Master in Signal Theory and Communications Master's

MASTER IN SIGNAL THEORY AND COMMUNICATIONS MASTER’S THESIS

DESIGN AND CHARACTERIZATION OF W-BAND RADAR COMPONENTS

MARTA FERRERAS MAYO 2017

MASTER’S THESIS

Title: Design and Characterization of W-Band Radar Components Author: Marta Ferreras Mayo Tutor: Jes´us Grajal de la Fuente Department: Se˜nales, Sistemas y Radiocomunicaciones

Group: Grupo de Microondas y Radar

COMPOSITION OF THE TRIBUNAL

President: Mariano Garc´ıaOtero Vocal: José Manuel Riera Sal´ıs Secretary: Manuel Sierra Castañer Substitute: Pedro Zufiria Zatarain

Date of defense and evaluation: 25th July 2017 Grading: 10-MH

UNIVERSIDAD POLITECNICA´ DE MADRID

ESCUELA TECNICA´ SUPERIOR DE INGENIEROS DE TELECOMUNICACION´

MASTER IN SIGNAL THEORY AND COMMUNICATIONS MASTER’S THESIS

DESIGN AND CHARACTERIZATION OF W-BAND RADAR COMPONENTS

MARTA FERRERAS MAYO 2017

Abstract

This Master’s Thesis summarizes the work that has been performed in the frame of the SPADERADAR-CM Project for the ultimate purpose of developing a W-band space debris radar operating at 94 GHz. The main goal of this type of radars consists of detecting and tracking particles, with sizes ranging from 1 to 10 cm, that are orbiting around the Earth at speeds up to 15 km/s and that could cause severe damage in case of collision against manned spacecraft. Particularly, the work performed within the realization of this Thesis has contributed to the progress of the space debris radar in several aspects of the hardware architecture of the system. On one side, part of the work has been concerned with the characterization and integration of the millimeter-wave receiving subsystem of the radar. On the other side, different pre-designs for the antenna system have been simulated and analyzed, and the performance of a reflectarray, that could be used in the future to obtain electronic scanning, has been characterized. Apart from studying the available literature, the utilized methodology has required the familiarization with measurement equipment to characterize devices at millimeter wavelengths. Furthermore, the use of several high level simulation tools specialized in high frequency modelling, such as Grasp, ADS or HFSS, has been required. As a summary, this Master’s Thesis describes a real application of engineering, which includes coping with literature, designing according to specifications, simulating and performing experimental validation through measurements.

Keywords

Radar, space debris, W-Band, millimeter-wave, quasi-optical, Cassegrain, reﬂectarray, Gaussian beam, receiver, S-parameters, noise ﬁgure.

Resumen

Este Trabajo de Fin de Máster expone el trabajo realizado en el marco del Proyecto SPADERADAR-CM, cuyo objetivo últimoes el desarrollo de un radar de basura espacial embarcado que funcione a 94 GHz. Este tipo de radares tienen el propósitode detectar y realizar el seguimiento de pequeñas part´ıculas de diámetrosde 1 a 10 cm que orbitan alrededor de la Tierra a velocidades del orden de 15 km/s y que pueden ocasionar graves daños en caso de colisión. En particular, este Trabajo de Fin de Másterha contribuido al avance del Proyecto en diversos aspectos de la arquitectura hardware del sistema. Por una parte, se ha caracterizado el comportamiento lineal de la parte de milimétricasdel subsistema receptor del radar. Por otra parte, se ha abordado el diseñoy simulación del sistema de antenas y se ha caracterizado el funcionamiento de un reflectarray que, en el futuro, podr´ıa incorporarse al radar para conseguir explorar el espacio mediante escaneo electrónico. Aparte del estudio de la literatura existente sobre antenas y sistemas radar, la metodolog´ıa utilizada ha requerido la familiarización con equipos de medida para frecuencias milimétricas. Además, ha sido necesario el manejo de diferentes programas de simulación especializados en el diseñoy análisis en alta frecuencia, como son Grasp, ADS o HFSS. Por todo ello, el trabajo expuesto en esta memoria supone un trabajo de ingenier´ıa real, que incorpora investigación,diseño,simulaciones y medidas experimentales, y que por tanto, lleva a la práctica muchos de los aspectos que han sido tratados en las asignaturas del Másteren Teor´ıa de la Señal y Comunicaciones.

Palabras clave

Radar, basura espacial, banda W, milimétricas, cuasi-óptica, Cassegrain, reflectarray, haz gaussiano, receptor, parámetros S, figura de ruido.

Contents

Abstract iii

Keywords iii

Table of contents vii

List of Figures xi

List of Tables xvii

List of Acronyms xxi

1 Introduction and Objectives 1 1.1MotivationandContext...... 1 1.2Objectives...... 1 1.3Methodology...... 2 1.4Structure...... 2

2 The Space Debris Radar 3 2.1TheSpaceDebrisProblem...... 3 2.2SpaderadarSpeciﬁcations...... 4 2.3SpaderadarArchitecture...... 5 2.3.1 Basicarchitecture...... 5 2.3.2 Noiseanddynamic-rangeconsiderations...... 6 2.3.3 Monopulseradar...... 6 2.3.4 Antennasystem...... 7

3 Antenna System Design 9 3.1TheSpaderadarAntennaSystem...... 9 3.1.1 Cassegrainreﬂectorsystem...... 10 3.1.2 Monopulsefeed...... 11 3.2DesignCriteria...... 11

vii viii CONTENTS

3.2.1 Restrictingdimensions...... 12 3.2.2 Casestudies...... 14 3.3AnalyticalSolution...... 14 3.3.1 Analyticalequations...... 14 3.3.2 Analysisoftheresults...... 15 3.4NumericalSolution...... 16 3.4.1 Simulationset-up...... 16 3.4.2 Simulationresultsofdifferentpre-designs...... 17 3.4.3 Analysisoftheresults...... 20 3.5FinalAntennaDesign...... 21 3.5.1 Geometricaldefinition...... 21 3.5.2 Simulationresults...... 22 3.5.3 Considerationsonthefinalantennasystem...... 23

4 Simulation of Quasi-optical Measurement Systems 25 4.1TheoreticalBackgroundonQuasi-OpticalSystems...... 25 4.1.1 Gaussian beam propagation in free space ...... 25 4.1.2 Gaussianbeamtransformation...... 27 4.2DevelopedGaussianBeamTracingTool...... 30 4.2.1 Running the software ...... 30 4.2.2 Step-by-step simulation process ...... 30 4.2.3 Simulationresultsandoutputﬁles...... 31 4.2.4 Limitationsofthesimulationtool...... 31 4.3 Application Example: 45◦ Incidence...... 32 4.3.1 Designcriteria...... 32 4.3.2 Simulatedopticalconﬁgurations...... 33 4.3.3 Criticalanalysisofthesimulationresults...... 33

5 Characterization of a W-band reflectarray 35 5.1TheoreticalBackgroundonReflectarrayAntennas...... 35 5.1.1 Reflectarrayantennasbasedonpatches...... 36 5.1.2 Reconfigurable reflectarrays based on liquid crystal ...... 36 5.2ReflectarraySampleUnderTest...... 37 5.3Quasi-opticalTestBenches...... 38 5.3.1 Utilizedopticalcomponents...... 39 5.3.2 Optical set-up for 30◦ incidence...... 39 5.3.3 Optical set-up for 45◦ incidence...... 40 5.3.4 Comparison of lens-based and mirror-based set-ups for 45◦ incidence . . 43 CONTENTS ix

5.4ReﬂectarrayCharacterization...... 45 5.4.1 Measurementplan...... 45 5.4.2 Statichomogeneouscontrol...... 46 5.4.3 Dynamiccontrolbasedontime-multiplexing...... 51 5.4.4 Discussionoftheresults...... 54 5.4.5 Futuremeasurements...... 56

6 Radar Receiving Chain Characterization. 57 6.1 The Millimeter-Wave Receiving Subsystem ...... 57 6.2CharacterizationofIndividualComponents...... 58 6.3 Characterization of the Receiver Isolation Chain ...... 59 6.3.1 Transmit insertion losses...... 60 6.3.2 Isolationbetweenthetransmitterandthereceiver...... 60 6.3.3 Power transfer from the antenna to the receiver...... 62 6.4 Noise Performance of the Receiver Chain ...... 64 6.4.1 AnalyticalestimationusingFriisformula...... 65 6.4.2 Noise budget analysis ...... 67 6.4.3 Noisemeasurements...... 68 6.4.4 Conversion losses ...... 70 6.5OverallConclusionsfromtheMeasurements...... 71 6.5.1 Transmit-receive isolation ...... 71 6.5.2 Maximumoutputpowerofthetransmitter...... 72 6.5.3 Receivernoiseﬂoor...... 72 6.5.4 Receiver sensitivity ...... 73

7 Summary and Conclusions 75 7.1Summary...... 75 7.2Conclusions...... 75

A Simulations in Grasp 77 A.1POandPTD...... 77 A.2 Grasp conﬁguration for simulating a Cassegrain system ...... 77 A.2.1Cassegrainantennamodel...... 78 A.2.2Commandlist...... 78

B Optical Test Benches for 45◦ Incidence 81 B.1OpticalSet-upUsingTwoDielectricLenses...... 81 B.2 Optical Set-up Using Two 45◦ Oﬀ-axisMirrors...... 83 B.2.1 Option with available 45◦ oﬀ-axismirrors...... 83 x CONTENTS

B.2.2 Option with alternative 45◦ off-axismirrors...... 84 B.3 Optical Set-up Using Two 90◦ Off-axisMirrors...... 85 B.4 Optical Set-up Using 45◦ Off-axisMirrorsandLenses...... 87 B.5 Optical Set-up Using 45◦ and 90◦ Off-axisMirrors...... 89 B.5.1Resultsforoption1 ...... 90 B.5.2Resultsforoption2 ...... 92

C Phase Center Calculation 93 C.1RPGFH-PP-100PotterHorn...... 93 C.2 Millitech SGH-08 Conical Horn ...... 96

D Measurement Set-ups and Equipment Conﬁgurations 99 D.1S-ParametersCharacterizationofW-bandDevices...... 99 D.2NoiseMeasurements...... 101 D.3Free-SpaceMeasurements...... 102

E Free-space Post-processing Techniques 105 E.1RecalibrationwithaReference...... 105 E.2Time-domainAnalysis...... 106 E.3 Smoothing vs Time-domain Processing ...... 107

F Characterization of Millimeter-wave Components 109 F.1RPGWFI-110Isolator...... 110 F.2 RPG WPD-110 Hybrid Power Divider ...... 111 F.3 ELVA CR-1094 Circulator ...... 114 F.4 Quinstar QAL-W00000 Variable Attenuator ...... 116 F.5 ELVA SPST-10 Switch ...... 118 F.6JointResponseoftheIsolatorandtheSwitch...... 120 F.7 RPG W-LNA75110 Low Noise Ampliﬁer ...... 123

G Millimeter Wave Components Datasheets 125

Bibliography 141 List of Figures

2.1Blockdiagramofthepreliminaryradararchitecture...... 5 2.2 Modiﬁed block diagram of the radar architecture using and two channels for monopulsetracking...... 7 2.3 Classical Cassegrain antenna schematic...... 7

3.1 Centred Cassegrain antenna geometry...... 10 3.2Gaincurveswithrespecttothemainreflectordiameter...... 12 3.3Positionandapproximatedimensionsofthemonopulsehorn...... 12 3.4 Feed directivity model...... 13 3.5 Analyzed Cassegrain geometries from Table 3.2...... 17 3.6Simulatedfarfieldresultsforgeometricaldesign1...... 17 3.7Simulatedfarfieldresultsforgeometricaldesign2...... 18 3.8Simulatedfarfieldresultsforgeometricaldesign3...... 18 3.9Simulatedfarfieldresultsforgeometricaldesign4...... 19 3.10Geometryofthefinaldesignofthedualantennasystem...... 22 3.11 Simulated farfield of the final design illuminated by C = −10dB...... 23

4.1 Evolution of the beam radius and phase radius of curvature for a Gaussian beam that propagates in a certain direction...... 26 4.2Gaussianbeamtransformationbylens...... 28 4.3 Example of an afocal system for quasi-optical beam propagation...... 29

5.1Schematicofareflectarrayantenna...... 36 5.2Schematicofthemanufacturedreflectarray...... 37 5.3Photographsofthereflectarraysample...... 38 5.4 Test bench configuration for 30◦ incidenceat94GHz...... 40 5.5 Test bench configuration for 45◦ incidence at 94 GHz using lenses...... 41 5.6 Test bench configuration for 45◦ incidenceat94GHzusingmirrors...... 42 5.7 Optical thru in the quasi-optical test bench utilized to measure vertical incidence response for 45◦ incidence...... 43 ◦ 5.8 Measured S21 of the measured optical thru for 45 incidence...... 44

xi xii LIST OF FIGURES

5.9 Reflectarray in the quasi-optical test bench utilized to measure vertical orientation response for 30◦ incidence...... 46 5.10 Reflectarray measurements using sinusoidal excitation, 30◦ incidence and vertical orientation...... 46 5.11 Reflectarray measurements using square excitation for 30◦ incidence and vertical orientation...... 47 5.12 Reflectarray in the quasi-optical test bench utilized to measure vertical orientation response for 30◦ incidence...... 47 5.13 Reflectarray measurements using sinusoidal excitation, 30◦ incidence and horizontalorientation...... 48 5.14 Reflectarray measurements using square excitation for 30◦ incidence and horizontalorientation...... 48 5.15 Reflectarray in the quasi-optical test bench utilized to measure vertical orientation response for 45◦ incidence...... 49 5.16 Reflectarray measurements using sinusoidal excitation for 45◦ incidence and verticalorientation...... 49 5.17 Reflectarray measurements using square excitation for 45◦ incidence and vertical orientation...... 49 5.18Comparisonofthemeasuredphaserangesat94GHzand100GHz...... 50 5.19Comparisonofthemeasuredlossesat94GHzand100GHz...... 50 5.20 Reflectarray performance for the four analyzed dynamic states for vertical orientation:strategy1...... 53 5.21 Reflectarray performance for the four analyzed dynamic states for horizontal orientation:strategy1...... 53 5.22 Reflectarray performance for the four analyzed dynamic states for horizontal orientation:strategy2...... 54 5.23 Mean values of the phase curves for the different dynamic excitation strategies. . 55

6.1 Millimeter-wave receiving subsystem options...... 58 6.2 Important situations of the receiver that need to be analyzed...... 60 6.3 Measurement set-up for the isolation chain collocating the load at port 2 of the circulator...... 61 6.4 Isolation chain performance from the transmitter to the receiver: S-parameters. . 61 6.5 Isolation chain performance from the transmitter to the receiver: insertion and return losses...... 62 6.6 Measurement set-up for the isolation chain collocating the load at port 1 of the circulator...... 62 6.7 Isolation chain performance from the antenna port to the LNA port: S-parameters. 63 6.8 Isolation chain performance from the antenna port to the LNA port: insertion andreturnlosses...... 63 6.9Blockdiagramofthereceiver...... 64 6.10 Receiver schematic for the ADS noise budget analysis...... 67 LIST OF FIGURES xiii

6.11 Noise budget analysis of the receiver...... 68 6.12 Measurement set-up for the characterization of the receiver chain noise performance. 69 6.13 Noise power measurement at the output of the receiver chain when the transmitter and the antenna are matched (Ta =290K)...... 69 6.14Impactofusingdiﬀerentinputpowervaluestothemultiplier...... 70 6.15Schematicoftheisolationchain...... 71

B.1Proposedopticalarrangementusinghornsandlenses...... 82 B.2 Simulation results for the sample size that obtains =17.4 dB taper using two dielectric lenses...... 82 B.3 Proposed optical set-up using horns and 45◦ off-axismirrors...... 83 B.4 Simulation results for the sample size that obtains =17.4 dB taper using 45◦ off-axis mirrors with 101.6 mm diameter ...... 84 B.5 Simulation results for the sample size that obtains =17.4 dB taper using 45◦ off-axismirrorswith76.2mmdiameter...... 85 B.6 Proposed optical arrangements using of horns and 90◦ off-axis mirrors to measure reflectivity at 45◦ incidence...... 86 B.7 Simulation results for the sample size that obtains =17.4 dB taper using 90◦ off-axismirrors...... 86 B.8 Proposed optical set-up using of horns, 45◦ off-axis mirrors and lenses...... 88 B.9 Simulation results for the sample size that obtains =17.4 dB taper using two lenses and two 45◦ off-axismirrors...... 88 B.10 Proposed optical arrangements using of horns, 45◦ and 90◦ off-axis mirrors. . . . 90 B.11 Simulation results for the sample size that obtains =17.4 dB taper using 45◦ and 90◦ off-axismirrors(option1)...... 91 B.12 Simulation results for the sample size that obtains =17.4 dB taper using 45◦ and 90◦ off-axismirrors(option2)...... 92

C.1HFSSmodeloftheRPGhornusingsymmetries...... 94 C.2 Phase of the copolar component of the electric field at 94 GHz when the coordinate system is at z =20.5mminsidethehorn...... 94 C.3 Phase of the copolar component of the electric field at 100 GHz when the coordinate system is at z =24.5mminsidethehorn...... 95 C.4 Directivity at 94 GHz...... 95 C.5 Directivity at 100 GHz...... 95 C.6 HFSS model of the Millitech horn using symmetries...... 96 C.7 Phase of the copolar component of the electric field at 94 GHz when the coordinate system is at z =6.6mminsidethehorn...... 97 C.8 Phase of the copolar component of the electric field at 100 GHz when the coordinate system is at z =7.9mminsidethehorn...... 97 C.9 Directivity at 94 GHz...... 97 xiv LIST OF FIGURES

C.10 Directivity at 100 GHz...... 98

D.1 Measurement set-up used for the acquisition of the S-parameters of millimeter-wave devices...... 100 D.2MeasurementofaQuinstarW-bandload...... 101 D.3 Measurement set-up for the acquisition of the noise power level at the output of the receiving chain ...... 102 D.4 Coaxial cable and WR-10 transitions between the horns and the VNA (Vector NetworkAnalyzer)ports...... 103 D.5ThruoftheTRLcalibrationkitaftercalibration...... 104

E.1Photographoftheset-uptomeasuretheopticalthru...... 105 E.2Calibrationofthetransmissioncoeﬃcientwithanopticalthru...... 106 E.3 Time domain transformation of the S-parameters of the 30◦-incidence optical test bench...... 107 E.4 Post-processing of the transmission coeﬃcient...... 108

F.1Measurementset-upfortheRPGWFI-110isolator...... 110 F.2RPGWFI-110isolator:S-parameters...... 110 F.3RPGWFI-110isolator:othermeasurements...... 111 F.4 Measurement set-up for the RPG WPD-110 power divider...... 112 F.5 RPG WPD-110 hybrid power divider: S-parameters...... 112 F.6 RPG WPD-110 hybrid power divider: insertion and return losses...... 113 F.7 RPG WPD-110 hybrid power divider: phase balanced and group delay...... 113 F.8 Measurement set-up for the ELVA CR-1094 circulator...... 114 F.9 ELVA CR-1094 circulator: S-parameters...... 115 F.10 ELVA CR-1094 circulator: other measurements...... 116 F.11 Measurement set-up for the Quinstar QAL-W00000 variable attenuator...... 116 F.12 Quinstar QAL-W00000 attenuator: return losses...... 117 F.13 Quinstar QAL-W00000 attenuator: attenuation and phase shift...... 117 F.14 Measurement set-up for the ELVA SPST-10 switch...... 118 F.15 ELVA SPST-10 switch: S-parameters...... 119 F.16 ELVA SPST-10 switch: insertion losses...... 119 F.17 ELVA SPST-10 switch: return losses...... 120 F.18 Measurement set-up to characterize the joint response of the isolator and the switch.121 F.19Isolator+switch:S-parameters...... 121 F.20 Isolator + switch: return losses...... 122 F.21 Isolator + switch: insertion losses...... 122 F.22 Measurement set-up for the RPG W-LNA75110 low noise ampliﬁer...... 123 F.23 RPG W-LNA75110 low noise ampliﬁer: S-parameters...... 123 LIST OF FIGURES xv

F.24 RPG W-LNA75110 low noise ampliﬁer: gain and return losses...... 124 xvi LIST OF FIGURES List of Tables

2.1Preliminaryoperationalparametersoftheradarsystem...... 4 2.2 Radar capabilities expected from the pre-design values...... 4

3.1Generalspecificationsoftheradarantennasystem...... 9 3.2StudycasesfortheCassegrainantennasystem...... 14 3.3Analyticalresultsfordifferentspecifications...... 15 3.4 Gaussian feed configuration for each of the four compared geometries so that illumination at the edge of the subreflector is =10dB...... 16 3.5Comparisonoftheresultsobtainedfordifferentpre-designs...... 19 3.6Geometricalandsimulatedresultsofthechosenconfiguration...... 21 3.7 Geometrical parameters of the final Cassegrain system...... 22 3.8 Simulation results for the final Cassegrain design optimally illuminated by a Gaussianfeed...... 22

4.1 Recommended sample sizes for using diﬀerent free-space measurement systems (usingRPGhorns)...... 34

5.1Specificationsofthereflectarraysample...... 37 5.2 Element positions for the proposed optical test bench for 30◦ incidence...... 40 5.3 Simulated results of the proposed test bench configuration to measure the reflectarray with an angle of incidence of 30◦...... 40 5.4 Element positions for the proposed optical test bench for 45◦ incidence using lenses. 41 5.5 Simulated results of the test bench configuration to measure the reflectarray with an angle of incidence of 45◦ using lenses...... 42 5.6 Element positions for the proposed optical test bench for 45◦ incidence using mirrors...... 42 5.7 Simulated results of the alternative test bench configuration to measure the reflectarray with an angle of incidence of 45◦ usingmirrors...... 43 5.8Commonparameterstoallthemeasurements...... 45 5.9 Summary of both excitation strategies for dynamic time-multiplexed control of thereflectarraystates...... 52 5.10Summaryofthereflectarrayperformancewhentime-multiplexingisused..... 56

xvii xviii LIST OF TABLES

6.1 Summary of the measured responses of the receiving chain millimeter-wave componentsat94GHz...... 59 6.2Transmitter-to-antennaperformanceat94GHz...... 60 6.3 Transmitter-to-receiver performance results at 94 GHz...... 62 6.4 Antenna-to-receiver performance results at 94 GHz...... 64 6.5Friisformulaparametersat94GHz...... 66 6.6 Output noise results at 94 GHz for different receiver bandwidths obtained using Friisformula...... 67 6.7 Noise budget analysis results at 94 GHz at the output of the IF (Intermediate Frequency) active filter for different receiver bandwidths...... 68 6.8 Noise power level at the output of the receiver chain for an antenna temperature of Ta ≈ Tamb ≈ 290K...... 70 6.9 Most relevant measurement results of the receiving chain at 94 GHz...... 71 6.10 Comparison of noise power results at the output of the receiver chain according toanalyticalcalculations,simulationsandmeasurements...... 72

6.11 Receiver sensitivity for a swerling 5 target without pulse integration and Ta = 290 K. 73

A.1TextualreproductionoftheGraspcommandlist...... 78

B.1Elementpositionsfortheproposedarrangementusinghornsandlensese..... 82 B.2 Results at 94 GHz and 100 GHz obtained using a configuration that utilizes horns and dielectric lenses for 45◦ incidence...... 83 B.3 Element positions for the proposed set-up using horns and 45◦ off-axis mirrors. . 83 B.4 Results at 94 GHz and 100 GHz obtained using a configuration that uses horns and 45◦ off-axis mirrors with 101.6 mm diameter...... 84 B.5 Results at 94 GHz and 100 GHz obtained using a configuration that uses horns and 45◦ off-axismirrorswith76.2mmdiameter...... 85 B.6 Element positions for the proposed arrangement (option 2) using horns and 90◦ off-axis mirrors to measure reflectivity at 45◦ incidence...... 86 B.7 Results at 94 GHz and 100 GHz obtained using a configuration that uses horns and 90◦ off-axismirrors...... 87 B.8 Element positions for the proposed set-up using horns, 45◦ off-axis mirrors and lenses...... 88 B.9 Minimum sample diameter at 94 GHz and 100 GHz obtained using a configuration thatutilizeshornsanddielectriclenses...... 89 B.10 Element positions for the proposed arrangement using horns, 45◦ and 90◦ off-axis mirrors...... 90 B.11 Results at 94 GHz and 100 GHz obtained using a configuration that uses horns, 45◦ and 90◦ off-axismirrors(option1)...... 90 B.12 Results at 94 GHz and 100 GHz obtained using a configuration that uses horns, 45◦ and 90◦ off-axismirrors(option2)...... 92 LIST OF TABLES xix

C.1 Phase center at diﬀerent frequencies measured from the aperture (z>0isinside thehorn)...... 94 C.2 Phase center at diﬀerent frequencies measured from the aperture (z>0isinside thehorn)...... 96

D.1 Anritsu VNA configuration for the measurement of S-parameters at W-band. . . 100 D.2 Agilent spectrum analyzer configuration for the measurement of noise level of the receiving chain...... 102 D.3AnritsuVNAconfigurationforthefree-spacemeasurementsatW-band...... 103

F.1 RPG WFI-110 isolator measurement results at 94 GHz in comparison with those providedbythemanufacturer...... 111 F.2 RPG WPD-110 hybrid power divider measurement results at 94 GHz in comparisonwiththoseprovidedbythemanufacturer...... 114 F.3 ELVA CR-1094 circulator measurement results at 94 GHz in comparison with thoseprovidedbythemanufacturer...... 115 F.4 Quinstar QAL-W00000 attenuator measurement results at 94 GHz in comparison withthoseprovidedbythemanufacturer...... 118 F.5 ELVA SPST-10 switch: biasing and power consumption...... 118 F.6 ELVA SPST-10 switch measurement results at 94 GHz in comparison with those providedbythemanufacturer...... 120 F.7Measurementresultsoftheswitchandtheisolatorat94GHz...... 123 F.8 RPG W-LNA75110 low noise ampliﬁer measurement results at 94 GHz in comparisonwiththoseprovidedbythemanufacturer...... 124 xx LIST OF TABLES List of Acronyms

ADC Analog Digital Converter

ADS Advanced Design System R

DDS Direct Digital Synthesis

DSB Double-Side Band

DUT Device Under Test

FEM Finite Element Method

FFT Fast Fourier Transform

GEA Applied Electromagnetism Group

GMR Microwave and Radar Group

GR Radiation Group

Grasp General Reﬂector and Antenna Farm Analysis Software R

HFSS High Frequency Structural Simulator R

HPA High Power Ampliﬁer

IF Intermediate Frequency

LC Liquid Crystal

LCD Liquid Crystal Display

LFM Linear Frequency Modulation

LHCP Left-Hand Circular Polarization

LNA Low Noise Ampliﬁer

LO local oscillator

MMIC Monolithic Microwave Integrated Circuit

OMT Orthomode Transducer

xxi xxii List of Acronyms

PLO Phased Locked Oscillator

PO Physical Optics

PRI Pulse Repetition Interval

PTD Physical Theory of Diﬀraction

PW Pulse Width

RBW Resolution Bandwidth

RF Radiofrequency

RHCP Right-Hand Circular Polarization

RMS Root Mean Square

SNR Signal to Noise Ratio

SSB Single-Side Band

TRL Through-Reﬂect-Line

UPM Technical University of Madrid

VBW Video Bandwidth

VNA Vector Network Analyzer

VSWR Voltage Standing Wave Ratio Chapter 1

Introduction and Objectives

1.1 Motivation and Context

In the frame of the SPADERADAR-CM Project [1, 2, 3], a W-band space debris radar is being developed by a consortium lead by the GMR (Microwave and Radar Group) of UPM (Technical University of Madrid). This type of radars must be capable of detecting targets with sizes in the range of 1 to 10 cm that are orbiting around the Earth at speeds of 15 km/s and that can cause severe damage in case of collision [4]. Particularly, the Spaderadar Project is focused on the development of spaceborne radars, which are able to detect and track tiny particles that approximate dangerously to the infrastructure that is being protected. Therefore, their angular resolution, maximum range and frame rate must be suﬃciently high to produce real-time responses to incoming threats [2]. This Master’s Thesis summarizes the work that has been performed in the GMR for the purpose of developing, characterizing and integrating part of the millimeter-wave receiving subsystem of the space debris radar that is being deployed.

1.2 Objectives

This Master’s Thesis will be concerned with three diﬀerent tasks related to the space debris radar:

1. The ﬁrst task will consist of making a proposal for the antenna system that will be integrated in the radar prototype. The basic system will take the form of a Cassegrain antenna fed by a monopulse horn. In particular, the geometrical deﬁnition of the Cassegrain system will be tackled taking into account the application requirements.

2. In order to avoid the mechanical scanning that is inherent to the basic exploration approach, it has been considered the substitution of the hyperbolic subreflector by a reflectarray antenna. To this end, the second task of this Thesis will consist of characterizing a reflectarray (already manufactured) at W-band. As a preliminary step, it will be necessary to design an optical bench set-up for free-space reflectivity measurements, for which a software based on Gaussian beam propagation has been developed.

3. The last goal of this Thesis is the characterization of the components of one of the receiving channels of the radar. The intended characterization includes the acquisition of some of

1 2 1.3. METHODOLOGY

the most representative ﬁgures of merit of electronic devices, such as the S-parameters or the noise factor.

1.3 Methodology

The methodology that has been followed is similar for all the tasks described in Section 1.2:

1. Documentation on the subject by investigating the available literature.

2. Design and/or simulation using high level software tools specialized for high frequency designs, such as Grasp, ADS or HFSS. Matlab has been used for the development of the Gaussian beam tracing tool.

3. Realization of measurements using adequate equipment for characterizing high frequency devices. Processing and presentation of the results are performed using Matlab.

4. Critical analysis of the obtained results, both from simulations and from measurements, in comparison to what it was speciﬁed or simulated.

1.4 Structure

From this point, the document is divided into six chapters:

• Chapter 2 oﬀers an overview of the general speciﬁcations and topology of the Spaderadar Project emphasizing those aspects that will be developed along the rest of the Thesis.

• Chapter 3 describes the design procedure of the dual reflector system, the results from different iterations and the different trade-offs that had to be balanced in order to obtain the final pre-design of the Cassegrain antenna system.

• Chapter 4 describes the work realized in relation to the development of a software tool based on Gaussian Beam Theory to predict the behaviour of waves in quasi-optical systems.

• Chapter 5 summarizes the results that have been obtained after characterizing a reﬂectarray at W-band using a free-space measurement system.

• Chapter 6 summarizes the results that have been obtained after the characterization of one of the channels of the millimeter-wave receiving subsystem of the radar.

• Chapter 7 presents some general conclusions about the work performed within the realization of this Thesis.

Appendices A through G compliment the information included along these chapters. Chapter 2

The Space Debris Radar

This chapter describes the speciﬁcations, functionality and architecture of the space debris radar that is being developed in the frame of the SPADERADAR-CM Project [1, 2] and it introduces some of the tasks that will be covered along the rest of the document.

2.1 The Space Debris Problem

Space debris consists of micrometeoroids (natural) and remnants of spacecraft and vehicles (man-made). The growing number of spaceborn missions and applications has produced tenths of millions of particles that are polluting the orbital environment[4]. Since the hazards associated with space debris are continuously increasing, it is only a matter of time until a manned system is hit with potentially catastrophic consequences. Indeed, collisions with space debris are a reality of space ﬂight today. Therefore, risks associated to such collisions must be managed, which is becoming a crucial task for the national and international space agencies [4]. Two diﬀerent strategies exist to combat orbital debris:

• Protection through debris shielding.

• Avoidance through debris detection.

New spacecraft now incorporate debris shields. However, debris protection is limited to small particles (< 1 cm) and old spacecraft are still vulnerable. Therefore, attention is also being paid to the deployment of early detection systems that can produce a warning long before the collision. Radar systems have a fundamental role in the observation of space debris. However, currently deployed terrestrial radars are not able to detect and track objects with sizes below 10 cm [5]. As an alternative or complement to the surveillance capabilities provided by terrestrial radars, spaceborne radars may be used:

• They do not suﬀer from atmospheric attenuation, so millimeter waves can be utilized to increase resolution up to 0.1 to 1 cm.

• They are closer to the targets, so they require less transmitted power and smaller antennas.

3 4 2.2. SPADERADAR SPECIFICATIONS

• Real-time processing of the acquired data could trigger autonomous threat-avoidance processes in case particles were approaching dangerously to the platform that is being protected .

[5, 6] summarize the characteristics of some of the currently deployed radars which would be capable of space debris detection.

2.2 Spaderadar Speciﬁcations

The ultimate purpose of the SPADERADAR-CM Project is to develop a W-band space debris radar operating at 94 GHz [1, 2, 3]. The projected system will be a prototype of a spaceborne radar that must be capable of detecting targets with sizes in the range of 1 to 10 cm that are orbiting around the Earth at speeds up to 15 km/s and that can cause severe damage in case of collision with any manned spacecraft [2]. The preliminary design of the space debris radar is described in [2]. That document concludes that the radar system will be a pulse radar using LFM (Linear Frequency Modulation) pulses and working at 94 GHz. The preliminary operative parameters of the radar system are summarized in Table 2.1. Those values might vary in case any limitations are found along the implementation process.

Parameter Value Operating frequency 94 GHz Transmitted bandwidth ≈ 50 MHz Antenna gain > 55 dB Transmitted power 30 dBm [1] PRI (Pulse Repetition Interval) 100 µs [1] PW (Pulse Width) 24 µs [1] Sampling frequency 100 MHz

Table 2.1: Preliminary operational parameters of the radar system.

Those parameters would yield the system-level capabilities presented in Table 2.2 [2].

Parameter Value Maximum range (d=10 cm, SNR=13 dB) 10.82 km Maximum Doppler frequency 10 MHz Spatial resolution 3 m Angular resolution 0.3◦

Table 2.2: Radar capabilities expected from the pre-design values.

[1]These parameters are yet to be decided. CHAPTER 2. THE SPACE DEBRIS RADAR 5

2.3 Spaderadar Architecture

2.3.1 Basic architecture

Figure 2.1 shows a block diagram of the proposed pulsed LFM radar architecture using an heterodyne receiver.

Pulsed LFM Signal Pulsed LFM Signal Pulsed LFM Signal Pulsed LFM Signal (916.667- 918.7 MHz ) (3.916667- 3.9187 GHz ) (15.6667 – 15.675 GHz ) (94 -94.05 GHz )

Generador Transmitter/ señal x4 MPA x6 MPA HPA Receiver Antenna Filter 1 3 GHz Filter 2 Filter 3 DDS CTL CH1 PLO Master Oscillator LO (93-94 GHz) CLK 3 GHz (10 MHz) x6

PLO LNA 3.875 GHz LO (15,5 GHz) PC x4 MPA IF (0-1 GHz)

LO2 (3.875 GHz) Digital Microwave Millimiter – wave Electronics Subsystem Subsystem

I Samples IQ Receiver Subsystem Q Samples

Figure 2.1: Block diagram of the preliminary radar architecture [3].

Digital electronics: DDS (Direct Digital Synthesis) is a technique to generate LFM signals. In this case, sawtooth pulsed chirp signals of 50 MHz are generated every 100 µs at 917 MHz using a commercial DDS.

Microwave subsystem: The microwave subsystem comprises the RF (Radiofrequency) circuitry up to 20 GHz. Components are based on planar technologies and they can incorporate commercial MMIC (Monolithic Microwave Integrated Circuit) resulting in low-cost compact designs. A 3 GHz PLO (Phased Locked Oscillator) and a ×4 multiplier upconvert the signal and the LO (local oscillator) to 15.67 GHz.

Millimeter-wave subsystem: The millimeter-wave subsystem involves the components operating above 20 GHz, which are usually based on waveguide technology. The goals of this subsystem are frequency multiplication (×6) and ampliﬁcation of the pulsed signal. The receiver utilizes a mixer to downconvert the received pulses to an IF of 0 - 1 GHz (to be decided).

IQ receiver subsystem: Its principal task is to transform the IF signal into IQ samples, either in analog or digital domain.

Antenna system: The antenna system will consist of a dual reﬂector antenna with a gain of 55 - 60 dB. The simplest system utilizes a mechanical scanning approach to explore the space.

In the previous design, the LO frequency is a pure tone that downconverts the RF signal to an IF that can be digitalized by the ADC (Analog Digital Converter). Signal pulse compression is then performed entirely in the digital domain. 6 2.3. SPADERADAR ARCHITECTURE

2.3.2 Noise and dynamic-range considerations

Receivers generate internal noise that can mask weak signals. The strategy to maintain a low noise figure consists of introducing an LNA (Low Noise Amplifier) at the input of the receiving chain, so that this LNA establishes the noise floor of the receiver [7]. However, since this is a monostatic radar, two problems may arise: the high transmitted power reaching the receiver through the circulator or after reflecting at the antenna, and the received power being too high due to early targets. To avoid damages on the receiver components, the receiver must remain switched-off during the time the transmitter is active. For this purpose, an isolation chain formed by a circulator, an isolator and a switch is introduced before the LNA. This will degrade the overall noise figure, since the LNA no longer is the first component of the receiver [8]. On the other hand, the noise introduced by the ADC is usually analyzed as a separate contribution to the overall radar noise. If the quantification noise introduced by the ADC is higher than the receiver noise power, low energy echoes could be obscured, thus reducing the dynamic range of the system [7]. In order to ensure that the receiver dynamic range is limited by thermal noise, an IF active filter has been included after the mixer. All these problems will be analyzed in Chapter 6 after characterizing the receiver performance.

2.3.3 Monopulse radar

Monopulse tracking is based on the minimization of an error signal that is dependent on the target displacement from the pointing axis [7]. For this radar, a multi-mode horn is being designed along with a waveguide mode extractor, allowing a much flexible design than a multi-horn structure. This design is not part of the work included in this Thesis. A monopulse system based on amplitude comparison would require three different receiving channels to provide tracking error signals for two dimensions: sum, elevation-difference and azimuth-difference. On the other hand, if the system is designed to use circular polarization, it will be possible to obtain azimuth and elevation control using the sum pattern and a single difference signal [9]. The introduction of monopulse tracking requires modifications on the receive subsystems of the radar architecture. Basically, the new architecture must duplicate or triplicate (depending on the number of channels that are finally utilized) the receiving chains, so that every output signal of the monopulse comparator is downconverted and digitalized. The new architecture is shown in Figure 2.2. CHAPTER 2. THE SPACE DEBRIS RADAR 7

Pulsed LFM Signal Pulsed LFM Signal Pulsed LFM Signal Pulsed LFM Signal (916.667- 918.7 MHz ) (3.916667- 3.9187 GHz ) (15.6667 – 15.675 GHz ) (94 -94.05 GHz )

Generador Transmitter/ señal Mono x4 MPA x6 MPA HPA Receiver pulse Antenna Filter 1 Filter 2 HMC370LP4 HMC451LP1Filter 3 RPG Farran Farran FPA-10-0002 FPA-10-0005 DDS CTL 3 GHz AFM6-110 Synergy CH1 PLO LFSN200400-100 Master Oscillator LO (93 GHz) Elva CLK 3 GHz Switch Elva (10 MHz) Switch x6 PLO 3.875 GHz RPG Synergy LO (15,5 GHz) AFM6-110 PC LFSN200400-100 x4 MPA LNA RPG LO (3.875 GHz) HMC451LP1 WLNA-75-110 Digital Microwave IF (0-1 GHz) LNA Electronics Subsystem Quinstar QMB-9999WS RPG WLNA-75-110 Quinstar I Samples QMB-9999WS IQ Receiver Millimiter – wave Subsystem Subsystem Q Samples

I Samples IF (1-1.04 GHz) IQ Receiver Subsystem Q Samples

Figure 2.2: Modiﬁed block diagram of the radar architecture using and two channels for monopulse tracking [3].

2.3.4 Antenna system

The application requires an antenna with more than 55 dB gain at W-band that can perform three-dimensional scanning. Besides, this is a spaceborne application, so it is also considerably important that the entire antenna system is as compact as possible. Considering this, the space debris radar will utilize an axially symmetric Cassegrain conﬁguration [10] whose schematic is presented in Figure 2.3. Some pre-designs of this reﬂector antenna system are analyzed along Chapter 3.

Main reflector

F1 F2

Subreflector Feed

Figure 2.3: Classical Cassegrain antenna schematic.

As a ﬁrst approximation, exploration and target tracking will be performed using a mechanical approach that re-steers the main beam by rotating the entire antenna in azimuth and elevation, according to the monopulse error signals. In the future, diﬀerent possibilities will be evaluated in order to substitute this mechanical scanning by an electronic exploration scheme. 8 2.3. SPADERADAR ARCHITECTURE

Chapter 5 includes the characterization of a reflectarray that could substitute the hyperbolic subreflector of the Cassegrain system to provide electronic beamsteering in two dimensions [11]. There is still much work to be done since the reflectarray sample that has been characterized is the just first prototype of the final antenna that could be employed in the radar. Chapter 3

Antenna System Design

This chapter describes the design of an antenna system at 94 GHz for the space debris radar. Considering the radar specifications, a Cassegrain antenna system has been optimized for the application. Different antenna geometries are analytically evaluated in Section 3.3 according to traditional design criteria [12]. Then, those designs are numerically evaluated in Section 3.4 using the simulation tool Grasp (General Reflector and Antenna Farm Analysis Software R ). At the end of the chapter, in Section 3.5, the final design for the Cassegrain antenna system is presented.

3.1 The Spaderadar Antenna System

This application requires an antenna capable of producing an extremely narrow beam with more than 55 dB gain at 94 GHz. Besides, the system will be monopulse to gain target tracking precision. Table 3.1 presents a summary of the antenna system speciﬁcations.

Parameter Value Operating frequency 94 GHz Bandwidth > 2GHz Gain > 55 dB Polarization RHCP Weight/Size Minimum Exploration Mechanical Monopulse Tracking Yes

Table 3.1: General speciﬁcations of the radar antenna system.

The necessary antenna gain to maintain a moderate transmitted power and still cover more than 10 km range was determined in [2]. Besides, since this is a space-borne application, it is considerably important that the entire antenna system is as compact and light in weight as possible.

9 10 3.1. THE SPADERADAR ANTENNA SYSTEM

3.1.1 Cassegrain reﬂector system

Double reflector antennas are utilized for different applications, since they retain some advantages with respect to ordinary single-reflectors [13]. For this specific radar application, an axially symmetric Cassegrain antenna configuration has been selected due to its compactness and the possibility of placing the feed and the transceiver behind the main reflector. A schematic of the classical Cassegrain configuration is presented in Figure 3.1. The feed would be directly connected to the transmitter/receiver and pointed at a hyperbolic subreflector which is suspended in front of a larger main parabolic reflector. This antenna is designed to achieve a uniform phase front in the aperture of the paraboloid and it can obtain efficiencies of 65 - 80 % (if surfaces are shaped [14]).

Figure 3.1: Centred Cassegrain antenna geometry [12].

The analysis of this antenna system is simple and can be described by only four independent parameters [10]:

• The main reflector profile depends on the parameter F , its focal distance. In [12], its surface is defined by Equation 3.1.

• The subreflector is characterized by its eccentricity e and its focal distance f. Alternatively, Granet [12] uses the semi-transverse axis a of the hyperbola instead of the eccentricity. The surface of the subreflector is defined by Equation 3.2.

x2 + y2 D2 z + F = with: x2 + y2 ≤ (3.1) 4F 4 x2 + y2 d2 f z + f = a 1+ with: x2 + y2 ≤ S and e = > 1 (3.2) f 2 − a2 4 a

Through geometrical optics, it can be shown that this arrangement folds the rays so that the waves that emanate from the phase center of the feed illuminate the subreflector and are reflected by it towards the other focus of the hyperboloid. Since this other focus of the hyperboloid is co-located with the focus of the paraboloid, rays propagate towards the primary reflector as if CHAPTER 3. ANTENNA SYSTEM DESIGN 11 they were originated at the focal point of the paraboloid. Therefore, these rays are reflected by the primary reflector and transformed into parallel rays [10]. Any dual reflector system can be considered as being replaced by an equivalent single focusing surface, which in the case of a Cassegrain system is another paraboloid with larger focal length (since the hyperboloid slows the beam divergence). The focal distance of the equivalent single paraboloid Fe depends on the eccentricity of the subreflector e through the magnification parameter M [15].

e +1 M = (3.3) e − 1 Fe = M · F (3.4)

3.1.2 Monopulse feed

Different proposals for the monopulse feed of the Cassegrain system are already being designed by the GEA (Applied Electromagnetism Group). It will consist of a multiflare horn attached to a mode extractor that will produce the sum and difference responses that are required in a monopulse system. These designs are not part of the objectives of this Thesis, though it is important to know that first pre-designs are producing return losses of 20 - 25 dB and isolation between ports above 30 dB [16].

3.2 Design Criteria

The gain of a Cassegrain antenna, in which the shadow of the subreflector over the main dish is larger than the feed aperture, is given by Equation 3.5. Overall antenna efficiency η is usually 65 - 80 % and it includes different effects such as illumination efficiency, spillover losses, losses in the conductors, diffraction losses, blockage by the struts, etc. 2 2 2 4π π D − dS G = Aeff = η (3.5) λ2 λ2

The following list summarizes some design criteria that maximize the overall eﬃciency of a Cassegrain antenna for a certain application [12, 17]:

• Main dish should have at least 50λ diameter and F/D ratios between 0.25 and 0.8.

• The subreﬂector diameter dS should be larger than 5λ in order to avoid excessive diﬀraction losses.

• The subreflector diameter dS should be smaller than 20% of the size of the main reflector diameter, for the purpose of obtaining high blockage efficiency and avoiding excessively high sidelobe levels.

2 • The subreflector must be in the farfield of the feed (f + a>2dS/λ). Otherwise, there will be significant phase errors.

• The semi-subtended angle ΨS with which the feed illuminates the subreﬂector should be chosen to obtain an edge illumination at the subreﬂector in the range of −10 to =12 dB. 12 3.2. DESIGN CRITERIA

3.2.1 Restricting dimensions

Section 3.1 establishes some speciﬁcations on the antenna system that is being developed. Analyzing this speciﬁcations from the point of view of a Cassegrain geometry produces some restrictions on certain dimensions of the design [2].

Gain −→ Main diameter

Figure 3.2 has been obtained using Equation 3.5 to obtain an estimation of the Cassegrain antenna gain. Since the specification for the gain involved having at least 55 dB, a main reflector diameter of 900 mm has been chosen as fixed dimension for the pre-designs. This value leaves some margin of about 2 dB to face possible reduction in the performance.

Gain vs Diameter 62

56 G (dB) Eff=0.8, ds=10% 54 Eff=0.7, ds=10% Eff=0.6, ds=10% Eff=0.8, ds=20% 52 Eff=0.7, ds=20% Eff=0.6, ds=20% 50 400 600 800 1000 1200 1400 D (mm)

Figure 3.2: Gain curves with respect to the main reﬂector diameter.

Feed position

The dimensions for the future horn can be approximated by the schematic from Figure 3.3. As observed, the feed must be close to the apex of the main paraboloid so that the monopulse comparator and the transceiver lie behind the main reﬂector. For the following pre-designs the feed phase center has been assumed to be located 20 mm in front of the main reﬂector.

20-30 mm

28-30 mm 24-26 mm

30-40 mm

Figure 3.3: Position and approximate dimensions of the monopulse horn. CHAPTER 3. ANTENNA SYSTEM DESIGN 13

Feed directivity −→ Semi-subtended angle

Currently there are two possible pre-designs of the feed horn that are being developed in parallel and their performance will be compared in the following pre-designs.

• Feed with 21.5 dB directivity in the sum pattern.

• Feed with 24.8 dB directivity in the sum pattern.

Approximating the radiation patterns of those feeds as an ideal cosq model [10], it can be ◦ shown that the semi-subtended angle ΨS to obtain =10 dB taper is 14.6 for the horn with 21.5 dB directivity and 10◦ for the horn with 24.8 dB directivity. The derivation is presented in Equation 3.6 and the resulting directivity in Figure 3.4.

q 4π D0 − 2 E(Φ,θ)=cos (θ)with:D0 = =2(2q +1) −→ q = (3.6) Ω 4

Feed directivity model 0

-5

-10

-15

-20 E (dB) -25

-30

-35 21.5 dB (q = 34.81) 24.8 dB (q = 75) -40 -30 -20 -10 0 10 20 30 (º)

Figure 3.4: Feed directivity model.

Compactness and cost −→ Focal length

Since this is a spaceborne application, it is important that the ﬁnal system is as compact and light in weight as possible. The total length of a Cassegrain system is calculated with Equation 3.7 [12]. 2 dS Ltot = F + a 1+ − f (3.7) 4(f 2 − a2)

Total length is highly dependent on the focal distance of the main reﬂector, so lower F/D ratios are expected to produce more compact systems. Indeed usual F/D ratios for Cassegrain antennas range between 0.3and0.5, although for satellite and monopulse applications shallower dishes are used with F/D up to 1. The reason lies on the fact that lower proﬁle paraboloids are easier to support and to move mechanically, since they require less material for their fabrication, which also makes them lower-prized [18]. The following sections will compare the performance of F/D ratios of 0.4and0.75 in order to decide which range of F/D is best for this application. 14 3.3. ANALYTICAL SOLUTION

3.2.2 Case studies

According to the antenna system restrictions detailed along this section, Cassegrain optimum designs for two different feed directivities and two different F/D ratios will be compared in Section 3.3 and Section 3.4. Feed location and main dish diameter have been set to reasonable values given the system specifications. The four different combinations that will be analyzed along following sections are presented in Table 3.2.

Main dish Feed Edge taper Feed Case F/D ratio diameter position illumination directivity

1 0.4 21.5 dB 2 0.4 24.8 dB 900 mm 20 mm =10 dB 3 0.75 21.5 dB 4 0.75 24.8 dB

Table 3.2: Study cases for the Cassegrain antenna system.

3.3 Analytical Solution

The purpose of this section is to determine the geometrical dimensions and the expected performance of the four cases proposed in Table 3.2 using analytical expressions.

3.3.1 Analytical equations

According to Section 3.2, for this application there are four parameters that restrict the system geometry : D, F , Lm and ΨS (see Figure 3.1). For those four input parameters, Granet [12] provides a set of equations to ﬁnd the rest of the variables that deﬁne the geometry of the system:

ΨS (Lm − F ) −D +4F tan 1 2 a = (3.8) 2 ΨS D +4F tan 2 D(Lm − F ) Ls = − (3.9) ΨS D +4F tan 2 1 f = (F − Lm) (3.10) 2 ΨS 16 sin(ΨS)DF(Lm − F ) −D +4F tan 2 dS = (3.11) ΨS 2 2 ΨS 8FD D +4F tan +(D +16F )sin(ΨS) D +4F tan 2 2 CHAPTER 3. ANTENNA SYSTEM DESIGN 15

Using Granet’s Equations 3.8, 3.9, 3.10 and 3.11 optimal Cassegrain geometries have been found for the four cases from Table 3.2. The obtained results are presented in Table 3.3.

Case 1 Case 2 Case 3 Case 4 Input parameters Main dish diameter, D 900 mm 900 mm 900 mm 900 mm Main dish focal distance, F 360 mm 360 mm 675 mm 675 mm Directivity, D0 21.5 dB 24.8 dB 21.5 dB 24.8 dB ◦ ◦ ◦ ◦ Semi-subtended angle ΨS at C = −10 dB 14.65 10.01 14.65 10.01 Feed position, Lm 20 mm 20 mm 20 mm 20 mm

Output parameters Subreflector diameter, dS (3.11) 157.7 mm 110.5 mm 253.9 mm 187.2 mm Subreflector semi-transverse axis, a (3.8) 112 mm 128.2 mm 145.2 mm 191.2 mm Subreflector focal distance, f (3.10) 170 mm 170 mm 327.5 mm 327.5 mm Eccentricity, e (3.2) 1.52 1.33 2.26 1.71 Distance from feed to subreflector, Ls (3.9) 282 mm 298.2 mm 472.7 mm 517.7 mm Total length of the antenna, Ltot (3.7) 302.2 mm 317.8 mm 492.8 mm 535.8 mm Estimated gain (3.5) 57.84 dB 57.91 dB 57.62 dB 57.79 dB Equivalent focal distance, Fe (3.4) 1750 mm 2569 mm 1750 mm 2569 mm Magnification, M (3.3) 4.86 7.14 2.59 3.81

Table 3.3: Analytical results for diﬀerent speciﬁcations.

3.3.2 Analysis of the results

• A Cassegrain system using an F/D =0.4 results in an antenna system much more compact than the shallower system with F/D =0.75. However, lower proﬁle paraboloids will be lighter in weight so one advantage may compensate the other.

• Subreflector diameters are sufficiently large in terms of wavelengths (dS > 5λ)sothat diffraction losses are below 0.2 dB.

• When the feed position is ﬁxed, large focal lengths or low feed directivities produce larger subreﬂector diameters. Therefore, those designs are producing higher blockage, which explains the small loss in performance observed in the estimated gain.

• Estimated antenna gain is very similar for all the designs, obtaining a maximum of 57.9 dB for the case of F/D =0.4 with a 24.8 dB horn. The utilized overall eﬃciency is a coarse estimation of spillover, illumination and blockage eﬃciency.

The estimated performance of these designs has been evaluated in terms of the estimated gain. This ﬁgure of merit is neither suﬃcient, nor accurate for making a decision, so further analysis is required by using a numerical simulator. 16 3.4. NUMERICAL SOLUTION

3.4 Numerical Solution

Since reflector antennas usually have 10 - 1000 λ, the sub-wavelength gridding that is required in full-wave solutions would produce extremelly large problems. In order to reduce computational complexity, it is necessary to resort to approximate methods. This section utilizes the simulation tool Grasp to characterize more accurately the performance for the different cases proposed in Table 3.2. Grasp is a trademark reflector analysis tool from TICRA that is able to predict the electromagnetic fields produced by high frequency reflector systems. This is attained by solving the time-variant Maxwell’s equations using highly efficient numerical approximations known as PO (Physical Optics) and PTD (Physical Theory of Diffraction) [19]. Appendix A summarizes the behaviour of those algorithms when they are used to simulate reflector antennas.

3.4.1 Simulation set-up

Appendix A details how to conﬁgure Grasp to simulate the farﬁeld of a Cassegrain system.

• Simulations that are performed within this section include:

– Spillover efficiency. – Illumination efficiency. – Subreflector blockage efficiency. – Diffraction at the reflector edges.

• Simulations that are performed within this section do not include:

– Blockage and diﬀraction caused by the supporting structures (they will be very similar for the four cases). – Losses and roughness of the conductor surfaces. – Other possible non-idealities.

The ideal Gaussian feed model parameters to simulate each case are described in Table 3.2 are presented in Table 3.4.

Taper Case Taper angle illumination Polarization

1 14.6◦ 2 10◦ =10 dB RHCP 3 14.6◦ 4 10◦

Table 3.4: Gaussian feed conﬁguration for each of the four compared geometries so that illumination at the edge of the subreﬂector is =10 dB.

The analyzed theta range from =180◦ to 180◦ is conﬁgured to use 10001 points. Since both the feed and the reﬂector system have circular symmetry, all the cuts of the radiation pattern in phi are equal. CHAPTER 3. ANTENNA SYSTEM DESIGN 17

3.4.2 Simulation results of diﬀerent pre-designs

Geometrical dimensions determined in Table 3.3 for the four pre-design cases are introduced in Grasp and simulated. The distinct geometries are illustrated in Figure 3.5, where each pre-design is fed as indicated in Table 3.4.

(a) (b) (c) (d)

Figure 3.5: Analyzed Cassegrain geometries from Table 3.2: (a) case 1, (b) case 2, (c) case 3 and (d) case 4.

Results obtained after having simulated each of the four proposed cases are summarized in Table 3.5. The resulting radiation patterns are respectively illustrated in: • Figure 3.6 for case 1 −→ F/D =0.4 and 21.5 dB-feed. • Figure 3.7 for case 2 −→ F/D =0.4 and 24.8 dB-feed. • Figure 3.8 for case 3 −→ F/D =0.75 and 21.5 dB-feed. • Figure 3.9 for case 4 −→ F/D =0.75 and 24.8 dB-feed.

Copolar component at 94 GHz Crosspolar component at 94 GHz 60 60 50 50 40 40 30 30 20 20 10 10 0 0 -10 -10 Amplitude (dB) Amplitude (dB) -20 -20 -30 -30 -40 -40 -50 -50 -90 -75 -60 -45 -30 -15 0 15 30 45 60 75 90 -90 -75 -60 -45 -30 -15 0 15 30 45 60 75 90 (º) (º) (a) (b) Farfield versus frequency 60 50 Copolar 92 GHz Crosspolar 92 GHz 40 Copolar 94 GHz 30 Crosspolar 94 GHz Copolar 96 GHz 20 Crosspolar 96 GHz 10 0 -10 Amplitude (dB) -20 -30 -40 -50 -5-4-3-2-1012345 (º) (c) Figure 3.6: Simulated farﬁeld results for geometrical design 1: (a) Copolar, (b) crosspolar and (c) zoomed response. 18 3.4. NUMERICAL SOLUTION

Copolar component at 94 GHz Crosspolar component at 94 GHz 60 60 50 50 40 40 30 30 20 20 10 10 0 0 -10 -10 Amplitude (dB) Amplitude (dB) -20 -20 -30 -30 -40 -40 -50 -50 -90 -75 -60 -45 -30 -15 0 15 30 45 60 75 90 -90 -75 -60 -45 -30 -15 0 15 30 45 60 75 90 (º) (º) (a) (b) Farfield versus frequency 60 50 Copolar 92 GHz Crosspolar 92 GHz 40 Copolar 94 GHz 30 Crosspolar 94 GHz Copolar 96 GHz 20 Crosspolar 96 GHz 10 0 -10 Amplitude (dB) -20 -30 -40 -50 -5-4-3-2-1012345 (º) (c) Figure 3.7: Simulated farﬁeld results for geometrical design 2: (a) Copolar, (b) crosspolar and (c) zoomed response.

Copolar component at 94 GHz Crosspolar component at 94 GHz 60 60 50 50 40 40 30 30 20 20 10 10 0 0 -10 -10 Amplitude (dB) Amplitude (dB) -20 -20 -30 -30 -40 -40 -50 -50 -90 -75 -60 -45 -30 -15 0 15 30 45 60 75 90 -90 -75 -60 -45 -30 -15 0 15 30 45 60 75 90 (º) (º) (a) (b) Farfield versus frequency 60 50 Copolar 92 GHz Crosspolar 92 GHz 40 Copolar 94 GHz 30 Crosspolar 94 GHz Copolar 96 GHz 20 Crosspolar 96 GHz 10 0 -10 Amplitude (dB) -20 -30 -40 -50 -5-4-3-2-1012345 (º) (c) Figure 3.8: Simulated farﬁeld results for geometrical design 3: (a) Copolar, (b) crosspolar and (c) zoomed response. CHAPTER 3. ANTENNA SYSTEM DESIGN 19

Figure 3.9: Simulated farﬁeld results for geometrical design 4: (a) Copolar, (b) crosspolar and (c) zoomed response.

Parameter Case 1 Case 2 Case 3 Case 4

Focal distance, F/D 0.4 0.4 0.75 0.75 Feed directivity 21.5 dB 24.8 dB 21.5 dB 24.8 dB Gain 57.4 dB 57.56 dB 56.59 dB 57.22 dB Side Lobe Level =19.18 dB =20.96 dB =14.8 dB =17.85 dB Crosspolar ratio =58.01 dB =55.61 dB =60.8 dB =60.6 dB Beamwidth 0.231◦ 0.235◦ 0.221◦ 0.226◦

Subreﬂector diameter, dS/D 17.5 % 12.3 % 28.2 % 20.8 % Total length of the antenna 302.2 mm 317.8 mm 492.8 mm 535.8 mm Overall eﬃciency 70 % 72.6 % 58.1 % 67.2 %

Table 3.5: Comparison of the results obtained for diﬀerent pre-designs.

Overall efficiencies have been calculated by comparing the simulated gain to the directivity of a paraboloid the same size as the main reflector. Values larger than 70 % are very good designs. Some times the reflectors can be shaped to obtain up to 80 %. 20 3.4. NUMERICAL SOLUTION

3.4.3 Analysis of the results

Main results obtained within this section are summarized in Table 3.5.

• A main reﬂector with F/D =0.4 produces better results, in terms of gain and secondary lobes, than a main reﬂector with F/D =0.75.

• All the analyzed cases obtain simulated gains larger than the speciﬁcation. As observed in the radiation patterns, neither is the bandwidth restriction an issue.

• Obtained crosspolar ratios are quite low for all the designs, although they are better for the lower proﬁle antennas of F/D =0.75.

• As it was obtained within Section 3.3, the overall length Ltot of the antenna system is smaller for F/D =0.4. Besides, lower directivity feeds do also produce more compact systems, since the beam has to be interrupted sooner to prevent it from diverging too much.

• Since it has been required that the feed is considerably close to the apex of the main reﬂector, for F/D =0.75, imposing this criterion and obtaining the required subtended angle generates a subreﬂector diameter that is considerably large. This produces higher blockage and, therefore, performance losses in terms of gain and sidelobe levels.

• For the same reason as the previous point, when the low directivity feed is used, the subreﬂector diameter tends to grow to accommodate to the larger subtended angle that is required to maintain an optimal illumination of C==10 dB.

As a summary, these simulations show that the best performance is expected to be obtained for a Cassegrain system using a main paraboloid of F/D =0.4 illuminated by a feed with 24.8 dB directivity. Shallower paraboloids produce higher secondary lobes and blockage losses due to their large subreﬂectors. The geometrical and electrical parameters for this best pre-design (case 2) are collected in Table 3.6. CHAPTER 3. ANTENNA SYSTEM DESIGN 21

Parameter Value Speciﬁcations Main dish diameter, D 900 mm Main dish focal distance, F 360 mm Feed directivity, D0 24.8 ◦ Semi-subtended angle, ΨS 10.01 Feed position, Lm 20 mm

Geometrical parameters Subreflector diameter, dS 110.5 mm Subreflector semi-transverse axis, a 128.2 mm Subreflector focal distance, f 170 mm Eccentricity, e 1.33 Distance from feed to subreflector, Ls 298.2 mm Total length of the antenna, Ltot 317.8 mm Equivalent focal distance, Fe 2569 mm Magnification, M 7.14

Simulated results Gain 57.56 dB Side Lobe Level =20.96 dB Crosspolar ratio =55.61 dB Beamwidth 0.235◦ Eﬃciency 72.6 %

Table 3.6: Geometrical and simulated results of the chosen conﬁguration.

3.5 Final Antenna Design

After having encountered the range of focal distances and feed directivies for which the antenna system works the best, the ﬁnal optimization has been performed by experts from the GR (Radiation Group) of UPM. Although the optimization process is not part of the work performed within this Thesis, this section presents the ﬁnal antenna geometry for the space debris radar and the simulated results.

3.5.1 Geometrical deﬁnition

The geometrical parameters of the final reflector system are presented in Table 3.7. The resulting geometry is shown at Figure 3.10. Conformation strategies over the reflector and subreflector dishes were also considered for obtaining a more uniform illumination while maintaining low spillover losses, thus increasing the overall efficiency. However, the application of conformation has been finally dismissed, because it would increase the secondary side lobes. 22 3.5. FINAL ANTENNA DESIGN

Parameter Value

Main dish diameter, D 900 mm Main dish focal distance, F/D 0.36 Main dish focal distance, F 324 mm ◦ Semi-subtended angle, ΨS 9.35

Feed position, Lm 34 mm

Subreﬂector diameter dS/D 10 %

Subreflector diameter, dS 90 mm Subreflector semi-transverse axis, a 114 mm Subreflector focal distance, f 145 mm Eccentricity, e 1.27 Distance from feed to subreflector, Ls 259 mm

Total length of the antenna, Ltot 293 mm

Table 3.7: Geometrical parameters of the ﬁnal Cassegrain system.

Figure 3.10: Geometry of the ﬁnal design of the dual antenna system.

3.5.2 Simulation results

The proposed geometry has been simulated in Grasp utilizing the conﬁguration described in Appendix A. The simulation results are presented in Table 3.8 and Figure 3.11.

Parameter Value

Gain 57.5 dB Side Lobe Level =20.71 dB Crosspolar ratio =52.67 dB Beamwidth 0.235◦ Eﬃciency 71.6 %

Table 3.8: Simulation results for the ﬁnal Cassegrain design optimally illuminated by a Gaussian feed. CHAPTER 3. ANTENNA SYSTEM DESIGN 23

Amplitude (dB) -20 -30 -40 -50 -5 -4 -3 -2 -1 0 1 2 3 4 5 (º) (c)

Figure 3.11: Simulated farﬁeld of the ﬁnal design illuminated by C = −10 dB: (a) Copolar (RHCP), (b) crosspolar (LHCP) and (c) zoomed frequency response.

3.5.3 Considerations on the ﬁnal antenna system

This design was optimized by the Radiation Group taking into account further aspects of the design than those observed in Table 3.8. For instance, ease of fabrication, supporting structures, conductor losses or blockage by the struts were considered. Therefore, the simulated results should not be compared with those obtained in previous sections, since they are based on more complex considerations. Besides, the design was optimized for a third model of feed horn with a directivity of 24.55 dB, to which a correcting lens might be attached to improve overall system efficiency. As a task for the future, the fields produced by the monopulse feed that is being designed will be validated for this reflector system. For this purpose, a Grasp object called “tabulated feed” can be used to introduce the real sum and difference patterns of the monopulse horn as a feed of the Cassegrain antenna. 24 3.5. FINAL ANTENNA DESIGN Chapter 4

Software Tool Design for Simulating Quasi-optical Measurement Systems

The simplest free-space measurement system consists of a pair of horns and a sample located between them. However, in most optical applications it is necessary to focus, modify, or shape the beam by using lenses, mirrors and other optical elements. For this reason, this chapter develops a Matlab software tool based on Gaussian beam propagation theory that can be utilized for the analysis and synthesis of quasi-optical test bench designs. In order to examine the capabilities of the developed tool, Section 4.3 offers different examples of reflection-based measurement test benches that could be utilized to measure the reflection coefficient of a sample at W-band.

4.1 Theoretical Background on Quasi-Optical Systems

Quasi-optical systems are a suitable alternative to guided transmission lines at sub-millimeter wavelengths, since not only do they provide exceptionally low losses, but they can also handle multiple polarizations and large bandwidths. Quasi-optical system design is based on Gaussian beam propagation theory. By means of re-focalizing the beam using lenses or mirrors, Gaussian propagation can distribute the input power through a region of several wavelengths [20].

4.1.1 Gaussian beam propagation in free space

Considering that diffraction is small with respect to a wavelength and that axial variations of the field are negligible, the wave equation is reduced to what is called the paraxial wave equation. This approximation can be applied when the angular divergence of the beam is reasonably confined to 30◦. The solution of the paraxial equation are the Gaussian beam modes, which are used as the basis of quasi-optical design [21]. The fundamental and most simple transverse Gaussian mode has the normalized Gaussian field presented in Equation 4.1. 2 jπr2 r2 E(r, z)= exp −jkz − − (4.1) πw2(z) λR(z) w2(z)

The ﬁrst exponential factor of Equation 4.1 describes the phase of a plane wave, the second

25 26 4.1. THEORETICAL BACKGROUND ON QUASI-OPTICAL SYSTEMS factor is responsible for the phase front curvature and the last exponential factor determines the field intensity in the transverse direction [22]. There are some basic parameters that describe a Gaussian beam according to this model: w(z): The radius w of a Gaussian beam is defined as the lateral distance from the propagation axis of the beam where the field amplitude has decayed by exp(−1). The “beamwaist” w0 is the minimum beam radius of the beam.

R(z): The radius of curvature R is deﬁned as the radius of curvature of the spherical wavefronts that describe the equiphase surfaces of the diﬀerent modes.

θ0: The variation of the beam radius w as a function of distance z from the beamwaist has the form of a hyperbola. The asymptotic growth angle of the beam radius is θ0. zc: Rayleigh distance zc is the distance relative to the beamwaist position, in which the beam can be said to be approximately collimated. It is a useful quantity to approximate the beam parameters in two diﬀerent regions: z<>zc is the farﬁeld region.

The parameter z deﬁnes the propagation axis. As the beam propagates towards the beamwaist position, the beam is said to be converging, and after the beamwaist, the beam is diverging. At the beamwaist position, the beam radius is minimum and the radius of curvature is ±∞ (see Figure 4.1).

Beam Beam converges diverges

w = √2 w0 Beamwaist w = √2 w0 w0

θ0 -zc zc

Plane Rmin = 2 zc Rmax = -2 zc wavefront Spherical R→∞ Spherical wavefront wavefront

Figure 4.1: Evolution of the beam radius (black) and phase radius of curvature (green) for a Gaussian beam that propagates in a certain direction.

The variation of beam parameters with distance z, measured from the beamwaist, is given by the following equations[21]:

2 2 z z w(z)=w0 · 1+ (4.2) tan(θ0)= (4.4) zc zc 2 2 zc πw0 R(z)=z + (4.3) zc = (4.5) z λ CHAPTER 4. SIMULATION OF QUASI-OPTICAL MEASUREMENT SYSTEMS 27

4.1.2 Gaussian beam transformation

The treatment of rays in linear optical geometrical systems is based on ABCD transformation matrices, which are defined for each optical element. The quantities of interest are the position din and the slope din of the ray in the input plane, which are transformed into the corresponding quantities dout and dout of the ray in the output plane . Since the radius of curvature is defined as R = position/slope, the relationship from Equation 4.7 can be defined [23].

d AB d out · in = (4.6) dout CD din

dout ARin + B Rout = = (4.7) dout CRin + D

The extension of this ray transformation approach to Gaussian beams, leads to an ABCD law in which the same matrices operate on the complex radius of curvature q which is deﬁned in Equation 4.8 [24]. The complex radii of curvature of the beam at the input and the output planes of an optical structure are related by the transformation of Equation 4.9 [23].

λ 1 1 − 1 = i 2 = (4.8) q(z) R(z) πw (z) z +izc

Aqin + B qout = (4.9) Cqin + D

The equivalent matrix for a sequence of elements can be obtained by multiplying the individual ABCD matrices, starting with that for the ﬁrst element encountered by the beam and adding the matrix of each subsequent element on the left [21].

ABCDtotal = ABCDn · ABCDn−1 · (···) · ABCD2 · ABCD1 (4.10)

Gaussian Beam Sources

Waveguide horns are among the most common radiating elements that produce an approximately Gaussian radiation pattern. A complete list of the approximate beam radii at the aperture of various feed structures is presented by Goldsmith in [20]. This can be used when accurate measurements of the beam size are not available.

Knowing the beam radius at the aperture (w(zap)) and assuming that the radius of curvature attheaperture(R(zap)) is equal to the slant length of the horn, the beamwaist radius w0 and its position behind the aperture z0 can be approximated using Equation 4.11 and Equation 4.12 [21].

w(zap) w0 = (4.11) 2 πw (zap) 1+ 2 λR (zap) πw 0 2 2 z0 = w (zap) − w (4.12) λ 0 28 4.1. THEORETICAL BACKGROUND ON QUASI-OPTICAL SYSTEMS

Beam transformation by a lens

The ABCD matrix of a thin lens, whose surfaces have radii of curvature R1 and R2, is deﬁned using Equation 4.13 [24]. ⎡ ⎤ 10 ⎣ ⎦ 1 nlens − n0 1 1 ABCDlens = 1 with: = − (4.13) − 1 F n0 R2 R1 F

When this matrix is applied to Equation 4.9, the speciﬁc transformation produced on a Gaussian beam after going through a thin lens is found to be modelled by Equations 4.14 and 4.15.

⎡ ⎤ ⎢ din ⎥ ⎢ − 1 ⎥ ⎢ F ⎥ dout = F · ⎢1+ 2 2 ⎥ (4.14) ⎣ din zc ⎦ − 1 + F F

w0in w0 out = (4.15) 2 2 din zc − 1 + F F

A thick lens (it has a certain thickness d) can use those thin lens equations if a certain equivalent focal distance is deﬁned as indicated in Figure 4.2b. In practice, it is also important to know the front and back focal lengths of the lens, Ffv and Fbv [25].

h1 h2

w0in w0out

Ffv Fbv

Fe Fe din dout (a) (b)

Figure 4.2: Gaussian beam transformation by lens: (a) thin lens model and (b) modiﬁed model for a thick lens.

Beam transformation by a focusing mirror

In quasi-optical systems, mirrors provide an alternative to lenses as focusing elements for beam radiation. The beam transformation that occurs at the surface of a mirror is analogous to what happens in a thin lens, excepting for the folding of the propagation axis. Therefore, Equations 4.14 and 4.15 can be used to determine the reﬂected beam parameters of a mirror [23].

• A spherical mirror with a curvature radius R would have the ABCD matrix of 1 2 Equation 4.13, with = . F R CHAPTER 4. SIMULATION OF QUASI-OPTICAL MEASUREMENT SYSTEMS 29

1 1 1 • An ellipsoidal mirror would have the ABCD matrix of Equation 4.13, with = + , F D1 D2 being D1 and D2 the distances from each focus of the ellipsoid to the center of the mirror section.

• A paraboloid mirror is equivalent to an ellipsoid mirror that has a focus at the inﬁnity. Therefore, it has the ABCD matrix of an ellipsoid particularized for D2 = ∞ and D1 = Fparab/cos(θ), where θ is the oﬀ-axis angle of the mirror.

Mirrors usually have to be off-axis resulting in the beam suffering from cross-polarization and distortion effects, specially when the effective focal distance is small. These effects are quantified in [26] and will not be taken into account in the simulation tool.

Beam transformation by a telescope: the afocal system

Usually, when trying to take measurements over a large bandwidth, a non-frequency dependent optical configuration is desired. In general, the relationship between the input beamwaist radius win and the output beamwaist radius wout depends on their locations din and dout,andthey can be derived using the ray transfer matrices of Equation 4.9. A special case occurs when the input beamwaist position din is equal to the focal length F of the lens: Equation 4.14 shows that the output beamwaist position dout will be equal to this focal distance F , regardless of the frequency. This fact is the basis of a “telescope transformation”, in which the beamwaist radius and its position can be controlled by separating every two lenses by the sum of their focal lengths. This allows the creation of what is called an “afocal system”, since an object separated an infinite distance from the first lens will form an image at infinity [25]. A “beam-waveguide” is an afocal system that takes advantage of a telescope-based transformation to guide waves as waveguides do. It injects a Gaussian beam at the focal point of the first lens, so that the output beamwaist is located exactly at the output focal point of the last lens. If the output horn was located there, maximum power coupling from one horn to the other would be obtained. An example of an afocal quasi-optical system is presented in Figure 4.3. The sample (in green) that needs to be characterized is placed at the internal focal points of the lenses (they are coincident). In this way, it is guaranteed that a beamwaist or focusing point will occur exactly at the position of the sample, which means that it would be illuminated by a plane wave maximally collimated regardless of the frequency of operation [25].

w0 w0

F1 F1 F2

Figure 4.3: Example of an afocal system for quasi-optical beam propagation. 30 4.2. DEVELOPED GAUSSIAN BEAM TRACING TOOL

4.2 Developed Gaussian Beam Tracing Tool

A software tool based on Gaussian beam propagation theory has been developed using Matlab as a programming language. It propagates the beam in a two dimensional bench that can be freely conﬁgured using horns, lenses and mirrors as optical elements. This section explains how to correctly execute a simulation (Section 4.2.1), describes its operational ﬂow (Section 4.2.2) and details the simulation outputs (Section 4.2.3).

4.2.1 Running the software

The following enumeration summarizes the steps to make a proper use of the implemented software.

1. Open ﬁle MAIN.m.

2. Type frequency of operation in GHz.

3. Choose the exponent of the exponential ﬁeld decay that will be plotted in addition to the exponent decay -1 (it corresponds to =8.7 dB power decay).

4. Choose which optical system components to use from those available.

5. Choose an arrangement of the optical elements from those that are pre-deﬁned in the tool.

6. Choose separation between horns and lenses.

7. Choose separation between mirrors and the sample.

8. Execute ﬁle MAIN.m.

9. Wait for the results (see Section 4.2.3).

Some pre-designed configurations are already programmed and can be modified to test different situations. If any different optical configuration is needed or any new component has to be simulated, some files must be modified or created.

4.2.2 Step-by-step simulation process

This section summarizes the basic operations that are sequentially performed by the simulator during execution time.

1. The initial parameters are entered as indicated in Section 4.2.1.

2. The corresponding optical system ﬁle is loaded:

2.1. Characteristic parameters of each utilized optical element are obtained. 2.2. Each optical element is positioned and rotated in a two-dimensional bench according to the conﬁguration ﬁle.

3. Propagation axis is unfolded and beam parameters are iteratively calculated as the beam propagates between optical elements: CHAPTER 4. SIMULATION OF QUASI-OPTICAL MEASUREMENT SYSTEMS 31

3.1. Relative input beamwaist position din is obtained.

3.2. Beam parameters, din and w0in, are transformed using the corresponding the ABCD law (Equation 4.9) into the beam parameters referred to the output plane of the structure, dout and w out.

3.3. Paraxial approximation is checked (w0 >> 0.9λ)

3.4. Absolute output beamwaist position is calculated from the relative distance dout. 3.5. Go back to step 3.1.

4. Rays and optical elements are plotted in the unfolded one-dimensional test bench. This approximation makes mirrors behave as thin lenses.

5. Optical axis is re-folded according to the conﬁguration ﬁle and rays and optical elements are plotted in a schematic of a two-dimensional test bench.

6. Overall results of the simulation are calculated, plotted and saved in the corresponding ﬁles (see Section 4.2.3).

4.2.3 Simulation results and output ﬁles

When the simulation stops, results are stored into diﬀerent ﬁles:

Figure 1: two-dimensional propagating beam. This ﬁgure shows a scaled version of the optical bench in which the optical elements and the propagating beam are seen from above. The beam propagates from one element to the next. This ﬁgure is saved as Results/fig1.png and Results/fig1.fig.

Figure 2: simplified one-dimensional propagating beam. This figure unfolds the optical axis so that the beam propagates in a constant direction. This unfolding basically assumes normal incidence over each surface and makes mirrors behave as lenses. This figure is saved as Results/fig2.png and Results/fig2.fig.

Output text ﬁle. This text ﬁle includes all the important results generated during the simulation. These results include:

– Positions of the optical structures in the two-dimensional optical test bench. – Amplitude taper of the beam at the edges of each optical structure. – Beam parameters at the sample position. – Estimated fraction of power than impinges at the sample and at the output horn (it only considers spillover losses).

This ﬁle is saved as Results/output.txt.

4.2.4 Limitations of the simulation tool

The simulation tool that has been implemented along this chapter allows to predict the approximate behaviour of a fundamental Gaussian mode propagating through an optical bench. The tool has many limitations, so it is not intended to obtain a detailed and accurate response of the optical arrangements: 32 4.3. APPLICATION EXAMPLE: 45◦ INCIDENCE

• Beam transformations are calculated assuming normal incidence and that distances between elements are given by the distances between their centers. • For the calculation of the beam transformations along the optical axis, elements are assumed to be ideal: lossless, reflectionless and with an infinite diameter. • Cross-polarization and distortions caused by the feed and the optical structures are not being taken into account. • The pre-configured systems are perfectly aligned systems, since beams propagate along the unfolded optical axis of the system. • Horns are not ideal Gaussian beam radiators. Modifications are required if higher order Gaussian modes need to be taken into account.

As a summary, this tool implements a very simplified version of the Gaussian beam propagation theory. Modifications based on 3 × 3or4× 4 ABCD matrices are not difficult to incorporate in order to produce more accurate results that take into account misalignments, losses, reflections or crosspolarization [27]. Other approximations of Gaussian beam theory use a mode matching method to calculate the transmitted and reflected Gaussian modes at each optical structure [23].

4.3 Application Example: Reﬂection-based Optical Set-ups to Measure Samples at 45◦ Incidence

In order to examine the capabilities of the developed tool, this section proposes different optical configurations that could be used to measure the reflection coefficient of a sample impinged at an angle of 45◦ from boresight. Each configuration produces a different propagation pattern, ones being more collimated at the sample position and others less collimated. Therefore, each configuration will require a different minimum sample size to maintain a certain constraint on edge diffraction and transferred power. For the purpose of making this analysis extensible to any future measurements, the main goal of this analytical example has consisted of obtaining the range of sample sizes for which each quasi-optical bench could produce accurate measurements.

4.3.1 Design criteria

The criteria for the test bench designs of this section are summarized in the following list:

• In order to guarantee good results across different frequencies, these set-ups have been designed as afocal systems, whose characteristics were explained in Section 4.1.2. • Illumination at the edge of the optical elements should be as low as possible, so that most energy is transmitted to the next element and border diffraction effects are minimized. An usual requirement for this taper illumination is =17.4 dB at the border, which is equivalent to a exp(−2) field decay [21]. • Physical elements utilized in the optical bench must not overlap. • Optical elements should interact only once with the propagating beam. • The propagating beam should not intersect with itself. CHAPTER 4. SIMULATION OF QUASI-OPTICAL MEASUREMENT SYSTEMS 33

4.3.2 Simulated optical conﬁgurations

Considering the design criteria from Section 4.3.1, six different optical configurations are proposed for measuring the reflection coefficient of a flat sample impinged at an angle of 45◦ from boresight:

• Using two horns and two dielectric lenses: Section B.1.

• Using two horns and two 45◦ oﬀ-axis mirrors: Section B.2.

• Using two horns and two 90◦ oﬀ-axis mirrors: Section B.3.

• Using two horns, two lenses and two 45◦ oﬀ-axis mirrors: Section B.4.

• Usingtwohorns,two45◦ oﬀ-axis mirrors and two 90◦ oﬀ-axis mirrors: Section B.5

– Option 1: Section B.5.1. – Option 2: Section B.5.2.

These configurations have been simulated using the Matlab software described in Section 4.2, specifically at 94 GHz and 100 GHz, which are the frequencies at which the Spaderadar Project components usually operate. Besides, two different models of horns are compared: a pair of 23 dB RPG Potter horns and a pair of 21 dB Millitech standard conical horns. The selected optical elements are all available at the laboratory and their datasheets can be found in Appendix G. The detailed results of all the performed simulations belonging to each of the proposed configurations are presented in Appendix B.

4.3.3 Critical analysis of the simulation results

As an example of an scenario in which the developed Gaussian beam tracing tool could be utilized, different optical test benches have been designed to measure the reflection coefficient of a flat sample impinged from 45◦ with respect to its normal. The simulation results are presented in Appendix B and their analysis will be useful in Chapter 5 to choose the best free-space measurement system to characterize a reflectarray antenna. In all the designed set-ups the sample is located at a beamwaist position regardless of the frequency, which is a positive feature in case of a broadband measurement. Besides, the usual criteria to consider that the Gaussian beam approximation is sufficiently accurate for the application demands that the amplitude taper at the edges of every optical element is below =17.4 dB. If this is fulfilled, beam truncation effects are negligible [20]. Because of this the objective was to calculate the sample size that obtains exactly those =17.4 dB at its border. The following list summarizes some general conclusions that can be obtained from the analyzed examples:

• Millitech conical horns produce a smaller beamwaist at their phase center than the RPG dual mode horns. This is because the aperture of the RPG horns is larger [21]. It has been noticed that the beam radius at the sample position is smaller in case of:

– Using two focusing elements and the RPG horns. – Using four focusing elements and the Millitech horns. 34 4.3. APPLICATION EXAMPLE: 45◦ INCIDENCE

• In all the analyzed designs the beam radius at the sample position is smaller at 100 GHz than at 94 GHz. However, it has been noticed that, in a 5 % bandwidth, actual diﬀerences in the beam evolution throughout the bench are small.

• None of the optical conﬁgurations using 90◦ oﬀ-axis mirrors obtains less than =17.4 dB spillover losses at those mirrors. The reason for this is that the beam diverges too much when it propagates along the distance from the horn too the mirror (equivalent focal length of the mirror), which could be avoided using horns with larger beamwaist at their phase centers (e.g., with higher gain).

• Configurations using two 45◦ and two 90◦ off-axis mirrors do not comply with the paraxial approximation at the sample position, so the Gaussian beam approximation is not representative of the real behaviour of the fields.

As a summary, the sample under test has to be larger than the minimum sample size to avoid truncation effects. Besides, if it is too large, only the response of the central part of the sample will be actually measured. A good trade-off between maintaining low truncation effects and obtaining high illumination efficiency would demand from =17.4 dB to =25 dB at the edge of the sample. Therefore, different configurations would be optimum for measuring different samples depending on their sizes. The sample sizes for the most promising configurations, according to simulations, are presented in Table 4.1.

Sample size Configuration 94 GHz 100 GHz Lenses (×2) 57 - 69 mm 55 - 66 mm 45◦ off-axis mirrors (×2) 108 - 130 mm 104 - 125 mm Lenses (×2) + 45◦ off-axis mirrors (×2) 35 - 42 mm 34 - 41 mm

Table 4.1: Recommended sample sizes for using diﬀerent free-space measurement systems (using RPG horns).

Finally, another aspect to be considered in order to choose the best optical set-up is the avoidance of6 elements that introduce losses or uncontrolled distortions. For example, the lenses available at the laboratory introduce about 20 % losses according to their datasheet (see Appendix G). Chapter 5

Characterization of a W-band reﬂectarray

This chapter is aimed at the characterization of a reflectarray working at W-band. This antenna was designed by the Applied Electromagnetism Group and the Photonics Group of ETSIT (UPM) as a first prototype of a reflectarray to substitute the mechanical exploration scheme of the basic antenna system described in Chapter 3. The software tool developed in Chapter 4 will be utilized to design the quasi-optical test benches necessary to measure the reflectarray sample. According to simulations, those configurations expected to obtain the best performance will be implemented to perform the measurements (Section 5.3). The measurements performed within this chapter are intended to serve as a general overview of the behaviour of the reflectarray, in order to validate the designing and manufacturing methods [28]. The main goal of the measurements presented in Section 5.4 has been to establish which excitations to apply to produce a certain quasi-permanent state at each unit cell of the reflectarray. Once this is obtained, pattern synthesis theory could be applied to obtain beamforming and beamsteering capabilities.

5.1 Theoretical Background on Reﬂectarray Antennas

A reflectarray is an antenna consisting of a flat reflecting surface formed by many radiating elements that are illuminated by a feed antenna (see Figure 5.1). When the feed illuminates the reflectarray elements, most of the energy is re-radiated. By modifying certain geometrical parameters of the radiating elements, the incident field at each elemental cell will be scattered with the electric phase required to form a planar wavefront in the farfield distance [29]. Each elemental cell must introduce a phase shift to compensate for the phase differences associated to the different paths between the horn and the different cells. Besides, it is possible to introduce further phase shifts to apply array synthesis techniques and accurately tilt or conform the beam [30].

35 36 5.1. THEORETICAL BACKGROUND ON REFLECTARRAY ANTENNAS

Figure 5.1: Schematic of a reﬂectarray antenna [29].

5.1.1 Reﬂectarray antennas based on patches

The simplest elements that can be used in reflectarray antennas consist of variable-size printed patches. By varying the resonant dimensions of the patches, the phase shift introduced by each cell in the incident field can be modified [29]. A reflectarray made of a single layer of microstrip patches exhibits a narrowband behaviour. There are several techniques to increase the operational bandwidth:

• Increasing the substrate thickness (although this reduces the phase range).

• Stacking two or more array layers.

• Using more complex multi-resonant cells.

5.1.2 Reconﬁgurable reﬂectarrays based on liquid crystal

The principle of operation of a reconfigurable reflectarray is based on the possibility of varying the geometrical parameter that controls the phase shift (e.g., the resonant length) of the unit-cell elements. LC (Liquid Crystal) is a thin membrane material that has the ability to change its permittivity (dielectric anisotropy) when a quasi-static electric field is externally applied. This important feature is based on a property of nematic LC molecules to twist themselves to varying degrees depending on the applied voltage [31, 32]. If the LC is inserted in the gap between the printed patches layer and the ground layer of a reflectarray antenna, this tunable permittivity will modify the effective wavelength of the cell. Thus, LC properties can be exploited to transform each cell of the reflectarray antenna into an electronically controlled phase shifter [31, 33]. If each reflectarray cell can be biased independently with a certain voltage, the antenna could be used for 2D-scanning using array synthesis techniques [30]. Different strategies have already been successfully utilized to address the cells (pixels) of LCD (Liquid Crystal Display) screens [32]. They are usually based on time-multiplexing techniques, in which different cells are interconnected in rows at one side of the LC layer and in columns at the other side, and then sequentially biased as required. These techniques could be adapted to operate in reflectarray technology.

• Passive addressing: Due to the inherent capacitive behaviour of the LC, short pulses can be applied periodically to each column and row to maintain the molecular twisted state CHAPTER 5. CHARACTERIZATION OF A W-BAND REFLECTARRAY 37

of the LC inside each cell. Basically, the strategy relies on the switching-oﬀ speed of LC being longer than the refreshing period[32]. • Active addressing: It involves introducing an appropriate element with memory (capacitor, transistor) in each cell, so that it holds the charge for a limited period of time. The switching action of the external element helps the reﬂectarray cells to remain active until the next refreshing period [32].

5.2 Reﬂectarray Sample Under Test

The reflectarray antenna that needs to be characterized exploits the dielectric anisotropy of LC to produce a reconfigurable antenna. It has been designed to operate at 96 - 104 GHz and it is expected to generate about 440◦ phase variation and to introduce mean losses below 7 dB. Figure 5.2 depicts the topology of the reflectarray. The unit cells are composed of three dipoles of different lengths that are printed on a quartz wafer, which is separated from a metal ground by an LC layer. 52 × 54 cells are arranged in a rectangular lattice to form the reflectarray [34].

(a) (b)

Figure 5.2: Schematic of the manufactured reﬂectarray [34]: (a) Unit-cell and (b) reﬂectarray.

Table 5.1 summarizes the dimensions and the simulated results of the designed reﬂectarray [35].

Parameter Value Parameter Value

Operating frequency 96 - 104 GHz Number of column cells 54 cells Operating incidence angle 0 - 30◦ Number of row cells 52 cells Maximum reﬂection loss 12 dB Diameter of the reﬂectarray 60 mm Phase variation at 100 GHz 440◦ Total diameter of the sample 100 mm

Table 5.1: Speciﬁcations of the reﬂectarray sample. 38 5.3. QUASI-OPTICAL TEST BENCHES

Figure 5.3 presents a photograph of the manufactured reflectarray sample. As observed, the reflectarray cells are connected in rows and columns following a passive matrix addressing strategy. A cell is biased if a potential difference is present between the row and column to which it is connected. For independent excitation of each row and column, 52 + 54 biasing cables are extracted from the reflectarray and connected to the excitation source.

(a) (b)

Figure 5.3: Photographs of the reﬂectarray sample: (a) Front view and (b) rear view.

5.3 Quasi-optical Test Benches

This section presents the measurement set-ups that have been utilized for measuring the reﬂectarray for various angles of incidence. Quasi-optical set-ups for 30◦ and 45◦ incidence angles have been proposed and analyzed using the software developed in Chapter 4:

• Quasi-optical set-up for 30◦ incidence: (Section 5.3.2).

– Based on lenses.

• Quasi-optical set-up for 45◦ incidence: (Section 5.3.3).

– Based on lenses. – Based on mirrors.

All the utilized measurement systems are afocal systems (see Section 4.1.2) to which the VNA is connected. Therefore, the beam can be considered locally at the sample position as a plane wave regardless of the frequency. CHAPTER 5. CHARACTERIZATION OF A W-BAND REFLECTARRAY 39

It is also important to comment, that the calculated eﬃciencies are not representative of the real behaviour of the system, since they are only considering spillover losses and losses in the lenses. Other sources of losses, dispersion or reﬂections could cause a loss in performance.

5.3.1 Utilized optical components

Only those optical components that are already available at the laboratory are utilized to design the optical test benches:

1. Conical horns:

– 23 dB gain dual mode conical horns (×2).

2. Paraboloid oﬀ-axis mirrors:

◦ –45, ∅ = 101.6mmand Feq = 119.03 mm (×2).

3. Dielectric lenses:

– Teﬂon, ∅ =80mmandFeq =62.7mm(×2) .

4. Supporting structures.

5. 600 × 600 mm optical bench.

Available datasheets of these components can be found in Appendix G. Besides, the phase center of the horns has been calculated in Appendix C simulating them using HFSS (High Frequency Structural Simulator R ), so that they can be placed at their optimum positions according to the test bench designs.

5.3.2 Optical set-up for 30◦ incidence

Using the available material, the simplest test bench for measuring with 30◦ incidence consists of placing the sample obliquely between two horns and collimating the beam with two lenses at the output of the horns. Figure 5.4 illustrates the simulated behaviour of the beam through the proposed test bench at 94 GHz, which is the frequency of interest for which the beam radius at the sample is larger. Table 5.3 presents a summary of the obtained results for the proposed test bench.

• Edge diﬀraction is negligible since the amplitude taper at the sample and the rest of optical structures is below =17.4 dB.

• Spillover losses and other beam truncation eﬀects can also be neglected since the edge taper at every structure is suﬃciently low. The main source of losses are the lenses which introduce 19.6 % losses each.

• Lenses overlap, so in order to obtain a focused beam at the sample, their edges have been slightly trimmed so that they ﬁt in this conﬁguration. This adjustment is not expected to perturb the behaviour of the lenses. 40 5.3. QUASI-OPTICAL TEST BENCHES

Optical Bench Configuration

Optical element x(mm) y(mm) 0 Horn 1 (phase center) 00 Lens 1 (convex face) 69.10 (mm) -50 Sample (center) 131.80 Lens 2 (convex face) 89.8 −72.8 Horn 2 (phase center) 65.9 −114.1 -100

Beam e-1 Beam e-2

-50 0 50 100 150 (mm)

Figure 5.4: Test bench conﬁguration for 30◦ Table 5.2: Element positions for the proposed incidence at 94 GHz. optical test bench for 30◦ incidence.

Parameter 94 GHz 100 GHz Beam at the sample Beam radius 14.18 mm 13.65 mm ∞ Radius of curvature ∞ m m Efficiency Edge taper at the sample =28.99 dB =31.28 dB Maximum edge taper =19.94 dB =20.92 dB Losses in the lenses 35.3 % 35.3 % Spillover efficiency 98.35 % 99.78 % Total efficiency ≈ 63.6% ≈ 64.5%

Table 5.3: Simulated results of the proposed test bench conﬁguration to measure the reﬂectarray with an angle of incidence of 30◦.

5.3.3 Optical set-up for 45◦ incidence

According to the study developed in Section 4.3, there are different optical configurations that could produce satisfactory results for the measurement of the reflectarray sample with an angle of incidence of 45◦. The simplest test bench again consists of utilizing two lenses to collimate the beam emerging from the horns. However, each lens introduces about 1 dB loss, so an alternative set-up that uses off-axis mirrors as collimating elements has also been implemented. Empirical results of both measurement set-ups are compared in Section 5.3.4. CHAPTER 5. CHARACTERIZATION OF A W-BAND REFLECTARRAY 41

Proposed optical test bench using lenses

This optical set-up uses lenses to collimate the beam emerging from the horns. Figure 5.5 illustrates the simulated behaviour of the beam through the proposed test bench at 94 GHz, which is the the frequency of interest that produces the largest beam radius at the sample. Table 5.5 presents a summary of the obtained results for the proposed optical system. Optical Bench Configuration 50

0 Optical element x(mm) y(mm)

-50 Horn 1 (phase center) 00 Lens 1 (convex face) 47.70 (mm) . − . -100 Sample (center) 131 8 69 1 Lens 2 (convex face) 131.8 −84.1 Horn 2 (phase center) 131.8 −131.8 -150

Beam e-1 Beam e-2 -200 -50 0 50 100 150 200 (mm)

Figure 5.5: Test bench conﬁguration for 45◦ Table 5.4: Element positions for the proposed incidence at 94 GHz using lenses. optical test bench for 45◦ incidence using lenses.

• Edge diﬀraction is negligible since the amplitude taper at the sample and the rest of optical structures is below =17.4 dB.

• Spillover losses and other beam truncation eﬀects can also be neglected since the edge taper at every structure is suﬃciently low. Therefore, the estimated loss in performance is mainly due to the losses introduced by the lenses.

• The eﬀective beam radius at the sample is larger than in the case of 30◦ incidence, because the sample is impinged more obliquely. Therefore, spillover losses are larger. 42 5.3. QUASI-OPTICAL TEST BENCHES

Parameter 94 GHz 100 GHz Beam at the sample Beam radius 14.18 mm 13.65 mm ∞ Radius of curvature ∞ m m Spillover efficiency Edge taper at the sample =19.2 dB =20.72 dB Maximum edge taper =19.2 dB =20.72 dB Losses in the lenses 35.3 % 35.3 % Spillover efficiency 98.77 % 99.14 % Total efficiency ≈ 63.8% ≈ 64.1%

Table 5.5: Simulated results of the test bench conﬁguration to measure the reﬂectarray with an angle of incidence of 45◦ using lenses.

Proposed optical test bench using 45◦ oﬀ-axis mirrors

In contrast to the previous optical conﬁguration, this set-up is based on the use 45◦ oﬀ-axis mirrors to collimate the beam emerging from the horns. Figure 5.6 illustrates the behaviour of the beam through the proposed test bench for a frequency of 94 GHz, which is the frequency of interest that produces the largest beam radius at the sample position. Table 5.7 summarizes the obtained simulation results.

Optical Bench Configuration 100 Beam e-1 Beam e-2 50

0 Optical element x(mm) y(mm) Horn 1 (phase center) -50 00 ) Lens 1 (convex face) 119 0 mm ( -100 Sample (center) 34.9 −84.2 Lens 2 (convex face) 119 −168.3 -150 Horn 2 (phase center) 0 −168.3

-200

-250 -50 0 50 100 150 (mm)

Figure 5.6: Test bench conﬁguration for 45◦ Table 5.6: Element positions for the proposed incidence at 94 GHz using mirrors. optical test bench for 45◦ incidence using mirrors.

• Edge diﬀraction would be high at the borders of the sample, since they will be illuminated with about =5.5 dB with respect to the center of the sample.

• Spillover at the sample position will be large and it is the main reason for the loss in performance observed in the estimated eﬃciency. Other truncation eﬀects, such as beam CHAPTER 5. CHARACTERIZATION OF A W-BAND REFLECTARRAY 43

distortion, cannot be neglected, neither can they be evaluated using the implemented software.

• Figure 5.6 suggests that spillover may travel towards the horns corrupting the measurements. Indeed, the problem will be that the quartz frame in which the sample is inserted is 40 mm larger than the actual reﬂectarray. Therefore, the quartz will be illuminated and its response will partially obscure the reﬂectarray response.

Parameter 94 GHz 100 GHz Beam at the sample Beam radius 26.92 mm 13.65 mm ∞ Radius of curvature ∞ m m Eﬃciency Edge taper at the sample =5.4 dB =5.8 dB Maximum edge taper =5.4 dB =5.8 dB Spillover eﬃciency 70.31 % 73.46 %

Table 5.7: Simulated results of the alternative test bench conﬁguration to measure the reﬂectarray with an angle of incidence of 45◦ using mirrors.

5.3.4 Comparison of lens-based and mirror-based set-ups for 45◦ incidence

As stated in Section 5.3.3, two different optical set-ups could yield good results for the measurement of the reflectarray when it is impinged at an angle of 45◦. The first set-up is based on lenses and the second is based on 45◦ off-axis mirrors. Both proposed measurement systems have been implemented in the optical bench. In order to decide which of them yields the best results, an optical thru (flat metallic plate) with the same dimensions as the reflectarray is placed at the sample position. Photographs of the optical test benches utilized for these situations are presented in Figure 5.7.

(a) (b)

Figure 5.7: Optical thru in the quasi-optical test bench utilized to measure vertical incidence response for 45◦ incidence: (a) Based on lenses and (b) based on mirrors. 44 5.3. QUASI-OPTICAL TEST BENCHES

Figure 5.8 presents the response of the thru for both measurement systems in time and in frequency domains, where a rectangular window is used for the transformation and a Hamming ﬁlter for time gating.

Transmission coefficient in time domain Transmission coefficient in frequency domain after gating 0 60 S21-Lenses S21-Mirrors

50 -5

-10 (dB) 30 (dB)

20 -15 Raw S21-Lenses Gated S21-Lenses 10 Raw S21-Mirrors Gated S21-Mirrors 0 -20 0 2000 4000 6000 8000 10000 12000 88 90 92 94 96 98 100 102 104 106 Time (ps) Frequency (GHz) (a) (b)

◦ Figure 5.8: Measured S21 of the optical thru for 45 incidence: (a) Time domain and (b) frequency domain.

Even though less reﬂections and lower losses were expected from the mirror-based test bench, a S21 response with more ripples and lower mean level has been actually obtained. This can be explained understanding the multipath time response of Figure 5.8a:

• The earliest arriving signal corresponds to the response of the thru, since waves travel through the shortest path between both horns. This peak occurs latter for the mirror-based system due to the larger effective focal distance of the mirrors. • The rest of the peaks represent standing waves inside the system finally arriving to the horn after several reflections. It can be seen that they arrive every certain period of time according to the separation between optical elements in the test bench. • Transmission losses are about 4 dB higher in the case of the mirror-based system, which could be explained from the high spillover losses that are occurring when the Gaussian beam impinges at the sample (see Figure 5.6). However, spillover losses were included in the calculation of the expected efficiency, which yielded worst performance for the lens-based system (see from Section 5.3.3). • Another explanation is that in the case of mirrors, that energy is not lost; instead it arrives in the form of those powerful “late-arriving signals”, whose power is more blurred for the lens-based system. This means that part of the loss in performance of the mirror-based system is due to high return losses, which is an effect that was not not accounted for in the efficiency estimation from Section 5.3.3.

As it is commented in Appendix D and Appendix E, the dynamic margin obtained after calibrating the VNA is about 25 dB, a quantity from which the losses occurring inside the optical bench must be subtracted (losses of the thru). Therefore, when the mirror-based system is used, high resonances of more than 20 dB appearing in the reﬂectarray response are actually falling below the calibration precision, which corrupts the phase responses with noise and they cannot be recovered using the post-processing technique explained in Appendix E. For all these reasons, the measurements of the reﬂectarray that are based on mirrors have been ignored for the following analysis. CHAPTER 5. CHARACTERIZATION OF A W-BAND REFLECTARRAY 45

5.4 Reﬂectarray Characterization

This section presents the first set of measurements of the reflectarray sample described in Section 5.2. They are intended to obtain a general overview of the reflectarray response and validate the theoretical model and the manufacturing method.

5.4.1 Measurement plan

Reflectarrays behave very differently depending on how the cells are excited and the characteristics of the incident field. Therefore, the reflectarray behaviour can be characterized varying different parameters:

• For diﬀerent incident frequencies. • For diﬀerent signal shapes.

• For diﬀerent angles of incidence. • For diﬀerent control voltages.

• For diﬀerent polarizations. • For diﬀerent synthesized patterns.

• For diﬀerent addressing strategies. •···

The general parameters that are common for all the performed measurements are summarized in Table 5.8.

Parameter Value Range of frequencies 80 - 110 GHz Range of control voltages 0 - 300 Vpp Frequency of the excitation 1 kHz

Table 5.8: Common parameters to all the measurements.

Ranges of frequency and incidence angles for which to perform the measurements are chosen according to the speciﬁcations in Table 5.1, so that performance losses when being outside the operational ranges can also be appreciated. The following list summarizes the measurements that are presented along the rest of the section:

• Quasi-static homogeneous control: Cells are all excited with the same quasi-static control signal and they are characterized for diﬀerent biasing voltages (Section 5.4.2).

– 30◦ incidence for vertical orientation. – 30◦ incidence for horizontal orientation. – 45◦ incidence for vertical orientation.

• Dynamic control based on time-multiplexing: Short excitation pulses are sequentially applied to each row and column intending to maintain a certain quasi-permanent state in all the cells (Section 5.4.3):

– 30◦ incidence for vertical orientation. – 30◦ incidence for horizontal orientation. 46 5.4. REFLECTARRAY CHARACTERIZATION

Section 5.3 presents the designs of the quasi-optical test benches that have been utilized to measure the reﬂectarray for both 30◦ (see Figure 5.4) and 45◦ incidence (see Figure 5.5). On the other hand, the VNA conﬁguration and other measurement equipment is detailed in Appendix D and applied post-processing techniques are explained in Appendix E.

5.4.2 Static homogeneous control

For this ﬁrst set of measurements, every unit cell of the reﬂectarray is identically biased. In order to do this, the same quasi-static excitation has been simultaneously applied to every row and column biasing lines. Measurements have been performed for combinations of:

– Vertical and horizontal orientation. –30◦ and 45◦ incidence angles. – Sinusoidal and square excitation signals.

30◦ incidence for vertical orientation A photograph of the reﬂectarray placed in the quasi-optical test bench is presented in Figure 5.9.

Figure 5.9: Reﬂectarray in the quasi-optical test bench utilized to measure vertical orientation response for 30◦ incidence.

The results obtained after applying the same sinusoidal excitation to every cells are presented in Figure 5.10. Figure 5.11 shows the same experiment but for square excitation.

Sinusoidal excitation: |S21| Sinusoidal excitation: (S21) 0 0

-5 -200 -10 0.0 Vpp 62.8 Vpp 0.0 Vpp 62.8 Vpp 3.9 Vpp 66.6 Vpp -400 3.9 Vpp 66.6 Vpp -15 7.7 Vpp 70.5 Vpp 7.7 Vpp 70.5 Vpp 11.6 Vpp 78.0 Vpp 11.6 Vpp 78.0 Vpp -20 15.4 Vpp 86.0 Vpp -600 15.4 Vpp 86.0 Vpp 19.4 Vpp 93.8 Vpp 19.4 Vpp 93.8 Vpp 23.3 Vpp 102.0 Vpp S21 (º) 23.3 Vpp 102.0 Vpp S21(dB) -25 27.1 Vpp 111.0 Vpp 27.1 Vpp 111.0 Vpp 31.0 Vpp 117.0 Vpp -800 31.0 Vpp 117.0 Vpp 38.7 Vpp 127.0 Vpp 38.7 Vpp 127.0 Vpp -30 42.5 Vpp 134.0 Vpp 42.5 Vpp 134.0 Vpp 46.4 Vpp 142.0 Vpp 46.4 Vpp 142.0 Vpp 50.3 Vpp 150.0 Vpp -1000 50.3 Vpp 150.0 Vpp -35 54.2 Vpp 219.0 Vpp 54.2 Vpp 219.0 Vpp 58.1 Vpp 298.0 Vpp 58.1 Vpp 298.0 Vpp -40 -1200 80 85 90 95 100 105 110 80 85 90 95 100 105 110 Frequency (GHz) Frequency (GHz) (a) (b) Figure 5.10: Reﬂectarray measurements using sinusoidal excitation, 30◦ incidence and vertical orientation: (a) Amplitudes and (b) phase shifts. CHAPTER 5. CHARACTERIZATION OF A W-BAND REFLECTARRAY 47

Square excitation: |S21| Square excitation: (S21) 0 0

-5 -200 -10 0 Vpp 63.6 Vpp 0 Vpp 63.6 Vpp 5 Vpp 67.4 Vpp -400 5 Vpp 67.4 Vpp -15 7.95 Vpp 71.3 Vpp 7.95 Vpp 71.3 Vpp 11.9 Vpp 78.4 Vpp 11.9 Vpp 78.4 Vpp -20 15.7 Vpp 87.3 Vpp -600 15.7 Vpp 87.3 Vpp 19.7 Vpp 95.2 Vpp 19.7 Vpp 95.2 Vpp 23.6 Vpp 103 Vpp S21 (º) 23.6 Vpp 103 Vpp S21(dB) -25 27.5 Vpp 112 Vpp 27.5 Vpp 112 Vpp 31.4 Vpp 119 Vpp -800 31.4 Vpp 119 Vpp 39.2 Vpp 129 Vpp 39.2 Vpp 129 Vpp -30 43.1 Vpp 137 Vpp 43.1 Vpp 137 Vpp 47 Vpp 145 Vpp 47 Vpp 145 Vpp 51 Vpp 153 Vpp -1000 51 Vpp 153 Vpp -35 54.9 Vpp 223 Vpp 54.9 Vpp 223 Vpp 58.8 Vpp 307 Vpp 58.8 Vpp 307 Vpp -40 -1200 80 85 90 95 100 105 110 80 85 90 95 100 105 110 Frequency (GHz) Frequency (GHz) (a) (b) Figure 5.11: Reﬂectarray measurements using square excitation for 30◦ incidence and vertical orientation: (a) Amplitudes and (b) phase shifts.

30◦ incidence for horizontal orientation In order to measure the response when the reﬂectarray is horizontally oriented, both the horns and the sample are rotated by 90◦, so that TM polarization is maintained. A photograph of the reﬂectarray placed in the quasi-optical test bench is presented in Figure 5.12.

Figure 5.12: Reﬂectarray in the quasi-optical test bench utilized to measure vertical orientation response for 30◦ incidence. Figure 5.13 presents the results that have been obtained applying the same sinusoidal excitation voltage to every cell of the reﬂectarray. Figure 5.14 shows the results for square excitation. 48 5.4. REFLECTARRAY CHARACTERIZATION

Sinusoidal excitation: |S21| Sinusoidal excitation: (S21) 0 200

-5 0 -10 0.0 Vpp 62.8 Vpp 0.0 Vpp 62.8 Vpp 3.9 Vpp 66.6 Vpp -200 3.9 Vpp 66.6 Vpp -15 7.7 Vpp 70.4 Vpp 7.7 Vpp 70.4 Vpp 11.6 Vpp 77.3 Vpp 11.6 Vpp 77.3 Vpp -20 15.4 Vpp 85.9 Vpp -400 15.4 Vpp 85.9 Vpp 19.3 Vpp 93.7 Vpp 19.3 Vpp 93.7 Vpp 23.3 Vpp 102.0 Vpp S21 (º) 23.3 Vpp 102.0 Vpp S21(dB) -25 27.1 Vpp 110.0 Vpp 27.1 Vpp 110.0 Vpp 31.0 Vpp 117.0 Vpp -600 31.0 Vpp 117.0 Vpp 38.6 Vpp 127.0 Vpp 38.6 Vpp 127.0 Vpp -30 42.6 Vpp 134.0 Vpp 42.6 Vpp 134.0 Vpp 46.3 Vpp 142.0 Vpp 46.3 Vpp 142.0 Vpp 50.3 Vpp 150.0 Vpp -800 50.3 Vpp 150.0 Vpp -35 54.2 Vpp 219.0 Vpp 54.2 Vpp 219.0 Vpp 58.1 Vpp 297.0 Vpp 58.1 Vpp 297.0 Vpp -40 -1000 80 85 90 95 100 105 110 80 85 90 95 100 105 110 Frequency (GHz) Frequency (GHz) (a) (b) Figure 5.13: Reﬂectarray measurements using sinusoidal excitation, 30◦ incidence and horizontal orientation: (a) Amplitudes and (b) phase shifts.

Square excitation: |S21| Square excitation: (S21) 0 200

-5 0 -10 0.0 Vpp 63.6 Vpp 0.0 Vpp 63.6 Vpp 5.0 Vpp 67.4 Vpp -200 5.0 Vpp 67.4 Vpp -15 8.0 Vpp 71.3 Vpp 8.0 Vpp 71.3 Vpp 11.8 Vpp 78.4 Vpp 11.8 Vpp 78.4 Vpp -20 15.7 Vpp 87.2 Vpp -400 15.7 Vpp 87.2 Vpp 19.6 Vpp 95.0 Vpp 19.6 Vpp 95.0 Vpp 23.6 Vpp 103.0 Vpp S21 (º) 23.6 Vpp 103.0 Vpp S21(dB) -25 27.5 Vpp 112.0 Vpp 27.5 Vpp 112.0 Vpp 31.4 Vpp 119.0 Vpp -600 31.4 Vpp 119.0 Vpp 39.1 Vpp 129.0 Vpp 39.1 Vpp 129.0 Vpp -30 43.1 Vpp 136.0 Vpp 43.1 Vpp 136.0 Vpp 47.0 Vpp 144.0 Vpp 47.0 Vpp 144.0 Vpp 51.0 Vpp 153.0 Vpp -800 51.0 Vpp 153.0 Vpp -35 54.8 Vpp 223.0 Vpp 54.8 Vpp 223.0 Vpp 58.8 Vpp 308.0 Vpp 58.8 Vpp 308.0 Vpp -40 -1000 80 85 90 95 100 105 110 80 85 90 95 100 105 110 Frequency (GHz) Frequency (GHz) (a) (b)

Figure 5.14: Reﬂectarray measurements using square excitation for 30◦ incidence and horizontal orientation: (a) Amplitudes and (b) phase shifts.

45◦ incidence for vertical orientation

Photographs of the reﬂectarray placed in the proposed quasi-optical test benches are presented in Figure 5.15. As concluded in Section 5.3.4, the set-up that yields the best results is the one based on lenses. Therefore, the measurements taken using the optical set-up of Figure 5.15a are the ones that are post-processed and presented in this section. Figure 5.16 shows the results that have been obtained simultaneously applying the same sinusoidal excitation voltage to every cell of the reﬂectarray. Figure 5.17 presents the same results but for square excitation signals. CHAPTER 5. CHARACTERIZATION OF A W-BAND REFLECTARRAY 49

(a) (b)

Figure 5.15: Reﬂectarray in the quasi-optical test bench utilized to measure vertical orientation response for 45◦ incidence: (a) Based on lenses and (b) based on mirrors.

Sinusoidal excitation: |S21| Sinusoidal excitation: (S21) 0 0

-5 -200 -10 0.0 Vpp 0.0 Vpp 3.9 Vpp 63.0 Vpp -400 3.9 Vpp 63.0 Vpp -15 7.8 Vpp 66.8 Vpp 7.8 Vpp 66.8 Vpp 11.6 Vpp 70.6 Vpp 11.6 Vpp 70.6 Vpp -20 15.4 Vpp 77.5 Vpp -600 15.4 Vpp 77.5 Vpp 19.4 Vpp 85.0 Vpp 19.4 Vpp 85.0 Vpp 23.3 Vpp 93.9 Vpp S21 (º) 23.3 Vpp 93.9 Vpp S21(dB) -25 27.2 Vpp 102.0 Vpp 27.2 Vpp 102.0 Vpp 31.6 Vpp 117.0 Vpp -800 31.6 Vpp 117.0 Vpp 38.7 Vpp 127.0 Vpp 38.7 Vpp 127.0 Vpp -30 42.7 Vpp 135.0 Vpp 42.7 Vpp 135.0 Vpp 46.5 Vpp 142.0 Vpp 46.5 Vpp 142.0 Vpp 50.4 Vpp 151.0 Vpp -1000 50.4 Vpp 151.0 Vpp -35 54.3 Vpp 219.0 Vpp 54.3 Vpp 219.0 Vpp 58.2 Vpp 298.0 Vpp 58.2 Vpp 298.0 Vpp -40 -1200 80 85 90 95 100 105 110 80 85 90 95 100 105 110 Frequency (GHz) Frequency (GHz) (a) (b)

Figure 5.16: Reﬂectarray measurements using sinusoidal excitation for 45◦ incidence and vertical orientation: (a) Amplitudes and (b) phase shifts.

Square excitation: |S21| Square excitation: (S21) 0 0

-5 -200 -10 0.0 Vpp 63.7 Vpp 0.0 Vpp 63.7 Vpp 5.1 Vpp 67.5 Vpp -400 5.1 Vpp 67.5 Vpp -15 8.0 Vpp 71.3 Vpp 8.0 Vpp 71.3 Vpp 11.8 Vpp 78.5 Vpp 11.8 Vpp 78.5 Vpp -20 15.7 Vpp 87.4 Vpp -600 15.7 Vpp 87.4 Vpp 19.6 Vpp 95.4 Vpp 19.6 Vpp 95.4 Vpp 23.6 Vpp 103.0 Vpp S21 (º) 23.6 Vpp 103.0 Vpp S21(dB) -25 27.5 Vpp 112.0 Vpp 27.5 Vpp 112.0 Vpp 31.5 Vpp 119.0 Vpp -800 31.5 Vpp 119.0 Vpp 39.2 Vpp 129.0 Vpp 39.2 Vpp 129.0 Vpp -30 43.1 Vpp 137.0 Vpp 43.1 Vpp 137.0 Vpp 47.0 Vpp 145.0 Vpp 47.0 Vpp 145.0 Vpp 51.0 Vpp 153.0 Vpp -1000 51.0 Vpp 153.0 Vpp -35 54.9 Vpp 223.0 Vpp 54.9 Vpp 223.0 Vpp 58.9 Vpp 307.0 Vpp 58.9 Vpp 307.0 Vpp -40 -1200 80 85 90 95 100 105 110 80 85 90 95 100 105 110 Frequency (GHz) Frequency (GHz) (a) (b)

Figure 5.17: Reﬂectarray measurements using square excitation for 45◦ incidence and vertical orientation: (a) Amplitudes and (b) phase shifts.

Discussion of the results

This reﬂectarray was designed to work at 96 - 104 GHz with an angular range of 0 - 30◦ and TM polarization. However, there are disagreements with respect to simulations that cannot 50 5.4. REFLECTARRAY CHARACTERIZATION be explained from manufacturing tolerances, especially regarding the frequency band and the maximum phase diﬀerence (see Table 5.1). Therefore, the entire design and manufacturing process is being reconsidered [34].

Sinusoidal excitation Square excitation 0 0 =30º, 94 GHz, H-Pol =30º, 94 GHz, H-Pol =30º, 100 GHz, H-Pol =30º, 100 GHz, H-Pol =30º, 94 GHz, V-Pol =30º, 94 GHz, V-Pol -100 =30º, 100 GHz, V-Pol -100 =30º, 100 GHz, V-Pol (º) =45º, 94 GHz, V-Pol (º) =45º, 94 GHz, V-Pol =45º, 100 GHz, V-Pol =45º, 100 GHz, V-Pol -200 -200 ase range ase range

Ph -300 Ph -300

-400 -400 0 50 100 150 200 250 300 0 50 100 150 200 250 300 Voltage(Vpp) Voltage(Vpp) (a) (b)

Figure 5.18: Comparison of the measured phase ranges at 94 GHz and 100 GHz: (a) Sinusoidal excitation and (b) square excitation.

Sinusoidal excitation Square excitation 0 0

-5 -5

-10 -10

=30º, 94 GHz, H-Pol =30º, 94 GHz, H-Pol

S21(dB) -15 S21(dB) -15 =30º, 100 GHz, H-Pol =30º, 100 GHz, H-Pol =30º, 94 GHz, V-Pol =30º, 94 GHz, V-Pol -20 =30º, 100 GHz, V-Pol -20 =30º, 100 GHz, V-Pol =45º, 94 GHz, V-Pol =45º, 94 GHz, V-Pol =45º, 100 GHz, V-Pol =45º, 100 GHz, V-Pol -25 -25 0 50 100 150 200 250 300 0 50 100 150 200 250 300 Voltage(Vpp) Voltage(Vpp) (a) (b)

Figure 5.19: Comparison of the measured losses at 94 GHz and 100 GHz: (a) Sinusoidal excitation and (b) square excitation.

A shift has occurred on the center frequency of the antenna, opening the possibility of using the reflectarray at 94 GHz instead of at 100 GHz. This can be observed in Figure 5.18 and Figure 5.19, which present, respectively, the obtained phase difference and amplitude loss for different biasing voltages at 94 GHz and at 100 GHz.

• Phase linearity is approximately maintained in the range of 90 - 99 GHz, although the phase range was expected to be larger (about 440◦). At 100 - 104 GHz, phase curves fall steeply, so small bias variations will cause large phase shift changes. This forbids the use of the antenna at this frequency band. • Figure 5.18 shows that there is a threshold voltage from which the obtained phase shift saturates. Biasing voltages above the threshold will produce a faster response.

• Amplitude peaks observed in the measured S21 are caused by the diﬀerent resonance frequencies of the three dipoles of the cell. These peaks move when the excitation is CHAPTER 5. CHARACTERIZATION OF A W-BAND REFLECTARRAY 51

changed since resonance frequency of the cell varies, but they are excessively pronounced (< −20 dB) in the 100 - 104 GHz band (see Figures 5.10a, 5.11a, 5.13a and 5.14a).

• Even though at 94 GHz the measured range of phase shifts is shorter, the maximum amplitude losses are about 7 dB, in contrast to the more than 20 dB losses occurring for certain permittivity values at 100 GHz.

Maximum phase variation was expected to be about 440◦, but this value has significantly decreased to 350 - 380◦, with horizontal orientation measurements showing slightly larger phase differences. Besides, as expected, when the angle of incidence is 45◦, the phase range is shorter, since 45◦ lies outside the operating angular range (0 - 30◦). It can also be mentioned that a square excitation produces a phase shift range and amplitude response similar to that of a sinusoidal excitation, but displaced in the voltage dimension. This is compliant with the developed LC model, which shows that the effective permittivity is a monotonically increasing function of the RMS (Root Mean Square) voltage [34]. Considering all of the above, it has been concluded that this reflectarray prototype can be used for pattern synthesis experiments in the 92 - 96 GHz band and for both vertical and horizontal 30◦-incidence. Array pattern synthesis requires that each element of the reflectarray can be independently biased to produce all possible phase shifts from 0◦ to 360◦.At94GHz,the measured phase-shift variation barely reaches 240 - 270◦, so the 360◦ can not be covered. The solution to cover the entire 360◦-range without actually generating the highest phase-shift values consists of quantizing the states so that only a finite number of phase shifts are generated. In this case, a 270◦ phase variation allows to generate four maximally-separated states (0◦ ± 45◦, 90◦ ± 45◦, 180◦ ± 45◦ and 270◦ ± 45◦), which is equivalent to consider each reflectarray cell as an electronically-controlled two-bit phase-shifter. However, using a small number of finite phase shifts comes at the expense of higher side-lobe levels in the synthesized patterns [30] Generating those four phase-shift states will be the goal of Section 5.4.3. In that section, instead of polarizing the reflectarray cells with different biasing voltages, the effective permittivity is changed by rapid discontinuous excitations that control the dynamic transient response of the liquid crystal cells and maintain them in intermediate excitation states.

5.4.3 Dynamic control based on time-multiplexing

The reflectarray sample under test utilizes a passive addressing strategy to excite each cell (see Section 5.1.2). This technique is based on the fact that the decay times (on-to-off time) of the LC are slower than its rising times (off-to-on time). Therefore, a strategy based on time-multiplexed excitations over rows and columns can be applied to maintain each cell of the reflectarray independently biased on a certain state. It should be noticed, that cells on one row or column will only be receiving the necessary excitation to maintain the maximum voltage a fraction of the time. Therefore, LC will actually present an oscillating state in between the ON response (maximum voltage) and the OFF response (0 Vpp) [32]. Knowing the dynamic behaviour of the cells (transient response of the LC), the pulse duration and the refreshing period can be tuned to generate different quasi-permanent states [33]. Two different strategies that apply pulses of a certain fixed voltage and duration over the different columns (one-dimensional sweep) are tested along this section. Their most important parameters are summarized in Table 5.9. 52 5.4. REFLECTARRAY CHARACTERIZATION

Strategy 1: This excitation strategy has been developed by analyzing the dynamic behaviour of the LC cells according to the theoretical model [33]. Pulses of 300 Vpp are applied sequentially to the 52 columns. Maximum phase shift state uses the minimum possible refreshing period, which is 40 ms/column × 52 columns = 2.08 s. As it will be observed in the measurements, this strategy produces very unstable states due to the high peak voltage.

Strategy 2: This second excitation strategy is based on an empirical adjustment of the excitation parameters. Besides, in order to reduce the oscillations, the columns at the edges of the reﬂectarray are grouped and excited together, so that the equivalent number of columns in which to iterate is only 36. This allows to reduce the minimum refreshing period to 1.44 s. Furthermore, the excitation voltage is 225 Vpp so that rising and decaying times are slower and ﬂuctuations decrease.

Excitation duration / Refreshing period / Initial decay time Voltage State 1 State 2 State 3 State 4

#1 300 Vpp 0 ms/–/– 17 ms/8.32 s/20.8 s 13 ms/8.32 s/6.24 s 40 ms/2.08 s/0 s #2 225 Vpp 0 ms/–/– 17 ms/5.76 s/14.4 s 25 ms/5.76 s/4.32 s 40 ms/1.44 s/0 s

Table 5.9: Summary of both excitation strategies for dynamic time-multiplexed control of the reﬂectarray states.

The measurements presented within this section attempt to characterize the dynamic behaviour of the reflectarray cells when a time-multiplexed signal is used to maintain them all in the same orientation state. Since the responses oscillate, several captures have been taken for each state to observe their stability once the permanent regime of each particular state has been reached. The ultimate goal of these measurements is to find four excitation patterns that produce four different quasi-permanent reflectarray states (as a 2-bit phase-shifter) at 94 GHz and 30◦-incidence, for both antenna orientations.

30◦ incidence for vertical orientation

The measurement set-up for this conﬁguration was presented in Figure 5.9. The excitation strategy excites every cell periodically according to the theoretical model (strategy 1). Measurement results are presented in Figure 5.20. CHAPTER 5. CHARACTERIZATION OF A W-BAND REFLECTARRAY 53

Dynamic states: amplitude Dynamic states: phase shift 0 0

-5 -200 -10 -400 -15

-20 -600 S21 (º) S21(dB) -25 -800 0 Vpp 0 Vpp -30 State 2 State 2 State 3 State 3 -1000 -35 State 4 State 4 300 Vpp 300 Vpp -40 -1200 88 90 92 94 96 98 100 102 104 106 88 90 92 94 96 98 100 102 104 106 Frequency (GHz) Frequency (GHz) (a) (b)

Figure 5.20: Reﬂectarray performance for the four analyzed dynamic states for vertical orientation (strategy 1): (a) Amplitudes and (b) phase shifts.

30◦ incidence for horizontal orientation

The measurement set-up for this conﬁguration was presented in Figure 5.12. In this case, both strategies have been tested:

• The results for the ﬁrst strategy are presented in Figure 5.21.

• The results for the second strategy are presented in Figure 5.22.

Dynamic states: amplitude Dynamic states: phase shift 0 0

-5 -200 -10 -400 -15

Figure 5.21: Reﬂectarray performance for the four analyzed dynamic states for horizontal orientation (strategy 1): (a) Amplitudes and (b) phase shifts. 54 5.4. REFLECTARRAY CHARACTERIZATION

Dynamic states: amplitude Dynamic states: phase shift 0 0

-5 -200 -10 -400 -15 ) º ( -20 -600 S21 S21(dB) -25 -800 0 Vpp 0 Vpp -30 State 2 State 2 State 3 State 3 -1000 -35 State 4 State 4 225 Vpp 225 Vpp -40 -1200 88 90 92 94 96 98 100 102 104 106 88 90 92 94 96 98 100 102 104 106 Frequency (GHz) Frequency (GHz) (a) (b)

Figure 5.22: Reﬂectarray performance for the four analyzed dynamic states for horizontal orientation (strategy 2): (a) Amplitudes and (b) phase shifts.

5.4.4 Discussion of the results

Diﬀerent states of the reﬂectarray have been obtained using time-multiplexed excitations and their mean phase shifts can be observed in Figure 5.23.

• The ﬁrst strategy consisted of exciting each row and column with the same period and during the same time. However, the mean phase shift values that have been obtained are not suﬃciently separated to apply them for 2-bit-based pattern synthesis.

• A second approach utilized an empirical adjustment of the excitation parameters, so that the mean obtained phase shifts were maximally separated and more stable (see Figure 5.23c).

The frequency for which the excitation strategies were designed is 94 GHz and four well-diﬀerentiated states were expected.

• For vertical and horizontal orientation, the strategy based on the theoretical model produces two states that are almost equal in average, so indeed there are only 3 states. Errors in the theoretical model, the manufacturing process or the excitation circuitry are being considered.

• The second strategy has only been applied for horizontal orientation, but it achieves four well differentiated states that are separated by about 80◦. These results indicate that it is possible to use this passive addressing approach to obtain different quasi-permanent phase shifts. If different states could be independently applied to different cells, the reflectarray could be used to synthesize various radiation patterns.

• In the case of horizontal orientation, Figure 5.23 shows that phase responses are more diﬀerent at 96 GHz than at 94 GHz. This could already be seen in the static analysis from Figure 5.14.

Oscillations on the phase and amplitude responses are too large in comparison to what it would be required (±45◦). CHAPTER 5. CHARACTERIZATION OF A W-BAND REFLECTARRAY 55

Dynamic states: mean phases (V-pol) Dynamic states: mean phases (H-pol) 0 0

-200 -200

-400 -400

-600 -600 S21(º) S21(º)

-800 -800 0 Vpp 0 Vpp State 2 State 2 -1000 -1000 State 3 State 3 State 4 State 4 -1200 -1200 88 90 92 94 96 98 100 102 104 106 88 90 92 94 96 98 100 102 104 106 Frequency (GHz) Frequency (GHz) (a) (b) Dynamic states: mean phases (H-pol) 0

-200

-400

-600 S21(º)

-800 0 Vpp State 2 -1000 State 3 State 4 -1200 88 90 92 94 96 98 100 102 104 106 Frequency (GHz) (c)

Figure 5.23: Mean values of the phase curves for the diﬀerent dynamic excitation strategies: (a) vertical orientation (strategy 1), (b) horizontal orientation (strategy 1) and (c) horizontal orientation (strategy 2).

• Using the ﬁrst excitation strategy, vertical orientation produces states that oscillate more than 75◦. Horizontal orientation states oscillate more than 130◦.

• The second addressing strategy, as expected, produces less oscillations due to the reduction in the refreshing period and the peak voltage of the excitation pulses.

Finally, since a limited number of captures were randomly taken at diﬀerent excitation instants, some oscillation eﬀects may not have been observed. Results will be more representative when captures are taken automatically several times within a refreshing period, which is planned to be done in the future. Table 5.10 presents a summary of the results obtained for the measurements performed within this section, at 94 GHz for vertical orientation and at 96 GHz for horizontal orientation. 56 5.4. REFLECTARRAY CHARACTERIZATION

Parameter State 1 State 2 State 3 State 4

Vertical orientation (strategy 1) Mean relative phase shift 0◦ =118◦ =98◦ =219◦ Phase shift variation — 76◦ 71◦ 45◦ Mean amplitude =5.7 dB =9.7 dB =9.9 dB =4.7 dB Amplitude variation — 1.6 dB 0.7 dB 2dB Horizontal orientation (strategy 1) Mean relative phase shift 0◦ =154◦ =135◦ =246◦ Phase shift variation — 123◦ 139◦ 69◦ Mean amplitude =4.8 dB =9.4 dB =9.5 dB =6.9 dB Amplitude variation — 2.3 dB 2.3 dB 3.6 dB Horizontal orientation (strategy 2) Mean relative phase shift 0◦ =75◦ =175◦ =240◦ Phase shift variation — 26◦ 96◦ 58◦ Mean amplitude =4.6 dB =8.3 dB =9dB =6.9 dB Amplitude variation — 1.2 dB 3.6 dB 3 dB

Table 5.10: Summary of the reﬂectarray performance for the analyzed dynamic states at 94 GHz for vertical orientation and at 96 GHz for horizontal orientation.

5.4.5 Future measurements

There are still several features of the reflectarray performance that need to be characterized. These tasks are intended to be performed in the future and are not included in this document. The first important measurement that needs to be performed is the characterization of the dynamic behaviour of the reflectarray cell. Since the measurements of Section 5.4.3 have not produced the expected theoretical results, a more accurate model of the the rising (off-to-on time) and decaying (on-to-off time) speed of the LC is needed. The easiest way to obtain this is to configure the VNA to take periodic captures of the S-parameters during the transitional periods after switching on and off the excitation. Once four different phase shifts are obtained using the time-multiplexed technique, different radiation patterns could be synthesized. This would consist of applying a different biasing state to each cell of the reflectarray. LC molecules of a reflectarray cell would maintain different orientation states if their excitation is refreshed according to their required state. Crosstalk between nearby cells may occur, complicating the synthesis. Finally, once different excitation strategies have been validated, the reflectarray will be measured again in an anechoic chamber, in which the environment is more controlled and more accurate results could be obtained. Chapter 6

Radar Receiving Chain Characterization.

This chapter addresses the characterization of the millimeter-wave receiving subsystem of the radar. The ultimate goal of is to determine whether it is possible to build the receiving chain of the space debris radar using the waveguide components that are already available at the Microwave and Radar Group and to analyze the limitations and requirements of this choice. In particular, the following measurements have been performed:

• S-parameters characterization of active and passive devices (Section 6.2).

• S-parameters characterization of the isolation chain of the receiver (Section 6.3).

• Noise characterization (Section 6.4).

The experimental acquisitions obtained during the measurements will be post-processed using Matlab and ADS (Advanced Design System R ).

6.1 The Millimeter-Wave Receiving Subsystem

Considering the high cost of waveguide components, one of the main criteria for the design of the architecture was the utilization of W-band components that are already available at the laboratory [3]. The complete radar architecture was presented in Figure 2.1 and that basic design was modified in Figure 2.2 to include monopulse tracking capabilities. The main goal of the receiving subsystem of the radar is the amplification of the received signal and its downconversion to a band from which it can be digitalized. On the other hand, in order to maintain a low noise figure, an LNA is introduced at the input of the receiving chain, so that it establishes the noise floor of the receiver [7]. However, since this a monostatic radar that uses a single antenna for transmitting and receiving, the receiver must be switched-off during the time the transmitter is active to protect the devices of the receiver from being damaged by the high transmitted power. For this purpose, an isolation chain is introduced before the LNA [7]. This will degrade the overall noise figure, since the LNA no longer is the first component of the receiver. There are two different proposals for this isolation chain:

Circulator-based: This option is presented in Figure 6.1a. It is formed by a circulator,

57 58 6.2. CHARACTERIZATION OF INDIVIDUAL COMPONENTS

an isolator and a switch. It is the simplest option but it can only be used with the non-monopulse architecture.

OMT-based: This option is presented in Figure 6.1b. Isolation is procured by an OMT (Orthomode Transducer) followed by an isolator and a switch. This combination can be used in both monopulse and non-monopulse architectures (see Figure 6.1c).

OMT OMT 2 Antenna Antenna Antenna HPA HPA HPA CirculatorCirculator

Isolator Isolator Isolator Isolator mm-wave mm-wave mm-wave receiving receiving receiving subsystem Switch subsystem Switch subsystem Switch Switch

LO LNA LNA LNA LNA

Mixer Mixer LO LO Mixer Mixer Divider

Active Active Active Active IF filter IF filter IF filter IF filter

(a) (b) (c)

Figure 6.1: Millimeter-wave receiving subsystem options: (a) Circulator-based and (b) OMT-based and (c) OMT-based for monopulse.

The following sections will characterize the proposal of Figure 6.1a, since the OMT of Figure 6.1c is being designed together with the monopulse horn and is not yet available. Indeed, the monopulse horn has been speciﬁed to provide 6 dB higher isolation between ports than the circulator, so it will yield better performance if the manufacturing process is correct.

6.2 Characterization of Individual Components

Appendix F presents a detailed characterization of some of the available millimeter-wave components that may be used in the radar if their response is considered appropriate for the application. The speciﬁc devices that are proposed to be utilized in the receiver subsystem from Figure 6.1a are listed below:

• Circulator: ELVA CR-1094 (Section F.3)

• Isolator: RPG WFI-110 (Section F.1)

• Switch: ELVA SPST-10 (Section F.5)

• LNA: RPG W-LNA75110 (Section F.7)

• Mixer: Quinstar QMB-9999WS balanced mixer.

• Active base band ﬁlter: dependent on ADC requirements. CHAPTER 6. RADAR RECEIVING CHAIN CHARACTERIZATION. 59

Table 6.1 summarizes the performance of those components from the list whose S-parameters have been measured in Appendix F. The manufacturers’ datasheets corresponding to each device can be found in Appendix G.

Measured Datasheet Circulator Insertion losses 0.22 dB 0.7 dB Return losses 26.7 dB 20.8 dB Isolation 25 dB 23 dB Bandwidth[1] 7 GHz 2.5 GHz

Isolator Insertion losses 1.6 dB 1.3 dB Return losses 19.7 dB 14 dB Isolation 22.9 dB > 20 dB

Switch Insertion losses 0.96 dB 1 dB Isolation 35.1 dB > 30 dB Return losses (OFF) 0.55 dB —

LNA Gain 28 dB 26.5 dB Return losses (input) 9.2 dB 9.3 dB

Table 6.1: Summary of the measured responses of the receiving chain millimeter-wave components at 94 GHz.

6.3 Characterization of the Receiver Isolation Chain

As commented in Section 6.1, monostatic pulsed systems require an isolation chain to protect the receiver. This section will show the results obtained from the S-parameters characterization of the isolation scheme proposed in Figure 6.1a. The switch will be oﬀ-biased when the transmitter is active to protect the receiver and it will be on-biased during the time in which the transmitter is inactive to minimize receive insertion losses. There are four diﬀerent situations that need to be analyzed:

1. Power transfer from the transmitter to the antenna (transmit mode, OFF): Figure 6.2a. 2. Power transfer from the transmitter to the receiver (transmit mode, OFF): Figure 6.2b. 3. Power transfer from the antenna to the receiver (transmit mode, OFF): Figure 6.2c. 4. Power transfer from the antenna to the receiver (receive mode, ON): Figure 6.2c.

[1]The circulator response is actually what limits the bandwidth of the receiver. 60 6.3. CHARACTERIZATION OF THE RECEIVER ISOLATION CHAIN

(a) (b) (c)

Figure 6.2: Important situations that need to be analyzed: (a) Insertion loss in transmit mode, (b) transmit-receive isolation in transmit mode and (c) insertion loss in transmit and receive modes.

6.3.1 Transmit insertion losses.

Power transfer from the antenna to the transmitter is given by the insertion losses of the circulator when it is loaded at its third port by the receiving chain. This situation can be observed in Figure 6.2a. Considering that input return losses of the isolator are larger than 18.8 dB for the band of interest, transmit insertion losses will be very similar to the insertion losses of the circulator alone, which are presented in Figure F.10a. A summary of the obtained results when power is ﬂows from the transmitter to the antenna is presented in Table 6.2.

Parameter Measured

Insertion losses (S21) 0.15 dB Return loss (S11) 26.7 dB Isolation (S12) 36 dB Bandwidth 91 - 98 GHz

Table 6.2: Transmitter-to-antenna performance at 94 GHz.

6.3.2 Isolation between the transmitter and the receiver.

Power transfer from the transmitter to the receiver should be as low as possible in order to prevent damages on the receiver when the transmitter is active. The schematic for this situation is presented Figure 6.2b. Figure 6.3 shows the measurement set-up that has been utilized for the characterization of this ensemble. Since the horn is not available, the port where the antenna should be connected is matched with a load (characterized in Figure D.2). CHAPTER 6. RADAR RECEIVING CHAIN CHARACTERIZATION. 61

Figure 6.3: Measurement set-up for the isolation chain collocating the load at port 2 of the circulator.

Measured S-parameters for each state of the switch are shown in Figure 6.4. Even though the behaviour of both states of the switch has been characterized, the receiver will always be switched-oﬀ during transmission for its own protection, so only the oﬀ-state is relevant.

S-parameters (TX-OFF) S-parameters (TX-ON) 0 0

-10 -10

-20 -20

-30 -30 (dB) (dB)

-40 -40 S11 S11 S13 S13 -50 -50 S31 S31 S33 S33 -60 -60 85 90 95 100 105 85 90 95 100 105 Frequency (GHz) Frequency (GHz) (a) (b)

Figure 6.4: Isolation chain performance from the transmitter to the receiver: (a) S-Parameters amplitude when the switch is OFF and (b) S-Parameters amplitude when the switch is ON.

Insertion and return losses for each state are presented in detail in Figure 6.5, and the most relevant results obtained for this conﬁguration are summarized in Table 6.3.

• Figure 6.5a shows that insertion losses when the switch is oﬀ-biased are larger than 60 dB[2] in the band of interest (92 - 96 GHz). This high isolation is produced by the circulator and the oﬀ-biased switch.

• Obtained input return losses (Figure 6.5b) are larger than 22 dB in the band of interest and they are imposed by the return losses of the circulator (see Figure F.10b).

[2]Measurements below 40 dB are considered to be unreliable due to the ﬁnite precision of the calibration. 62 6.3. CHARACTERIZATION OF THE RECEIVER ISOLATION CHAIN

Insertion Losses (TX to RX) Input Return Losses (TX to RX) 70 50

60 45

50 40

40 35 IL (dB) RL (dB) 30 30

20 25 Total (OFF) Total (OFF) Total (ON) Total (ON) 10 20 90 91 92 93 94 95 96 97 98 90 91 92 93 94 95 96 97 98 Frequency (GHz) Frequency (GHz) (a) (b)

Figure 6.5: Isolation chain performance from the transmitter to the receiver: (a) Insertion losses and (b) return losses.

Parameter Measured

Insertion losses (S31 OFF) > 60 dB Return loss (S11 OFF) 23.7 dB

Table 6.3: Transmitter-to-receiver performance results at 94 GHz.

6.3.3 Power transfer from the antenna to the receiver.

Power transfer from the antenna port to the LNA should be maximum during the periods of time in which the receiver is listening to the echoes and minimum during the periods in which the transmitter is active. The schematic for this situation can be observed in Figure 6.2c. Figure 6.6 shows the measurement set-up that has been utilized for the characterization of this chain of devices. The port that would be connected to the transmitter is matched with a load and S-parameters are measured from port 2 of the circulator to the output of the switch.

Figure 6.6: Measurement set-up for the isolation chain collocating the load at port 1 of the circulator.

• During the periods of time is which the transmitter is inactive, the switch must be on-biased in order to minimize insertion losses. • During the periods of time in which the transmitter is active, the switch must be oﬀ-biased CHAPTER 6. RADAR RECEIVING CHAIN CHARACTERIZATION. 63

to increase isolation between the transmit and receive subsystems. The power originated at the transmitter will not only reach the receiver directly through the circulator, but also after reﬂecting at the antenna and going through the circulator again. • During a small period of time after the transmitter is deactivated, the switch will remain oﬀ-biased to prevent damages due to powerful early echoes (blanking).

Therefore, both switch positions are relevant and require characterization. Measured S-parameters for each state of the switch are presented in Figure 6.7.

S-parameters (RX-OFF) S-parameters (RX-ON) 0 0

-10 -10

-20 -20

-30 -30 (dB) (dB)

-40 -40 S22 S22 S23 S23 -50 -50 S32 S32 S33 S33 -60 -60 85 90 95 100 105 85 90 95 100 105 Frequency (GHz) Frequency (GHz) (a) (b)

Figure 6.7: Isolation chain performance from the antenna port to the LNA port: (a) S-Parameters amplitude when the switch is OFF and (b) S-Parameters amplitude when the switch is ON.

Insertion and return losses for each state can be observed in detail in Figure 6.8, and the most relevant results have been summarized in Table 6.4.

Insertion Losses (Antenna to RX) Input Return Losses (Antenna to RX) 40 Total (OFF) 45 Total (OFF) Total (ON) Total (ON) 35 40 30

25 35

20 30 IL (dB) RL (dB) 15 25 10 20 5

0 15 90 91 92 93 94 95 96 97 98 90 91 92 93 94 95 96 97 98 Frequency (GHz) Frequency (GHz) (a) (b)

Figure 6.8: Isolation chain performance from the antenna port to the LNA port: (a) Insertion losses and (b) return losses at the antenna port.

• Figure 6.8a shows that insertion losses of the isolation chain (receiving mode) are approximately constant and below 2.8 dB in all the band of interest (92 - 96 GHz). This is consistent with the expected 0.7+1.3 + 1 = 3 dB insertion losses extracted from the datasheets (see Appendix G). 64 6.4. NOISE PERFORMANCE OF THE RECEIVER CHAIN

• Total isolation (transmit mode) from the power coming from the antenna is larger than 32 dB in the band of interest (Figure 6.8a). Therefore, transmitted power reflected at the antenna or at early targets will be attenuated by that value. Indeed, the analysis of Section 6.5 will show that reflections at the antenna are the main limitation to protect the receiver. This means that, if the antenna is damaged or improperly connected, the receiver might suffer irreparable damage.

• Obtained input return losses (Figure 6.8b) are larger than 22 dB in the band of interest. They are equal for both on and oﬀ switch states and they are imposed by the input return losses of the circulator (see Figure F.10b).

Parameter Measured

Insertion losses (S32 ON) 2.2 dB Return loss (S22 ON) 23.7 dB Isolation (S32 OFF) 35.6 dB Return loss (S22 OFF) 23.7 dB

Table 6.4: Antenna-to-receiver performance results at 94 GHz.

6.4 Noise Performance of the Receiver Chain

This section deals with the calculation (Section 6.4.1), simulation (Section 6.4.2) and measurement (Section 6.4.3) of the noise power level at the input of the digitalizer. In order to do this, the noise internally generated by the proposed receiving chain must be estimated. The schematic for the complete receiver is presented in Figure 6.9.

Figure 6.9: Block diagram of the receiver.

The noise power spectral density of a system must be integrated across the receiver bandwidth. In the case of a radar system, the receiver bandwidth is equivalent to the bandwidth CHAPTER 6. RADAR RECEIVING CHAIN CHARACTERIZATION. 65 of a bin of the FFT (Fast Fourier Transform), which should be approximately equal to the inverse of the pulse width (assuming rectangular windowing). Since the pulse duration is yet to be selected, the noise performance of several receiver bandwidths will be characterized along this section. In order to guarantee that the receiver noise floor is not being limited by the digitalizer noise floor, it has been necessary to include an active filter as the last component of the receiver (see Section 6.4.1).

6.4.1 Analytical estimation using Friis formula

Friis formula is the easiest and most direct analytical approach to estimate the receiver noise performance. However, it does not take into account mismatches between components [36] and is not valid in this case due to the lack of an image rejection strategy. Therefore, an alternative formulation has been derived [37]. The equivalent noise temperature at the output of the mixer referenced to the input of the chain is calculated in Equation 6.1:

isol sw LNA mix circ Te Te Te Te Te = T + + + + (6.1) e Gcirc GcircGisol GcircGisolGsw GcircGisolGswGLNA Assuming that the noise of the desired and the image bands are added incoherently in the IF band, the noise at the output of the mixer can be calculated with Equation 6.2. Both sidebands will be very close together (IF is very low), so it has been assumed that they have the same gain and the same noise ﬁgure.

S S S I I I N0mixer = kB(Te + Ta )G + kB(Te + Ta )G ≈ k2B(Ta + Te)G (6.2)

S I – Te and Te are the equivalent noise temperatures of the mixer at the desired and image bands.

S I – Ta and Ta are the input noise temperatures at the desired and image bands. – GS and GI are the gains at the desired and image bands from the ﬁrst component of the chain up to the mixer.

Equation 6.3 defines an equivalent SSB (Single-Side Band) noise figure of the chain from the first component up to the mixer, that can be directly used in the classical Friis formulation [37]. It is exactly 3 dB higher than the original DSB (Double-Side Band) noise figure [3].

SNRin Nout k2B(Ta + Te)G 2Te FSSB |Ta = = = =2+ =2FDSB |Ta (6.3) SNRout NinG kBTaG Ta By using the adaptation from Equation 6.3, the noise ﬁgure of the chain and its equivalent noise temperature can be calculated. The necessary parameters to calculate Friis formula can be found in Table 6.5. These have been obtained from measurements (Appendix F) and datasheets (Appendix G).

[3] In Equation 6.3 and the following derivations, noise ﬁgures are referenced to the antenna temperature Ta instead of to the reference temperature T0 = 290 K. This permits using Equation 6.7 regardless of the antenna temperature. 66 6.4. NOISE PERFORMANCE OF THE RECEIVER CHAIN

Noise ﬁgure for Component Gain T0 = 290 K

Circulator 0.22 dB =0.22 dB Isolator 1.6 dB =1.6 dB Switch (ON) 0.96 dB =0.96 dB LNA 3.8dB 28dB DSB Mixer 6.5 dB =6.5 dB

Table 6.5: Friis formula parameters at 94 GHz.

The noise figure of passive components is considered to be equal to their attenuation, which is valid when the reference temperature T0 is equal to the room temperature Tamb. Besides, the DSB noise figure of the mixer has been assumed to be equal to its conversion losses, since its datasheet does not provide this information. These conversion losses are not entirely due to thermal noise, so the real value for the mixer noise figure is likely to be lower [38]. Equations 6.4, 6.5 and 6.6 present, respectively, the noise figure, equivalent temperature and total available gain of the receiver chain.

F . SSB |T0 =959 dB (6.4) Te = 2058.9K (6.5)

Gtotal =18.72 dB (6.6)

Since the antenna is going to be pointed at the sky, antenna noise temperature will be assumed to be Ta = 60 K. Besides, the output noise for the case in which the antenna noise temperature is Ta = 290 K has also been calculated, for the purpose of comparing this result with the measurements described in Section 6.4.3. Equation 6.7 can be used to calculate the noise at the output of the mixer for both cases.

Nout = kTaF |Ta BRXGtotal (6.7)

The obtained values (Table 6.6) are below the digitalizer quantization noise, which (according to models under consideration: LTM9004 and AD9655) will introduce about =100 dBm in a bandwidth of 40 kHz. In order to increase the dynamic range of the receiver, a 20 dB gain amplifier will be included at its output. This amplifier will not have much effect on the receiver noise figure because it is the last element of the chain. However, it will increase the overall gain of the system and therefore, the total output noise. Assuming that the amplifier design obtains F . a noise figure better than 4 dB, the new noise figure will be SSB |T0 =961 dB, which is almost equivalent to the value obtained in Equation 6.4. Table 6.6 presents the noise power levels obtained for different receiver bandwidths, with and without IF amplifier. It can be noticed that the obtained output noise power after the introduction of the 20 dB active filter is more than 10 dB above the noise floor of the digitalizer. CHAPTER 6. RADAR RECEIVING CHAIN CHARACTERIZATION. 67

Output noise (without Output noise (with IF Receiver Pulse IF ampliﬁer) ampliﬁer) bandwidth width Ta=60 K Ta=290 K Ta=60 K Ta=290 K

39 kHz 26 µs =100.15 dBm =99.75 dBm =80.13 dBm =79.74 dBm 24 kHz 42 µs =102.26 dBm =101.86 dBm =82.24 dBm =81.85 dBm 10 kHz 10 µs =106.06 dBm =105.66 dBm =86.04 dBm =85.65 dBm

Table 6.6: Output noise results at 94 GHz for diﬀerent receiver bandwidths obtained using Friis formula.

6.4.2 Noise budget analysis

Friis formulation does not take into account the effects of mismatches between the receiver components. A noise budget simulation has been performed in ADS, in order to obtain a better estimation of the real noise figure and output noise power level of the receiver subsystem. Figure 6.10 shows the schematic of the receiver chain that has been drawn in ADS in order to carry out the simulation at 94 GHz. RF frequency has been chosen to be 2 MHz above the LO frequency in order to simulate a target producing a beat frequency of 2 MHz. Besides, the simulation has already been performed assuming the use of a 20 dB-gain IF amplifier at the output of the chain.

Var VAR Noise Figure Budget Analysis Eqn VAR1 Power_RF=-85 Component and input/output noise figure RFfreq=94.002 GHz LOfreq=94 GHz IFfreq=RFfreq-LOfreq RBW=39 KHz Ta=290

RF Input RF IF 12 12 12 Te r m Ref Ref Ref Te r m 2 Num=2 P_1Tone Amplifier2 MixerWithLO Amplifier2 S2P S2P S2P Z=50 Ohm PORT1 LNA MIXER AMP_IF Circulator Isolator Switch Noise=no Num=1 S21=dbpolar(28,0) ZRef=50 Ohm S21=dbpolar(20,0) Te m p = 2 7 Z=50 Ohm S11=dbpolar(-9.2,0) DesiredIF=RF minus LO S11=polar(0,0) P=dbmtow(Power_RF) S22=dbpolar(-9.2,0) ConvGain=dbpolar(-6.5,0) S22=polar(0,180) Freq=RFfreq S12=0 S12=0 Noise=yes Temp=Ta-273

Figure 6.10: Receiver schematic for the ADS noise budget analysis.

• Obtained noise ﬁgure is Ftotal =9.59 dB, which is approximately equal to the result obtained using the modiﬁed Friis equation from the previous section.

• As expected, Figure 6.11a shows how the ADS and modiﬁed noise ﬁgure calculation are about 3 dB above the classical Friis formula result (see Figure 6.11a).

• The obtained output noise is about 2 dB larger than the one that would be obtained just by applying the noise ﬁgure deﬁnition (Nout = kT0BFG). Instead, ADS noise calculation is taking into account mismatches between components in order to calculate a more realistic output noise value. Noise at the output of each receiver component can be observed in Figure 6.11b. 68 6.4. NOISE PERFORMANCE OF THE RECEIVER CHAIN

Simulated Noise Figure Simulated Output Noise Power 10 -70 ADS noise budget RBW=39KHz-Ta=290K Friis formula -80 RBW=24KHz-Ta=290K 8 Modified Friis formula RBW=10KHz-Ta=290K -90 RBW=39KHz-Ta=60K RBW=24KHz-Ta=60K 6 -100 RBW=10KHz-Ta=60K

(dBm) -110 out NF (dB) 4 N -120

-130 2 -140

0 -150 Circulator Isolator Switch LNA Mixer IF-AMP Circulator Isolator Switch LNA Mixer IF-AMP (a) (b)

Figure 6.11: Noise budget analysis of the receiver: (a) noise ﬁgure referred to 290 K and (b) output noise power for Ta=290 K.

Figure 6.11b and Table 6.7 summarize the results obtained for the diﬀerent receiver bandwidths that have been considered along the simulations.

Output noise Receiver Pulse (after IF ampliﬁer) bandwidth width Ta=60 K Ta=290 K

39 kHz 25.6 µs =78.74 dBm =77.92 dBm 24 kHz 41.7 µs =80.85 dBm =80.03 dBm 10 kHz 10 µs =84.65 dBm =83.83 dBm

Table 6.7: Noise budget analysis results at 94 GHz at the output of the IF active ﬁlter for diﬀerent receiver bandwidths.

6.4.3 Noise measurements

Noise measurements of the receiving chain have been performed following the technique and configurations explained in Appendix D. Figure 6.12 shows the particular set-up that has been used for measuring the noise at the output of the receiver chain. This set-up already includes a 20 dB-gain IF amplifier at its output to maximize the dynamic range, although a new amplifier will be designed in the future. The IF frequency in which the system will work is yet to be decided (0 - 1 GHz), but there will be no big differences on the results as long the mixer is working at its operating band. Oscillator frequency is generated by multiplying by 6 a 16.667 GHz signal produced with a signal generator. CHAPTER 6. RADAR RECEIVING CHAIN CHARACTERIZATION. 69

Figure 6.12: Measurement set-up for the characterization of the receiver chain noise performance.

As previously commented, the receiver bandwidth is given by the width of an FFT bin, which is approximately equal to the inverse of the pulse duration. Since the RBW (Resolution Bandwidth) of the spectrum analyzer is the bandwidth over which power is integrated, this is the parameter that is modiﬁed in order to characterize the performance for diﬀerent pulse durations. The obtained measurement results for each of the receiver bandwidths that have been characterized are presented in Figure 6.13.

• Figure 6.13 shows that noise is quite ﬂat, without noticeable spurious signals, at least in the range 0.5 - 5 MHz.

• Measured noise power levels are about 1 dB higher than what was expected from the noise budget simulation in ADS (see Table 6.7).

• The power decay occurring at 5 MHz is due to the active filter (IF amplifier) at the output of the mixer. The future IF amplifier will have at least 50 MHz bandwidth.

Noise traces at the filter output (LO=7dBm) -70 RBW=39KHz - LO OFF RBW=39KHz - LO ON -80 RBW=24KHz - LO OFF RBW=24KHz - LO ON RBW=10KHz - LO OFF -90 RBW=10KHz - LO ON (dBm)

out -100 P

-110

-120 12345678910 Frequency (MHz)

Figure 6.13: Noise power measurement at the output of the receiver chain when the transmitter and the antenna are matched (Ta = 290 K).

Assuming that the loads are perfectly matched resistors (T = T0), the degradation on the output SNR (Signal to Noise Ratio) due to the introduction of the receiver components can be estimated from the measurement. In all the cases, the noise level curve (LO ON traces) is well 70 6.4. NOISE PERFORMANCE OF THE RECEIVER CHAIN above the noise ﬂoor (LO OFF traces). This guarantees that the impact of the noise internally generated by the spectrum analyzer is negligible with respect to the measurement (excepting at very low frequencies). A summary of the obtained results is shown in Table 6.8.

Output Output Receive Pulse width noise at noise at Degradation bandwidth 1MHz 2MHz 39 kHz 25.6 µs =76.8 dBm =76.8 dBm 12.57 dB 24 kHz 41.7 µs =78.8 dBm =78.9 dBm 12.58 dB 10 kHz 10 µs =82.7 dBm =82.7 dBm 12.58 dB

Table 6.8: Noise power level at the output of the receiver chain for an antenna temperature of Ta ≈ Tamb ≈ 290 K.

6.4.4 Conversion losses

The datasheet of the multiplier (see Appendix G) indicates that the optimum input power value for this device is 7 dBm. Utilizing the same measurement set-up of Figure 6.12, the output power of the signal generator has been swept in order to characterize its impact on the downconversion process.

Noise traces at the filter output (RBW=10KHz) Noise traces at the filter output (RBW=24KHz) -70 -70 LO=0dBm LO=0dBm LO=2dBm LO=2dBm -80 LO=4dBm -80 LO=4dBm LO=6dBm LO=6dBm LO=7dBm LO=7dBm -90 LO=8dBm -90 LO=8dBm Noise floor Noise floor (dBm) (dBm)

out -100 out -100 P P

-110 -110

-120 -120 12345678910 12345678910 Frequency (MHz) Frequency (MHz) (a) (b) Noise traces at the filter output (RBW=39KHz) -70 LO=0dBm LO=2dBm -80 LO=4dBm LO=6dBm LO=7dBm -90 LO=8dBm Noise floor (dBm)

out -100 P

-110

-120 12345678910 Frequency (MHz) (c) Figure 6.14: Impact of using diﬀerent input power values to the ×6 multiplier: (a) RBW=10 kHz, (b) RBW=24 kHz and (c) RBW=39 kHz. CHAPTER 6. RADAR RECEIVING CHAIN CHARACTERIZATION. 71

All the noise traces of interest have been measured and results can be observed in Figure 6.14. They show that conversion losses of the multiplier+mixer saturate at about =6 dBm.

6.5 Overall Conclusions from the Measurements

6.5.1 Transmit-receive isolation

The characterization of the ensemble shown in Figure 6.15 has been performed. It produces more than 60 dB isolation between the transmitter (port 1) and the receiver (port 3) during the time in which the transmitter is active. A summary of the obtained results is presented in Table 6.9.

Figure 6.15: Schematic of the isolation chain.

Parameter Measured

Transmit insertion losses (S21) 0.15 dB Receive insertion losses (S32 ON) 2.2 dB Receive insertion losses (S32 OFF) 35.6 dB Transmitter-to-receiver isolation (S31 OFF) 60 dB Operating band 91 - 98 GHz

Table 6.9: Most relevant measurement results of the receiving chain at 94 GHz.

Transmitter-to-receiver isolation could also be influenced by the amount of reflection occurring at the antenna and going through the circulator towards the receiver. However, because the monopulse feed is not yet manufactured, a perfect load was placed at port 2 and this effect was not accounted for. 72 6.5. OVERALL CONCLUSIONS FROM THE MEASUREMENTS

6.5.2 Maximum output power of the transmitter

Maximum input power rating to avoid permanent damage on the LNA is =20 dBm according to the datasheet. Therefore, the maximum output power that the transmitter HPA (High Power Ampliﬁer) should generate must be estimated.

• Power coming from the transmitter might be leaked to the receiver through the circulator: Equation 6.8.

• Power coming from the transmitter that is reﬂected at the antenna goes through the circulator again reaching the receiver: Equation 6.9.

off PHPA +20log S31 < −20 dBm (6.8) off ANT off PHPA +20log S21 +20log S11 +20log S32 < −20 dBm (6.9) ANT ANT PHPA < min −20 + 60, −20 + 0.15 + 35.6 − S11 (dB) =min 40, 15.75 − S11 (dB) (6.10)

Considering that the first pre-designs for the feed feature return losses of 20 - 25 dB, the limiting factor to the maximum transmitted power will be probably imposed by this feed reflection coefficient[4]. Therefore, until the feed is manufactured and measured, transmitter designs should assume an output power no larger than 35 dBm.

6.5.3 Receiver noise ﬂoor

The noise figure of the whole receiving chain has been calculated, simulated and measured. Table 6.10 presents a comparison of between the results obtained with those three methods. An IF active filter has been included at the end of the receiving chain in order to increase the noise floor of the receiver so that it lies above the floor of the digitalizer. A new active filter will be designed in the future in order to enlarge the operating band of the system, which should have at least 50 MHz. This change will not have much effect on the noise internally generated by the chain since it is located at the last position.

Receive Pulse Output noise for Ta=290 K bandwidth width Friis ADS Measurement

39 kHz 25.6 µs =79.74 dBm =77.92 dBm =76.8 dBm 24 kHz 41.7 µs =81.85 dBm =80.03 dBm =78.9 dBm 10 kHz 10 µs =85.65 dBm =83.83 dBm =82.7 dBm

Table 6.10: Comparison of noise power results at the output of the receiver chain according to analytical calculations, simulations and measurements.

[4]Indeed, the monopulse comparator and the horn for the monopulse-based receiver (Figure 6.1c) are being designed together in order to optimize the isolation between input and output ports of the complete set [16]. CHAPTER 6. RADAR RECEIVING CHAIN CHARACTERIZATION. 73

6.5.4 Receiver sensitivity

Receiver sensitivity is the minimum received power at the input of the receiver from which the system can decide that a target is present. As a reference, in the case of a swerling 5 target, the SNR threshold for detection is 13 dB. In case pulse integration were used, minimum required power would be lower. Assuming that the noise ﬂoor is limited by thermal noise and taking into account previously taken noise measurements at the output of the chain, the sensitivity of the receiver can be calculated as Sin = Nout + SNRmin − Grx. Results are presented in Table 6.11.

Receiver sensitivity Receive Minimum power at (minimum power at bandwidth the ADC the antenna)

39 kHz =63.8 dBm =102.5 dBm 24 kHz =65.9 dBm =104.6 dBm 10 kHz =69.7 dBm =108.4 dBm

Table 6.11: Receiver sensitivity for a swerling 5 target without pulse integration and Ta = 290 K. 74 6.5. OVERALL CONCLUSIONS FROM THE MEASUREMENTS Chapter 7

Summary and Conclusions

This chapter summarizes the work that has been performed within the realization of this Master’s Thesis, along with some of the most important conclusions.

7.1 Summary

This Master’s Thesis has been concerned with the realization of several tasks related to the millimeter-wave subsystem of the space debris radar at 94 GHz that is being developed in the frame of the Spaderadar Project [1, 2]. The contributions to this Project that are included in this document can be summarized in three diﬀerent tasks:

1. Design of the dual reﬂector antenna system that will be utilized in millimeter-wave radar.

2. Contribution to the characterization of a reﬂectarray antenna operating at W-Band.

3. Characterization of the millimeter-wave receiver subsystem of the radar.

The work has been performed in the GMR (Microwave and Radar Group) and the GEA (Applied Electromagnetism Group) of ETSIT-UPM, with punctual collaborations with the GR (Radiation Group).

7.2 Conclusions

Chapter 3 is concerned with the design of the Cassegrain reflector antenna system that will be utilized in the radar. Several simulations have been performed in Grasp yielding a final antenna system of 900×900×293 mm from which a gain of 57.5 dB is expected. The Cassegrain system is already being manufactured and, in the future, its performance will be measured in an anechoic chamber and compared to the simulations. Work is currently underway on the final design of a monopulse feed for the antenna system. Chapter 5 presents the first measurements that have been performed to characterize a reflectarray antenna designed to operate at W-Band. As a previous step, the quasi-optical test bench for performing free-space measurements had to be designed, for which Chapter 4 presents a software based on Gaussian beam propagation theory. This tool was proved to have many limitations specially because it does not consider reflections and other non-idealities. The obtained measurement results of the reflectarray show disagreements with respect to what it

75 76 7.2. CONCLUSIONS was expected from the theoretical model [34]. Even though the phase variation and operational frequency range are lower than expected, there are still many measurements that need to be performed for the purpose of finding the causes of those disagreements and improving the design and manufacturing procedures. Finally, Chapter 6 involves the characterization of a proposal for the millimeter-wave receiving subsystem of the radar. On the one hand, the isolation chain has been proved to introduce about 60 dB isolation, which could effectively protect the receiver if it transmits less than 35 dBm. On the other hand, the noise at the output of the receiver chain has been measured and the introduction of an IF amplifier has been found to be necessary in order to ensure that the noise floor of the system is limited by thermal noise. Considering the measurement results, there are still some operative parameters of the radar that have to be selected, such as the transmitted power or the duration of the pulses. A non-linear characterization of the receiving chain will also have to be performed in the future. Appendix A

Simulations in Grasp

Grasp is a simulation software from TICRA that uses PO (Physical Optics), PTD (Physical Theory of Diffraction) and other numerical methods, to compute scattered fields from surfaces that are electrically large. This appendix offers a brief introduction on those numerical methods (Section A.1) and details how to configure the software so that a Cassegrain antenna can be accurately simulated (Section A.2).

A.1 PO and PTD

PO is a numerical method utilized to find the field scattered by a body from the knowledge of the incident fields at the part of its surface that is illuminated [19]. PO propagates the fields in terms of rays as in an optical method. The following list summarizes the process for obtaining the total field outside of a scatterer:

• Fields are propagated from source objects towards the scatterers via geometrical optics (ray propagation).

• The induced currents on the surface of scatterers can be determined from the incident magnetic ﬁeld over the surface of the body: JS =2ˆn × Hi

• The scattered ﬁeld due to the induced currents can be calculated by integrating the currents over the surface of the object.

• If the scattered field is evaluated asymptotically (farfield), the total field outside the body can be described in terms of geometrical optics (rays) by adding it to the incident field.

PO assumes that the scatterers have flat and infinite surfaces. PTD is an extension of PO method that corrects the PO solution by adding the fields due to the currents close to edges of the scatterers [19].

A.2 Grasp conﬁguration for simulating a Cassegrain system

This section details the process to simulate a dual Cassegrain system using Grasp.

77 78 A.2. GRASP CONFIGURATION FOR SIMULATING A CASSEGRAIN SYSTEM

A.2.1 Cassegrain antenna model

The modeling of the dual reﬂector system is started using the wizard to produce a Cassegrain system with default parameters. Then, any object of the system including the feed can be modiﬁed to match the requirements of the simulation.

A.2.2 Command list

Table A.1 illustrates the Grasp commands used for the estimation of the farﬁeld of a Cassegrain antenna system [39].

Command Objects Arguments Type

Field accuracy: -80 dB Auto convergence of PO: on Source: feed Convergence on scatterer: main reflector 1 Get Currents Target: subreflector Convergence on output grid: farfield cut Maximum bisections: 5 Integration grid limit: on Field accuracy: -80 dB Auto convergence of PO: on Source: subreflector Convergence on scatterer: subreflector 2 Get Currents Target: main reflector Convergence on output grid: farfield cut Maximum bisections: 5 Integration grid limit: on Source: main reflector 3 Get Field Target: farfield cut Source: feed + subreflector 4 Add Field Target: farfield cut Field accuracy: -80 dB Auto convergence of PO: on Source: main reflector Convergence on scatterer: 5 Get Currents Target: subreflector Convergence on output grid: farfield cut Maximum bisections: 5 Integration grid limit: on Source: subreflector 6 Add Field Target: farfield cut

Table A.1: Textual reproduction of the Grasp command list.

Simulating the main component of the farﬁeld

The currents induced in the subreflector by fields propagated from the feed (Grasp command 1) produce a scattered field that illuminates the main reflector. This induces other currents in the surface of the main reflector (Grasp command 2) that scatter to create a pencil-like radiation pattern in broadside direction (Grasp command 3). APPENDIX A. SIMULATIONS IN GRASP 79

Simulating spillover losses

Spillover and some diffraction effects are considered by adding, to the scattered field from the main reflector, those fields produced at the feed that propagate at an angle close to or greater than the semi-subtended angle ΨS, and thus diffract or do not even interact with the reflectors (Grasp command 4).

Simulating blockage from subreﬂector

Blockage effects have been considered by calculating the currents produced by letting the main reflector scattered field illuminate again the subreflector (Grasp command 5). The backwards-propagating field produced by the induced currents is then added to the main reflector farfield (Grasp command 6). 80 A.2. GRASP CONFIGURATION FOR SIMULATING A CASSEGRAIN SYSTEM Appendix B

Simulation Results of Diﬀerent Reﬂection-based Optical Test Benches for 45◦ Incidence

This appendix presents the simulation results that have been obtained for the different quasi-optical set-ups that were proposed in Section 4.3 to measure the reflection coefficient of a sample impinged at an angle of 45◦ from broadside. The quasi-optical set-ups are analyzed at 94 GHz and at 100 GHz and the results are compared for two different types of horns: Millitech 21 dB horns and RPG 23 dB horns. These are the six different afocal quasi-optical systems that are analyzed within the following sections:

• Using two horns and two dielectric lenses: Section B.1.

• Using two horns and two 45◦ oﬀ-axis mirrors: Section B.2.

• Using two horns and two 90◦ oﬀ-axis mirrors: Section B.3.

• Using two horns, two lenses and two 45◦ oﬀ-axis mirrors: Section B.4.

• Usingtwohorns,two45◦ oﬀ-axis mirrors and two 90◦ oﬀ-axis mirrors: Section B.5

– Option 1: Section B.5.1. – Option 2: Section B.5.2.

B.1 Optical Set-up Using Two Dielectric Lenses

The optical structures that will be used for this conﬁguration are:

• Two conical horns:

– Millitech smooth wall conical horns with 21 dB in W-band. – RPG dual mode conical horns with 23 dB in W-band.

• Two plano-convex dielectric lenses of Feq =62.7mm.

• An ideal ﬂat sample modelled as a plane mirror.

81 82 B.1. OPTICAL SET-UP USING TWO DIELECTRIC LENSES

Figure B.1 shows the schematic of the geometrical arrangement that has been proposed to obtain a beam maximally collimated at the sample position to measure its reﬂection coeﬃcient.

Ffv Fbv Sample Lens Optical element x(mm) y(mm) 45º Input horn Horn 1 (phase center) 00 Fbv Lens 1 (convex side) 47.70 Lens Sample 131.80 Lens 2 (convex side) 131.8 −84.4 Ffv Horn 2 (phase center) 131.8 −131.8 Output horn

Figure B.1: Proposed optical arrangement Table B.1: Element positions for the proposed using horns and lenses. arrangement using horns and lensese.

Simulations have been run at 94 GHz and 100 GHz for the proposed configuration using both types of horns. Simulated results are presented in Figure B.2. In each simulation, the minimum sample diameter that ensures an exp(−2) field decay (=17.4 dB) at its edges has been configured. Obtained minimum sample sizes are presented in Table B.2.

Optical Bench Configuration Optical Bench Configuration 50 50 Beam e-1 Beam e-1 Beam e-2 Beam e-2

0 0

-50 -50 (mm) (mm)

-100 -100

-150 -150 -50 0 50 100 150 200 -50 0 50 100 150 200 (mm) (mm) (a) (b) Optical Bench Configuration Optical Bench Configuration 50 50 Beam e-1 Beam e-1 Beam e-2 Beam e-2

0 0

-50 -50 (mm) (mm)

-100 -100

-150 -150

-200 -200 -50 0 50 100 150 200 -50 0 50 100 150 200 (mm) (mm) (c) (d)

Figure B.2: Simulation results for the sample size that obtains =17.4 dB taper using two dielectric lenses: (a) 21 dB horns at 94 GHz, (b) 21 dB horns at 100 GHz, (c) 23 dB horns at 94 GHz and (d) 23 dB horns at 100 GHz. APPENDIX B. OPTICAL TEST BENCHES FOR 45◦ INCIDENCE 83

21 dB-directivity horns 23 dB-directivity horns Parameter 94 GHz 100 GHz 94 GHz 100 GHz

Beamwaist (w0) 17.8 mm 17.26 mm 14.18 mm 13.65 mm

Sample diameter for 50.5 mm 48.9 mm 40.25 mm 38.8 mm exp(−1) ﬁeld decay Sample diameter for 71.5 mm 69.3 mm 56.95 mm 54.9 mm exp(−2) ﬁeld decay

Table B.2: Results at 94 GHz and 100 GHz obtained using a conﬁguration that utilizes horns and dielectric lenses for 45◦ incidence.

B.2 Optical Set-up Using Two 45◦ Oﬀ-axis Mirrors

The optical structures that will be used in this conﬁguration are:

• Two conical horns:

– Millitech smooth wall conical horns with 21 dB in W-band. – RPG dual mode conical horns with 23 dB in W-band.

• Two 45◦ oﬀ-axis mirrors:

◦ – 45 , ∅ = 101.6mmand Feq = 119.03 mm. ◦ – 45 , ∅ =76.2mmand Feq =89.28 mm (purchase proposal).

• An ideal ﬂat sample modelled as a plane mirror.

B.2.1 Option with available 45◦ oﬀ-axis mirrors

The schematic for the proposed optical arrangement to measure the reflection coefficient of the sample using horns and the largest 45◦ off-axis mirrors is presented in Figure B.3.

Feq

Input horn Paraboloid mirror Optical element x(mm) y(mm) 45º Horn 1 (phase center) 00

45º Paraboloid mirror 1 119.03 0 Sample Feq Sample 34.86 −84.17 Paraboloid mirror 2 0 −168.33 Output horn 45º Paraboloid Horn 2 (phase center) 0 −168.33 mirror

Feq

Figure B.3: Proposed optical set-up using Table B.3: Element positions for the proposed horns and 45◦ oﬀ-axis mirrors. set-up using horns and 45◦ oﬀ-axis mirrors. 84 B.2. OPTICAL SET-UP USING TWO 45◦ OFF-AXIS MIRRORS

Simulations have been run at 94 GHz and 100 GHz for the proposed configuration using both types of available horns. In each simulation, the minimum sample diameter that ensures an exp(−2) field decay at its edges has been configured. Results are presented in Figure B.4 and Table B.4.

Optical Bench Configuration Optical Bench Configuration Optical Bench Configuration Optical Bench Configuration 100 100 100 100 Beam e-1 Beam e-1 Beam e-1 Beam e-1 Beam e-2 Beam e-2 Beam e-2 Beam e-2 50 50 50 50

0 0 0 0

-50 -50 -50 -50 (mm) (mm) (mm) (mm) -100 -100 -100 -100

-150 -150 -150 -150

-200 -200 -200 -200

-250 -250 -250 -250 -50 0 50 100 150 -50 0 50 100 150 -50 0 50 100 150 -50 0 50 100 150 (mm) (mm) (mm) (mm) (a) (b) (c) (d)

Figure B.4: Simulation results for the sample size that obtains =17.4 dB taper using 45◦ oﬀ-axis mirrors with 101.6 mm diameter: (a) 21 dB horns at 94 GHz, (b) 21 dB horns at 100 GHz, (c) 23 dB horns at 94 GHz and (d) 23 dB horns at 100 GHz.

21 dB-directivity horns 23 dB-directivity horns Parameter 94 GHz 100 GHz 94 GHz 100 GHz

Beamwaist (w0) 33.8 mm 32.76 mm 26.91 mm 25.91 mm

Sample diameter for 95.65 mm 92.7 mm 76.2 mm 73.4 mm exp(−1) ﬁeld decay Sample diameter for 135.35 mm 131.15 mm 108 mm 103.8 mm exp(−2) ﬁeld decay

Table B.4: Results at 94 GHz and 100 GHz obtained using a conﬁguration that uses horns and 45◦ oﬀ-axis mirrors with 101.6 mm diameter.

B.2.2 Option with alternative 45◦ oﬀ-axis mirrors

The purchase of an smaller model of the 45◦ oﬀ-axis paraboloid mirrors has been proposed, in order to measure smaller samples. These new mirrors would have an smaller eﬀective focal distance (89.28 mm), which would truncate the beam before it diverges too much. As a downside, the mirrors are smaller: 76.2 mm. Results are presented in Figure B.5 and Table B.5. APPENDIX B. OPTICAL TEST BENCHES FOR 45◦ INCIDENCE 85

0 0 0 0

-50 -50 -50 -50 (mm) (mm) (mm) (mm)

-100 -100 -100 -100

-150 -150 -150 -150

-200 -200 -200 -200 -50 0 50 100 150 -50 0 50 100 150 -50 0 50 100 150 -50 0 50 100 150 (mm) (mm) (mm) (mm) (a) (b) (c) (d)

Figure B.5: Simulation results for the sample size that obtains =17.4 dB taper using 45◦ oﬀ-axis mirrors with 76.2 mm diameter: (a) 21 dB horns at 94 GHz, (b) 21 dB horns at 100 GHz, (c) 23 dB horns at 94 GHz and (d) 23 dB horns at 100 GHz.

21 dB-directivity horns 23 dB-directivity horns Parameter 94 GHz 100 GHz 94 GHz 100 GHz

Beamwaist (w0) 25.35 mm 24.57 mm 20.19 mm 19.44 mm

Sample diameter for 71.8 mm 69.6 mm 57.2 mm 55.3 mm exp(−1) ﬁeld decay Sample diameter for 101.6 mm 98.45 mm 81 mm 77.95 mm exp(−2) ﬁeld decay

Table B.5: Results at 94 GHz and 100 GHz obtained using a conﬁguration that uses horns and 45◦ oﬀ-axis mirrors with 76.2 mm diameter.

B.3 Optical Set-up Using Two 90◦ Oﬀ-axis Mirrors

The optical structures that will be used in this conﬁguration are:

• Two conical horns:

– Millitech smooth wall conical horns with 21 dB in W-band. – RPG dual mode conical horns with 23 dB in W-band.

• Two 90◦ oﬀ-axis mirrors.

◦ – 90 , ∅ = 101.6mmand Feq = 152.4 mm.

• An ideal ﬂat sample modelled as a plane mirror.

The schematic for the proposed optical arrangement to measure the reflection coefficient of the sample using horns and 90◦ off-axis mirrors is presented in Figure B.6. Two different but equivalent structures could be used to obtain the beamwaist at the sample position. 86 B.3. OPTICAL SET-UP USING TWO 90◦ OFF-AXIS MIRRORS

Feq Paraboloid Feq mirror Paraboloid Input horn mirror

90º Output horn 90º

Feq Feq Paraboloid Paraboloid Feq mirror mirror

45º

90º Sample Sample 90º Feq

Feq Feq

Output horn Input horn

(a) (b)

Figure B.6: Proposed optical arrangements using horns and 90◦ oﬀ-axis mirrors: (a) Option 1 and (b) option 2.

Optical element x(mm) y(mm)

Horn 1 (phase center) 00 Paraboloid mirror 1 152.40 Sample 152.4 −152.4 Paraboloid mirror 2 0 −152.4 Horn 2 (phase center) 0 −304.8

Table B.6: Element positions for the proposed arrangement (option 2) using horns and 90◦ oﬀ-axis mirrors to measure reﬂectivity at 45◦ incidence.

Simulations have been run at 94 GHz and 100 GHz for the proposed configuration using both types of available horns. On each simulation, the minimum sample diameter that ensures an exp(−2) field decay at its edge has been configured. Results are presented in Figure B.7 and Table B.7.

Optical Bench Configuration Optical Bench Configuration Optical Bench Configuration Optical Bench Configuration 50 50 50 50

0 0 0 0

-50 -50 -50 -50

-100 -100 -100 -100

-150 -150 -150 -150 (mm) (mm) (mm) (mm)

-200 -200 -200 -200

-250 -250 -250 -250

-300 -300 -300 -300 Beam e-1 Beam e-1 Beam e-1 Beam e-1 Beam e-2 Beam e-2 Beam e-2 Beam e-2 -350 -350 -350 -350 -50 0 50 100 150 200 -50 0 50 100 150 200 -50 0 50 100 150 200 -50 0 50 100 150 200 (mm) (mm) (mm) (mm) (a) (b) (c) (d)

Figure B.7: Simulation results for the sample size that obtains =17.4 dB taper using 90◦ oﬀ-axis mirrors: (a) 21 dB horns at 94 GHz, (b) 21 dB horns at 100 GHz, (c) 23 dB horns at 94 GHz and (d) 23 dB horns at 100 GHz. APPENDIX B. OPTICAL TEST BENCHES FOR 45◦ INCIDENCE 87

21 dB-directivity horns 23 dB-directivity horns Parameter 94 GHz 100 GHz 94 GHz 100 GHz

Beamwaist (w0) 43.28 mm 41.95 mm 34.46 mm 33.18 mm

Sample diameter for 122.5 mm 118.7 mm 97.6 mm 93.9 mm exp(−1) ﬁeld decay Sample diameter for 173.2 mm 167.87 mm 138 mm 132.85 mm exp(−2) ﬁeld decay

Table B.7: Results at 94 GHz and 100 GHz obtained using a conﬁguration that uses horns and 90◦ oﬀ-axis mirrors.

Indeed, simulation results show that truncation eﬀects are not limited by the sample size but by the diameter of the mirrors. Therefore, in all the cases, high spillover losses and diﬀraction will occur at the edges of the mirror, regardless of the size of the sample.

B.4 Optical Set-up Using Two 45◦ Oﬀ-axis Mirrors and Two Dielectric Lenses

The optical structures that will be used in this conﬁguration are:

• Two conical horns:

– Millitech smooth wall conical horns with 21 dB in W-band. – RPG dual mode conical horns with 23 dB in W-band.

• Two 45◦ oﬀ-axis paraboloid mirrors:

◦ – 45 , ∅ = 101.6mmand Feq = 119.03 mm.

• Two plano-convex dielectric lenses of Feq =62.7 mm.

• An ideal ﬂat sample modelled as a plane mirror.

Maximum collimation at the sample can be obtained using these optical structures if they are arranged as indicated in the schematic presented in Figure B.8. 88 B.4. OPTICAL SET-UP USING 45◦ OFF-AXIS MIRRORS AND LENSES

Ffv Fbv Feq Optical element x(mm) y(mm) Lens Paraboloid mirror 45º Horn 1 (phase center) 00 Input horn Lens 1 (convex side) 47.73 0

45º Paraboloid mirror 1 250.82 0 Sample Sample 166.66 −84.17 Paraboloid mirror 2 250.82 −168.33 Output horn Lens 45º Paraboloid Lens 2 (convex side) 47.73 −168.33 mirror Horn 2 (phase center) 0 −168.33

Ffv Fbv Feq

Figure B.8: Proposed optical set-up using of Table B.8: Element positions for the proposed horns, 45◦ oﬀ-axis mirrors and lenses. set-up using horns, 45◦ oﬀ-axis mirrors and lenses.

Simulations have been run at 94 GHz and 100 GHz for the proposed configuration using both types of horns. Simulation results are presented in Figure B.2. On each simulation, the minimum sample diameter that ensures an exp(−2) field decay (=17.4 dB) at its edges has been configured. Obtained minimum sample sizes for a successful measurement are presented in Table B.9.

Optical Bench Configuration Optical Bench Configuration 100 100 Beam e-1 Beam e-1 Beam e-2 Beam e-2 50 50

0 0

-50 -50 (mm) (mm) -100 -100

-150 -150

-200 -200

-250 -250 -50 0 50 100 150 200 250 300 -50 0 50 100 150 200 250 300 (mm) (mm) (a) (b) Optical Bench Configuration Optical Bench Configuration 100 100 Beam e-1 Beam e-1 Beam e-2 Beam e-2 50 50

0 0

-50 -50 (mm) (mm) -100 -100

-150 -150

-200 -200

-250 -250 -50 0 50 100 150 200 250 300 -50 0 50 100 150 200 250 300 (mm) (mm) (c) (d)

Figure B.9: Simulation results for the sample size that obtains =17.4 dB taper using two lenses and two 45◦ oﬀ-axis mirrors: (a) 21 dB horns at 94 GHz, (b) 21 dB horns at 100 GHz, (c) 23 dB horns at 94 GHz and (d) 23 dB horns at 100 GHz. APPENDIX B. OPTICAL TEST BENCHES FOR 45◦ INCIDENCE 89

21 dB-directivity horns 23 dB-directivity horns Parameter 94 GHz 100 GHz 94 GHz 100 GHz

Beamwaist (w0) 6.79 mm 6.59 mm 8.53 mm 8.33 mm

Sample diameter for 19.5 mm 18.9 mm 24.3 mm 23.75 mm exp(−1) ﬁeld decay Sample diameter for 27.8 mm 26.95 mm 34.65 mm 33.8 mm exp(−2) ﬁeld decay

Table B.9: Minimum sample diameter at 94 GHz and 100 GHz obtained using a conﬁguration that utilizes horns and dielectric lenses.

B.5 Optical Set-up Using Two 45◦ Oﬀ-axis Mirrors and Two 90◦ Oﬀ-axis Mirrors

The optical structures that will be used in this conﬁguration are:

• Two pairs of conical horns:

– Millitech smooth wall conical horns with 21 dB in W-band. – RPG dual mode conical horns with 23 dB in W-band.

• Two pairs of oﬀ-axis mirrors.

◦ – 45 , ∅ = 101.6mmand Feq = 119.03 mm. ◦ – 90 , ∅ = 101.6mmand Feq = 152.4 mm.

• An ideal ﬂat sample modelled as a plane mirror.

The schematics for the proposed optical arrangements to measure the reflection coefficient of the sample using horns, 45◦ and 90◦ off-axis mirrors are presented in Figure B.10. They are not equivalent since 45◦ and 90◦ mirrors are not positioned in the same order. Simulations have been run at 94 GHz and 100 GHz for the proposed configurations using both types of available horns. On each simulation, the minimum sample diameter that ensures an exp(−2) field decay at its edges has been configured. Results are presented in:

• Figure B.11 and Table B.11 for option 1.

• Figure B.12 and Table B.12 for option 2.

Simulation results show that, in both configurations, truncation effects are not limited by the sample size, but by the diameter of the 90◦ off-axis mirrors, which is too small. Besides, in the case of option 2, Millitech horns produce an extremely narrow beamwaist at the sample, which doesn’t comply with the paraxial approximation. 90 B.5. OPTICAL SET-UP USING 45◦ AND 90◦ OFF-AXIS MIRRORS

F45

90º 90º F90 F90 Paraboloid Paraboloid mirror mirror Sample 45º Input horn 45º Paraboloid mirror Input horn 90º 90º Output horn

45º 90º

90º F90 + F45 Sample F90 + F45

90º 90º Paraboloid Paraboloid mirror mirror 45º 45º 45º

F45

45º 45º 45º 45º Paraboloid Paraboloid Paraboloid mirror mirror mirror

(a) (b)

Figure B.10: Proposed optical arrangements using of horns, 45◦ and 90◦ oﬀ-axis mirrors: (a) Option 1 and (b) option b.

Option 1 Option 2 Optical element x(mm) y(mm) x(mm) y(mm)

Horn 1 (phase center) 0000 45◦ off-axis mirror 1 119.03 0 152.4 −271.43 90◦ off-axis mirror 1 −72.9 −191.93 152.40 Sample 180.784.17 236.57 −187.26 45◦ off-axis mirror 2 −288.4 −191.9 320.73 0 90◦ off-axis mirror 2 96.5 −383.9 320.73 −271.43 Horn 2 (phase center) 215.5 383.9 473.13 0

Table B.10: Element positions for the proposed arrangement using horns, 45◦ and 90◦ oﬀ-axis mirrors.

B.5.1 Results for option 1

21 dB-directivity horns 23 dB-directivity horns Parameter 94 GHz 100 GHz 94 GHz 100 GHz

Beamwaist (w0) 4.58 mm 4.44 mm 5.76 mm 5.62 mm

Sample diameter for 13.3 mm 12.9 mm 16.6 mm 16.2 mm exp(−1) ﬁeld decay Sample diameter for 19.5 mm 18.7 mm 23.8 mm 23.2 mm exp(−2) ﬁeld decay

Table B.11: Results at 94 GHz and 100 GHz obtained using a conﬁguration that uses horns, 45◦ and 90◦ oﬀ-axis mirrors (option 1). APPENDIX B. OPTICAL TEST BENCHES FOR 45◦ INCIDENCE 91

Optical Bench Configuration Optical Bench Configuration 100 100

50 50

0 0

-50 -50

-100 -100

-150 -150

-200 -200 (mm) (mm) -250 -250

-300 -300

-350 -350

-400 -400

Beam e-1 Beam e-1 -450 -450 Beam e-2 Beam e-2 -500 -500 -300 -250 -200 -150 -100 -50 0 50 100 150 200 -300 -250 -200 -150 -100 -50 0 50 100 150 200 (mm) (mm) (a) (b) Optical Bench Configuration Optical Bench Configuration 100 100

50 50

0 0

-50 -50

-100 -100

-150 -150

-200 -200 (mm) (mm) -250 -250

-300 -300

-350 -350

-400 -400

Beam e-1 Beam e-1 -450 -450 Beam e-2 Beam e-2 -500 -500 -300 -250 -200 -150 -100 -50 0 50 100 150 200 -300 -250 -200 -150 -100 -50 0 50 100 150 200 (mm) (mm) (c) (d)

Figure B.11: Simulation results for the sample size that obtains =17.4 dB taper using 45◦ and 90◦ oﬀ-axis mirrors (option 1): (a) 21 dB horns at 94 GHz, (b) 21 dB horns at 100 GHz, (c) 23 dB horns at 94 GHz and (d) 23 dB horns at 100 GHz. 92 B.5. OPTICAL SET-UP USING 45◦ AND 90◦ OFF-AXIS MIRRORS

B.5.2 Results for option 2

Optical Bench Configuration Optical Bench Configuration 100 100

50 50

0 0

-50 -50

-100 -100 (mm) (mm)

-150 -150

-200 -200

-250 -250 Beam e-1 Beam e-1 Beam e-2 Beam e-2 -300 -300 -100 -50 0 50 100 150 200 250 300 350 400 450 500 -100 -50 0 50 100 150 200 250 300 350 400 450 500 (mm) (mm) (a) (b) Optical Bench Configuration Optical Bench Configuration 100 100

50 50

0 0

-50 -50

-100 -100 (mm) (mm)

-150 -150

-200 -200

-250 -250 Beam e-1 Beam e-1 Beam e-2 Beam e-2 -300 -300 -100 -50 0 50 100 150 200 250 300 350 400 450 500 -100 -50 0 50 100 150 200 250 300 350 400 450 500 (mm) (mm) (c) (d)

Figure B.12: Simulation results for the sample size that obtains =17.4 dB taper using 45◦ and 90◦ oﬀ-axis mirrors (option 2): (a) 21 dB horns at 94 GHz, (b) 21 dB horns at 100 GHz, (c) 23 dB horns at 94 GHz and (d) 23 dB horns at 100 GHz.

21 dB-directivity horns 23 dB-directivity horns Parameter 94 GHz 100 GHz 94 GHz 100 GHz

Beamwaist (w0) 2.79 mm 2.71 mm 3.51 mm 3.43 mm

Sample diameter for 9.5 mm 8.2 mm 10.4 mm 10.1 mm exp(−1) ﬁeld decay Sample diameter for 13.1 mm 12.55 mm 15.4 mm 14.95 mm exp(−2) ﬁeld decay

Table B.12: Results at 94 GHz and 100 GHz obtained using a conﬁguration that uses horns, 45◦ and 90◦ oﬀ-axis mirrors (option 2). Appendix C

Phase Center Calculation

The phase center location of the horns utilized as feeds has to be known ir order to place them at their optimum positions. Even though there are some analytical approaches to ﬁnd the phase center location of a horn [10], in this case, a numerical approach based on simulations has been preferred. HFSS, which is a simulator based on FEM (Finite Element Method), has been used. The procedure that has been followed can be summarized in the following four steps:

• Creation of the HFSS model of the antenna.

• Deﬁnition of a relative coordinate system that is oﬀset from the global coordinate system in z-dimension. Its origin must be located at a certain distance pos from the aperture of the horn (if pos > 0, then the origin of the relative coordinate system is inside the horn).

• Creation of a rectangular plot for the phase of the main cuts of the E-ﬁeld copolar component multiplied by the distance R.

• Modiﬁcation of the position of the relative coordinate system until the ﬂattest possible response is obtained in the phase plot. A parametric study is also possible.

C.1 RPG FH-PP-100 Potter Horn

The phase center of the RPG FH-PP-100 conical horn is calculated in this section. The datasheet of this horn, which includes its dimensions, can be found in Appendix G. Figure C.1 presents the HFSS model that has been used to simulate the horn. Taking advantage of the modal and geometrical symmetries of the antenna, it was only necessary to simulate a quarter of the model. Magnetic and electric symmetries must be applied carefully at the corresponding splitting planes.

93 94 C.1. RPG FH-PP-100 POTTER HORN

Figure C.1: HFSS model of the RPG horn using symmetries.

After several iterations looking for the coordinate system origin for which the phase of the electric ﬁeld is maximally planar, the phase center of the horn has been found. The horn response has been studied at 94 GHz and 100 GHz, since these are the center frequencies at which the horn will be used. A summary is presented in Table C.1. Phases at 94 GHz and 100 GHz are presented in Figure C.2 and Figure C.3 and directivities in Figure C.4 and Figure C.5.

Phase center Maximum variation Frequency Directivity position in a 16◦-beamwidth

94 GHz 20.5 mm 9.81◦ 23.14 dB 100 GHz 24.5 mm 13.29◦ 23.43 dB

Table C.1: Phase center at diﬀerent frequencies measured from the aperture (z>0 is inside the horn).

Figure C.2: Phase of the copolar component of the electric ﬁeld at 94 GHz whenthecoordinatesystemisatz =20.5 mm inside the horn. APPENDIX C. PHASE CENTER CALCULATION 95

Figure C.3: Phase of the copolar component of the electric ﬁeld at 100 GHz when the coordinate system is at z =24.5 mm inside the horn.

Figure C.4: Directivity at 94 GHz.

Figure C.5: Directivity at 100 GHz. 96 C.2. MILLITECH SGH-08 CONICAL HORN

C.2 Millitech SGH-08 Conical Horn

The phase center of a Millitech SGH-08 conical horn is calculated in this section. The datasheet of this horn, which includes its dimensions, can be found in Appendix G. Figure C.6 presents the HFSS model that has been used to simulate this horn. Taking advantage of the modal and geometrical symmetries only a quarter of the antenna is simulated. Magnetic and electric symmetries must be applied carefully at the corresponding splitting planes.

Figure C.6: HFSS model of the Millitech horn using symmetries.

After several iterations looking for the coordinate system origin for which the phase of the electric ﬁeld is maximally planar, the phase center of the horn has been found. The horn response has been studied at 94 GHz and 100 GHz, since these are the center frequencies at which the horn will be used. A summary is presented in Table C.2. Phases at 94 GHz and 100 GHz are presented in Figure C.7 and Figure C.8 and directivities in Figure C.9 and Figure C.10.

Phase center Maximum variation Frequency Directivity position in a 20◦-beamwidth

94 GHz 6.6 mm 4.75◦ 20.67 dB 100 GHz 7.9 mm 6.17◦ 21.08 dB

Table C.2: Phase center at diﬀerent frequencies measured from the aperture (z>0 is inside the horn). APPENDIX C. PHASE CENTER CALCULATION 97

Figure C.7: Phase of the copolar component of the electric ﬁeld at 94 GHz whenthecoordinatesystemisatz =6.6 mm inside the horn.

Figure C.8: Phase of the copolar component of the electric ﬁeld at 100 GHz when the coordinate system is at z =7.9 mm inside the horn.

Figure C.9: Directivity at 94 GHz. 98 C.2. MILLITECH SGH-08 CONICAL HORN

Figure C.10: Directivity at 100 GHz. Appendix D

Measurement Set-ups and Equipment Conﬁgurations

This appendix summarizes the measurement equipment, set-ups and conﬁgurations that have been used along the thesis to characterize some of the components belonging to the millimeter-wave subsystem of the radar.

D.1 S-Parameters Characterization of W-band Devices

An Anritsu broadband VNA has been used for the characterization of S-parameters of active and passive devices at W-Band (75 - 110 GHz). All the equipment used for this measurement is summarized below:

• An Anritsu ME7838B broadband VNA operational from 70 kHz to 110 GHz. It consists of the following items:

– A MS4647B VectorStar VNA, 70 kHz to 70 GHz. – Two 3743A millimeter-wave modules to extend the band up to 110 GHz. – A 3739B broadband millimeter-wave test set and interface cables.

• SAGE Millimeter SWC-101F-E1 1 mm-coaxial (F) to WR-10 waveguide transitions.

• TRL (Through-Reﬂect-Line) calibration kit in WR-10.

• WR-10 waveguide terminations to match the ports.

• WR-10 straight pieces of waveguide to facilitate connections.

The measurement set-up for any of the measurements is shown in Figure D.1. Basically, the DUT (Device Under Test) must be connected to the output ports of the VNA. A short straight waveguide is collocated between the DUT and port 2 in order to facilitate connections (see Figure D.1b).

99 100 D.1. S-PARAMETERS CHARACTERIZATION OF W-BAND DEVICES

VNA VNA display control

Test Set

mm-Wave mm-Wave DUTDUT module module

Coax to WR-10 (a) (b)

Figure D.1: Measurement set-up used for the acquisition of the S-parameters of millimeter-wave devices.

Table D.1 summarizes the VNA conﬁguration for which the calibration and the S-parameters measurements are performed.

Parameter Value

Sweep mode Frequency sweep Frequency range 75 - 110 GHz RF Power =30 dBm IF bandwidth 10 kHz Number of points 3201 points Calibration Manual TRL Trace averaging None

Table D.1: Anritsu VNA conﬁguration for the measurement of S-parameters at W-band.

Calibrating the VNA in frequency allows compensation of all those time-invariant measurement errors of the system. Finally, *.s2p ﬁles are post-processed using Matlab. The whole measuring process has the following steps:

1. Calibration of the VNA.

2. S-Parameters acquisition in the whole calibrated band (75 - 110 GHz).

3. Correction of measurement imperfections.

4. Application of a smoothing ﬁlter to the traces in order to eliminate residual noise. This ﬁltering consists of a 2 % averaging window.

5. Zooming into the band of interest of 88 - 102 GHz. For this particular radar application the band of interest is even narrower, being 92 - 96 GHz. APPENDIX D. MEASUREMENT SET-UPS AND EQUIPMENT CONFIGURATIONS 101

A W-band load is needed to match ports that are not being measured during the S-parameters characterization of devices with more than 2 ports, and also as a noise source to produce noise at W-band. A Quinstar W-band load has been used for those two purposes. Obtained results (Figure D.2) are consistent with the expected VSWR (Voltage Standing Wave Ratio) from the datasheet and prove the usefulness of the load as a 50 Ω “perfect” resistive load.

S-Parameter VSWR 10 1.16 S11 Measured 0 1.14 Datasheet -10 1.12 -20 1.1 -30 1.08

(dB) -40 VWSR 1.06 -50 1.04 -60

-70 1.02

-80 1 75 80 85 90 95 100 105 110 75 80 85 90 95 100 105 110 Frequency (GHz) Frequency (GHz) (a) (b)

Figure D.2: Measurement of a Quinstar W-band load: (a) Reﬂection coeﬃcient and (b) VSWR.

D.2 Noise Measurements

Since a W-band noise source is not currently available in the laboratory, noise at W-band is generated using the W-band load from Figure D.2. Noise performance of the whole receiving chain has been characterized by obtaining the noise power level at the intermediate frequency (after downconversion by the mixer) using a microwave spectrum analyzer. All the equipment used for this measurement is summarized below:

• Signal generator from Keysight.

• An Agilent EXA N9010 spectrum analyzer.

• WR-10 waveguide terminations to match the ports.

• WR-10 straight pieces of waveguide to facilitate connections.

Basically, loads of 50 Ω are used to match those ports of the millimeter-wave subsystem that are not connected to the receiver. These (ideally) perfect matched loads would act as noise sources with a noise temperature of T = 290 K. Afterwards, the obtained response will be compared to the expected values from Friis formula and ADS noise budget simulations. The measurement set-up for any of the noise measurements that have been performed is presented in Figure D.3, and Table D.2 summarizes the spectrum analyzer conﬁguration for which the noise measurements are performed. 102 D.3. FREE-SPACE MEASUREMENTS

Signal generator

mm-wave IF components components RF IF Z0 mixer Spectrum analyzer

Figure D.3: Measurement set-up for the acquisition of the noise power level at the output of the receiving chain

Parameter Value Number of points 1001 points Frequency span 0 - 10 MHz RBW (Resolution Bandwidth) FFT bin width VBW (Video Bandwidth) 1000 Attenuation 0 dB Trace averaging 100 passes Detector type Average RMS

Table D.2: Agilent spectrum analyzer conﬁguration for the measurement of noise level of the receiving chain.

Obtained measurements will be post-processed using Matlab. The whole noise characterization process has the following steps:

1. Conﬁguration of the spectrum analyzer, so that the noise ﬂoor level is at least 10 dB below the measurements.

2. Noise power level acquisition.

3. Correction of measurement imperfections.

4. Application of a smoothing ﬁlter to the traces in order to eliminate residual noise.

5. Zooming into de band of interest and comparison of the measured results with the calculated and simulated results.

D.3 Free-Space Measurements

In Section 5.3, different optical configurations have been designed to measure the reflection coefficient of a reflectarray sample impinged from different angles. In order to capture the response of the reflectarray sample, the output of the horns has been connected to an Anritsu broadband VNA. APPENDIX D. MEASUREMENT SET-UPS AND EQUIPMENT CONFIGURATIONS 103

The measurement set-up is similar to what has been used in Section D.1. Although, in this case, the DUT of Figure D.1 would be the entire quasi-optical system. 1 mm-long coaxial cables are connected between the horns and the output ports of VNA in order to facilitate connections. This condition can be observed in Figure D.4.

Figure D.4: Coaxial cable and WR-10 transitions between the horns and the VNA ports.

Table D.3 summarizes the VNA conﬁguration for which the calibration and the S-parameter measurements are performed.

Parameter Value

Sweep mode Frequency sweep Frequency range 80 - 110 GHz RF Power =30 dBm IF bandwidth 10 kHz Number of points 3001 points Calibration Manual TRL Trace averaging None

Table D.3: Anritsu VNA conﬁguration for the free-space measurements at W-band.

Calibration of the VNA is performed at the input port of the horns, due to the lack of a standard procedure to calibrate a reﬂection-based quasi-optical system. This compensates the time-invariant measurement errors, that occur up to the input waveguide of the horns. Calibration accuracy is limited to about 25 dB, since coaxial cables had to be moved during the calibration to connect the thru. This can be observed in Figure D.5. 104 D.3. FREE-SPACE MEASUREMENTS

Calibration 0

-10

-20 (dB) -30

S11 -40 S12 S21 S22 -50 80 85 90 95 100 105 110 Frequency (GHz) Figure D.5: Thru of the TRL calibration kit after calibration.

Post-processing is performed using Matlab and it is explained in detail in Appendix E. The whole measurement process can be summarized in the following steps:

1. Calibration of the VNA.

2. S-parameters acquisition of the thru.

3. S-Parameters acquisition of the sample under test.

4. Re-calibration of the measured S21 of the sample with the measured S21 of the thru.

5. Correction of measurement imperfections:

– Time domain processing for the removal of uncalibrated reﬂections. – Application of a smoothing ﬁlter to the traces in order to eliminate residual noise. Appendix E

Free-space Post-processing Techniques

This appendix summarizes the post-processing techniques that have been utilized to correct the measurement errors, reﬂections and residual noise that are present on the free-space acquisitions.

E.1 Recalibration with a Reference

As commented in Appendix D, calibration of the measurement system has been performed at the input waveguide of the horns. Therefore, reﬂections and losses occurring inside the quasi-optical bench are not being compensated. Three measurements would be necessary for a complete free-space calibration. But due to the lack of three accurate calibration standards for this set-up, a single optical thru has been utilized as reference sample to compensate the losses and part of the ripple associated to quasi-optical elements. This “optical thru” consists of a ﬂat metallic surface which has the same size as the sample under test. A photograph of the measurement set-up for acquiring the response of the thru is presented in Figure E.1.

Figure E.1: Photograph of the set-up to measure the optical thru.

The response of the reﬂectarray is embedded in the transmission coeﬃcient of the measured S-parameters. Therefore, the losses and phase shifts introduced by the optical system can be coarsely compensated using Equation E.1, which yields the results observed in Figure E.2.

105 106 E.2. TIME-DOMAIN ANALYSIS

S21 sample S21 corr = (E.1) S21 thru The measured reﬂectarray response will always lie below the losses of the reference thru. On the other hand, if any resonance peak falls below the calibration precision in a certain band, the curve will be corrupted with noise in that band. Therefore, in order to maximize the dynamic margin of the measurement system, the optical test bench should introduce the lowest possible thru losses (S21 → 0 dB) and the calibration level must as low as possible.

Re-calibrated amplitude of the transmission coefficient Re-calibrated angle of the transmission coefficient 0 150 Sample -5 Thru 100 Calibrated sample

-10 50

-15 0 (dB) (dB)

-50 -20

-100 Sample -25 Thru Calibrated sample -150 -30 88 90 92 94 96 98 100 102 104 106 88 90 92 94 96 98 100 102 104 106 Frequency (GHz) Frequency (GHz) (a) (b)

Figure E.2: Calibration of the transmission coeﬃcient with an optical thru: (a) Amplitude and (b) phase.

E.2 Time-domain Analysis

As it can be observed in Figure E.2, ripple associated to reﬂections occurring inside the measurement system is not completely eliminated by Equation E.1. A time domain analysis has been performed, for the purpose of observing the most powerful reﬂections of the system. Time domain responses obtained using a rectangular window are presented in Figure E.3:

• Sample response zone is marked in both Figure E.3a and Figure E.3b. It is approximately coincident for S11 and S21 due to the symmetry of the optical conﬁguration. That zone would be the gated-in band after time-domain processing.

• The positions of the identiﬁed discontinuities are consistent with their real position in the measurement system.

• The reflectarray introduces a delay with respect to the thru. This is because the reflectarray is formed by several layers (with different and tunable permittivities) and the thru is aligned with the quartz superstate (see Figure 5.2). APPENDIX E. FREE-SPACE POST-PROCESSING TECHNIQUES 107

Reflection coefficient in time domain 50 Input face of lens 1 Output face of lens 2 Input face of lens 2 Ffv Fbv Aperture of the horn Output face of lens 2 Lens 40 Sample

Sample Input 30º response 30 horn

Lens (dB) 20

10 Output horn S11-Thru S11-Sample 0 0 500 1000 1500 2000 2500 3000 Time (ps) (a) Transmission coefficient in time domain

60 Thru Sample Ffv Fbv response Lens Sample 50 Dipoles layer Ground plane Input 30º 40 horn Superstrate layer LC layer Lens

(dB) 30

20 Output horn 10 S21-Thru S21-Sample 0 0 500 1000 1500 2000 2500 3000 Time (ps) (b)

Figure E.3: Time domain transformation of the S-parameters of the ◦ 30 -incidence optical test bench: (a) S11 and (b) S21.

E.3 Smoothing vs Time-domain Processing

Two diﬀerent procedures are proposed to eliminate the uncalibrated reﬂections and residual errors:

• Smoothing filter: 1. Calibration of the sample measurement with the thru. 2. Application of a smoothing filter to the corrected transmission coefficient. This filter would consist of an averaging window of length 5 % of the samples. • Time domain processing: 1. Filtering of the time-domain response of the thru measurement. 2. Filtering of the time-domain response of the sample measurement. 3. Transformation of time-gated responses of the thru and the sample back to frequency domain. 108 E.3. SMOOTHING VS TIME-DOMAIN PROCESSING

4. Calibration of the time-gated sample with the time-gated thru.

Results from both methods are compared in Figure E.4. It can be concluded that they both yield very similar responses and both reduce the ripple present on the measured S21 curve.

Post-processed amplitude of the transmission coefficient Post-processed phase of the transmission coefficient 0 150

-5 100

50 -10

0 (dB) (dB) -15 -50

-100 -20 Calibrated Calibrated Smoothed Smoothed Time-filtered -150 Time-filtered -25 88 90 92 94 96 98 100 102 104 106 88 90 92 94 96 98 100 102 104 106 Frequency (GHz) Frequency (GHz) (a) (b)

Figure E.4: Post-processing of the transmission coeﬃcient: (a) Amplitude and (b) phase. Appendix F

Characterization of Millimeter-wave Components

This appendix presents the detailed characterization of some of the most relevant components that will be used in the radar receiving chain, if their response is considered appropriate for the application:

• Passive devices:

– RPG WFI-110 isolator. – RPG WPD-110 hybrid power divider. – ELVA CR-1094 circulator. – Quinstar QAL-W00000 variable attenuator. – ELVA SPST-10 switch.

• Active devices:

– RPG W-LNA75110 low noise ampliﬁer.

In particular, the S-parameters of each speciﬁc component have been measured:

• Measurements and conclusions can be found in the sections associated to each component.

• The necessary equipment and its speciﬁc conﬁguration can be found in Appendix D.

• The manufacturers’ datasheets corresponding to each millimeter-wave component can be found in Appendix G.

109 110 F.1. RPG WFI-110 ISOLATOR

F.1 RPG WFI-110 Isolator

This RPG isolator will be used at the input of the reflective switch to attenuate its reflections when it is switched-off.

• Figure F.1 shows the measurement set-up that has been used for its characterization.

• Measured S-parameters are presented in Figure F.2.

• Insertion losses, return losses and isolation and group delay can be observed in detail in Figure F.3.

Figure F.1: Measurement set-up for the RPG WFI-110 isolator.

S-Parameters 0 S-Parameters (phase)

150 S11 S21 -10 100

50 -20

(º) 0 (dB) S11 measured -30 S12 measured -50 S21 measured S22 measured -40 RL datasheet -100 IS datasheet IL datasheet -150 -50 85 90 95 100 105 85 90 95 100 105 Frequency (GHz) Frequency (GHz) (a) (b)

Figure F.2: RPG WFI-110 isolator: (a) S-Parameters amplitude and (b) S-Parameters phase.

As shown in Figure F.3a, this device presents insertion losses in the band of interest (92 - 96 GHz) of 1.6 dB, which are 0.3 dB above the manufacturer speciﬁcation. Isolation (Figure F.3c) is higher than 20 dB across the whole W-band. Additionally Figure F.3b shows return losses better than 16.5 dB in the band of interest. Group delay presents a ﬂat response (Figure F.3d) across the whole band of interest, which is positive in case of using wideband signals. Table F.1 presents a summary of the measurement results that have been obtained for this device. APPENDIX F. CHARACTERIZATION OF MILLIMETER-WAVE COMPONENTS 111

Insertion Losses Return Losses 2 35 Measured Datasheet 1.8 30

1.6 25 IL (dB) 1.4 RL (dB) 20

1.2 15 Input Port Output Port Datasheet 1 10 90 91 92 93 94 95 96 97 98 90 91 92 93 94 95 96 97 98 Frequency (GHz) Frequency (GHz) (a) (b) Isolation Group delay 30 0.5

0.4

25 0.3 (ns) g 0.2

Isolation (dB) 20

0.1 Measured Datasheet Measured 15 0 90 91 92 93 94 95 96 97 98 90 91 92 93 94 95 96 97 98 Frequency (GHz) Frequency (GHz) (c) (d)

Figure F.3: RPG WFI-110 isolator: (a) Insertion losses, (b) return losses, (c) isolation and (d) group delay.

Parameter Measured Datasheet

Insertion Losses 1.6 dB 1.3 dB Return losses 19.7dB 14dB Isolation 22.9 dB > 20 dB

Table F.1: RPG WFI-110 isolator measurement results at 94 GHz in comparison with those provided by the manufacturer.

F.2 RPG WPD-110 Hybrid Power Divider

This hybrid power divider might be used to divide the LO signal, so that it can be used to down-convert the diﬀerent channels of the monopulse architecture. Figure F.4 shows the measurement set-up that has been used for the characterization of this RPG power divider. As observed, a straight piece of rectangular waveguide is strictly necessary, in order to collocate the load at the corresponding port. The load used for matching is characterized in Appendix D and it can be thought as an ideal Z0.

• Measured S-parameters are presented in Figure F.5. It was not possible to measure the 112 F.2. RPG WPD-110 HYBRID POWER DIVIDER

Figure F.4: Measurement set-up for the RPG WPD-110 power divider.

isolation between ports 2 and 3 because of their physical closeness (see Figure F.4).

• Insertion and return losses are shown with more detail in Figure F.6.

• Relative phase shift between both paths and group delays are presented in Figure F.7.

S-parameters S-parameters (phase) 0 150

-10 100

50 -20

(º) 0 (dB) S11 -30 S12 -50 S13 S21 -40 S22 -100 S31 S21 S33 -150 S31 -50 85 90 95 100 105 85 90 95 100 105 Frequency (GHz) Frequency (GHz) (a) (b)

Figure F.5: RPG WPD-110 hybrid power divider: (a) S-Parameters amplitude and (b) S-Parameters phase.

Insertion losses (Figure F.6a) of the power divider are slightly higher at 94 GHz than those provided by the manufacturer. Amplitude balance between both ports is in agreement with the expected hybrid behaviour, since the diﬀerence ranges from 0.3 to 0.8 dB in the band of interest (92 - 96 GHz). In addition, input return losses (Figure F.6b) are better than 13 dB across the whole band of interest, limiting on the lower part of this band (92 GHz). In general their value is much higher than what is indicated by the manufacturer. APPENDIX F. CHARACTERIZATION OF MILLIMETER-WAVE COMPONENTS 113

Insertion Losses Return Losses 5.5 30 S21 S31 5 25 Datasheet S21 Datasheet S31 4.5 20

4 15 IL (dB) RL (dB) 3.5 10 Port 1 Port 2 3 5 Port 3 Datasheet 2.5 0 90 91 92 93 94 95 96 97 98 90 91 92 93 94 95 96 97 98 Frequency (GHz) Frequency (GHz) (a) (b)

Figure F.6: RPG WPD-110 hybrid power divider: (a) Insertion losses and (b) return losses.

◦ The phase responses of S21 and S31, shown in Figure F.7a, present a deviation of 180 ± 10 in the band of interest (92 - 96 GHz). Therefore the divider is designed as a 180◦-hybrid, which is not indicated in the datasheet. Calculated group delay (Figure F.7b) is very small and quite flat across the whole band and for both traces. Besides, group delay balance ensures that two signals coming from different ports would suffer more or less the same delay.

Phase balance Group delay 200 250

195 200 190

185 150 (S31)|(º)

180 (ps) g 100 175 (S21)- | 170 50 165 S21 S31 160 0 90 91 92 93 94 95 96 97 98 90 91 92 93 94 95 96 97 98 Frequency (GHz) Frequency (GHz) (a) (b)

Figure F.7: RPG WPD-110 hybrid power divider: (a) phase balance and (b) group delay.

Table F.2 summarizes the measurement results obtained for this device at 94 GHz. 114 F.3. ELVA CR-1094 CIRCULATOR

Parameter Measured Datasheet

Insertion Losses (1 → 2) 3.28 dB 3 dB Coupling Losses (1 → 3) 3.81 dB 3.6 dB Return losses > 16.1dB 6.5dB Phase balance 176◦ —

Table F.2: RPG WPD-110 hybrid power divider measurement results at 94 GHz in comparison with those provided by the manufacturer.

F.3 ELVA CR-1094 Circulator

This ELVA narrow band circulator is meant to isolate the transmit and receive subsystems. The circulator response has been obtained connecting a pair of its ports to the VNA and matching the third port with a waveguide termination which is characterized in Appendix D. Three measurements are performed to cover any possible combination of ports. Measurement set-ups can be observed in Figure F.8.

3 3 3 2 2 1

1 1 2

(a) (b) (c)

Figure F.8: Measurement set-up for the ELVA CR-1094 circulator: (a) ports 1-2, (b) ports 1-3 and (c) ports 2-3.

Measured S-parameters are presented in Figure F.9 before and after load correction [1].As observed, there are no major changes in the curves after load correction(Figure F.9b), which is coherent with the fact that an almost perfect load (ρL ≈ 0) has been used to match the unused port at each measurement.

[1]Load correction refers to a correction technique that compensates the use of imperfect loads to match the unused ports during a two-port measurement of a device with more than two ports. APPENDIX F. CHARACTERIZATION OF MILLIMETER-WAVE COMPONENTS 115

S-parameters S-parameters 0 0

-10 -10

-20 -20 S11 S11 S12 S12 (dB) S13 (dB) S13 -30 -30 S21 S21 S22 S22 S23 S23 -40 S31 -40 S31 S32 S32 S33 S33 -50 -50 85 90 95 100 105 85 90 95 100 105 Frequency (GHz) Frequency (GHz) (a) (b)

Figure F.9: ELVA CR-1094 circulator: (a) Measured S-Parameters amplitude (referred to the real load) and (b) S-Parameters amplitude after load correction (referred to Z0).

Insertion losses, return losses and isolation are shown in Figure F.10. This device presents very low insertion losses (Figure F.10a) of only 0.3 dB and return losses (Figure F.10b) better than 26.5 dB, which are values above the speciﬁcation. In addition, it features an isolation (Figure F.10c) better than 22 dB across the whole band of interest. In general, it can be observed that the band in which the circulator works correctly ranges from 91 to 98 GHz. Table F.3 summarizes the measurement results obtained for this device.

Parameter Measured Datasheet

Insertion Losses 0.22 dB 0.7 dB Return Losses 26.7 dB 20.8 dB Isolation 25 dB 23 dB Bandwidth 7 GHz 2.5 GHz

Table F.3: ELVA CR-1094 circulator measurement results at 94 GHz in comparison with those provided by the manufacturer. 116 F.4. QUINSTAR QAL-W00000 VARIABLE ATTENUATOR

Insertion Losses Return Losses 1 50 S21 Port 1 S32 45 Port 2 0.8 S13 Port 3 Datasheet Datasheet 40

0.6 35

IL(dB) 30 0.4 RL (dB)

25 0.2 20

0 15 90 91 92 93 94 95 96 97 98 90 91 92 93 94 95 96 97 98 Frequency (GHz) Frequency (GHz) (a) (b) Isolation 45 S12 40 S23 S31 Datasheet 35

25 Isolation (dB) 20

10 90 91 92 93 94 95 96 97 98 Frequency (GHz) (c)

Figure F.10: ELVA CR-1094 circulator: (a) Insertion losses, (b) return losses and (c) isolation.

F.4 Quinstar QAL-W00000 Variable Attenuator

Figure F.11 shows the measurement set-up that has been used for the characterizations of this Quinstar variable attenuator.

Figure F.11: Measurement set-up for the Quinstar QAL-W00000 variable attenuator.

Different measurements have been taken to compare the response of different attenuation positions. Obtained results for different positions are presented in Figure F.12 and Figure F.13. APPENDIX F. CHARACTERIZATION OF MILLIMETER-WAVE COMPONENTS 117

Input Return Losses Output Return Losses 45 45 Position 0 Position 0 40 Position 5 40 Position 5 Position 10 Position 10 Position 15 Position 15 35 35 Position 20 Position 20 Position 25 Position 25 30 Datasheet (max) 30 Datasheet (max)

25 25 RL (dB) RL (dB)

20 20

15 15

10 10 90 91 92 93 94 95 96 97 98 90 91 92 93 94 95 96 97 98 Frequency (GHz) Frequency (GHz) (a) (b)

Figure F.12: Quinstar QAL-W00000 attenuator: (a) Input return losses and (b) output return losses

Input and output return losses (Figure F.12a and Figure F.12b, respectively) are above 17 dB across the whole W-band, which is in agreement with the expected values extracted from the datasheet.

Attenuation Attenuation 20 92-96 GHz 25

15 20

15 10 Position 0 Att (dB) Att (dB) 10 Position 5 Position 10 Position 15 5 5 Position 20 Position 25 Datasheet (max) 0 0 90 91 92 93 94 95 96 97 98 0 5 10 15 20 25 30 Frequency (GHz) Micrometer position (a) (b) Phase Shift

150 Position 0 Position 5 Position 10 100 Position 15 Position 20 50 Position 25

0 S21 (º) -50

-100

-150

90 91 92 93 94 95 96 97 98 Frequency (GHz) (c)

Figure F.13: Quinstar QAL-W00000 attenuator: (a) Attenuation vs. frequency, (b) attenuation vs. micrometer position and (c) phase shift. 118 F.5. ELVA SPST-10 SWITCH

Figure F.13a shows that the maximal attenuation that can be obtained with this device is 20 dB (position 0), which is 5 dB lower than the manufacturer speciﬁcation. In addition, it can be observed (Figure F.13a) that the micrometer position is not linearly related to the obtained attenuation. Figure F.13b presents an approximate correspondence between each micrometer position and the mean attenuation level that would be obtained for that position in the band of interest (92 to 96 GHz). Table F.4 summarizes the measurement results obtained for this device.

Parameter Measured Datasheet

Return Losses 23 dB 14 dB Maximum attenuation 20 dB 25 dB

Table F.4: Quinstar QAL-W00000 attenuator measurement results at 94 GHz in comparison with those provided by the manufacturer.

F.5 ELVA SPST-10 Switch

This ELVA switch is used in reception, just after the circulator, in order to provide higher isolation to the active components of the receiver during transmitting periods. It will be in the oﬀ-state during transmission periods and in the on-state during reception periods. Figure F.14 shows the measurement set-up that has been used for its characterization.

Figure F.14: Measurement set-up for the ELVA SPST-10 switch.

The necessary biasing conditions to obtain oﬀ- and on-states are presented in Table F.5.

Positive Negative Reference Total power State supply (5 V) supply (=9V) voltage consumption current current

OFF 0 V 34 mA 29 mA 0.43 W ON 5 V 100 mA 20 mA 0.68 W

Table F.5: ELVA SPST-10 switch: biasing and power consumption.

• Measured S-parameters are shown in Figure F.15. APPENDIX F. CHARACTERIZATION OF MILLIMETER-WAVE COMPONENTS 119

• Insertion losses for each state can be seen in detail in Figure F.16.

• Return losses are presented in Figure F.17.

S-parameters (OFF) S-parameters (ON) 0 0

-10 -10

-20 -20 (dB) (dB) -30 -30

S11 S11 -40 S12 -40 S12 S21 S21 S22 S22 -50 -50 85 90 95 100 105 85 90 95 100 105 Frequency (GHz) Frequency (GHz) (a) (b)

Figure F.15: ELVA SPST-10 switch: (a) S-Parameters amplitude when the switch is OFF and (b) S-Parameters amplitude when the switch is ON.

This switch shows insertion losses (Figure F.16b) lower than 1.1 dB in the band of interest (92 to 96 GHz) when it is biased in the closed state (reference voltage level of 5 V). When the switch is off-biased (reference voltage level of 0 V) an isolation larger than 31 dB is obtained for the whole band of interest (Figure F.16a). This high level of isolation will protect the receiver from leakage of transmit power occurring during transmission periods. As observed in Figure F.17a, this is a reflective switch, since most of the RF power that is not being transmitted in the off-state is actually being reflected. Its extremely low return losses show the necessity of an isolator at the input of the switch, to prevent reflected power from being re-radiated. (see Section F.6).

Insertion Losses (OFF) Insertion Losses (ON) 45 1.5 S21(ON) S12(ON) Datasheet (typ) 40

35 1 IL (dB) IL (dB)

30 S21(OFF) S12(OFF) Datasheet (typ) 25 0.5 90 91 92 93 94 95 96 97 98 90 91 92 93 94 95 96 97 98 Frequency (GHz) Frequency (GHz) (a) (b)

Figure F.16: ELVA SPST-10 switch: (a) Insertion losses when the switch is OFF and (b) insertion losses when the switch is ON.

Table F.6 summarizes the measurement results obtained for this device. 120 F.6. JOINT RESPONSE OF THE ISOLATOR AND THE SWITCH

Return Losses (OFF) Return Losses (ON) 1 30 S11(OFF) S11(ON) S22(OFF) S22(ON) 0.8 25

0.6 20 RL (dB) RL (dB) 0.4

15 0.2

0 10 90 91 92 93 94 95 96 97 98 90 91 92 93 94 95 96 97 98 Frequency (GHz) Frequency (GHz) (a) (b)

Figure F.17: ELVA SPST-10 switch: (a) Return losses when the switch is OFF and (b) return losses when the switch is ON.

Parameter Measured Datasheet

Insertion losses (S21 ON) 0.96 dB 1 dB Isolation (S21 OFF) 35.1 dB > 30 dB Return loss (S11 OFF) 0.55 dB —

Table F.6: ELVA SPST-10 switch measurement results at 94 GHz in comparison with those provided by the manufacturer.

F.6 Joint Response of the Isolator and the Switch

The extremelly low return losses of the oﬀ-biased switch (see Section F.5) demand an isolator at its input to attenuate reﬂected power. Therefore, this ensemble is expected to achieve:

• Improved return losses during the oﬀ-state thanks to the attenuation of the reﬂected power from the switch in the isolator.

• Low insertion losses in the on-state because of the low losses provided by both the switch and the isolator.

The joint response of both devices will be presented in this section for both states of the switch. Figure F.18 shows the measurement set-up that has been utilized for the characterization. APPENDIX F. CHARACTERIZATION OF MILLIMETER-WAVE COMPONENTS 121

Isolator

Switch

Figure F.18: Measurement set-up to characterize the joint response of the isolator and the switch.

• Measured S-parameters are shown in Figure F.19.

• Return losses are presented in detail for each state Figure F.20.

• Insertion losses for each state are presented in detail in Figure F.21.

S-parameters (OFF) S-parameters (ON) 0 0

-10 -10

-20 -20

-30 -30 (dB) (dB)

-40 -40 S11 S11 S12 S12 -50 S21 -50 S21 S22 S22 -60 -60 85 90 95 100 105 85 90 95 100 105 Frequency (GHz) Frequency (GHz) (a) (b)

Figure F.19: Isolator + switch: (a) S-Parameters amplitude when the switch is OFF and (b) S-Parameters amplitude when the switch is ON. 122 F.6. JOINT RESPONSE OF THE ISOLATOR AND THE SWITCH

Input Return Losses (OFF) Input Return Losses (ON) 30 30

28 25 26 20 24

15 22

RL (dB) RL (dB) 20 10 18 Isolator+Switch Isolator+Switch 5 Switch 16 Switch Isolator Isolator 0 14 90 91 92 93 94 95 96 97 98 90 91 92 93 94 95 96 97 98 Frequency (GHz) Frequency (GHz) (a) (b)

Figure F.20: Isolator + switch: (a) Return losses when the switch is OFF and (b) return losses when the switch is ON.

Insertion Losses (OFF) Insertion Losses (ON) 42 Isolator+Switch 2.5 Switch 40

2 38

36 1.5 IL (dB) IL (dB)

34 1 Isolator+Switch 32 Switch Isolator 30 0.5 90 91 92 93 94 95 96 97 98 90 91 92 93 94 95 96 97 98 Frequency (GHz) Frequency (GHz) (a) (b)

Figure F.21: Isolator + switch: (a) Insertion losses when switch is OFF and (b) insertion losses when the switch is ON.

Figure F.20a shows that input return losses in the off-state have improved by 15 dB with respect to the return losses provided by the switch alone. This is compliant with the 20 dB reverse attenuation and 14 dB input reflection coefficient provided by the isolator. In both, off- and on-states, reflections coming from the switch or the LNA can be neglected in comparison with those directly connected to the isolator reflection coefficient. At the same time, insertion losses in the on-state (Figure F.21b) have not been severely worsened. The switch alone has 1 dB insertion loss and the isolator, 1.3 dB. Both devices together obtain 2.2 - 2.5 dB insertion losses in the band of interest, as expected. As a whole, the ensemble works as an absorptive switch, which is a device that is not currently commercialized at W-band. Table F.7 summarizes the obtained measurement results. APPENDIX F. CHARACTERIZATION OF MILLIMETER-WAVE COMPONENTS 123

Parameter Measured

Insertion losses (S21 ON) 2dB Isolation (S21 OFF) 35.3 dB Return loss (S11 OFF) 18.8 dB

Table F.7: Measurement results of the switch and the isolator at 94 GHz.

F.7 RPG W-LNA75110 Low Noise Ampliﬁer

The LNA is the ﬁrst active device of the receiver chain. It should be located as close as possible to the antenna to reduce the noise ﬁgure of the chain. Figure F.22 shows the measurement set-up that has been used for the characterization of this LNA.

Figure F.22: Measurement set-up for the RPG W-LNA75110 low noise ampliﬁer.

Measured S-parameters are presented in Figure F.23 and gain and return losses can be observed in detail in Figure F.24.

S-Parameters S-Parameters 30 150 S11 20 S21 100 10 50 0

(º) 0

(dB) -10

-20 -50

-30 S11 S12 -100 -40 S21 S22 -150 -50 85 90 95 100 105 85 90 95 100 105 Frequency (GHz) Frequency (GHz) (a) (b)

Figure F.23: RPG W-LNA75110 low noise ampliﬁer: (a) S-Parameters amplitude and (b) S-Parameters phase. 124 F.7. RPG W-LNA75110 LOW NOISE AMPLIFIER

Gain Return Losses 35 15 Input Port Output Port Input Datasheet Output Datasheet 30 10 G (dB) RL (dB) 25 5

Measured Datasheet 20 0 90 91 92 93 94 95 96 97 98 90 91 92 93 94 95 96 97 98 Frequency (GHz) Frequency (GHz) (a) (b)

Figure F.24: RPG W-LNA75110 low noise ampliﬁer: (a) Gain (20 log|S21|) and (b) return losses.

This device features a gain (Figure F.24a) of 26 - 31 dB in the band of interest, which is slightly above the manufacturer curve. Input return losses (Figure F.24b) are 8.4 - 11.2 dB. All this is compliant with the speciﬁcation. It is also important to note that power rating of this device is =20 dBm, so a complete protecting network will be needed at its input to isolate it from the transmitter power. Table F.8 summarizes the measurement results obtained for this device.

Parameter Measured Datasheet

Gain 28 dB 26.5 dB Input return losses 9.2 dB 9.3 dB

Table F.8: RPG W-LNA75110 low noise ampliﬁer measurement results at 94 GHz in comparison with those provided by the manufacturer. Appendix G

Millimeter Wave Components Datasheets

The datasheets collected in this appendix have been organized as follows:

1. RF components:

• Passive devices: – RPG WFI-110 isolator. – RPG WPD-110 hybrid power divider. – ELVA CR-1094 circulator. – Quinstar QAL-W00000 variable attenuator. – ELVA SPST-10 switch. • Active devices: – RPG W-LNA75110 low noise ampliﬁer. – Quinstar QMB-9999WS balanced mixer. – RPG AFM6-110 ×6 frequency multiplier.

2. Optical structures:

• Edmund Optics aluminium off-axis mirrors. – 84-585 45◦ off-axis paraboloid mirror. – 84-569 45◦ off-axis paraboloid mirror. – 84-975 90◦ off-axis paraboloid mirror. • W-band Teflon lenses.

3. Antennas:

• Millitech SGH-08 conical horn in WR-08. • RPG FH-PP-100 Potter horn in WR-10.

125 126 APPENDIX G. MILLIMETER WAVE COMPONENTS DATASHEETS 127 128

x 26.5-220 GHz operating frequency x High isolation x Narrow band and full band types x Compact size x Low insertion losses

x Laboratory measurement and test equipment x Junction of some parts of sub-systems x Matching of several waveguide components x Base of multi-junction devices (injection-locked amplifier)

26.5-220GHz Circulators and Isolators are ferrite waveguide components. There are two kinds of the products operating within narrow frequency band (1-4 GHz) and full waveguide band. Junction circulators /isolators are narrow band. Wideband devices base on Faraday rotation effect. Used in many waveguide schemes for junction their parts and for matching different components and protecting against reflected mm-wave power. Standard line of ELVA-1’s circulators CR-XX/CF/BW series provide low insertion losses and high isolation for all three ports. They have operation frequency band up to 4 GHz. Better performances of the circulators can be provided within narrow frequency band. The IS-XX/CF/BW isolators realized by terminating of one port of the junction circulators. Ideally suit for suppression of reflected power coming from any waveguide devices with high VSWR. Full band isolators IF-XX have good performances within full waveguide range. Mainly used in wideband sources or receivers for suppression mm-wave power propagating in one fixed direction. Have small insertion losses.

Narrow band circulators CR-XX/CF/BW series:

1 2

CR-XX/CF/BW Central frequency: Fixed from 26.5- 110 GHz Fixed from 110- 170 GHz Bandwidth: 2.5 GHz 0.5 GHz 2.5 GHz 0.5 GHz Insertion losses: 0.7 dB 0.5 dB 1 dB 0.7 dB 1 to 2, 2 to 3, 3 to 1 Isolation: 23 dB (min) 30 dB 20 dB (min) 25 dB 2 to 1, 3 to 2, 1 to 3 VSWR 1.2 (typ) 1.3 (typ)

APPENDIX G. MILLIMETER WAVE COMPONENTS DATASHEETS 129 130

x Low insertion losses x Fast switching time x High isolation x More then 10% bandwidth operation x Low cost x Easy to use

x Radars x Fast protection system x AM of microwave signals. x Lock-in detection systems

ELVA-1 series fast SPST switches is built on slim film PIN diodes. Built-in driver provides switching time 4-6 ns and unique technology allows to get more then 10% operation with small insertion losses and isolation more then 30 dB.

Model SPST-42 SPST-28 SPST-22 SPST-19 SPST-15 SPST-12 SPST-10 SPST-08 SPST-06 Frequency Band K Ka Q U V E W F D Range, GHz 18-26.5 26-40 33-50 40-60 50-75 60-90 75-110 90-140 110-150 Insertion Loss, dB (typ) 0,7 0,7 0,8 0,8 0,8 1,0 1,0 1,5 1,5 Isolation, dB (min) 30* 30* 30* 30* 30* 30* 30* 30* 30* Peak Power, W(max) 1,0 1,0 1,0 1,0 1,0 1,0 1,0 1,0 0,8 Switching Time, ns** 4-6 4-6 4-6 4-6 4-6 4-6 4-6 4-6 4-6

Supply +/-5V DC Control signal TTL Control Input impedance 50 Ohm

*The models with 60 dB Isolation are available upon request **Guaranteed for Rise Time 0-90% RF and Fall Time 100-10% RF. Typical data for different models are presented below.

SPST-10/94 '0', Isolation '1', Loss Sw itch SPST-06/140 Isolation Losses

0 0 -5 -5 -10 -10 -15 -15 -20 -20 -25 -30 Loss, dB

Loss, dB -25 -35 -30 -40 -35 -45 -40 -50

90 90,5 91 91,5 92 92,5 93 93,5 94 94,5 95 95,5 96 96,5 97 97,5 98 98,5 99 99,5 100 110 112 114 116 118 120 122 124 126 128 130 132 134 136 138 140 142 144 146 148 150 Frequency, GHz Frequency, GHz

Specify Model Number SPST-XX/AA/BB - XX- waveguide band (WR-Number) - AA – Center operation frequency (fo), GHz - BB – Operation bandwidth (fo+/-BB), GHz

APPENDIX G. MILLIMETER WAVE COMPONENTS DATASHEETS 131 132 APPENDIX G. MILLIMETER WAVE COMPONENTS DATASHEETS 133 134 APPENDIX G. MILLIMETER WAVE COMPONENTS DATASHEETS 135 136

W-Band Dielectric Lenses

Parameter Value

Material Teﬂon (r =2.1, tan(δ)=0.006) Focal length 62.7 mm Input radius ∞ Output radius 26.961 mm Lens thickness 21.41 mm Losses 19.6 % Back-vertex focal length 48 mm Front-vertex focal length 62.7 mm APPENDIX G. MILLIMETER WAVE COMPONENTS DATASHEETS 137

SERIES SGH Millimeter-Wave Technology & Solutions

ELECTRICAL SPECIFICATIONS*

Pyramidal Horns Model Number SGH-42 SGH-28 SGH-22 SGH-19 SGH-15 SGH-12 SGH-10 SGH-08 SGH-06 SGH-05 SGH-04 SGH-03 Frequency band K Ka Q U V E W F D G - - and range (GHz) 18-26.5 26.5-40 33-50 40-60 50-75 60-90 75-110 90-140 110-170 140-220 170-260 220-325 Gain (dB) 24 24 24 24 24 24 24 24 24 24 24 24 VSWR 1.2:1 1.2:1 1.2:1 1.2:1 1.2:1 1.2:1 1.2:1 1.25:1 1.25:1 1.25:1 1.25:1 1.25:1 Conical Horns Gain (dB) 21 21 21 21 21 21 21 21 21 21 21 21 VSWR 1.2:1 1.2:1 1.2:1 1.2:1 1.2:1 1.2:1 1.2:1 1.25:1 1.25:1 1.25:1 1.25:1 1.25:1 *All specifications listed are typical values.

TYPICAL PERFORMANCE

OUTLINE DRAWINGS*

*The outlines shown may not reflect the latest information. Please contact Millitech for current outline drawings.

IS000025 REV07 ECO #1606-29-03 www.millitech.com 138

SERIES SGH Millimeter-Wave Technology & Solutions

MECHANICAL SPECIFICATIONS

Circular Waveguide Output – Conical Horns Diameter (in) Frequency Range A (in/mm) B (in/mm) Flange MIL.F-3922 0.455 17.5-20.5 2.300/58.420 5.000/127.000 /54-001* 0.396 20.0-24.5 2.660-67.564 4.976/126.390 /54-001* 0.328 24.0-26.5 2.350/59.690 4.384/111.354 /54-001* 0.315 26.5-33.0 1.800/45.720 3.300/83.820 /54-003* 0.250 33.0-38.5 1.660/42.164 3.097/78.664 /54-003* 0.219 38.5-40.0 1.512/38.405 2.821/71.653 /54-003* 0.250 33.0-38.5 1.440/36.576 2.700/68.580 /67B-006 0.219 38.5-43.0 1.456/39.982 2717/69.012 /67B-006 0.188 43.0-50.0 1.276/32.410 2.381/60.477 /67B-006 0.210 40.0-43.0 1.180/29.972 2.250/57.150 /67B-007 0.188 43.0-50.0 1.276/32.410 2.381/60.477 /67B-007 0.165 50.0-60.0 1.079/27.407 2.013/51.130 /67B-007 0.165 50.0-58.0 0.950/24.130 1.900/48.260 /67B-008 0.141 58.0-68.0 0.942/23.927 1.757/44.628 /67B-008 0.125 68.0-75.0 0.830/21.082 1.548/39.319 /67B-008 0.136 60.0-66.0 0.784/19.914 1.600/40.640 /67B-009 0.125 66.0-88.0 0.770/19.558 1.438/36.525 /67B-009 0.094 88.0-90.0 0.667/16.942 1.244/31.598 /67B-009 0.112 75.0-88.0 0.644/16.358 1.300/33.020 /67B-010 0.094 88.0-110.0 0.599/15.215 1.118/28.397 /67B-010 0.089 90.0-115.0 0.514/13.056 1.100/27.940 /67B-M08 0.075 115.0-140.0 0.465/11.811 0.868/22.047 /67B-M08 0.073 110.0-140.0 0.418/10.617 0.900/22.860 /67B-M06 0.059 140.0-160.0 0.396/10.058 0.738/18.745 /67B-M06 0.058 140.0-220.0 0.328/8.331 0.750/19.050 /67B-M05 0.049 170.0-260.0 0.276/7.010 0.650/16.510 /67B-M04 0.039 220.0-325.0 0.218/5.537 0.550/13.970 --- Rectangular Waveguide Output – Pyramidal Horns Model Number A (in/mm) B (in/mm) C (in/mm) Flange MIL.F-3922 SGH-42 4.068/103.327 3.093/78.562 7.480/189.992 /54-001* SGH-28 2.712/68.885 2.062/52.375 5.087/129.210 /54-003* SGH-22 2.170/55.118 1.650/41.910 4.070/103.378 /67B-006 SGH-19 1.821/46.253 1.385/35.179 3.480/88.392 /67B-007 SGH-15 1.434/36.424 1.090/27.686 2.775/70.485 /67B-008 SGH-12 1.182/30.023 0.898/22.809 2.348/59.639 /67B-009 SGH-10 0.969/24.613 0.736/18.694 1.938/49.225 /67B-010 SGH-08 0.775/19.685 0.589/14.961 1.561/39.649 /67B-M08 SGH-06 0.630/16.002 0.479/12.167 1.265/32..131 /67B-M06 SGH-05 0.494/12.548 0.376/9.550 1.036/26.314 /67B-M05 SGH-04 0.417/10.592 0.317/8.052 0.855/21.717 /67B-M04 SGH-03 0.329/8.357 0.250/6.350 0.707/17.958 --- * With #4-40 threaded holes.

IS000025 REV07 ECO #1606-29-03 www.millitech.com APPENDIX G. MILLIMETER WAVE COMPONENTS DATASHEETS 139 140 Bibliography

[1] Comunidad Aut´onomade Madrid, “Space Debris Radar project (Ref. S2013/ICE3000 SPADERadar-CM),” 2017.

[2] V. Iglesias, J. Grajal, and G. Rubio-Cidre, “Radar para detecci´on de basura espacial (SPADERADAR-CM). Dise˜nodel sistema,” tech. rep., GMR (UPM), 2015.

[3] M. Ram´ırez and J. Grajal, “Radar para detecci´onde basura espacial (SPADERADAR-CM). Arquitectura del sistema,” tech. rep., GMR (UPM), 2017.

[4] D. Heimerdinger, “Orbital debris and associated space ﬂight risks,” in Reliability and Maintainability Symposium, 2005. Proceedings. Annual, pp. 508–513, IEEE, 2005.

[5] C. L. Stokely, J. L. Foster, E. G. Stansbery, J. R. Benbrook, and Q. Juarez, “Haystack and HAX Radar Measurements of the Orbital Debris Environment,” Tech. Rep. November, Lyndon B. Johnson Space Center, 2006.

[6] D. Walsh, “A survey of radars capable of providing small debris measurements for orbit prediction,” tech. rep., -, 2013.

[7] M. I. Skolnik, Radar Handbook. McGraw-Hill, 2008.

[8] D. M. Pozar, Microwave engineering. John Wiley & Sons, 2009.

[9]S.M.ShermanandD.K.Barton,Monopulse principles and techniques. Artech House, 2011.

[10] C. A. Balanis, Antenna theory: analysis and design. John Wiley & Sons, 2016.

[11] M. Arrebola, J. A. Encinar, R. Cahill, and G. Toso, “Dual-reflector antenna with a reflectarray subreflector for wide beam scanning range at 120GHz,” in Proc. Int. Conf. Electromagnetics in Advanced Applications, pp. 848–851, Sept. 2012.

[12] C. Granet, “Designing axially symmetric Cassegrain or Gregorian dual-reﬂector antennas from combinations of prescribed geometric parameters,” IEEE Antennas and Propagation Magazine, vol. 40, pp. 82–89, June 1998.

[13] S. Ashwyn, “Introduction to Cassegrain antenna,” June 2009.

[14] M. Soe, Z. M. Aung, Z. M. Naing, and K. Theingi Oo, “Performance analysis and design consideration of cassegrain for satellite communication,” in International MultiConference of Engineers and Computer Scientists, 2009.

[15] P. Hannan, “Microwave antennas derived from the Cassegrain telescope,” IRE Transactions on Antennas and Propagation, vol. 9, no. 2, pp. 140–153, 1961.

141 142 BIBLIOGRAPHY

[16] M. Barba, “Radar para detecci´onde basura espacial (SPADERADAR-CM). Monopulse radar horns.,” tech. rep., ETC (UPM), 2017.

[17] P. Wade, “Multiple reﬂector dish antennas,” 2004.

[18] T. A. Milligan, Modern antenna design. John Wiley & Sons, 2005.

[19] P. Uﬁmtsev, Fundamentals of the Physical Theory of Diﬀraction. Wiley, 2014.

[20] P. F. Goldsmith, I. of Electrical, E. Engineers, M. Theory, and T. Society, Quasioptical systems: Gaussian beam quasioptical propagation and applications. IEEE press New York, 1998.

[21] P. F. Goldsmith, “Quasi-optical techniques,” Proceedings of the IEEE, vol. 80, no. 11, pp. 1729–1747, 1992.

[22] B. Guenther, Modern optics. OUP Oxford, 2015.

[23] H. Kogelnik and T. Li, “Laser beams and resonators,” Proceedings of the IEEE, vol. 54, pp. 1312–1329, Oct. 1966.

[24] D. Marcuse, Light transmission optics. Van Nostrand Reinhold New York, 1972.

[25] R. Easton, “Ray optics for imaging systems. course notes.,” tech. rep., Chester F. Carlson Center for Imaging Science (Rochester Institute of Technology), 2013.

[26] J. A. Murphy, “Distortion of a simple Gaussian beam on reﬂection from oﬀ-axis ellipsoidal mirrors,” International Journal of Infrared and Millimeter Waves, vol. 8, pp. 1165–1187, Sept. 1987.

[27] A. A. Tovar and L. W. Casperson, “Generalized beam matrices: Gaussian beam propagation in misaligned complex optical systems,” JOSA A, vol. 12, no. 7, pp. 1522–1533, 1995.

[28] G. Perez-Palomino, R. Florencio, J. A. Encinar, M. Barba, R. Dickie, R. Cahill, P. Baine, M. Bain, and R. R. Boix, “Accurate and eﬃcient modeling to calculate the voltage dependence of liquid crystal-based reﬂectarray cells,” IEEE Transactions on Antennas and Propagation, vol. 62, no. 5, pp. 2659–2668, 2014.

[29] J. Huang and J. A. Encinar, Reﬂectarray Antennas. A John Wiley & Sons, 2008.

[30] R. J. Mailloux, Phased array antenna handbook, vol. 2. Artech House Boston, 2005.

[31] W. Hu, M. Ismail, R. Cahill, J. Encinar, V. Fusco, H. Gamble, D. Linton, R. Dickie, N. Grant, and S. Rea, “Liquid-crystal-based reﬂectarray antenna with electronically switchable monopulse patterns,” Electronics Letters, vol. 43, no. 14, 2007.

[32] I. Fujitsu Microelectronics America, “Fundamentals of Liquid Crystal Displays. How They Work and What They Do. White Paper,” tech. rep., Fujitsu Microelectronics America, Inc., 2006.

[33] G. Pérez Palomino, Contribution to the analysis and design of reflectarray antennas for reconfigurable beam applications at frequencies above 100 GHz using liquid crystal technology. PhD thesis, Telecomunicacion, 2015. BIBLIOGRAPHY 143

[34] G. Perez-Palomino, P. Baine, R. Dickie, M. Bain, J. A. Encinar, R. Cahill, M. Barba, and G. Toso, “Design and experimental validation of liquid crystal-based reconﬁgurable reﬂectarray elements with improved bandwidth in F-band,” IEEE Transactions on Antennas and Propagation, vol. 61, no. 4, pp. 1704–1713, 2013.

[35] G. Perez-Palomino, M. Barba, J. A. Encinar, R. Cahill, R. Dickie, P. Baine, and M. Bain, “Design and demonstration of an electronically scanned reﬂectarray antenna at 100 GHz using multiresonant cells based on liquid crystals,” IEEE Transactions on Antennas and Propagation, vol. 63, no. 8, pp. 3722–3727, 2015.

[36] S. A. Maas, Noise in linear and nonlinear circuits. Artech House Publishers, 2005.

[37] C. Razell, “System Noise-Figure Analysis for Modern Radio Receivers: Part 1, Calculations for a Cascaded Receiver,” Microwave Journal, 2013.

[38] D. N. Held and A. R. Kerr, “Conversion Loss and Noise of Microwave and Millimeter-wave Mixers: Part 1 - Theory,” IEEE Transactions on Microwave Theory and Techniques, 1978.

[39] TICRA GRASP, User Manual: ”GRASP”, 2016.

[40] G. Carpintero, E. Garc´ıa-Muñoz, H. Hartnagel, S. Preu, and A. Räisänen, Semiconductor Terahertz Technology: Devices and Systems at Room Temperature Operation. John Wiley & Sons, 2015.

[41] W. D. Fitzgerald, “A 35-GHz beam waveguide system for the millimeter-wave radar,” The Lincoln Laboratory Journal, vol. 5, no. 2, pp. 245–272, 1992.

[42] N. Gagnon, Design and study of a free-space quasi-optical measurement system.University of Ottawa (Canada), 2002.

[43] E. H˚akansson, A. Amiet, and A. Kaynak, “Dielectric characterization of conducting textiles using free space transmission measurements: Accuracy and methods for improvement,” Synthetic Metals, vol. 157, no. 24, pp. 1054–1063, 2007.

[44] W. Hu, R. Cahill, J. A. Encinar, R. Dickie, H. Gamble, V. Fusco, and N. Grant, “Design and measurement of reconﬁgurable millimeter wave reﬂectarray cells with nematic liquid crystal,” IEEE Transactions on Antennas and Propagation, vol. 56, no. 10, pp. 3112–3117, 2008.

[45] A. Kazemipour, M. Hudlicka, S. K. Yee, M. A. Salhi, D. Allal, T. Kleine-Ostmann, and T. Schrader, “Design and Calibration of a Compact Quasi-Optical System for Material Characterization in Millimeter/Submillimeter Wave Domain,” IEEE Transactions on Instrumentation and Measurement, vol. 64, pp. 1438–1445, June 2015.

[46] R. K. May, The Development of Quasi-Optical Techniques for Log Wavelength Imaging. PhD thesis, National University of Ireland Maynooth, 2008.

[47] B. M. Oliva, Desarrollo y aplicaciones de radares de alta resolución en bandas milimétricas. PhD thesis, Universidad Politécnica de Madrid, 2014.

[48] S. H. Sánchez, “Análisis y desarrollo de sistemas de medida cuasi-ópticosen la banda de ondas milimétricas. Aplicaciónpara la medida de constantes dieléctricasy reflectividad a 100 GHz.,” Master’s thesis, Escuela TécnicaSuperior de Ingenieros de Telecomunicación, Universidad Politécnica de Madrid, 2013. 144 BIBLIOGRAPHY

[49] J. A. Scheer and W. L. Melvin, Principles of modern radar. The Institution of Engineering and Technology, 2013.

[50] Anritsu, Application notes MS4640A VectorStar VNA.