UNIVERSITÄT STUTTGART INSTITUT FÜR HOCHFREQUENZTECHNIK PROF. DR. JAN HESSELBARTH

Master Thesis

Cavity Stabilized Microwave Oscillator

Josep Canals Casals

Start Date : 15.10.2012 Submission Date : 17.05.2013

Supervisor : Prof. Jan Hesselbarth

Erklärung

Hiermit erkläre ich, dass die vorliegende Masterarbeit selbständig verfasst wurde und keine anderen als die angegebenen Quellen und Hilfsmittel benutzt worden sind.

Stuttgart, den 23.05.2013

Josep Canals Casals

Acknowledgments

I would like to express my gratitude to my supervisor, Dr Jan Hesselbarth, who gave me the opportunity of doing this master’s thesis and whose expertise, understanding, and patience, were essential for this work.

I would like to thank other members and students at the Institut für Hochfrequenztechnik (IHF) of University of Stuttgart for their time, patience, guidance and company.

I also want to thank all my childhood friends from Berga, those who I shared class during my degree in Polytechnical Univertiy of Catalunya (UPC) and those friends who I have met the lasts months here in Stuttgart.

Finally special acknowledgment for my parents, Maria and Lluís, and all my family for the support they provided me through my entire life, encouragement and love.

Zusammenfassung

In der vorliegenden Arbeit wird ein stabilisierter C-Band-Oszillator beschrieben. Dafür werden zwei unterschiedene zwei Hohlraumresonatoren realisieren, ein durch zwei

Abschlussebenen geschlossener Rechteckhohlleiter, der einen TE101-Hohlraumresonator bildet. Zum Anderen ein durch zwei Abschlussebenen geschlossener Rundhohlleiter, der einen TM010-Hohlraumresonator bildet. Die Hohlraumresonatoren werden über zwei Aperturen an die Mikrostreifenleitung einer planaren Schaltung gekoppelt.

Der Oszillator besteht aus zwei kaskadierten GaAs pHEMT MMIC rauscharmen Verstärkern, einem Phasenschieber und einem der zwei o.g. Hohlraumresonatoren. Die Ausgangsleistung lässt sich über einem integrierten Koppler messen.

Der Oszillator mit dem Rundhohlraumresonator besitzt eine Ausgangsleistung von etwa –4 dBm. Die Kurzzeit- Frequenzstabilität beträgt –97.38 dBc/Hz bei einer Frequenzversatz von 1 kHz und einer Oszillationsfrequenz von 5,97 GHz.

Abstract

In this work, a C-band oscillator stabilized by a high-Q waveguide cavity is designed and realized. Firstly; rectangular waveguide closed for two shorting planes defining a rectangular cavity resonator is used. On the other hand, circular waveguide closed for two shorting planes defining a circular cavity resonator. Both cavities are coupled to microstrip lines of the planar circuit through two apertures in the cavity.

Feedback configuration consists of two GaAs pHEMT MMIC Low Noise Amplifiers in cascade, one phase shifter and a cavity. Output power can be measured with a coupling configuration.

Oscillator with circular resonator has an output power about –4 dBm. Short term stability is –97.38 dBc/Hz at 1 kHz offset frequency and oscillation frequency of 5.97 GHz.

Contents

I

1 INTRODUCTION ...... 1

1.1 STATE OF THE ART ...... 1 1.2 PRESENTATION OF THE WORK ...... 2 1.3 STRUCTURE OF THE WORK ...... 2 2 THEORETICAL BACKGROUND ...... 3 2.1 RESONANCE ...... 3 2.1.1 EQUIVALENT CIRCUIT ...... 3 2.1.2 LOADED AND UNLOADED Q FACTOR (Q) ...... 4 2.1.3 WAVEGUIDE RESONATORS ...... 5 2.2 MICROSTRIP LINES ...... 13 2.3 DIRECTIONAL COUPLER ...... 14 2.4 OSCILLATOR CIRCUIT ...... 16 2.4.1 OSCILLATION CONDITIONS ...... 16 3 DESIGN ...... 18 3.1 SIMULATIONS ...... 18 3.1.1 RESONANT CAVITY ...... 18 3.1.2 SMA CONNECTORS AND TRANSMISSON LINES ...... 55 3.1.3 DIRECTIONAL COUPLER ...... 58 3.1.4 AMPLIFIER ...... 60 3.1.5 PHASE SHIFTER ...... 66 3.1.6 MICROSTRIP BENDING ...... 66 3.2 BUILDING AND MEASUREMENTS ...... 69 3.2.1 AMPLIFIER ...... 69 3.2.2 RESONANT CAVITY ...... 76 3.2.3 DIRECTIONAL COUPLER ...... 82 3.2.4 OSCILLATOR PLANAR CIRCUIT ...... 84 3.2.5 PHASE NOISE ...... 90 4 CONCLUSIONS ...... 92 APPENDIX ...... 96 A.SOFTWARE ...... 96 ADVANCED DESIGN SYSTEM 2012.08 (ADS) ...... 96 CST MICROWAVE STUDIO 2012 ...... 96 EAGLE 4.16 (Easily Applicable Graphical Layout Editor) ...... 96 MATLAB R2012a ...... 97 B.EQUIPMENT ...... 97 SPECTRUM ANALYZER R&S FSL6 and HEWLETT PACKARD 8563E ...... 97 NETWORK ANALYZER WILTRON 360B ...... 98 SOLDERING EQUIPMENT ...... 100 PCB MANUFACTORING ...... 104

i ii Contents

SIGNAL GENERATOR GIGA-TRONICS 900 ...... 104 BIBLIOGRAPHY ...... 105

List of Figures

Figure 2-1: Series and parallel resonant circuit with lumped elements ...... 3 Figure 2-2: Series resonance with microstrip line ended with open circuit (left). Parallel resonance with microstrip line ended with short circuit ...... 4 Figure 2-3:Resonant circuit loaded by external circuit ...... 4 Figure 2-4: Rectangular cavity structure ...... 6 Figure 2-5: Air dimension inside brass ...... 6 Figure: 2-6: Circular cavity structure ...... 9 Figure 2-7: Air dimension inside brass ...... 10 Figure 2-8: Probe used to excite waveguides and cavity resonators ...... 12 Figure 2-9: A loop used to excite waveguides and cavity resonators...... 12 Figure 2-10: Aperture used to excite waveguides and cavity resonators ...... 13 Figure 2-11: Microstrip line cross section electric and magnetic fields distribution ...... 13 Figure 2-12: Equivalent geometry of a quasi-TEM microstrip line. (left) Original geometry.

Equivalent geometry, where the dielectric substrate of relative permittivity is replaced with a homogeneous medium of effective relative permittivity (Right) ...... 14 Figure 2-13: Directional coupler plot ...... 15 Figure 2-14: Feedback oscillator circuit ...... 16 Figure 3-1:Electric Field in cross section cavity in frequency 6.029 GHz ...... 20 Figure 3-2: Electric Field in cross section cavity in frequency 6.029 GHz ...... 20 Figure 3-3: Insertion loss for different rectangular cavity height ...... 21 Figure 3-4: Magnetic Field in cavity cross section in frequency 7.526 GHz ...... 22 Figure 3-5: Electric Field in cavity cross section in frequency 7.526 GHz ...... 22 Figure 3-6:Electric Field in cavity cross section in frequency 7.853 GHz ...... 23 Figure 3-7:Electric Field in cavity cross section in frequency 7.853 GHz ...... 23 Figure 3-8: Rectangular cavity dielectric dimensions ...... 24 Figure 3-9: Resonant mode chart for a cylindrical cavity obtained from ...... 25

Figure 3-10: Magnetic field in TM010 simulated circular cavity in frequency 6.08 GHz ...... 26 Figure 3-11: Electric field in TM010 simulated circular cavity in frequency 6.08 GHz ...... 26 Figure 3-12: Insertion loss for different cavity height ...... 27

Figure 3-13: Electric field in TE111 simulated circular cavity in frequency 7.839 GHz ...... 28 Figure 3-14: Electric field in TE111 simulated circular cavity in frequency 7.839 GHz ...... 29 Figure 3-15: Circular air shape ...... 29 Figure 3-16: Final Brass rectangular cavity ...... 30 Figure 3-17: Final Brass circular cavity ...... 31 Figure 3-18: Rectangular cavity with PCB (left) and coupling wires. circular cavity(right) ... 31 Figure 3-19: Coupling wires and Electric field representation in cavity cross-section ...... 32 Figure 3-20: Length wire sweep in rectangular cavity ...... 32 Figure 3-21: Length wire sweep in circular cavity...... 33 Figure 3-22: Different strip line disc radius in rectangular cavity holding the coupling wires 34 radius in rectangular cavity holding the coupling wires ...... 34

iii iv List of Figures

Figure 3-23: Different strip line disc radius in circular cavity holding the coupling wires ..... 34 Figure 3-24: Top view PCB surface (Top).Top PCB ground (center), Cavity cross section for circular holes coupling (bottom) ...... 36 Figure 3-25: Top view PCB surface (Top). Top PCB ground (center), Cavity cross section for rectangular holes coupling (bottom) ...... 37

Figure 3-26: Surface currents in TE101 mode in rectangular cavity ...... 38 Figure 3-27: Insertion loss with different holes position in the top surface cavity (x,y,z) ...... 38 Figure 3-28: Insertion loss with different holes width in the top surface cavity ...... 39 Figure 3-29: Insertion loss with different holes length in the top surface cavity ...... 39 Figure 3-30: Insertion loss for different holes radius (z=12) ...... 40 Figure 3-31: Rectangular cavity with circular coupling holes depending on holes position ... 41

Figure 3-32: Surface currents in TM011 mode in circular cavity ...... 42 Figure 3-33: Insertion loss circular cavity for different position (x,y,z)...... 43 Figure 3-34: Insertion loss circular cavity for different hole radius with x holes=12 mm ...... 43 Figure 3-35: Insertion loss circular cavity using rectangular holes varying holes width ...... 44 Figure 3-36: Insertion loss circular cavity using rectangular holes varying holes length ...... 44 Figure 3-37: Coupling coefficinet ...... 46

Figure 3-38: S21 and S11 parameters in rectangular cavity with and without resistor as matching network ...... 47

Figure 3-39: S21 and S11 parameters in circular cavity with and without resistor as matching network...... 48 Figure 3-40: Reflection using matching network with R=47 ohms and R=50 ohms ...... 49 Figure 3-41:.Top view of strip lines and ground plane in PCB (top). Rectangular S parameters with resistor and stub (bottom) ...... 50 Figure 3-42: Final rectangular cavity design plot ...... 52 Figure 3-43: Final circular cavity design plot ...... 52 Figure 3-44: Theoretical unloaded Q for Rectangular (red line) and Circular (blue line) cavity ...... 53 Figure 3-45: SMA Straight Jack PCB 32K101-400L5 layout pattern ...... 56 Figure 3-46: SMA Right Angle Jack layout pattern ...... 56 Figure 3-47: SMA Straight Jack PCB 32K101-400L5 ...... 57 Figure 3-48: SMA Right Angle Jack of Rosenberger representation ...... 57 Figure 3-49: Simulated SMA connectors reflection parameters...... 58 Figure 3-50: Directional coupler plot in CST ...... 59 Figure 3-51: Simulated coupler S-parameters ...... 60 Figure 3-52:QFN16 Layout pattern connected to 50  line ...... 61 Figure 3-53: HMC717LP3 evaluation PCB. (top) Amplifier and bias circuit layout. (bottom) Reference line circuit...... 62 Figure 3-54:ST089 PAD with 50 ohms microstrip line...... 63 Figure 3-55:RF3376 evaluation PCB. a) Amplifier and bias circuit layout. b) Reference line circuit...... 64 Figure 3-56: Blocking RF structure...... 65 Figure 3-57: Phase shifter plot ...... 66 Figure 3-58: Mitered Bend. W50=1.8 mm; a=3 mm...... 67 Figure 3-59: Swept Bend. W50=1.8 mm; R=2 mm ...... 67 List of Figures v

Figure 3-60: S parameters of 90 degrees mitered bend ...... 68 Figure 3-61: Simulated S parameters of 90 degrees swept bend (R=2 mm) ...... 68 Figure 3-62: Test PCB for HMC717LP3 ...... 69 Figure 3-63: Test PCB for RF3376 ...... 70

Figure 3-64: S21 and S11 of HMC717LP3 ...... 71 Figure 3-65: S21 and S11 of RF3376 (52) ...... 71 Figure 3-66: S21 and phase of HMC717LP3 ...... 72 Figure 3-67: S21 and phase of RF3376 ...... 72 Figure 3-68: Compression point measurement ...... 73 Figure 3-69: Measurement Setup ...... 74 Figure 3-70: Hittite Power Response ...... 74 Figure 3-71: RF3376 Power Response ...... 75

Figure 3-72: Measured S21 for rectangular cavity ...... 77 Figure 3-73: Measured S21 for rectangular cavity ...... 77 Figure 3-74: Measured S21 and S11 with silver painting ...... 78 Figure 3-75: Measured S21 and S11 ...... 79 Figure 3-76: Measured S21 phase silver painting ...... 79 Figure 3-77: Measured S21 phase ...... 80 Figure 3-78: Measured S21 and S11 with silver glue ...... 81 Figure 3-79: Directional coupler photo ...... 82 Figure 3-80: Directional Coupler measured S parameters ...... 83 Figure 3-81: Oscillator circuit with rectangular cavity ...... 84 Figure 3-82: Obtained resonant frequencies with rectangular oscillator ...... 85 Figure 3-83: Oscillator circuit with circular cavity ...... 86 Figure 3-84: Phase shifter procedure scheme ...... 87 Figure 3-85: Phase shifter proper wire position ...... 87 Figure 3-86: Spectrum analyzer measure for circular cavity oscillator ...... 88 Figure 3-87: Oscillator measurement ...... 89 Figure 3-88: Obtained measurement with spectrum analyzer ...... 90 Figure 4-1: Proposed cavity structure ...... 93 Figure 4-2: Mitered bending ...... 93 Figure 4-3: swept bending ...... 93 Figure 4-4: Directional coupler improvement ...... 94 Figure 4-5: Possible improvement in oscillator planar circuit with circular cavity ...... 95 Figure B-1: (a) R&S FSL6 (b) HEWLETT PACKARD 8563E ...... 98 Figure B-2: Network Analyzer Photo ...... 98 Figure B-3: Calibration Kit ...... 99 Figure B-4: Connectors used to have proper measurements ...... 100 Figure B-5: Microscope to soldering process ...... 101 Figure B-6: Paste syringe photo ...... 102 Figure B-7: Condensation oven photo ...... 103 Figure B-8: Proper soldering of SMA connector and PCB ground ...... 103 Figure B-9: Used signal generator ...... 104

List of tables

Table 2-1: Values of for TE Modes of a circular waveguide ...... 11 Table 2-2: Values of for TM Modes of a circular waveguide ...... 11 Table 3-1: Coupling coefficient for each coupling way in each cavity and coupling parameters ...... 46 Table 3-2: Stubs dimension for rectangular resonators matching network ...... 51 Table 3-3: Rectangular cavity design parameters ...... 51 Table 3-4: Circular cavity design parameters ...... 51 Table 3-5: Coupling coefficient, insertion loss and Q-factor in a cavity with and without matching network using different coupling parameters...... 54 Table 3-6: Coupling coefficient, insertion loss and Q-factor in a cavity with and without matching network using the same coupling parameters...... 55 Table 3-7: Final directional coupler dimensions ...... 59 Table 3-8: HMC717LP3 Features ...... 60 Table 3-9: RF3376 Features ...... 63 Table 3-10: Final parameters for RF signal blocker ...... 65 Table 3-11: Amplifiers characteristics in resonant frequency...... 73 Table 3-12: 1 dB input compression point and saturated output power for each amplifier ..... 75 Table 3-13: Advantages and inconvenient of both amplifiers ...... 76 Table 3-14: Measured S parameters in resonant frequency ...... 81 Table 3-15: Computed Coupler characteristics obtained from the measurement ...... 83 Table 3-16: Oscillator Phase noise in circular cavity ...... 91

vi

1 Introduction

RF and microwave oscillators are found in all modern wireless communications, radar, and remote sensing systems to provide signal sources for frequency conversion and carrier generation. A solid-state oscillator uses an active nonlinear device, such as a diode or transistor, in conjunction with a passive circuit to convert DC to a sinusoidal steady-state RF signal. Basic transistor oscillator circuits can generally be used at low frequencies, often with crystal resonators to provide improved frequency stability and low noise performance. At higher frequencies, diodes or transistors biased to a negative resistance operating point can be used with cavity, transmission line, or dielectric resonators to produce fundamental frequency oscillations up to 100 GHz. Alternatively, frequency multipliers, in conjunction with a lower frequency source, can be used to produce power at millimeter wave frequencies.

The IEEE C-band (4 GHz to 8 GHz) and its slight variations contains frequency ranges that are used for many satellite communications transmissions, some Wi-Fi devices, some cordless telephones, and some weather radar systems. For satellite communications, the microwave frequencies of the C-band perform better under adverse weather conditions in comparison with Ku-band (11.2 GHz to 14.5 GHz) microwave frequencies. 1.1 STATE OF THE ART

Oscillator stability is enhanced with the use of a high-quality factor (Q) tuning network. The unloaded Q of a resonant network using lumped elements or microstrip lines and stubs is typically limited to a few hundred [1], waveguide cavity resonators can have unloaded Q of or more. However, they are not well suited for integration in miniature microwave integrated circuitry. Another disadvantage of metal cavities is the significant frequency drift caused by dimensional expansion due to temperature variations. Some studies to improve these variations are done as in [2] [3].

The dielectric cavity resonator [4] overcomes most of these disadvantages, as it can have an unloaded Q as high as several thousand, it is compact and easily integrated with planar circuitry, and it can be made from ceramic materials that have excellent temperature stability.

Another method of oscillator stabilization is a substrate integrated cavity scheme, which consist of metalized via holes made in dielectric substrates [5]. This method is useful for lower frequencies because the size and pitch of the via-holes are normally large, which might result in a radiation loss at high frequency and an inaccurate resonant frequency.

1

2 Chapter 1 Introduction

1.2 PRESENTATION OF THE WORK

The objective of this work is design a prototype oscillator which will be designed, built and measured for students in a laboratory. Several options for each part in the circuit are evaluated in order to know which one provides the best result.

Due to the academically finality of this work, high Q-factor resonator is needed in order to have an oscillator with good stability properties. However, a cavity integrated in a miniature circuit is not required, hence microwave resonator is used. Influence of thermal expansion on the resonant frequency of cavity is not studied.

Oscillator’s performance is evaluated in terms of phase noise. The phase noise is governed by the loaded Q factor of the resonator, active circuit form and oscillator’s output power. Following Leeson’s equation improved by Rogers [6]

(1-1)

Where PN is the phase noise, F is the active device noise figure at operating power, kT is the thermal noise, is the oscillation frequency, is the output power and is the offset frequency from at which the phase noise is evaluated. 1.3 STRUCTURE OF THE WORK

This work is divided in 4 chapters: Chapter 1 gives to the reader a wide vision about what an oscillator is, how can be built, and some utilities. Theoretical background is summarized in chapter 2 in order to introduce to the subject to the reader. In chapter 3, all design of the oscillator including simulations, building and measurements steps. Firstly each part of the circuit is treated separately and afterwards, joined in oscillator planar circuit description. Finally, chapter 4 summarizes the conclusions obtained from the work and tries to solve the found difficulties.

2 Theoretical Background

2.1 RESONANCE

2.1.1 EQUIVALENT CIRCUIT [1]

Resonant circuits are circuits, which offer a high impedance or low impedance (for parallel and series resonance respectively) to the source at a particular frequency of operation. The frequency at which the resonant circuit has very high or low impedance is called resonant frequency.

Resonant circuits can be built either using lumped elements or distributed elements. Figure 2-1 shows series and parallel resonant circuits using lumped elements. In lumped elements resonant circuits, capacitors store the electric energy and the inductors store the magnetic energy, while the resistance shows up as loss. Resonance occurs when the average stored magnetic and electric energies are equal and hence, input impedance become real.

Figure 2-1: Series and parallel resonant circuit with lumped elements

Another type of resonant circuit is the distributed resonant circuit, which utilizes an open or shorted transmission line as in Figure 2-2. The resonance occurs in the form of standing waves due to superposition of the forward and reverse traveling waves. Even in the distributed resonant circuit, energy transfer happens every quarter cycle. As the resonant circuit needs a standing wave along the transmission line, its dimensions are comparable with the wavelength.

3

4 Chapter 2 Theoretical Background

Figure 2-2: Series resonance with microstrip line ended with open circuit (left). Parallel resonance with microstrip line ended with short circuit (right) Any form of transmission line of suitable length can be used as a resonator. When the transmission line used is a waveguide, the resulting resonator is called a cavity resonator and the resonator is called a strip resonator when a microstrip is used as the transmission line.

2.1.2 LOADED AND UNLOADED Q FACTOR (Q) [1]

Another important parameter of a resonant circuit is its Quality factor (Q), which represents the sharpness in the frequency response of a resonator and it is defined as (2-1)

(2-1)

Resonator losses may be due to conductor loss, dielectric loss, or radiation loss, and are represented by the resistance, R, in equivalent circuit in Figure 2-1. An external connecting network may introduce additional loss.

Unloaded Q or is the quality factor in the absence of any loading effects caused by external circuitry. When the resonant cavity is connected to an external circuitry with its Q,

as shown in Figure 2-3, the Q of the overall circuitry, QL is computed as (2-2) or (2-3).

Figure 2-3:Resonant circuit loaded by external circuit

2.1 RESONANCE 5

In (2-2) f is the difference in the frequency where falls to 3dB and is the center frequency. f is also one criteria to define bandwidth.

(2-2) 

(2-3)

This method to find the loaded Q of a resonant circuit can be used in general to any form of resonator, it may be a waveguide resonator, a strip resonator or a lumped element resonator.

 -Lumped element resonators have several limitations over waveguide resonators as following.

 Values of Q that can be achieved by lumped elements are usually limited to hundreds. Q values of several tens of thousands are achievable with waveguide resonators.

 Power dissipation capability is far lesser than waveguide resonators. This can be felt intuitively, lumped element resonators have a very small surface area and hence power dissipation is less whereas, waveguide resonators have a larger surface area and hence can dissipate more power.

2.1.3 WAVEGUIDE RESONATORS [1]

Waveguide resonators in its simplest forms are metallic enclosures or cavities. Electric and magnetic energy is stored in this volume thus establishing a resonance condition. The power dissipation is through the surface current loss of the waveguide and the dielectric filling loss.

RECTANGULAR RESONATOR

Rectangular resonator in its simplest form is a rectangular waveguide with shorting plates at both ends as in Figure 2-4. Lowest mode for a rectangular waveguide, which is TE10 is first studied. For the resonant frequency analysis the side walls will be considered to be having infinite conductivity and then will be perturbed by adding a finite conductivity for Q calculations. 6 Chapter 2 Theoretical Background

Figure 2-4: Rectangular cavity structure Although one could begin with the Helmholtz wave equation and the method of separation of variables to solve for the electric and magnetic fields that satisfy the boundary conditions of the cavity [1], it is easier to start with the fields of the TE or TM waveguide modes since these already satisfy the necessary boundary conditions on the side walls (x = 0, a and y = 0, b) of the cavity in Figure 2-5. Then it is only necessary to enforce the boundary conditions that

Ex = Ey = 0 on the end walls at z = 0 and z=d in Figure 2-5.

Figure 2-5: Air dimension inside brass 2.1 RESONANCE 7

From [1] the transverse electric fields (Ex , Ey) of the TEmn or TMmn rectangular waveguide mode can be written as (2-4)

(2-4)

In (2-4) e(x,y) is the transverse variation of the mode, and are arbitrary amplitudes of the forward and backward traveling waves. Propagation constant of the m, nth TE or TM mode is (2-5) where k=

(2-5)

To satisfy the boundary conditions that = 0 at z = 0 implies . Then condition z=d leads to equation (2-6)

(2-6)

The only solution of (2-6) taking into consideration that is (2-7)

(2-7)

The resonant frequency of the TEmnl or TMmnl mode is given by (2-8)where the indices m, n, l indicate the number of variations in the standing wave pattern in the x, y, z directions, respectively.

(2-8)

From (2-8) can be observed that different modes can have the same resonant frequency irrespective of the actual field distribution. Modes with different field patterns but having the same resonant frequency are called degenerate modes.

From (2-6) and total fields for TE10l resonant mode can be written as (2-9), (2-10) and (2-11) where is the wave impedance of the waveguide. On the other hand is the wave impedance in free space.

(2-9)

8 Chapter 2 Theoretical Background

(2-10)

(2-11)

Equations above can be simplified using and (2-12), (2-13) and (2-14) are obtained.

(2-12)

(2-13)

(2-14)

Unloaded Q from this mode can be computed finding stored electrical and magnetic energies, and the power lost in the conducting walls and the dielectric filling as [1]. Formula (2-15) is

QC associated to conductive material losses and (2-16) to dielectric losses. Afterward Q0 is computed with (2-17).

(2-15)

(2-16)

(2-17)

When air is used as a dielectric material as in this work, dielectric loss tangent of air is

=0. Hence QD tents to infinity and with (2-17) can be seen that Q0=QC.

Following observation can be made about rectangular cavities.

- For a given box size, resonant frequency increases with increasing mode. Intuitively the explanation is like this; once the dimension is fixed and some lower order modes are getting excited, if is desired to increase the mode number, then more number of waves have to be accommodated in the same given dimension. This is possible only if the wavelength gets shorter (as the dimension is fixed) which means that frequency has to increase. 2.1 RESONANCE 9

- For a given resonant frequency, box dimension has to be increased to accommodate higher modes. The explanation parallels our earlier logic. If is desired to put in more waves in a box, box dimensions must be increased if the waves cannot be made shorter.

- Higher Q can be obtained by going for higher modes for a given resonant frequency. As the box becomes bigger, the volume to surface area ration increases and thus losses are reduced.

CIRCULAR RESONATOR

A cylindrical cavity resonator can be constructed from a section of circular waveguide shorted at both ends as shown in Figure: 2-6. Because the dominant circular waveguide mode is the

TE11 mode, the dominant cylindrical cavity mode is the TE111 mode.

Figure: 2-6: Circular cavity structure 10 Chapter 2 Theoretical Background

Figure 2-7: Air dimension inside brass The geometry of a cylindrical cavity is shown in Figure: 2-6. As in the case of the rectangular cavity, the solution is simplified by beginning with the circular waveguide modes, which already satisfy the necessary boundary conditions on the wall of the circular waveguide. From

[1] the transverse electric fields (E, E) of the TEnm or TMnm circular waveguide mode can be written as:

    (2-18)

Where e( ) represents the transverse variation of the mode, and A+ and A− are arbitrary amplitudes of the forward and backward traveling waves. The propagation constant of the

TEnm mode is (2-19) while the propagation constant of the TMnm mode is (2-20).

(2-19)

(2-20)

Where are defined as the roots of Bessel equation  and are defined as the roots of  . These values are given in mathematical tables; the first few values from

are listed in Table 2-1 and in Table 2-2 [1].

2.1 RESONANCE 11

Table 2-1: Values of for TE Modes of a circular waveguide

n 0 3.832 7.016 10.174 1 1.841 5.331 8.5336 2 3.054 6.706 9.970

Table 2-2: Values of for TM Modes of a circular waveguide

n 0 2.405 5.520 8.654 1 3.832 7.016 10.174 2 5.135 8.417 11.620

In order to have = 0 at z = 0 and z= d, A = , sin d=0 or d=l for l= 0, 1, 2, 3 must be selected, which implies that the waveguide must be an integer number of half-guide wavelengths long.

Some procedure to find the Q as in rectangular cavity is done. Equation to compute is the same as in rectangular cavity and is as:

(2-21)

CAVITY COUPLING [1]

Cavity resonators will be useful as circuit elements only if they can be coupled to other circuit elements. Energy has to be fed into the cavity and taken out from it to be useful as a filtering element. Excitation techniques used for launching waves into the waveguide can be used for coupling or exciting waves in a resonator as well. Following are the common methods used for coupling:

- A probe or an antenna oriented in the direction of electric field as shown in Figure 2-8. The position of the probe in the waveguide is chosen according to the coupling required and the impedance matching.

12 Chapter 2 Theoretical Background

Figure 2-8: Probe used to excite waveguides and cavity resonators

- A current carrying loop oriented in the plane normal to the magnetic field as shown in Figure 2-9.

Figure 2-9: A loop used to excite waveguides and cavity resonators.

- Current coupling consists on making a slit or an aperture in a wall of the cavity with the finality of perturb the currents which are in the conductor surface shown in Figure 2-10. Then, the superficial currents became different and the electric and magnetic field that they produce change as well. The slot must be situated where it can modify more surface current. 2.2 MICROSTRIP LINES 13

Figure 2-10: Aperture used to excite waveguides and cavity resonators 2.2 MICROSTRIP LINES Microstrip line [1] is one of the most popular types of planar transmission lines primarily because it can be fabricated by photolithographic processes and is easily miniaturized and integrated with both passive and active microwave devices

The geometry of a microstrip line is shown in Figure 2-11 A conductor of width W is printed on a thin, grounded dielectric substrate of thickness h and relative permittivity r , a sketch of the field lines is shown in Figure 2-11 as well.

Figure 2-11: Microstrip line cross section electric and magnetic fields distribution

The presence of the dielectric, particularly the fact that the dielectric does not fill the region above the strip, complicates the behavior and analysis of microstrip line.

Unlike stripline, where all the fields are contained within a homogeneous dielectric region, microstrip has some (usually most) of its field lines in the dielectric region between the strip conductor and the ground plane and some fraction in the air region above the substrate. For this reason microstrip line cannot support a pure TEM wave since the phase velocity of TEM fields in the dielectric region would be / while the phase velocity of TEM fields in the air region would be , so a phase-matching condition at the dielectric–air interface would be impossible to enforce. 14 Chapter 2 Theoretical Background

Actuality, the exact fields of a microstrip line constitute a hybrid TM-TE wave and require more advanced analysis techniques. In most practical applications, however, the dielectric substrate is electrically very thin (h <<) and so the fields are quasi-TEM. In other words, the fields are essentially the same as those of the static (DC) case. Thus, good approximations for the phase velocity, propagation constant and characteristic impedance can be obtained from static, or quasi-static, solutions.

(2-22)

(2-23)

where is the effective dielectric constant of the microstrip line (2-24)Because some of the field lines are in the dielectric region and some are in air, the effective dielectric constant satisfies the relation .

(2-24)

The effective dielectric constant can be interpreted as the dielectric constant of a homogeneous medium that equivalently replaces the air and dielectric regions of the microstrip line, as shown in Figure 2-12

Figure 2-12: Equivalent geometry of a quasi-TEM microstrip line. (left) Original geometry. Equivalent geometry, where the dielectric substrate of relative permittivity is replaced with a homogeneous medium of effective relative permittivity (Right)

2.3 DIRECTIONAL COUPLER

Power dividers and directional couplers [1] are passive microwave components used for power division or power combining. In power division, an input signal is divided into two (or more) output signals, while a power combiner accepts two or more input signals and 2.3 DIRECTIONAL COUPLER 15 combines them at an output port. Directional couplers can be designed for arbitrary power division.

The increasing use of planar lines also led to the development of couplers and dividers, such as the Wilkinson divider, the branch line hybrid, and the coupled line directional coupler.

The basic operation of a directional coupler can be illustrated with the aid of Figure 2-13

Figure 2-13: Directional coupler plot Power supplied to port 1 is coupled to port 3 (the coupled port) with the coupling factor (2-25), while the remainder of the input power is delivered to port 2 (the through port) with the coefficient (2-28). In an ideal directional coupler, no power is delivered to port 4 (the isolated port).

The following quantities are commonly used to characterize a directional coupler:

(2-25)

(2-26)

(2-27)

(2-28)

The coupling factor indicates the fraction of the input power that is coupled to the output port. The directivity is a measure of the coupler’s ability to isolate forward and backward waves (or the coupled and uncoupled ports). The isolation is a measure of the power delivered to the uncoupled port. These quantities are related as I = D + C dB 16 Chapter 2 Theoretical Background

The insertion loss accounts for the input power delivered to the through port, diminished by power delivered to the coupled and isolated ports. The ideal coupler has infinite directivity and isolation (S14 = 0).

2.4 OSCILLATOR CIRCUIT

Oscillator [7] is a feedback circuit with its output fed back into its input through a frequency selective electronic filter to provide positive feedback as can be seen in Figure 2-14. When the power supply to the amplifier is first switched on, electronic noise in the circuit provides a signal to get oscillations started. The noise travels around the loop and is amplified and filtered until very quickly it becomes a sine wave at a single frequency.

Figure 2-14: Feedback oscillator circuit

2.4.1 OSCILLATION CONDITIONS

The used amplifier is fed back by a cavity resonator. The described circuit oscillates, if the complex voltages at an arbitrary point of the oscillation loop are equal. This condition can be viewed as a gain and phase condition [7]. 2.4 OSCILLATOR CIRCUIT 17

(2-29)

(2-30)

in (2-29) is the gain and is the phase difference of the oscillator loop at the oscillation frequency . The gain of the loop is defined by the amplifier gain , the transmission factor of the resonant cavity and the losses of planar transmission lines have influence on as in (2-31)

(2-31)

3 Design 3.1 SIMULATIONS

3.1.1 RESONANT CAVITY

OPERATING MODE AND RESONANT FREQUENCY

The behavior of the amplifier frequency response has to be taken into consideration to make the choice because only one resonant frequency inside the amplifier working zone (amplifier bandwidth) is required. Thus, knowing that an amplifier acts as a low pass filter, peaks above the resonant frequency must be avoided. Working in any mode that it is not the fundamental one, resonant frequencies of the lower working modes below are presents if cutoff frequency is lower as the first mode, hence the design first idea is work in fundamental mode in both cavities. If undesired peaks were inside the amplifier bandwidth, they would be amplified as well, and the oscillator would have more than one resonant frequency. In addition, intermodulation distortion and harmonics would appear.

Rectangular Resonator

Considering a conventional rectangular resonator with height b, width a, and length d. The analytical expressions for modal resonant frequency and quality factors have been seen in chapter 2.

First of all, width a is found to have a cutoff frequency lower than 6 GHz. The fundamental mode is TE101 because of this mode is smaller than of TM11 mode, which is the one of smaller cutoff frequency of Transversal Magnetic modes. Moreover a>b, hence fundamental mode is TE10 and not TE01.

(3-1)

Using (3-1) it is seen that a > 25 mm to have fC10<6 GHz. Selected cavity width is a=28.5 mm which have a cutoff frequency =5.26 GHz. Height b is smaller than a if TE10 is the desired fundamental mode.

Next step is design the length d in order to have the resonant frequency in 6 GHz imposing the operation mode of the resonator (n, m, l). Electric field distribution inside the resonator is drawn in Figure 3-1 and Figure 3-2 .

(3-2)

18

3.1 SIMULATIONS 19

Equation (2-8) with (n=1,m=0,l=1) is used to find cavity length d. All parameters are known, except d which is isolated and computed as .

(3-3)

Where

(3-4)

Using (3-3) and (3-4) knowing is air electrical permittivity and speed of light, cavity length d = 52 mm. It can be also checked in (3-5) that d = guide/2. Observing the expression above is seen that neither the resonant frequency nor the cutoff frequency depend on the cavity height b. If cavity height is increased, cavity losses will decrease and hence Q- factor becomes bigger.

(3-5)

It can be checked that TE101 is the propagation mode in the resonator in Figure 3-1 and Figure 3-2 where electrical field inside the cavity in f=6.029 GHz is drawn using the commercial software computer simulation technology-Microwave Studio ® (CST-MWS).

Parameters a, b, and d are air rectangular dimensions inside the conductor cavity. Surface current flows for internal surfaces of conductor which enclose the air. 20 Chapter 3 Design

Figure 3-1:Electric Field in cross section cavity in frequency 6.029 GHz

Figure 3-2: Electric Field in cross section cavity in frequency 6.029 GHz Once a and d are determinate, simulation in CST-MWS is done with different cavity height b which is shown in Figure 3-3 in order to know which the proper design is.

3.1 SIMULATIONS 21

Simulated cavity insertion loss 0

-10

-20

-30

-40

[dB] 21

S -50

-60 b =14 mm cavity -70 b =20 mm cavity b =26 mm -80 cavity

-90 5 5.5 6 6.5 7 7.5 8 f [GHz]

Figure 3-3: Insertion loss for different rectangular cavity height With b=26 mm there is one peak in f=7.52 GHz. As it has said before, any resonance mode is not desired below 8 GHz, hence this peak cannot be in f=7.52 GHz. Electric and magnetic field inside the cavity in this frequency are analyzed with CST-MWS (Figure 3-4 and Figure 3-5).

Can be seen that this peak corresponds to the resonant frequency of TM110 mode. The resonant frequency of TM110 can be also calculated with (2-8) and check that it matches with Figure 3-3. Due to structure modification explained further, cavity height is 2 mm bigger. This height increment is because central part of brass top surface has been removed.

Resonant frequency of this mode depends on b, hence this frequency can be placed over 8 GHz decreasing b. On the other hand, will be seen further, than bigger b, better Q-factor. Hence, there is a compromise between good Q-factor and do not have any resonant frequency too closer to 6 GHz. 22 Chapter 3 Design

Figure 3-4: Magnetic Field in cavity cross section in frequency 7.526 GHz

Figure 3-5: Electric Field in cavity cross section in frequency 7.526 GHz Other peak in f=7.853 GHz is seen in Figure 3-3 as well. Simulated electric fields inside the cavity with CST-MWS are plotted in Figure 3-6 and Figure 3-7 . This field distribution corresponds to TE102 and resonant frequency calculated with (2-8) matches with the Figure 3-3 .

However, this frequency cannot be modified as previous case, because TE102 does not depend on the b. Variation of a or d should be done, but if these parameters are modified, initial 3.1 SIMULATIONS 23 design would change. That is why this peak appears in b=14 mm and b=20 mm as well. This resonant frequency is quite far of 6 GHz, hence any other modification is done.

Figure 3-6:Electric Field in cavity cross section in frequency 7.853 GHz

Figure 3-7:Electric Field in cavity cross section in frequency 7.853 GHz

In Figure 3-8 final resonator dimensions are described. 24 Chapter 3 Design

Figure 3-8: Rectangular cavity dielectric dimensions Circular Resonator

Considering a conventional circular resonator with radius a, height d, resonant frequency is calculated with (3-6) for TM modes and (3-7) for TE modes.

(3-6)

(3-7)

Fundamental mode for a circular waveguide is TE111. However, this mode, resonant frequency depends on the cavity height d because l 0 in (3-6). One working mode independent of cavity height is desired in order to change this parameter and have desired Q-factor without modifies the resonant frequency. That is why TM010 is selected.

2 In Figure 3-9 is seen that with a higher (2a/d) ratio than 1, resonant frequency for TM010 is lower than in TE111, hence first acts as a fundamental mode. 3.1 SIMULATIONS 25

x 1017 3

2.5

2 2

1.5 (Hz-m) TE 2 111 TM

010 (2af) TM 1 011 TE 211 TM 0.5 110 TE TM 011 111 TE 112 0 0 1 2 3 4 5 6 (2a/d)2

Figure 3-9: Resonant mode chart for a cylindrical cavity obtained from [8]

8 Isolating a from (3-6) and substituting =6 GHz, l=0 and =3·10 m/s following results are obtained.

(3-8)

(3-9)

With this radius a, desired TM010 with resonant frequency in 6 GHz is obtained. Electrical and magnetic fields distributions are plotted in Figure 3-10 and Figure 3-11 . 26 Chapter 3 Design

Figure 3-10: Magnetic field in TM010 simulated circular cavity in frequency 6.08 GHz

Figure 3-11: Electric field in TM010 simulated circular cavity in frequency 6.08 GHz In order to know the best cavity height d, CST-MWS simulation with different d is done in Figure 3-12. 3.1 SIMULATIONS 27

Simulated cavity insertion loss

-10

-20

-30

-40

-50

[dB]

21 S -60

-70

d =16 mm -80 cavity d =20 mm -90 cavity d =24 mm cavity -100 5 5.5 6 6.5 7 7.5 8 f [GHz]

Figure 3-12: Insertion loss for different cavity height As is seen in rectangular cavity, if d is too big, appears one tone below 8 GHz. This tone is resonant frequency mode TE111 as can be seen in electric and magnetic fields representation in Figure 3-13 and Figure 3-14. As in rectangular cavity, to increment resonant frequency of mode TE111 cavity height d must be reduced. 28 Chapter 3 Design

Figure 3-13: Electric field in TE111 simulated circular cavity in frequency 7.839 GHz

3.1 SIMULATIONS 29

Figure 3-14: Electric field in TE111 simulated circular cavity in frequency 7.839 GHz Final selected cavity height is d=20 mm as shows Figure 3-15.

Figure 3-15: Circular air shape

30 Chapter 3 Design

CAVITY CONDUCTOR MATERIAL

Once the cavity air dimensions have been found, the fitting conductor material which surrounds the cavity must be chosen. The better material’s conductivity, the less loss it would have. The workshop sets Copper (5.813 x 107 S/m), Aluminum (3.816 x 107 S/m) and Brass (2.564 x 107 S/m) [1].

The first one is very expensive and it is not used for such a big structure as our cavity. It is more common use for strip conductors, grounds in micro strips lines, which they have a very small thickness (around 17 m ~35 m) or even for wires. Aluminum has the problem that it cannot be soldered with the conventional mode using tin, which can be a big mechanical problem. Finally, brass has not any soldering problem and it is the selected material.

Brass thickness does not affect our design, but it is very important for the coupling of the cavity to the external circuit. Thus, all surface brass thickness are selected just taking into consideration mechanical construction point of view except for the top wall, where the coupling between cavity and microstrip line and PCB is done.

For the rectangular cavity, first idea was build a rectangle using six plane surface with a certain thickness each one and put the external circuit in the top using screws to maintain them joined. In order to have 90 degrees corners inside the cavity, the structure must be done soldering different brass parts.

Once the cavity was built, it was seen that it could have problems if between the top brass surface and the PCB ground (copper) remain some air gaps. Hence, one hole in top cavity surface was made as in Figure 3-16.

Can be also seen that edges of top surface are kept in order to put screws which keep the cavity and PCB joined.

Figure 3-16: Final Brass rectangular cavity Circular cavity is built just with one part as in Figure 3-17. 3.1 SIMULATIONS 31

Figure 3-17: Final Brass circular cavity

COUPLING BETWEEN RESONATOR AND PRINTED CIRCUIT BOARD (PCB)

Field Coupling

Geometry of this coupling method for rectangular and circular cavity can be seen in Figure

3-18. Two wires are introduced into the cavity through holes of length lwire. These wires are soldered to the microstrip lines leaving an air gap between it and cavity walls.

Figure 3-18: Rectangular cavity with PCB (left) and coupling wires. circular cavity(right) Due to different modes in each cavity, electric and magnetic fields inside the cavity are different as can be seen before. Thus, some coupling parameters must be taken into consideration to choose the best solution in each case. The wire inside the cavity must be parallel with the electric field inside the waveguide as can be seen in Figure 3-19. 32 Chapter 3 Design

Figure 3-19: Coupling wires and Electric field representation in cavity cross-section Other important parameter is the length which the coupling posts go inside the cavity. Due to the high current density on the coupling ports, their length also influences Q-factor and the resonant frequency of the resonator. Figure 3-20 and Figure 3-21 show in CST-MWS simulated insertion loss of the rectangular cavity and circular cavity respectively. The different plots represent simulations with different length of the posts.

Simulated cavity insertion loss 0 l =1 mm wire l =2 mm -10 wire l =3 mm wire

-20

[dB] -30

21 S

-40

-50

-60 5.9 5.92 5.94 5.96 5.98 6 f [GHz]

Figure 3-20: Length wire sweep in rectangular cavity 3.1 SIMULATIONS 33

Simulated cavity insertion loss -5 l =1 mm -10 wire l =2 mm wire -15 l =3 mm wire -20

-25

[dB] -30

21 S -35

-40

-45

-50

-55 6.06 6.07 6.08 6.09 6.1 6.11 6.12 6.13 6.14 f [GHz]

Figure 3-21: Length wire sweep in circular cavity

It can be seen that the insertion loss of the resonance is reduced for long posts. As mentioned, less loss implies bigger Q-factor which can be seen in S21 plots. Narrow the peak, higher QL. Wider the peak is, lower QL.

To connect the posts with microstrip line, circular strip conductor surrounding the wire with radius is used as in Figure 3-19. These discs introduce a capacitance behavior in transmission line and modify external impedance and hence as well. It can be observed in Figure 3-22 and Figure 3-23 for rectangular and circular cavities respectively that the bigger

is more insertion loss inside the cavity. 34 Chapter 3 Design

Simulated cavity insertion loss -5 r =2 mm disc -10 r =3 mm disc r =4 mm -15 disc

-20

-25

[dB] 21

S -30

-35

-40

-45

-50 5.9 5.95 6 6.05 6.1 f [GHz]

Figure 3-22: Different strip line disc radius in rectangular cavity holding the coupling wires

Simulated cavity insertion loss 0 r =2 mm -5 disc r =3 mm disc -10 r =4 mm disc -15

-20

[dB] -25

21 S -30

-35

-40

-45

-50 6 6.02 6.04 6.06 6.08 6.1 f [GHz]

Figure 3-23: Different strip line disc radius in circular cavity holding the coupling wires 3.1 SIMULATIONS 35

Current Coupling

For this coupling procedure, two holes must be done in the top face of the cavity as can be seen in Figure 3-24. The holes must be big enough to disturb surface current and hence modify electric and magnetic fields. Holes must be also situated  to open circuit of the microstrip feeding line because it is where the currents in strip conductor are higher and hence, the coupling is better.

(3-10)

With formula (3-10) and (2-24), knowing Substrate Rogers ® RO6002 permittivity =2.94, line width W50=1.8mm, substrate height h=0.762 mm and  mm is derived =3.23 and  7 mm. Coupling holes dimension and position of these holes in the cavity are simulated in CST-MWS in order to know how they affect insertions losses and resonant frequency. 36 Chapter 3 Design

Figure 3-24: Top view PCB surface (Top).Top PCB ground (center), Cavity cross section for circular holes coupling (bottom) 3.1 SIMULATIONS 37

Figure 3-25: Top view PCB surface (Top). Top PCB ground (center), Cavity cross section for rectangular holes coupling (bottom)

Rectangular Resonator

Surface currents distribution in a rectangular cavity in fundamental working mode TE101 is represented in Figure 3-26. Depending on these currents, position and shape of the holes can modify insertion loss and resonant frequency. Coordinates origin are situated in the cavity center in order to define holes position (x,y,z). Some simulations are plotted in order to identify which are the most critical parameters and to know how to fit our final design in to desired cavity insertion loss. 38 Chapter 3 Design

Figure 3-26: Surface currents in TE101 mode in rectangular cavity In Figure 3-27 insertion loss using rectangular holes varying holes position (x,y,z) with holes dimensions (width=3.5 mm and length=4.5 mm) is drawn. Coordinates center is defined in the middle of the cavity and x and y are kept constant.

Simulated cavity S parameters -10

-15

-20

-25

-30

[dB] S S

-35

-40 z =7.5 mm hole z =10.0 mm -45 hole z =12.5 mm hole -50 6 6.02 6.04 6.06 6.08 6.1 f [GHz]

Figure 3-27: Insertion loss with different holes position in the top surface cavity (x,y,z) In Figure 3-28 and Figure 3-29 holes position is kept constant (z=10 mm) and height and length of the holes are modified respectively. 3.1 SIMULATIONS 39

Simulated cavity insertion loss 0 width =2.5 mm -5 hole width =3.5 mm hole -10 width =4.5 mm hole -15

-20

[dB] -25

21 S -30

-35

-40

-45

-50 6 6.02 6.04 6.06 6.08 6.1 f [GHz]

Figure 3-28: Insertion loss with different holes width in the top surface cavity

Simulated cavity insertion loss -10 lenght =2.5 mm hole lenght =3.5 mm -20 hole lenght =4.5 mm hole

-30

[dB] -40

21 S

-50

-60

-70 6 6.02 6.04 6.06 6.08 6.1 f [GHz]

Figure 3-29: Insertion loss with different holes length in the top surface cavity

40 Chapter 3 Design

It can be seen in Figure 3-28 and Figure 3-29 that loss variation is bigger with length variation than width variation. In Figure 2-10 can be seen that bigger the length of the aperture, more influence would have surface current and hence, insertion loss variation is more important.

Circular holes behavior is studied as well in rectangular cavity. Holes radius is varied in Figure 3-30. As in the last case using rectangular holes, more variation in surface current, less insertions loss is obtained.

Simulated cavity insertion loss 0 r =1.5 mm -5 hole r =2.0 mm hole -10 r =2.5 mm hole -15

-20

[dB] -25

21 S -30

-35

-40

-45

-50 6 6.005 6.01 6.015 6.02 6.025 6.03 6.035 6.04 f [GHz]

Figure 3-30: Insertion loss for different holes radius (z=12) 3.1 SIMULATIONS 41

Simulated cavity insertion loss 0 z =10.0 mm -5 hole z =12.5 mm hole -10 z =15.0 mm hole -15

-20

[dB] -25

21 S -30

-35

-40

-45

-50 5.95 6 6.05 f [GHz]

Figure 3-31: Rectangular cavity with circular coupling holes depending on holes position Holes position (x,y,z) is varied in Figure 3-31 keeping fixed holes radius as in Figure 3-27 but now with circular radius. As the previous case, dimension holes are more important in this coupling method than holes position.

Circular Resonator

Same study is made for circular cavity. Surface currents distribution in a circular cavity in fundamental working mode TM010 is represented in Figure 3-32. 42 Chapter 3 Design

Figure 3-32: Surface currents in TM011 mode in circular cavity Figure 3-33 plots insertion loss of circular cavity for different holes position (x,y,z). It can be seen that is similar than rectangular cavity results in Figure 3-27 because surface current in both cavities is similar. 3.1 SIMULATIONS 43

Simulated cavity insertion loss 0 x =9 mm -5 hole x =12 mm hole -10 x =15 mm hole -15

-20

[dB] -25

21 S -30

-35

-40

-45

-50 6.05 6.06 6.07 6.08 6.09 6.1 f [GHz]

Figure 3-33: Insertion loss circular cavity for different position (x,y,z)

Simulated cavity insertion loss 0 r =1.0 mm hole r =1.5 mm -10 hole r =2.0 mm hole -20

[dB] -30

21 S

-40

-50

-60 6 6.02 6.04 6.06 6.08 6.1 f [GHz]

Figure 3-34: Insertion loss circular cavity for different hole radius with x holes=12 mm 44 Chapter 3 Design

Simulated cavity insertion loss 20 width =2.5 mm hole width =3.5 mm 10 hole width =4.5 mm hole 0

-10

[dB] 21 S -20

-30

-40

-50 6 6.02 6.04 6.06 6.08 6.1 f [GHz]

Figure 3-35: Insertion loss circular cavity using rectangular holes varying holes width

Simulated cavity insertion loss 20 lenght =2.0 mm hole lenght =2.5 mm 10 hole lenght =3.5 mm hole

0

[dB] -10

21 S

-20

-30

-40 6.04 6.05 6.06 6.07 6.08 6.09 6.1 f [GHz]

Figure 3-36: Insertion loss circular cavity using rectangular holes varying holes length

3.1 SIMULATIONS 45

COUPLING COEFFICIENT

A measure of the level of coupling between a resonator and a feed is given by the coupling coefficient. To obtain maximum power transfer between a resonator and a feed line, the resonator should be matched to the line at the resonant frequency; the resonator is then said to be critically coupled to the feed.

In [1] can be seen that the external Q ( ) and unloaded Q ( ) are equal under the condition of critical coupling. The loaded Q ( ) is half this value.

Coupling coefficient can be defined as

(3-11)

Three cases are possible:

- k < 1: The resonator is said to be undercoupled to the feed line when more power is dissipated in the resonator than in the external circuit.

- k = 1: The resonator is critically coupled to the feed line when an equal amount of power is dissipated in the external circuit as in the resonator itself.

- k > 1: The resonator is said to be overcoupled to the feed line when more power is lost in the external circuit than in the resonator.

Using transmission-type measurement explained in [9] equation (3-12) is obtained.

(3-12)

I can be seen in Figure 3-37 how k increase with . Critical coupling (k=1) is obtained with and hence cavity insertion loss of . 46 Chapter 3 Design

10

9

8

7

6

k 5

4

3

2

1

0 0 0.2 0.4 0.6 0.8 1 S 21

Figure 3-37: Coupling coefficient In oscillator design, good matching is required between the resonator and the feeding line.

However, coupling coefficient k=1 implies = 3 dB insertion loss and hence, small .

In order to guarantee a good , cavity insertion loss of 12 dB is designed with parameters (lwire ,rcond , lengthhole , widthhole,and rhole) in Table 3-1. In this table can be also observed coupling coefficient and insertion loss in each coupling way for each cavity.

Table 3-1: Coupling coefficient for each coupling way in each cavity and coupling parameters

Coupling Field coupling Current coupling with Current coupling with rectangular holes circular holes Cavity Rectangular Circular Rectangular Circular Rectangular Circular Coupling 0.33 0.3 0.32 0.31 0.3 coefficient k Insertion loss 12.1 dB 12.6 dB 12.3 dB 12.45 dB 12.7 dB (dB)

Length hole - - 4.3 1 - - (mm)

Width hole (mm) - - 1.5 1.5 - - rhole(mm) - - - - 2 1.4 Lwire(mm) 1.7 0.65 - - - - Rdisc(mm) 1.8 1.8 - - - -

As coupling coefficient depends on insertion loss and not in coupling method, mechanical construction characteristics are taken into consideration to choose the coupling method. 3.1 SIMULATIONS 47

Current coupling is selected for resonators which are built because structure in Figure 3-24 is easier to build mechanically than Figure 3-18. Circulars holes are used for circular cavity and rectangular holes for rectangular cavity.

RESONATOR MATCHING NETWORK

Once coupling between the resonator and microstrip line circuit is done, it is seen that in port situated in the beginning of microstrip line, reflection coefficient (S11) is very big. That means that there is too much power which returns to the port and hence do not allow to have a matched circuit.

In Figure 3-38 can be seen that studied microstrip line is ended with two open circuits. S21 parameter says that output power of the resonator has decreased 12dB respect the input power. Most part of the input power is reflected in the open circuit and unsuitable matching between resonator an external circuit is obtained.

In order to avoid this behavior, a resistor with value of the characteristic impedance line

(Z0=50 ) in the end of the line is used to convert the open circuit to a matched load. In

Figure 3-38 and Figure 3-39 can be observed how S11 parameter increases with this modification in both cavities. Resistor of 50  is not in standard values and the closer one is R=47 . Other option is connect in parallel two R=100 .

Rectangular cavity S 11 0 without Resistor -5 with Resistor

[dB] -10

11 S -15

-20 5 5.5 6 6.5 7 7.5 8 f [GHz] Rectangular cavity S 21 0 without Resistor -20 with Resistor

[dB] -40

21 S -60

-80 5 5.5 6 6.5 7 7.5 8 f [GHz]

Figure 3-38: S21 and S11 parameters in rectangular cavity with and without resistor as matching network 48 Chapter 3 Design

Circular cavity S 11 0 without Resistor -10 with Resistor

[dB] -20

11 S -30

-40 5 5.5 6 6.5 7 7.5 8 f [GHz] Circular cavity S 21 0 without Resistor -20 with Resistor

[dB] -40

21 S -60

-80 5 5.5 6 6.5 7 7.5 8 f [GHz]

Figure 3-39: S21 and S11 parameters in circular cavity with and without resistor as matching network. However, this resistor must be connected to the ground plane, that it is not possible in any PCB. Then, one stripline and one hole must be used as explained further in annex. This hole has an inductive behavior and can affect expected behavior. It is seen in Figure 3-40 that using R=47  instead of R=50  S11 becomes 3 dB bigger in the worst case. Resistor of R=47  is used in order to avoid more vias in the PCB. 3.1 SIMULATIONS 49

Simulated cavity insertion loss -10 R=47  R=50  -15

-20

[dB] -25

11 S

-30

-35

-40 6 6.02 6.04 6.06 6.08 6.1 f [GHz]

Figure 3-40: Reflection using matching network with R=47 ohms and R=50 ohms

However, smaller parameter was expected in Figure 3-38. Thus, additional parallel stub with W50=1.8 mm is used. In Figure 3-41 matching network and ground plane are plotted. Blue element called R is resistor which goes from RF line to ground plane through one via in the PCB. In Figure 3-41 just input of the circuit is plotted, in the output there is the symmetric matching network. S-parameters of rectangular cavity with the resistor and described stub are also drawn.

50 Chapter 3 Design

Simulated cavity insertion loss 0 S [dB] 21 -10 S [dB] 11 -20

-30

-40

[dB] 21

S -50

-60

-70

-80

-90 5 5.5 6 6.5 7 7.5 8 f [GHz]

Figure 3-41:.Top view of strip lines and ground plane in PCB (top). Rectangular S parameters with resistor and stub (bottom) To find the best stub dimensions, Advanced Design System ® 2012.08 (ADS) software and CST-MWS are used. Once the best result is found, other CST simulation with optimal parameters is done.

Final matching network parameters for rectangular and circular cavity are in Table 3-2. 3.1 SIMULATIONS 51

Table 3-2: Stubs dimension for rectangular resonators matching network

Rectangular Cavity LT [mm] 21.55 L [mm] 1.8 Lstub [mm] 14

In order to have insertion loss of each cavity around 12 dB, coupling parameters must be modified again as in Table 3-3 and Table 3-4.

Table 3-3: Rectangular cavity design parameters

Holes position Length holes Width holes Cavity height Cavity Resonant (x,y,z) [mm] [mm] [mm] [mm] Insertion loss Frequency [dB] [GHz] (0,0,10) 4.5 3.5 20 12.8 6.024

Table 3-4: Circular cavity design parameters

Holes position Radius holes Cavity height Cavity Insertion Resonant (x,y,z) [mm] [mm] [mm] loss [dB] Frequency [GHz] (0,0,12) 2 20 13.49 6.08

One the other hand, in Figure 3-39 is good enough and any extra stub will be introduced in circular cavity.

In order to measure S-parameters of each cavity, two SMA connectors are introduced in both simulations as in Figure 3-42 and Figure 3-43 . Blue parts at the end of microstrip lines in both figures are resistors models used in CST. 52 Chapter 3 Design

Figure 3-42: Final rectangular cavity design plot

Figure 3-43: Final circular cavity design plot

3.1 SIMULATIONS 53

Q -FACTOR

Unloaded Q ( ) As it has been seen before, resonant frequency and hence working mode depends on width a and length d in rectangular (3-14), and radius a in circular cavity (3-15). Hence, these parameters cannot be modified to increase . However, height in both cavities b and d respectively can be modified.

 (3-13)

-7 7 =4 10 ,H/m r=1, BRASS=1.59 10 S/m, r,  120 

(3-14)

(3-15)

In Figure 3-44 can be observed the plot of these two formulas, hence, the variance of

versus the cavity height for rectangular and circular cavity.

Computed Q 0 7500 Rectangular cavity Circular cavity 7000

6500

0 6000 Q

5500

5000

4500 0.015 0.02 0.025 0.03 h [m] cavity

Figure 3-44: Theoretical unloaded Q for Rectangular (red line) and Circular (blue line) cavity 54 Chapter 3 Design

Now can be checked that circular resonator are better than rectangular in terms of getting a high Q factor with smaller dimensions. With b=20 mm in rectangular cavity =5440 and with the same height d= 20 mm in circular cavity =6023 is obtained.

Loaded Q ( ) In real case, cavity feeding is required; hence it is not possible to simulate unloaded Q. What can be done is measure loaded Q with transmission type measurement explained in [9] and

CST simulation. This method consist in computing simulated with (3-16) and then with (3-17)

(3-16)



(3-17)

In Table 3-5 unloaded Q with (3-14) and (3-15) are calculated. Loaded and unloaded Q with (3-16) and (3-17) using transmission type method are computed for rectangular and circular cavity without matching network with coupling parameters in Table 3-1 and with matching network with parameters in Table 3-2, Table 3-3 and Table 3-4. Rectangular cavity with rectangular holes and circular one with circular holes are only studied in Table 3-5.

Table 3-5: Coupling coefficient, insertion loss and Q-factor in a cavity with and without matching network using different coupling parameters.

Rectangular cavity Circular cavity With matching Without matching With matching Without matching network network network network Theorical 5668 5668 6023 6023 Simulated 3399 4542 3042 4530 Simulated 4469 5975 3873 5836 Insertion Losses 12.3 12.4 12.4 13 (f0) [dB] Coupling factor k 0.32 0.32 0.32 0.3

It can be seen in [9] that accuracy of this method is seriously reduced when coupling is larger than critical. In this case that should not be any problem because the cavity is underloaded (k<1). In Table 3-5 comparisons between cavities with and without matching network with same coupling parameters in - Table 3-3 and Table 3-4 are done.

3.1 SIMULATIONS 55

Table 3-6: Coupling coefficient, insertion loss and Q-factor in a cavity with and without matching network using the same coupling parameters.

Rectangular cavity Circular cavity With matching Without matching With matching Without matching network network network network Theorical 5668 5668 6023 6023 Simulated 3399 2412 3042 2049 Simulated 4469 5866 3873 5663 Inserion Losses 12.3 dB 4.6 dB 12.4 dB 3.9 dB (f0) Coupling factor 0.32 1.42 0.32 1.76 k

Loaded Q is bigger with presence of matching network because the resistors in matching network increment .and hence in (2-7) increases. It can be seen that unloaded Q factor obtained from (3-16) and (3-17) and obtained with transmission method and simulated results is very different. In [10] this method is widely analyzed and some corrections are introduced.

3.1.2 SMA CONNECTORS AND TRANSMISSON LINES

In order to interconnect all the elements of the oscillator, microstrip lines are used. As it has been seen before, this technology is widely used in radio frequency circuitry.

Taking into consideration that used material is Rogers 6002 with dielectric permittivity 2.94 and h=0.762 mm, width of the line W50 must be found to have a characteristic line impedance of 50 . This calculation can be done manually, but there is a tool in ADS software called LinCal, which computes directly this parameter. Obtained value is W50=1.92 mm. Afterwards, the same line is simulated in CST-MWS and W50 is adjusted until W50=1.8 mm when input impedance of each port is 50 .

In addition, a SMA connector in each port that must be measured is needed to connect signal in the microstrip line with coaxial cables in measuring devices. SMA Straight Jack PCB 32K101-400L5 and SMA Right Angle Jack PCB of Rosenberger are studied. Both layout patterns are in Figure 3-45 and Figure 3-46. These connectors must be matched to Z0=50 , thus suitable values of W1START , L1START ,W2START and L2START must be found in order to have good matching between the connector and the line. 56 Chapter 3 Design

Figure 3-45: SMA Straight Jack PCB 32K101-400L5 layout pattern

Figure 3-46: SMA Right Angle Jack layout pattern The line is simulated with CST-MWS getting W1=2.2 mm and L1=1.4 mm and W2=1.25 mm and L2=3 mm.

When the SMA Straight Jack PCB 32K101-400L5 is soldered in the PCB, distance Dist1 in Figure 3-47 between both elements must be kept, hence one cable with diameter Dist1=1mm is used to keep the distance while the soldering process is done. Dist2=1mm and h is substrate thickness which is 0.762 mm. In Figure 3-47 SMA Right Angle Jack is showed. 3.1 SIMULATIONS 57

Figure 3-47: SMA Straight Jack PCB 32K101-400L5

Figure 3-48: SMA Right Angle Jack of Rosenberger representation

Simulation with CST-MWS of two connectors SMA Right Angle Jack (connector 1) and SMA Straight Jack PCB 32K101-400L5 (connector 2) joined with one transmission line is done. S11 parameter is plotted in Figure 3-48. 58 Chapter 3 Design

Simulated S 11 -20 Connector 1 -25 Connector 2

-30 [dB]

-35

11 S

-40

-45

-50 0 1 2 3 4 5 6 7 8 f [GHz]

Figure 3-49: Simulated SMA connectors reflection parameters. Second connector is selected to work because it is easier to solder and it does not require any hole in the PCB. Moreover, in Figure 2-1 can be seen that his frequency behavior is a little bit better.

3.1.3 DIRECTIONAL COUPLER

Oscillator circuit is a closed circuit with feedback alimentation, hence, for itself has neither an input port nor output port. One component to have an output signal is needed. That is why directional coupler as in Figure 3-50.

3.1 SIMULATIONS 59

Figure 3-50: Directional coupler plot in CST In Figure 3-50, one SMA connector is situated in each port in order to measure coupler S-parameters. In oscillator circuit, port 1 and 2 are connected to looping circuit and port 3 is connected with one SMA connector. Port 3 allows connect output oscillator tone with attenuation of the coupling factor.

In order to design coupler with C=15 dB, ADS has been used. Most important problem is high S33 value due to big reflections in transmission line bending. In order to improve this parameter, one resistor in port 4, and one stub are placed in the design. Design dimensions are in Table 3-7 and the simulation results with CST-MWS are plotted in Figure 3-51. Distance between two coupled lines is defined as s in Table 3-7.

Table 3-7: Final directional coupler dimensions

r s L 15.5 mm 2 mm 15.6 mm 0.3 mm 3 mm 5 mm 1.8 mm 60 Chapter 3 Design

Simulated Directional Coupler S-parameters 0

-5

-10

-15

-20

-25

[dB] S S -30 S 11 S -35 21 S -40 31 S 33 -45 S 32 -50 5 5.5 6 6.5 7 7.5 8 f [GHz]

Figure 3-51: Simulated coupler S-parameters 3.1.4 AMPLIFIER

HMC717LP3 of Hittite in Figure 3-52 and RF3376 of RF Micro Devices in Figure 3-54 models have been selected to measure their behavior and determine which the best for the final circuit is.

To measure the gain and phase variation, PCB must be designed following indications in their respective datasheets [11] [12].

HMC717LP3

In Table 3-8 there are main Features of HMC717LP3.

Table 3-8: HMC717LP3 Features

Noise Figure 1.1 dB

Gain 16.5 dB

Output IP3 +31.5 dBm

Single Supply +3V to +5V

Package QFN 16 Lead 3x3mm 3.1 SIMULATIONS 61

Schematics of biasing circuits in each amplifier can be found in[11] [12]. In Figure 3-53 there is layout pattern and bias circuit for HMC717LP3. Despite most important information in datasheet, several issues must be taken into consideration.

Firstly, QFN16 package in Figure 3-52 must be introduced in the design [13]. Microstrip line is used as a connector between the amplifier and other components in PCB. Amplifier’s PADs have a width of WPAD=0.25 mm, hence with the substrate Rogers 6002 ( =2.94) the characteristic line impedance is Z0=124 .

In PCB width of W50=1.8 mm is required; hence, it is impossible to avoid mismatching between amplifier pin and transmission line. What can be done is design the amplifier pad of

WPAD=0.25 mm as short as possible in order to reduce these reflections.

Difference phase measurement must be done very carefully. If it is only measured the top circuit in Figure 3-53, only the phase variation of the global circuit (amplifier+microstrip lines+capacitors+connector) can be known. The circuit below in Figure 3-53 is needed to compute phase variation of the circuit without amplifier. Thus, making the difference between both measurements, amplifier variation phase can be obtained. It can be seen that in reference line, part occupied for the amplifier is deleted, hence, there is the same transmission line length in both figures.

Figure 3-52:QFN16 Layout pattern connected to 50  line 62 Chapter 3 Design

Figure 3-53: HMC717LP3 evaluation PCB. (top) Amplifier and bias circuit layout. (bottom) Reference line circuit.

RF3376

Features of this amplifier are in Table 3-9. The Recommended Layout pattern needed in this amplifier is called ST089 [14]. The PAD amplifiers sizes are 1.5 mm, hence characteristic impedance is Z0=58  instead of Z0=50 . As it had been mentioned with the other amplifier, it is not possible an input impedance of 50 , and length of WPAD=1.5 mm line must be as short as possible.

In Figure 3-54 is shown ST089 PAD with 50  microstrip line. Same procedure than has been done for HMC717LP3 is done to measure the amplifier gain and phase difference as can be seen in Figure 3-55. 3.1 SIMULATIONS 63

Figure 3-54:ST089 PAD with 50 ohms microstrip line.

Table 3-9: RF3376 Features

Noise Figure 2 dB

Gain 22 dB

Single Supply +3V to +5V

Package ST089

64 Chapter 3 Design

Figure 3-55:RF3376 evaluation PCB. a) Amplifier and bias circuit layout. b) Reference line circuit. BIAS CIRCUIT

Biasing is the method of establishing predetermined voltages or currents at various points of an electronic circuit for the purpose of establishing proper operating conditions in electronic components. This work does not specify how the transistors inside the amplifier chip work, but in [15] it can be seen how an amplifier design and transistor working point is found. This proper design requires certain biasing which is explained in datasheet.

In RF3376 is seen that bias tension and RF signal share the same transmission line, hence some considerations must be taken into account. C1 and C2 block DC signal (with f=0 one capacitor is seen as a open circuit). Design of bias circuit explanation can be extended in 3.1 SIMULATIONS 65

On the other hand, RF signal cannot be present in DC node. Two stubs have been used as a

RF blocker in this design. Stub width WSTUB must be quite smaller than 50  line because most part of electrons must go on to the direct way (RF OUT). Also for the same reason the angle between these two lines is =90. To reach our blocker, in y=0 in Figure 3-56 must be seen as an open circuit in RF.

Hence, a line with LSTUB=/4 ended with a short is needed. If there is a short at the end of the line, the bias tension could not be connected so other geometry is needed. Butterfly structure

[16] [17] is used with LBUTERFLY=/4 ended with an open. DC line is connected in x=/4 with an angle of =90o. Angle  is also important in butterfly stub design.

Figure 3-56: Blocking RF structure. First design is done with ADS, and then optimized with CST-MWS. Final obtained parameters are written in Table 3-10: Final parameters for RF signal blocker.

Table 3-10: Final parameters for RF signal blocker

LSTUB WSTUB LBUTTERFLY 

7 mm 0.25 mm 7.5 mm 60

66 Chapter 3 Design

3.1.5 PHASE SHIFTER

In order to satisfy phase condition, structure in Figure 3-57 is designed. This structure allows us to modify circuit electric length just soldering one cooper wire with width 1.4 mm in correct position. Procedure to find the proper position of the wire is explained further.

Figure 3-57: Phase shifter plot

3.1.6 MICROSTRIP BENDING

In order to build closed oscillator circuit, it is necessary for the path of a strip to turn through a large angle. Discontinuities and bends in a microstrip line will cause a significant portion of the signal on the strip to be reflected back towards its source. This is because such discontinuities introduce parasitic reactances that can lead to phase and amplitude errors, input and output mismatch, and possibly spurious coupling or radiation.

The straightforward right-angle bend shown below has a parasitic discontinuity capacitance caused by the increased conductor area at the corner of the bend. This effect could be eliminated by making a smooth, “swept” bend with a radius R> 3W, but this takes up more space.

Alternatively, the right-angle bend can be compensated by mitering the corner, which has the effect of reducing the excess capacitance at the bend. As shown later, this technique can be applied to bends of arbitrary angle. The optimum value of the miter length, a, depends on the characteristic impedance and the bend angle, but a value of a = 1.8W50 is often used in practice. 3.1 SIMULATIONS 67

As it can be seen in [18], the first one is the best option. Moreover, in “swept” bend r< 3W50 has been used in order to not use such a big surface. CST simulation from S-parameters structures in Figure 3-58 and Figure 3-59 have been represented in Figure 3-60 and Figure 3-61 and this fact has been tested.

Figure 3-58: Mitered Bend. W50=1.8 mm; a=3 mm

Figure 3-59: Swept Bend. W50=1.8 mm; R=2 mm 68 Chapter 3 Design

Simulated Transmission Line bending -21

-22

-23

-24

-25 [dB]

-26

11 S -27

-28

-29

-30

-31 3 4 5 6 7 8 f [GHz]

Figure 3-60: S parameters of 90 degrees mitered bend

Simulated Transmission Line bending -20

-25

[dB]

11 S

-30

-35 3 4 5 6 7 8 f [GHz]

Figure 3-61: Simulated S parameters of 90 degrees swept bend (R=2 mm) 3.2 BUILDING AND MEASUREMENTS 69

3.2 BUILDING AND MEASUREMENTS

3.2.1 AMPLIFIER

Once the PCB has been built in the workshop photolithographic processes, SMD components must be soldered. Due to their small dimensions (0603 and 0402 in this design are classified according to their footprint size in mils, or in this case 0.060 inches by 0.030 inches.) one microscope, soldering paste and hot air solder are used as it will explain chapter 4.

Afterwards, paste must be introduced in chip pins and put into the condensation oven. The last components which must be introduced in PCB are SMA connectors and DC pins using tin soldering. Check that every component is correctly fitted in their PAD is very important.

Figure 3-62: Test PCB for HMC717LP3 70 Chapter 3 Design

Figure 3-63: Test PCB for RF3376 GAIN AND PHASE

Amplifier S-parameters are measured with Wiltron 306B Network Analyzer with previous calibration (see annex). With S-parameters, amplifier gain and phase difference can be known using the method explained further.

Before the measure, you must be sure that any DC signal cannot arrive to Network analyzer because it can damage the device. Hence, DC blocker must be checked before doing the measure with one multimeter. Last thing that must be taken into account is that one amplifier is an active circuit. That means that output power can be higher than the device maximum allowed power (20 dBm). Maximum gain expected for HMC717LP3 is 16.5 dB and 22 dB for RF3376. Hence, 4 attenuators of 6 dB are connected between PCB output SMA connector and port 2 coaxial cables.

To extract amplifier gain and phase, reference line in below the amplifier PCB prove in Figure 3-53 and Figure 3-55 are first measured. Afterwards, this data is saved in Network analyzer internal memory. Then amplifier test PCB in top part in Figure 3-53 and Figure 3-55 are measured and normalized with the option DATA%MEM in network analyzer.

As it has seen, S21 is the transmission coefficient for any device, hence, module of S21 can be presented as amplifier gain and S21 phase can be understood as phase difference between amplifiers input and output. On the other hand, S11 is reflection coefficient and shows us how the matching is. Network analyzer allows us to observe the frequency response of the amplifier just for the selected input power (0 dBm). 3.2 BUILDING AND MEASUREMENTS 71

In Figure 3-64 and Figure 3-65 S21 parameter module and S11 parameter module from 2.5 to 8 GHz is showed in dB for both amplifiers respectively. S21 parameter phase difference in resonant frequency is shown in Figure 3-66 and Figure 3-67.

Hittite amplifier S-Paramaters 25 S 20 21 S 11 15

10

5 [dB]

S S 0

-5

-10

-15

-20 0 1 2 3 4 5 6 7 8 f [GHz]

Figure 3-64: S21 and S11 of HMC717LP3

RF3376 amplifier S-parameters 30 S 11 S 20 21

10

0 [dB] S S -10

-20

-30

-40 0 1 2 3 4 5 6 7 8 f [GHz]

Figure 3-65: S21 and S11 of RF3376 72 Chapter 3 Design

Hittite amplifier S phase difference 21 200

150

100

50

0 [Degrees]

-50 Phase

-100

-150

-200 0 1 2 3 4 5 6 7 8 f [GHz]

Figure 3-66: S21 and phase of HMC717LP3

RF3376 amplifier S phase difference 21 200

150

100

50

[Degrees]

0 Phase -50

-100

-150 0 1 2 3 4 5 6 7 8 f [GHz]

Figure 3-67: S21 and phase of RF3376 3.2 BUILDING AND MEASUREMENTS 73

Table 3-11: Amplifiers characteristics in resonant frequency

S11 [dB] S21 [dB] Phase S21 [degrees] HMC717LP3 7.14 11.6 114 RF3376 8.3 12.3 -53

Keep in mind that S-parameters measured are for PIN = 0 dBm. With this input power, amplifier is in lineal zone, hence, amplifier S-parameters modules can be compared with diagrams in amplifiers datasheet [11][12].

Resonant cavities insertion loss has been designed of 13 dB. Using one amplifier in closed circuit of the oscillator gives not gain enough and hence, two amplifiers in cascade are used. One of the most important parameter of amplifiers is compression gain.

GAIN COMPRESSION

1 dB input compression point determines which is the maximum input power that guarantees that amplifier does not saturate. When amplifier is saturated, there is a non linear behavior and S-parameters are completely different as computed in above [19]. Undesired spurious peaks can appear in frequency domain and hence this behavior must be avoided.

This chapter shows how compression gain of both amplifiers is computed using Spectrum Analyzer 8563E from Hewlet and Packard, Signal generator Giga-Tronics and two coaxial cables as in Figure 3-68.

Figure 3-68: Compression point measurement In Figure 3-69 can be seen one scheme of the measure and coaxial cables measured loss. Loss in cables (measured with network analyzer) and spectrum analyzer offset value must be taken into account before the measure. 74 Chapter 3 Design

Figure 3-69: Measurement Setup Once the connections in Figure 3-69 are done, input power in signal generator is modified and each output power is observed in spectrum analyzer. The obtained results are plotted in Figure 3-70 and Figure 3-71. Red dotted line indicates lineal ideal gain response whereas the measured gain is in blue.

Measured Hittite Power Response 25

20

15

[dBm] OUT

P 10

5

0 -10 -5 0 5 10 P [dBm] IN

Figure 3-70: Hittite Power Response 3.2 BUILDING AND MEASUREMENTS 75

Measured RF3376 Gain Response 20

18

16

14

12

[dBm] 10 OUT

P 8

6

4

2

0 -10 -5 0 5 P [dBm] IN

Figure 3-71: RF3376 Power Response

To know 1 dB input compression point, power PIN that give a POUT power 1 dB lower than ideal case (red line) must be computed. Results for both amplifiers are in Table 3-12.

PIN plotted in the graph are the values in the output of signal generator. If it is considered that the cable 2 in Figure 3-69 has 1 dB attenuation. Hence this value must be subtracted of 1dB compression point computed with Figure 3-70 and Figure 3-71.

Table 3-12: 1 dB input compression point and saturated output power for each amplifier

1 dB Input Compression Output Saturation Power Point HMC717LP3 9.5 dBm 21 dBm RF3376 0 dBm 12 dBm

It can be seen that the computed gain with spectrum analyzer for PIN =0 dBm is GSA=10.6 dBm while with network analyzer the obtained gain was GNA=11.6 dB in Hittite amplifier. In RF3376 the GSA=10 dBm and GNA=12.3 dB. This small difference is because of PCB transmission line losses which are not taken into account with Network analyzer.

As it has been previously mentioned, in oscillator closed circuit, two used amplifiers should work in their lineal zone. Two HMC717LP3 in cascade are selected for the oscillation closed circuit because allows us having more power in oscillator circuit without saturate the second amplifier. This is the main characteristic to select two HMC717LP3. However, in Table 3-13 there are other advantages and inconvenient. 76 Chapter 3 Design

Table 3-13: Advantages and inconvenient of both amplifiers

HMC717LP3 RF3376 Advantages Inconvenient Advantages Inconvenient

Lower gain over Bigger S11 module in Lower S11 module in Higher gain over 7.5 GHz resonance frequency resonance frequency 7.5 GHz

S-Parameters Lower S21 module in Bigger S21 module in S-Parameters not available in Hittite resonant frequency resonant frequency available in RF Website MicroDevices Website Lower Noise Factor A lot of SMD Few SMD Bigger noise Factor components in bias components in bias circuit circuit

3.2.2 RESONANT CAVITY

As it has been seen before, PCB which feeds the resonator and waveguides resonators must be joined allowing that the surface current which flows inside the cavities does not find any interruption except the coupling holes. 14 screws are used in circular cavity and the results obtained further are very acceptable. In rectangular cavity, the fact that use two pieces instead of only one piece, makes this contact more difficult. Moreover, screws can only be situated in two sides when the ideal design should be with screws along x and z axis. These designing mistakes make use expensive solutions as silver glue and silver conducting painting.

In rectangular cavity, first cavity building is pasted to PCB with silver painting to improve the electrical connectivity between the two parts and 8 screws.

S21 and S11 module are computed with Network analyzer using different frequency ranges. In Figure 3-72 and Figure 3-73 measured S-parameters of rectangular resonator and circular from 500 MHz to 8 GHz is plotted. 3.2 BUILDING AND MEASUREMENTS 77

Measured rectangular cavity insertion loss -25

-30

-35

-40

-45

[dB] -50

21 S -55

-60

-65

-70

-75 0 1 2 3 4 5 6 7 8 f [GHz]

Figure 3-72: Measured S21 for rectangular cavity

Measured circular cavity insertion loss -10

-20

-30

-40

[dB] -50

21 S -60

-70

-80

-90 0 1 2 3 4 5 6 7 8 f [GHz]

Figure 3-73: Measured S21 for rectangular cavity 78 Chapter 3 Design

This first plot is done to compare measured to simulated parameters in Figure 3-3 and Figure 3-12 and check if other propagation modes are too near to fundamental resonant frequency. However, network analyzer computes only 501 point in all selected band. Hence, measured resonant frequency with this band is quite inexact and the swept frequency range must be hardly reduced. For rectangular cavity S21 module in Figure 3-74 is defined from 6 GHz to 6.05 GHz and S21 phase in Figure 3-76. For circular cavity in S21 module in Figure 3-75 is defined from 5.95 GHz to 6 GHz and S21 phase in Figure 3-77 .

Measured Rectangular cavity S-parameter -15 S 21 S -20 11

-25

-30

[dB] S S

-35

-40

-45 6 6.01 6.02 6.03 6.04 6.05 f [GHz]

Figure 3-74: Measured S21 and S11 with silver painting 3.2 BUILDING AND MEASUREMENTS 79

Measured circular cavity S-parameters -10 S -15 21 S -20 11

-25

-30

-35

[dB] S S -40

-45

-50

-55

-60 5.95 5.96 5.97 5.98 5.99 6 f [GHz]

Figure 3-75: Measured S21 and S11

Measured rectangular cavity phase difference 200

150

100

50

0 [Degrees]

-50 Phase

-100

-150

-200 6 6.005 6.01 6.015 6.02 6.025 6.03 6.035 6.04 f [GHz]

Figure 3-76: Measured S21 phase silver painting 80 Chapter 3 Design

Measured circular cavity phase difference 150

100

50

0

[degrees] Phase -50

-100

-150 5.95 5.955 5.96 5.965 5.97 5.975 5.98 5.985 5.99 5.995 6 f [GHz]

Figure 3-77: Measured S21 phase Rectangular resonator has still more losses than it is expected. Silver painting is changed for silver glue to joint all parts of the resonator and keep the parts mechanically and electrically joined. Figure 3-78 shows rectangular cavity S parameters using silver glue. It can be seen that the results are quite worst than using painting glue. That is not logical because silver glue 3.2 BUILDING AND MEASUREMENTS 81 has better properties than silver painting, hence this losses can have other origin. Measured Rectangular S-parameter -15 S 11 -20 S 21

-25

-30

-35

[dB] S S

-40

-45

-50

-55 6 6.02 6.04 6.06 6.08 6.1 f [GHz]

Figure 3-78: Measured S21 and S11 with silver glue In Table 3-14 there are measured values for both cavities in resonant frequency in each case. Q factor with transmission method in [9] from the measured results have been computed.

Table 3-14: Measured S parameters in resonant frequency

S11 [dB] S21 [dB] Phase S21 [GHz] QL Q0 [degrees]

Rectangular 20.75 18.74 127 6.024 1205 1362 cavity (silver painting)

Rectangular 25.3 29 152 6.044 1209 1253 cavity (silver glue)

Circular 16 13.7 24 5.976 2563 2075 cavity

Measured Q factor is quite lower than one computed in simulation. That can be for the limited points that network analyzer can get and the limitations of the method used. Other more accurate method is seen in [20]. 82 Chapter 3 Design

3.2.3 DIRECTIONAL COUPLER

Directional coupler S-parameters module in Figure 3-79 has been measured with Network analyzer as well and the obtained results are plotted in Figure 3-80. One must remember, that Network analyzer has just two ports and a 3-ports device has to be measured. In order to obtain a correct measurement is important to connect a 50  load in the port which is not connected to network analyzer coaxial cable due to not having an open circuit. Loads from calibrate kit cannot be used. Measured coupler parameters in resonant frequency are computed with (3-19) and written in Table 3-15 .

Figure 3-79: Directional coupler photo 3.2 BUILDING AND MEASUREMENTS 83

Measured Directional Coupler S-parameters 0

-10

-20

-30

[dB] S S

S -40 11 S 21 S -50 31 S 33 S 23 -60 1 2 3 4 5 6 7 8 f [GHz]

Figure 3-80: Directional Coupler measured S parameters

(3-18)

(3-19)

Table 3-15: Computed Coupler characteristics obtained from the measurement

Coupling [dB] Insertion loss [dB] [GHz]

Rectangular 12.85 1.063 6.024 cavity

Circular cavity 12.86 0.888 5.976

All parameters are similar as in the simulation except S33 which is around , and hence is better than in simulation.

84 Chapter 3 Design

3.2.4 OSCILLATOR PLANAR CIRCUIT

Power in closed circuit can be computed as (3-20) where is amplifier gain in resonant frequency are insertion loss of the cavity and are losses in transmission lines.

(3-20)

Once the waveguide cavity is fixed with screws and glue in each case, only work that must be done is solder the cooper wire in phase shifter structure as is said before in order to find the electrical length of the circuit that give phase difference between one arbitrary points in the circuit 2 n. Wire is soldered in one position and output signal of the oscillator is measured with spectrum analyzer.

RECTANGULAR OSCILLATOR

Oscillator with rectangular cavity has been measured using silver glue. Using silver glue circuit does not work as it was expected. The problem is that rectangular resonator has two much losses as it has been said and gain condition is not satisfied. In Figure 3-81 there is a photo of complete circuit. In this planar circuit circular microstrips bending have been used instead of mitered one which increase a little bit losses in the loop.

Figure 3-81: Oscillator circuit with rectangular cavity

3.2 BUILDING AND MEASUREMENTS 85

Second intent with an identical PCB and the same cavity is done with a different result. In Figure 3-82 one tone in 3.5 GHz can be observed and his respectively harmonics in 6.97 GHz and 10.47 GHz. The result is not a tone in 6 GHz because this oscillation is produced for the amplifier itself. Some output power of the amplifier is returning directly in his input and the amplifier becomes instable. On the other hand, any resonant frequency in 6 GHz is observed because insertion loss of the cavity is too large.

Figure 3-82: Obtained resonant frequencies with rectangular oscillator

CIRCULAR RESONATOR

In Figure 3-83 can be seen final planar circuit oscillator with circular cavity. 86 Chapter 3 Design

Figure 3-83: Oscillator circuit with circular cavity

Power in feedback circuit is computed with (3-20) getting POUT= 9.5 dBm just considering amplifier gain and cavity insertion loss. Small losses are present in transmission line, hence, neither amplifier 1 nor amplifier 2 are saturated. Thus, gain condition is satisfied.

Once the first condition is fulfilled, phase shifter must be modified in order to find the point where the phase condition is satisfied as well.

One wire of 1.4 mm diameter is soldered in position 0 in Figure 3-84. If the circuit does not oscillate, it means that phase difference between one arbitrary point after one loop corresponds with a resonator loss too big that circuit gain cannot compensate and hence there is no oscillation. Then, cooper wire must be collocated in position 1 and repeat the measure. When position where the circuit oscillates is found, position must be increased until the next position where the circuit does not oscillates. If there are some consecutive positions that the circuit oscillates, the proper position of the cable is the one in the middle because it would be the more stable. Final position of the wire can be seen in Figure 3-85. 3.2 BUILDING AND MEASUREMENTS 87

Figure 3-84: Phase shifter procedure scheme

Figure 3-85: Phase shifter proper wire position 88 Chapter 3 Design

In Figure 3-86 it can be seen output tone of designed oscillator using spectrum analyzer set as is shown in Figure 3-87. Resonant frequency as central frequency and one SPAN of 100 kHz are selected. In order to reduce outside influence in the measure, the circuit is shielded with aluminum paper. Small bandwidth of resolution filter in the spectrum analyzer is selected (RBW=3 kHz) in order to have more accurate measurement.

Figure 3-86: Spectrum analyzer measure for circular cavity oscillator

It can be seen in Figure 3-86 that a tone in 5.97 GHz, with POUT= 3.33 dBm is obtained.

This measure is done with spectrum analyzer Hewlett Packard. However, this device cannot do phase noise measurements and hence model R&S FSL6 must be used if resonant tone is below 6 GHz as in this case. 3.2 BUILDING AND MEASUREMENTS 89

Figure 3-87: Oscillator measurement It can be observed in Figure 3-88 that undesired spurious frequencies are present in all the band. These peaks are intermodulation distortion in amplifier due to different resonant modes in the resonator. 90 Chapter 3 Design

Figure 3-88: Obtained measurement with spectrum analyzer If strip conductors not used in phase shifter are removed with cutter, these spurious peaks have lower power (dBc) and hence, they are masked by noise. Hence, in frequency band there is just the desired resonant frequency with his correspondent harmonics.

3.2.5 PHASE NOISE

Phase noise refers to the short-term random fluctuation in the frequency (or phase) of an oscillator signal. Due to random fluctuations caused by thermal and other noise sources, appears as a broad, continuous distribution localized about the output signal.

Phase noise is defined as the ratio of power in one phase modulation sideband to the total signal power per unit bandwidth (1 Hz) at a particular offset, , from the signal frequency, and is denoted as ʆ ( ,). It is usually expressed in decibels relative to the carrier power per hertz of bandwidth (dBc/Hz).

Phase noise is computed with spectrum analyzer R&S FSL6 following indications in [21] and [22] with resolution bandwidth of the filter in spectrum analyzer of 30 kHz. Results obtained are in Table 3-16.

3.2 BUILDING AND MEASUREMENTS 91

Table 3-16: Oscillator Phase noise in circular cavity

fOFF [kHz] 0.001 0.01 0.1 1 100 1000 Phase noise 44 46.4 92.37 97.38 96.14 107.63 [dBc/Hz]

4 Conclusions

Implementation of one oscillator of 6 GHz has been described in this work. Oscillator is based in one microwave cavity which selects the desired frequency, two GaAs PHEMT MMIC Low Noise Amplifiers, one directional coupler to see the output signal and one phase shifter.

Oscillator with circular waveguide resonator has a resonant frequency of 5.97 GHz, output power about d m and short term stability of 97.38 dBc /Hz at 1 kHz offset frequency.

On the other hand, oscillator with rectangular waveguide resonator does not oscillate.

Some mistakes have been made in the design and some unexpected results have been measured. The aim of this chapter is summarize these problems and give one possible solution.

Mechanical design of the rectangular cavity was made with two brass pieces soldered plus the top part in order to use the screws to hold the PCB. This design was done in order to have perfect 90 degrees corner inside the cavities. However, obtained measure of S21 for this cavity are unsuitable and hence, the oscillator does not work. The optimal solution is to build this cavity just with one piece as circular cavity resonator. The inconvenience is that corners inside the cavity cannot have 90 degrees. Corners must have a circular curve (drill diameter) as in Figure 4-1 with radius R depending on the cavity height b desired. In this case which b=20 mm minimum available drill which can do the cavity has R=3 mm.

In working frequency of 6 GHz there is not any difference between the cavity with perfect 90 degrees corners simulated in this work and the new cavity proposed with circular corners. With this solution, cavity height is exactly b=20 mm not as in other case. Using silver glue, once the cavity is pasted to one PCB, two pieces cannot be separated without damaging PCB. Thus, using this solution und screws it is quite more manageable and cheaper solution.

It can be also observed in Figure 4-1 that in top part of the cavity, there is a relief which improve electrical connection between PCB and cavity.

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Figure 4-1: Proposed cavity structure With this cavity, screws in x-axis can be placed and the connection between cavity and PCB would be quite better. Moreover, the fact that having the cavity with just one piece, allows to use Aluminum instead of brass which have better conductivity.

Other detected problem is the flexibility of the dielectric substrate which was selected. When PCB is joined with microwave cavity with screws, due to its flexibility shape of the cavity can be slightly modified modification and hence, resonant frequency can have a small variation. Moreover, the more rigid is the PCB, the more manageable is the device. It would be a good idea make the design using a thicker substrate (h=3.18 mm) .

It has been seen that mitered bending in Figure 4-2 have better transmission and reflection behavior than swept bending in Figure 4-3. Hence in both oscillation circuits mitered bending should be used.

Figure 4-2: Mitered bending

Figure 4-3: swept bending Relating to the amplifiers, if the selected one would have bigger gain in 6 GHz, it would not be necessary using two amplifiers in cascade. Moreover, the soldering process would be faster 94 Chapter 4 Conclusions in this way or if the model selected would have less components in bias circuit. However, it is difficult to find an amplifier such that, hence other possibility should be design a resonant cavity with less losses even though it means worse Q factor and hence less stability in oscillator.

It has seen that the problem in directional coupler design was the difficulties to obtain an S33 low enough. One stub is designed in this work. However, other possible solution would be using mitered bending as in Figure 4-4 in order to reduce the reflections in the line. In this case should be studied if one stub is required.

Figure 4-4: Directional coupler improvement In final oscillator measurement, it can be seen that resonant frequency is not as stable as it could be expected. In order to improve this fact some changes in oscillator planar circuit can be done:

- Distribution of the planar circuit elements in PCB can be improved as in Figure 4-5.o avoid long DC line. Long line can produce small variations in DC signal. These variation produce amplifier gain variations and hence instability in oscillator.

- Coupling factor C in directional coupler small in order to do not reduce so much the power in closer circuit.

- One amplifier can be placed as in Figure 4-4 in order to increase of the oscillator. Moreover, it can give more isolation between closed circuit and the output [7] 0 95

Figure 4-5: Possible improvement in oscillator planar circuit with circular cavity -

In order to filter undesired resonant frequency harmonics, one pass band filter or low pass filter with cutoff frequency above 6 GHz can be designed as a part of feedback circuit. Due to the big distance between resonant frequency in 6 GHz and his harmonic of order two in 12 GHz, filter with a big transition band can be used.

Appendix

A.SOFTWARE

ADVANCED DESIGN SYSTEM 2012.08 (ADS)

ADS is very useful when some parameters in one circuit must be optimized to reach some goal. User can modify every parameter and observe in this moment how this change affects the design. For example, in this work it was used to design all matching networks and directional coupler structure.

Other interesting tools are available in this software. For example, LineCalc function which allows make very fast calculations of transmission line width and length of different structures introducing characteristic impedance of the line or electrical length (microstrip lines, coplanar lines,..).

Other interesting tool is Smith Chart Utility that introducing an unmatched load, different series and parallel stubs with variable length and width can be introduced and the program shows how characteristic impedance is modified, and hence how the matching network must be designed. More information can be searched in official web side [23]

CST MICROWAVE STUDIO 2012

This software was used to 3D field simulations for all designed passive structures, therefor it is not suitable to simulate the amplifier. The used version was CST Studio 2012. More information can be found in [24]. CST allows exporting SNP files to other programs in order to work with this information. For example, these fields have been exported to ADS in order to work faster or they have been also exported to Matlab so that plotting obtained graphs

EAGLE 4.16 (Easily Applicable Graphical Layout Editor)

This software allows an easy design of PCB layout using libraries available in internet (QFN16, ST089, 0603 or 0402 component pads) or creating your own libraries (phase shifter, coupler, SMA pads,…). In this work, easy design with just two layers is needed; hence not very difficult design is required. There are a couple of tricky things that must be known previously.

Firstly, in layout is very important work with Grid and change it in order to put each element where is desired. Be careful with working unities.

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Eagle allows to introduce structures using scripts with desired coordinates using SCR bottom in main menu. These files can be introduced directly in the board or in one created library. In order to create a new library, one project must be selected with mouse right bottom and select New/Library. Package, Symbol and connection between both called Device must be drawn. Once the new library is created, option Library/Use in main menu must be selected and this library appears in left side menu from schematic.

Other important thing is how to make the holes in ground plane. Layer 42 must be used to draw parts that will be removed in ground place. Layer 41 is used if some part has be removed from layer 1. More information can be consulted in Eagle Manual [25]

Designed PCB with Eagle must be converted with two different files extensions using CAM Processor option in main menu of schematic or board files: EXCELLON and GERBER. The first one contain all the coordinates required so that one special machine in workshop can make automatically all the holes. The second one is needed to create the film which is used to PCB fabrication process. One film for each layer must be done.

MATLAB R2012a

This software was only used to draw graphs from exported touchstone files from CST simulations or from obtained data from network analyzer measures.

B.EQUIPMENT

SPECTRUM ANALYZER R&S FSL6 and HEWLETT PACKARD 8563E

The first in Figure B-1 has a frequency resolution from 9 kHz to 6 GHz while the second in Figure B-1 from 9 kHz to 26.5 GHz. For this reason, the second one is used to observe if the circuit oscillates and to see the spurious peaks. In circular cavity oscillator, once it is checked that his resonant frequency is below 6 GHz, R&S model is used to compute phase noise.

Spectrum Analyzer does not compute any phase measurement; hence previous calibration is not necessary before his using. Only two considerations must be taken into consideration before doing the measure.

- Maximum input power allowed in both devices (can be seen below INPUT connector that this value is 30 dBm). This consideration must be done in all frequency range and not only the frequency range that can be seen in the screen. Attenuators must be used if the input power is bigger.

- Be sure that there is any DC voltage in Spectrum Analyzer Input. Device available in IHF lab, is it equipped which one DC blocker which must not be removed.

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Figure B-1: (a) R&S FSL6 (b) HEWLETT PACKARD 8563E NETWORK ANALYZER WILTRON 360B

This instrument in Figure B-2 is also called a VNA, or Vector Network Analyzer, to emphasize the complex nature of the measurements (as opposed to scalar). Simply stated, a network analyzer measures the N-port response of circuit over a specified frequency range.

Figure B-2: Network Analyzer Photo Most network analyzers are designed to measure two-port devices, since most filters, amplifiers, and other RF building blocks are two-ports. If only 1 port is used, then the network analyzer can measure the 1-port response, or the impedance of the device under test. Network analyzers incorporate directional couplers to decompose the voltages in each port into “incident" and “reflected" waves. The ratio between these waves is directly related to the scattering or S-parameters of the device. Inherently, therefore, the network analyzer is 99 measuring the S-parameters of the device under test. The S- parameters are easily converted into other parameter sets, such as impedance (Z) or admittance (Y) parameters.

Previous calibration using calibration kit in Figure B-3 must be done. Calibration steps are mentioned below:

- First of all input signal power must be selected in Measurement/Setup Menu/Test signals - Press Begin Calin calibration menu Calibration method must be Standart and transmission line type Coaxial. Once this options are selected press Next Cal Step. - In calibrate type menu select Full 12-Term and Exclude Isolation in the following step Normal (501 points Maximum) is selected on calibration data points menu. Next step frequency range must be selected. - Calibration parameters are PORT 1 CONN: SMA(M), PORT 2 CONN: SMA(M), REFLECTION PAIRING:MIXING and LOAD TYPE: BROADBAND. Afterwards press START CAL. - In this point, every component in calibration kit must be connected in port specified in screen using one screw.

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- Figure B-3: Calibration Kit

Any calibration can be saved in a disk and used when it is required with options Save/Recall.

In order to have a correct measures, connectors in Figure B-4 must be situated between SMA connector of the PCB and network analyzer coaxial cable. 100

Other important issue is that the maximum power of 20 dBm can not be exceeded. In this work, measures with actives devices are done, hence some attenuators must be also used. As in spectrum analyzer, DC signal can not arrive in internal device circuitry so must be checked previously that DC blockers in PCB are working properly.

Figure B-4: Connectors used to have proper measurements

SOLDERING EQUIPMENT

Due to the small dimensions of SMD components used in amplifier bias circuit, DC blockers, matching resistors and chip pads, solder paste and microscope in Figure B-5 is required. Paste heating is done with hot air pencil (365 degrees) in SMD components and using an oven for amplifiers chips. 101

Figure B-5: Microscope to soldering process

Solder paste consist in tiny solder balls floating in gel-like flux. Once the past is applied to the pads, components are placed in the top and then this paste must be heated until it is melted. Paste is applied with syringe in Figure B-6. Paste in the syringe top can became solid and hence does not flow easily, in this case one metallic cable thin and rigid enough is used to unblock the device. 102

Figure B-6: Paste syringe photo Chip used in PCB has some pads covered for the same chip, hence it is impossible to heat the paste with a hot air pencil. Vapour-Phase Soldering or condensation soldering is used with Quicky 450 Soldering machine from ASSCOM SYSTEMTECHNIK in Figure B-7. This soldering uses the latent heat of liquid vaporization to provide heat for soldering. This latent heat is released as the vapor of the inert liquid condenses on component leads and PCB lands. The peak soldering temperature is the boiling temperature of the inert liquid at atmosphere pressure. Machine heat uniformly all PCB and hence any part on the board exceeds the fluid boiling temperature [26] 103

Figure B-7: Condensation oven photo

On the other hand, conventional tin soldering has been used for SMA connectors and DC pins. SMA connectors must be soldered very carefully because in high frequency undesired air gaps can have big effect in reflection and transmission coefficients. Currents in SMA connector surface must flow to PCB ground as fast as possible. Hence solder in bottom side as in Figure B-8 must be done.

Figure B-8: Proper soldering of SMA connector and PCB ground 104

If the cooper of the soldering pads is dirty, solder cannot be properly done. For this reason cooper must be cleaned with Isopropanol. There is other liquid called flux, which can also be used. However, after cleaning the cooper this liquid must be cleaned again because it is corrosive. That is because using alcohol is the best option.

PCB MANUFACTORING

All circuits will be fabricated using a simple two-layer printed circuit board (PCB). The PCB consists of a dielectric material, Rogers 6002 ( r = 2.94) in this design, with a thickness of 0.762 mm and two layers of Cu metal layer. The metal layers have a thickness of 35μm. As has been said before, metal is pattern with films done with GERBER files obtained from EAGLE. The backside of the board is a solid ground plane. Connections to ground must travel through a “via" to reach the backside. The input and output microstrip transmission lines are interrupted periodically which allows you to place components in series or in shunt. Landing pads with vias to ground also appear periodically to allow shunt components to be soldered to ground.

SIGNAL GENERATOR GIGA-TRONICS 900

Signal generator in Figure B-9 is used to provide an input power to the amplifier when the saturation point is searched. Continues Wave must be selected pressing button CW. Signal frequency is selected in left top panel and signal power in right top panel. LED LEVERED must be always on because it means that the signal power is stable.

Figure B-9: Used signal generator

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