DOCSLIB.ORG

Aperture-Coupled Stripline-To-Waveguide Transitions for Spatial Power Combining

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Aperture-Coupled Stripline-To-Waveguide Transitions for Spatial Power Combining ACES JOURNAL, VOL. 18, NO. 4, NOVEMBER 2003 33 Aperture-Coupled Stripline-to-Waveguide Transitions for Spatial Power Combining Chris W. Hicks∗, Alexander B. Yakovlev#,andMichaelB.Steer+ ∗Naval Air Systems Command, RF Sensors Division 4.5.5, Patuxent River, MD 20670 #Department of Electrical Engineering, The University of Mississippi, University, MS 38677-1848 +Department of Electrical and Computer Engineering, North Carolina State University, Raleigh, NC 27695-7914 Abstract power. However, tubes are bulky, costly, require high operating voltages, and have a short lifetime. As an A full-wave electromagnetic model is developed and alternative, solid-state devices offer several advantages verified for a waveguide transition consisting of slotted such as, lightweight, smaller size, wider bandwidths, rectangular waveguides coupled to a strip line. This and lower operating voltages. These advantages lead waveguide-based structure represents a portion of the to lower cost because systems can be constructed us- planar spatial power combining amplifier array. The ing planar fabrication techniques. However, as the fre- electromagnetic simulator is developed to analyze the quency increases, the output power of solid-state de- stripline-to-slot transitions operating in a waveguide- vices decreases due to their small physical size. There- based environment in the X-band. The simulator is fore, to achieve sizable power levels that compete with based on the method of moments (MoM) discretiza- those generated by vacuum tubes, several solid-state tion of the coupled system of integral equations with devices can be combined in an array. Conventional the piecewise sinusodial testing and basis functions in power combiners are effectively limited in the num- the electric and magnetic surface current density ex- ber of devices that can be combined. To overcome pansions. Electric and magnetic dyadic Green’s func- these limitations and produce high power levels at mi- tions used in this integral equation formulation are de- crowave and millimeter-wave frequencies, in a past few veloped for an infinite rectangular waveguide in the years there has been a considerable activity in develop- form of partial expansion over the complete system ing spatial power combining systems [1], [2], [3]. The of eigenfunctions of a transverse Laplacian operator. output power of individual solid-state devices in a pla- Numerical results are obtained and compared with a nar array is combined to produce moderate-to-high commercial microwave simulator for a few represen- power levels. It is desirable to utilize a single solid- tative structures, including various configurations and state amplifier, however, as frequency increases, the /f 2 planar arrays of slotted waveguide modules coupled to output power levels become low due to the 1 fall- a strip line. off of available power [4]. By utilizing power combin- ing techniques light-weight, reliable, and low cost am- plifiers and oscillators can be potentially designed to I. Introduction meet the demand of military and civilian applications. Fundamental understanding of spatial power com- Military and civilian applications require sizable bining systems has primarily been done by experimen- power at microwave and millimeter-wave frequen- tal investigation. Several experimental free space and cies. Medium to high power levels are needed for dielectric quasi-optical power combiners and waveg- applications such as communications, active missile uide spatial power combiners have been successful at seekers, radar, and millimeter-wave imaging. To meet demonstrating the fundamental concept of generating this need, klystrons, traveling-wave tubes, and gridded usable output power levels using spatial and quasi- tubes are heavily utilized to generate medium to high optical techniques. Although great strides have been 1054-4887 © 2003 ACES 34 ACES JOURNAL, VOL. 18, NO. 4, NOVEMBER 2003 made, to date, quasi-optical/spatial power combin- between the middle and upper waveguides. The strips ing systems have not yet out performed conventional are located inside of the middle waveguide region. The power combiners. In order to capture the full potential objective of stripline-to-waveguide transition is to effi- of quasi-optical/spatial systems to generate high power ciently couple energy from the lower waveguide to the levels, numerical modeling and computer aid engineer- upper waveguide. An incident electromagnetic field is ing tools are needed to fully understand these systems illuminated at the input port of the lower waveguide. [5]. The development of computer models helps to re- This signal travels into the lower waveguide and in- duce the cost and time associated with experimental duces magnetic currents on the lower slots where the work, and computer models assist with designing ef- slots scatter energy into the lower, middle, and upper ficient quasi-optical/spatial power combining systems. waveguides. In the middle waveguide region the scat- Modeling a quasi-optical/spatial power combining sys- tered fields induce electric currents and standing waves tem is complex and challenging. There are several along the strips. The scattered energy from the strips major system components that must be modeled such along with the scattered energy from the lower slots as, the input and output sources, which are typically induce magnetic currents in the upper slots. The mag- waveguide horns with optical lenses inside, the input netic currents in the upper slots cause scattered fields and output antennas with associated transmission lines back into the middle waveguide and into the upper and control components, and the active integrated am- waveguide region. Optimum performance is achieved plifier circuitry. by varying the distance between the slots, adjusting the slot dimensions, rotating the slots, or varying the stripline dimensions. Upper Waveguide PLANAR WAVEGUIDE SPATIAL POWER COMBINING AMPLIFIER PLANE INPUT COUPLING AMPLIFIER ARRAYS OUTPUT COUPLING NETWORK NETWORK Port 3 Port 4 Output Slots Output ε r Stripline MMIC Input Slots Port 1 Input Port 2 GROUND PLANE OUTPUT PLANE a Pout AMPLIFIER PLANE b Dielectric Between Waveguides Bottom Waveguide INPUT PLANE Pin c MICROWAVE ABSORBER PHOTONIC MATERIAL Fig. 1. Aperture-coupled stripline-to-waveguide transition. Fig. 2. Aperture-coupled planar waveguide amplifier array. In this paper, an electromagnetic modeling environ- ment is developed for an aperture-coupled stripline- to-waveguide transition (with geometry shown in Fig. A full-wave electromagnetic model is developed for 1). This transition is the fundamental building block a structure that couples a waveguide to a stripline for two-dimensional spatial power combining amplifier through a set of slots and from the stripline through arrays shown in Fig. 2 and, in turn, for the planar another set of slots into a second waveguide. The sys- quasi-optical power combining systems. The transition tem modeling is based on an integral equation formu- consists of three infinite aperture-coupled rectangular lation for the induced electric and magnetic surface waveguides. The lower slots (apertures) are located current densities resulting in a coupled set of inte- on the surface between the lower and middle waveg- gral equations discretized via the method of moments uides, and the upper slots are located on the surface (MoM). The scattered electric and magnetic fields are Hicks, et al.: Aperture-Coupled Stripline-to-Waveguide Transitions for Power Combining 35 expressed in terms of dyadic Green’s functions and the S electric and magnetic surface currents. Electric and S m nˆ magnetic dyadic Green’s functions are developed for an infinite rectangular waveguide in the form of par- E , H tial expansion over the complete system of eigenfunc- i i tions of a transverse Laplacian operator. The surface Es , Hs S currents are discretized by overlapping piecewise sinu- Jimp e sodial subdomain basis functions in order to accurately model narrow longitudinal strips and transverse slots. Jind Vimp V In this formulation, a MoM matrix includes all possible self and mutual coupling effects between the slots and strips. The transition is excited with the TE10 dom- inant waveguide mode, and the scattering parameters are calculated from the forward and backward coupling Fig. 3. Geometry of a closed-boundary waveguiding structure coefficients in the waveguide regions. containing apertures and conducting strips in the presence Numerical results of the scattering characteristics of an impressed electric current source. are obtained and compared with a commercial mi- crowave simulator for a few representative structures, = ¯ including a single slot-strip-slot waveguide transition, −jωµ GEJ (r, r ) · Jind(r )dS Se multiple slot-strip-slot waveguide transitions, and pla- = nar arrays of slotted waveguide modules coupled to − GEM (r, r ) · M¯ (r )dS (1) strip lines. Sm = II. Theory H¯ (r )= GHJ (r, r ) · J¯imp(r )dV Vimp = A general electromagnetic formulation for a closed- + GHJ (r, r ) · J¯ind(r )dS boundary waveguiding structure containing arbitrarily Se shaped apertures and conducting strips (see Fig. 3) = is presented in this section. This structure is a gen- −jω GHM (r, r ) · M¯ (r )dS (2) S eral building block of the aperture-coupled stripline- m to-waveguide transition shown in Fig. 1. The formula- where tion is based on the integral representation of incident = = and scattered electric and magnetic fields in terms of GHJ (r, r )=∇× GEJ (r, r ), (3) dyadic Green’s functions
Load more

Recommended publications
  • Lowpass Lumped-Element Coplanar Waveguide-To- Coplanar Stripline Transitions
    LOWPASS LUMPED-ELEMENT COPLANAR WAVEGUIDE-TO- COPLANAR STRIPLINE TRANSITIONS Yo-Shen Lin1 and Chun Hsiung Chen2 1Department of Electrical Engineering, National Central University, Chungli 320, Taiwan, R.O.C. (email: [email protected]) 2Department of Electrical Engineering and Graduate Institute of Communication Engineering, National Taiwan University, Taipei 106, Taiwan, R.O.C. (email: [email protected]) ABSTRACT The lowpass coplanar waveguide-to-coplanar stripline transitions are proposed, using planar lumped-elements to realize the filter prototypes in the transition structures. The proposed transitions are very compact and can provide the combined functions of transition and filter. Simple equivalent-circuit models based on closed-form expressions are also established, from which the characteristics of various lowpass lumped-element transitions are investigated. INTRODUCTION Coplanar waveguide (CPW) and coplanar stripline (CPS) are widely used as building blocks in the design of uniplanar MMIC's [1]. To fully utilize the exclusive features of CPW and CPS, an effective interconnection between them is of crucial importance. This may allow the choice of different uniplanar line-based circuit elements in different parts of a system such that maximum circuit integration and optimal system performance may be accomplished. Various CPW-to-CPS transitions have been developed [2]-[7]. Most of these conventional transitions have bandpass behaviors [2]-[4]. The broadband transition [5] utilizing a slotline open structure has a lowpass frequency response but its insertion loss increases only gradually as the operating frequency increases. The ideally all-pass double-Y junction balun [2], in practice, also features a gradually increasing insertion loss with frequency.
    [Show full text]
  • The Stripline Circulator Theory and Practice
    The Stripline Circulator Theory and Practice By J. HELSZAJN The Stripline Circulator The Stripline Circulator Theory and Practice By J. HELSZAJN Copyright # 2008 by John Wiley & Sons, Inc. All rights reserved Published by John Wiley & Sons, Inc. Published simultaneously in Canada No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax (978) 750-4470, or on the web at www.copyright.com. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, (201) 748-6011, fax (201) 748-6008, or online at http:// www.wiley.com/go/permission. Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives or written sales materials. The advice and strategies contained herein may not be suitable for your situation. You should consult with a professional where appropriate. Neither the publisher nor author shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages.
    [Show full text]
  • 97/$10.00 260 Ii
    Lumped-element Sections for Modeling Coupling Between High-Speed Digital and I/O Lines W. Cui, H. Shi, X. Luo, F. Sha*, J.L. Drewniak, T.P. Van Doren and T. Anderson** ElectromagneticCompatibility Laboratory University of Missouri-Rolla Rolla, MCI 65401 * Northern Jiao Tong University EMC ResearchSection Beijing 100044,P.R.China * * HP-EEsof Division Hewlett-PackardCo. SantaRosa, CA 95403 Abstract: Lumped-elementsections are used for modeling designstage to estimateEM1 and minimize the noise coupling coupling betweenhigh-speed digital and I/O lines on printed to I/O lines on the PCB. As digital designs become more circuit boards (PCBs) in this paper. Radiatedelectromagnetic dense, flexibility in trace routing is reduced. Adherence to interference(EMI) is investigatedwhen the I/O line going off simple design maxims for avoiding adjacent segmentsof an the board is driven as an unintentional, but effective antenna. I/O line and a high-speeddigital line becomesmore difficult. Simulated results are compared with measurementsfor A meansfor estimatingEM1 at the design stageis desirableto coupled lines. A suitable number of lumped-elementsections maintainrouting flexibility while minimizing EM1 risk. for modeling is chosen based on the line length and the highestfrequency of interest. The three essentialcomponents for estimating EM1 resulting from coupling to I/O lines are suitable sourceand load models, a coupled transmission-line model, and an EM1 antenna I. INTR~DUC~~N model. Of particular interest at this stage are models for the coupled transmission lines, and the EM1 antenna. Two As the speed of digital designs continues to increase, approaches have been previously pursued for modeling unintentionalradiation from cablesattached to PCBs becomes coupled transmission-lines.One technique is to decouple the problematic.For clock speedsless than 50 MHz, a typical 1 m lines in the frequency domain by modal decomposition [l].
    [Show full text]
  • RF / Microwave PC Board Design and Layout
    RF / Microwave PC Board Design and Layout Rick Hartley L-3 Avionics Systems [email protected] 1 RF / Microwave Design - Contents 1) Recommended Reading List 2) Basics 3) Line Types and Impedance 4) Integral Components 5) Layout Techniques / Strategies 6) Power Bus 7) Board Stack-Up 8) Skin Effect and Loss Tangent 9) Shields and Shielding 10) PCB Materials, Fabrication and Assembly 2 RF / Microwave - Reading List PCB Designers – • Transmission Line Design Handbook – Brian C. Wadell (Artech House Publishers) – ISBN 0-89006-436-9 • HF Filter Design and Computer Simulation – Randall W. Rhea (Noble Publishing Corp.) – ISBN 1-884932-25-8 • Partitioning for RF Design – Andy Kowalewski - Printed Circuit Design Magazine, April, 2000. • RF & Microwave Design Techniques for PCBs – Lawrence M. Burns - Proceedings, PCB Design Conference West, 2000. 3 RF / Microwave - Reading List RF Design Engineers – • Microstrip Lines and Slotlines – Gupta, Garg, Bahl and Bhartia. Artech House Publishers (1996) – ISBN 0-89006-766-X • RF Circuit Design – Chris Bowick. Newnes Publishing (1982) – ISBN 0-7506-9946-9 • Introduction to Radio Frequency Design – Wes Hayward. The American Radio Relay League Inc. (1994) – ISBN 0-87259-492-0 • Practical Microwaves – Thomas S. Laverghetta. Prentice Hall, Inc. (1996) – ISBN 0-13-186875-6 4 RF / Microwave Design - Basics ) RF and Microwave Layout encompasses the Design of Analog Based Circuits in the range of Hundreds of Megahertz (MHz) to Many Gigahertz (GHz). ) RF actually in the 500 MHz - 2 GHz Band. (Design Above 100 MHz considered RF.) ) Microwave above 2 GHZ. 5 RF / Microwave Design - Basics ) Unlike Digital, Analog Signals can be at any Voltage and Current Level (Between their Min & Max), at any point in Time.
    [Show full text]
  • Reviewing the Basics of Microstrip
    DESIGN FEATURE Microstrip Lines Reviewing The Basics Of Microstrip An understanding of the fundamentals of Lines microstrip transmission lines can guide high- frequency designers in the proper application of this venerable circuit technology. Leo G. Maloratsky RINTED transmission lines are widely used, and for good reason. Principal Engineer They are broadband in frequency. They provide circuits that are Rockwell Collins, 2100 West Hibiscus Pcompact and light in weight. They are generally economical to pro- Blvd., Melbourne, FL 32901; (407) duce since they are readily adaptable to hybrid and monolithic inte- 953-1729, e-mail: lgmalora@ grated-circuit (IC) fabrication technologies at RF and microwave fre- mbnotes.collins.rockwell.com. quencies. To better appreciate printed transmission lines, and microstrip in particular, some of the basic principles of microstrip lines will be reviewed here. A number of different transmis- with respect to the others. In Fig. 1, sion lines are generally used for it should be noted that the substrate microwave ICs (MICs) as shown in materials are denoted by the dotted Fig. 1. Each type has its advantages areas and the conductors are indicat- ed by the bold lines. The microstrip line is a transmis- Basic lines Modifications sion-line geometry with a single con- W W t a ductor trace on one side of a dielectric H hhhW W substrate and a single ground plane line a h Suspended Inverted on the opposite side. Since it is an Microstrip Microstrip line Shielded microstrip line microstrip line microstrip line open structure, microstrip line has a t W W1 major fabrication advantage over b b t stripline.
    [Show full text]
  • Planar Transmission Line Method for Char- Acterization of Printed Circuit Board Di- Electrics
    Progress In Electromagnetics Research, PIER 102, 267{286, 2010 PLANAR TRANSMISSION LINE METHOD FOR CHAR- ACTERIZATION OF PRINTED CIRCUIT BOARD DI- ELECTRICS J. Zhang CISCO Systems, Inc. CA, USA M. Y. Koledintseva Missouri University of Science & Technology Rolla, MO, USA G. Antonini Department of Electrical Engineering University of L'Aquila Poggio di Roio, 67040 AQ, Italy J. L. Drewniak Missouri University of Science & Technology Rolla, MO 65401, USA A. Orlandi Department of Electrical Engineering University of L'Aquila Poggio di Roio, 67040 AQ, Italy K. N. Rozanov Institute for Theoretical and Applied Electromagnetics Russian Academy of Sciences Moscow 125412, Russia Corresponding author: M. Y. Koledintseva ([email protected]). 268 Zhang et al. Abstract|An e®ective approach to characterize frequency-dispersive sheet materials over a wide RF and microwave frequency range based on planar transmission line geometries and a genetic algorithm is proposed. S-parameters of a planar transmission line structure with a sheet material under test as a substrate of this line are measured using a vector network analyzer (VNA). The measured S-parameters are then converted to ABCD matrix parameters. With the assumption of TEM/quasi-TEM wave propagation on the measured line, as well as reciprocity and symmetry of the network, the complex propagation constant can be found, and the corresponding phase constant and attenuation constant can be retrieved. Attenuation constant includes both dielectric loss and conductor loss terms. At the same time, phase term, dielectric loss and conductor loss can be calculated for a known transmission line geometry using corresponding closed- form analytical or empirical formulas.
    [Show full text]
  • Planar Transmission Lines
    Adapted from notes by ECE 5317-6351 Prof. Jeffery T. Williams Microwave Engineering Fall 2018 Prof. David R. Jackson Dept. of ECE Notes 11 Waveguiding Structures Part 6: Planar Transmission Lines w ε0 ε r h 1 Planar Transmission Lines w w b ε h r εr Microstrip Stripline w w εr g g h εr g g h Coplanar Waveguide (CPW) Conductor-backed CPW s s εr h εr h Slotline Conductor-backed Slotline 2 Planar Transmission Lines (cont.) w w w w ε h εr s h r s Coplanar Strips (CPS) Conductor-backed CPS . Stripline is a planar version of coax. Coplanar strips (CPS) is a planar version of twin lead. 3 Stripline . Common on circuit boards ε,, µσd b . Fabricated with two circuit boards w . Homogenous dielectric (perfect TEM mode) TEM mode (also TE & TM Modes) Field structure for TEM mode: Electric Field Magnetic Field 4 Stripline (cont.) . Analysis of stripline is not simple. TEM mode fields can be obtained from an electrostatic analysis (e.g., conformal mapping). A closed stripline structure is analyzed in the Pozar book by using an approximate numerical method: b w b /2 ε,, µσd a ab>> 5 Stripline (cont.) Conformal mapping solution (S. Cohn): Exact solution: 30π Kk ( ) Z0 = K = complete elliptic Kk()′ integral of the first kind π /2 1 Kk( ) ≡ dθ ∫ 22 0 1− k sin θ π w k = sech 2b π w k′ = tanh 2b 6 Stripline (cont.) Curve fitting this exact solution: η b Z = 0 ln( 4) 0 ε ln(4) Note : = 0.441 4 r wb+ π e π Effective width Fringing term w 0 ;for ≥ 0.35 wwe b = − 2 bbww 0.35− ;for 0.1≤≤ 0.35 bb 1bb /2 η η b ideal 0 The factor of 1/2 in front is from the parallel Note: Z0 =η = = 24ww4w ε r combination of two ideal PPWs.
    [Show full text]
  • Microwave Filters
    EEE194 RF Microwave Filters Microwave Filters Passbands and Stopbands in Periodic Structures Periodic structures generally exhibit passband and stopband characteristics in various bands of wave number determined by the nature of the structure. This was originally studied in the case of waves in crystalline lattice structures, but the results are more general. The presence or absence of propagating wave can be determined by inspection of the k-β or ω-β diagram. For our purposes it's enough to know the generality that periodic structures give rise to bands that are passed and bands that are stopped. To construct specific filters, we'd like to be able to relate the desired frequency characteristics to the parameters of the filter structure. The general synthesis of filters proceeds from tabulated low-pass prototypes. Ideally, we can relate the distributed parameters to the corresponding parameters of lumped element prototypes. As we will see, the various forms of filter passband and stopband can be realized in distributed filters as well as in lumped element filters. Over the years, lumped element filters have been developed that are non-minimum phase; that is, the phase characteristics are not uniquely determined by the amplitude characteristics. This technique permits the design of filters for communications systems that could not be constructed using only minimum phase filter concepts. This generally requires coupling between multiple sections, and can be extended to distributed filters. The design of microwave filters is comprehensively detailed in the famous Stanford Research Institute publication1 Microwave Filters, Impedance Matching Networks and Coupling Structures. Richard's Transformation and Kuroda's Identities (λ/8 Lines) Richard's Transformation and Kuroda's Identities focus on uses of λ/8 lines, for which X = jZo.
    [Show full text]
  • Transmission Lines and Waveguides.Doc 1/3
    2/20/2009 3 Transmission Lines and Waveguides.doc 1/3 Chapter 3 – Transmission Lines and Waveguides First, some definitions: Transmission Line – A two conductor structure that can support a TEM wave. Waveguide – A one conductor structure that cannot support a TEM wave. Q: What is a TEM wave? A: An electromagnetic wave wherein both the electric and magnetic fields are perpendicular to the direction of wave propagation. HO: WAVEGUIDE 3.5 Coaxial Line Reading Assignment: p. 130 The most prevalent type of transmission line is the coaxial transmission line. HO: COAXIAL TRANSMISSION LINES Jim Stiles The Univ. of Kansas Dept. of EECS 2/20/2009 3 Transmission Lines and Waveguides.doc 2/3 Coaxial transmission lines are attached to devices using microwave connectors. HO: COAXIAL CONNECTORS 3.7 Stripline Reading Assignment: pp. 137-140 Often, microwave devices or networks are built on dielectric substrates (e.g., “printed circuit boards”). Connecting these devices require printed circuit board transmission lines. HO: PRINTED CIRCUIT BOARD TRANSMISSION LINES One of the most popular PCB transmission lines is stripline. HO: STRIPLINE 3.8 Microstrip Reading Assignment: pp. 143-146 Another popular PCB transmission line is microstrip. HO: MICROSTRIP Jim Stiles The Univ. of Kansas Dept. of EECS 2/20/2009 3 Transmission Lines and Waveguides.doc 3/3 3.11 Summary of Transmission Lines and Waveguides Reading Assignment: pp. 154-157 Let’s compare transmission line characteristics! HO: A COMPARISON OF COMMON TRANSMISSION LINES AND WAVEGUIDES Jim Stiles The Univ. of Kansas Dept. of EECS 2/19/2007 Waveguide 1/2 Waveguide A waveguide is not considered to strictly be a transmission line, as it is not constructed with two separate conductors.
    [Show full text]
  • Transmission Line Basics
    Transmission Line Basics Prof. Tzong-Lin Wu NTUEE 1 Outlines Transmission Lines in Planar structure. Key Parameters for Transmission Lines. Transmission Line Equations. Analysis Approach for Z0 and Td Intuitive concept to determine Z0 and Td Loss of Transmission Lines Example: Rambus and RIMM Module design 2 Transmission Lines in Planar structure Homogeneous Inhomogeneous Microstrip line Coaxial Cable Embedded Microstrip line Stripline 3 Key Parameters for Transmission Lines 1. Relation of V / I : Characteristic Impedance Z0 2. Velocity of Signal: Effective dielectric constant e 3. Attenuation: Conductor loss ac Dielectric loss ad Lossless case 1 L Td Z0 C V p C C 1 c0 1 V p LC e Td 4 Transmission Line Equations Quasi-TEM assumption 5 Transmission Line Equations R0 resistance per unit length(Ohm / cm) G0 conductance per unit length (mOhm / cm) L0 inductance per unit length (H / cm) C0 capacitance per unit length (F / cm) dV KVL : (R0 jwL0 )I dz Solve 2nd order D.E. for dI V and I KCL : (G0 jwC0 )V dz 6 Transmission Line Equations Two wave components with amplitudes V+ and V- traveling in the direction of +z and -z rz rz V V e V e 1 rz rz I (V e V e ) I I Z0 Where propagation constant and characteristic impedance are r (R0 jwL0 )(G0 jwC0 ) a j V V R0 jwL0 Z0 I I G0 jwC0 7 Transmission Line Equations a and can be expressed in terms of (R0 , L0 ,G0 ,C0 ) 2 2 2 a R0G0 L0C0 2a (R0C0 G0 L0 ) The actual voltage and current on transmission line: az jz az jz jwt V (z,t) Re[(V e e V e e )e ] 1 az jz az jz
    [Show full text]
  • Comparison of Embedded Coplanar Waveguide and Stipline for Multi-Layer Boards
    Comparison of Embedded Coplanar Waveguide and Stipline for Multi-Layer Boards Mohanad Abulghasim, Justin Tabatchnick, and Milica Markovic California State University Sacramento, Sacramento, CA, 95819, USA Abstract— In this paper we present comparison of relative capacitive and inductive coupling to be approxi- conductor-backed Coplanar Waveguide (CPW) with a cover mately equal [20]. Width of the signal strip to height of shield and Stripline for multi-layer boards using a full 3D the substrate must be fixed for a specific transmission line EM CAD software. It is important in High-Speed Digital Ap- plications to decrease the form factor and increase the signal impedance, which limits the design flexibility of striplines. density by reducing isolating metal layers while preserving An advantage of a CPW is in design flexibility. CPWs comparable crosstalk, loss and dispersion at the frequency of can be made on thick substrates. Design criteria in a CPW interest. Conductor, and dielectric losses of conductor-backed to achieve specific characteristic impedance is the ratio of CPW with a cover shield and Stripline are compared up to signal strip width and gap. The ratio of the width of the 25 GHz, for 5Gbps digital applications. Typical dimensions are used for Intel’s stripline SDRAM multilayer interconnect signal strip and the the height of the substrate does not boards, and equivalent dimensions are calculated for CPW. need to be fixed to produce a 50-Ω line. Characteristic Isolation and coupling is presented for tightly and loosely impedance is independent of the thickness of the substrate coupled edge and broadside coupled CPW and Stripline.
    [Show full text]
  • Transversely Compact Single-Ended and Balanced Bandpass Filters with Source–Load-Coupled Spurlines
    electronics Article Transversely Compact Single-Ended and Balanced Bandpass Filters with Source–Load-Coupled Spurlines Fang Yan 1,*, Yong Mao Huang 2 , Tao Huang 2, Shuai Ding 3 , Kenian Wang 1 and Maurizio Bozzi 4 1 Center of Airworthiness, Civil Aviation University of China, Tianjin 300300, China; [email protected] 2 School of Electrical and Electronic Information, Xihua University, Chengdu 610039, China; [email protected] (Y.M.H.); [email protected] (T.H.) 3 Institute of Applied Physics, and School of Physical Electronics, University of Electronic Science and Technology of China, Chengdu 610054, China; [email protected] 4 Department of Electrical, Computers and Biomedical Engineering, University of Pavia, 27100 Pavia, Italy; [email protected] * Correspondence: [email protected]; Tel.: +86-158-229-69896 Received: 18 March 2019; Accepted: 6 April 2019; Published: 10 April 2019 Abstract: Multi-function wireless systems demand multi-channel transmit/receive (TR) modules, particularly as multiple functions are required to operate simultaneously. In each channel, passive components, including bandpass filters, must be compact, or at least transversely compact; thus, the entire circuitry of the channel will be slender, and consequently multiple channels can be parallel-arranged conveniently. In this work, single-ended and balanced bandpass filters for multi-channel applications are presented. As a unique resonator, the U-shaped stepped impedance resonator (USIR) can achieve size miniaturization compared with its corresponding uniform impedance resonator (UIR) counterpart. Hence, with the utilization of USIRs, the proposed bandpass filters are able to acquire compact transverse sizes. Moreover, by using the source–load coupling scheme, two transmission zeros (TZs) are respectively generated at the lower and upper sides of the passbands, which is useful for improvement of the selectivity performance.
    [Show full text]