DOCSLIB.ORG

Ee217 Project

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Ee217 Project 1 An Analytical Approach to Broadband Matching David Sobel, Johan Vanderhaegen Abstract— The purpose of this project is to study differ- ent broadband matching techniques for microwave ampli- fiers. Two different methodologies for broadband amplifier design are developed and employed. The first method in- volves the design of a 6 dB/octave roll-up filter to com- pensate for the 6 dB/octave roll-off inherent to the active device. The second method seeks a closed form solution to the gain-matching problem with the use of second order matching networks. For each technique a two-octave gain- compensated amplifier is designed. I. Introduction HE ideal microwave amplifier would have constant Tgain and good input matching over the desired fre- Fig. 1. Broadband matching problem. quency bandwidth. Conjugate matching will give maxi- mum gain at the center of the band but results in unpre- dictable bandwidth and ripple. Another problem is the method is the use of two element matching networks. 6 dB/octave roll-off of S . Some of the common ap- 21 II. Network synthesis of sloped bandpass filters proaches to this problem| are| listed below[1] ; in each case an improvement in bandwidth is achieved only at the ex- This theory[2] assumes the transistor to be unilateral, pense of gain, complexity or other factors. so that the input and output networks can be designed seperately. In order to determine whether a transistor can A. Commonly used broadband techniques be considered unilateral from the standpoint of transducer Compensated matching networks: Input and output net- power gain, the unilateral figure of merit u can be used : • works can be designed to compensate for the gain roll-off in S21 , but generally at the expense of the input and output S S S S | | u = 11 22 12 21 (1) match. | | | 2 | | | | |2 Resistive matching networks: Good input and output 1 S11 1 S22 • − | | − | | matching can be obtained by using resitive matching net- If the transistor can be considered as unilateral, the in- works, with a corresponding loss in gain and increase in put can be approximated by a series RC-network and the noise figure. output by a parallel RC-network. In the case of discrete Negative feedback: Negative feedback can be used to flat- • transistor, inductors representing leads have to be added. ten the gain response of the transistor, improve the input and output match, and improve the stability of the device. A. General lumped broadband matching theory Amplifier bandwidths in excess of a decade are possible with this method, at the expense of gain and noise figure. Consider the broadband matching problem in figure 1, Balanced amplifiers: Two amplifer having 90◦ couples where N denotes a passive lossless matching network that • at their input and output can provide good matching over has to match ZL to R. Then an octave bandwidth, or more. The gain is equal to that 2 2 2 2 G(ω ) = S21(jω) = 1 S11(jω) = 1 S22(jω) of a single amplifier, however, and the design requires two | | − | | − | | transistors and twice the DC power. (2) Distributed amplifiers: Several transistors are cascaded • or (using analytic continuation) together along a transmission line, giving good gain, and 2 2 G( s ) = 1 S22(s) (3) noise figure over a wide bandwidth. The circuit is large, − − | | and does not give as much gain as a cascade amplifier with One can prove[2] that the same number of stages. Z2(s) ZL( s) B. This project S22(s) = − − (4) Z2(s) + ZL(s) The purpose of this project is to study different method- ologies to design matching networks that compensate for The poles of S22(s) in the right half plane are the poles of the 6 dB/octave roll-off of S21 . One method consists of ZL( s), since the other terms in equation (4) are positive- network synthesis of a sloped| bandpass| filter, i.e. a filter real− and cannot have poles in the right half-plane. Let with a 6 dB/octave roll-up over the passband. The second si (i = 1, 2, . , m) denote the the poles of ZL( s) (real − 2 or complex conjugate pairs). Define B(s) as low frequency 2 GHz high frequency 8 GHz m s si ripple 1 dB B(s) = − (5) Y s + s filter order 2 i=1 i TABLE I Then B(s) has only poles in the left half-plane, is real for Broadband amplifier specifications. real s and B(s)B( s) = 1 (B(s) is an all-pass function). Define then ρ(s) as− ρ(s) = B(s)S22(s) (6) would perform matching and 6 dB/octave roll-up at the same time. G(ω2) can be specified as : This reflection coefficient ρ(s) has only poles in the left 2 half-plane. Substituting equation (6) in equations (3) and 2 Kn (f/fc) G((2πf) ) = · 2 (14) (4) yields 2 f f f0 1 + ε Cn B f0 − f 2rL(s)B(s) Z2(s) = ZL(s) (7) f0 is the center frequency, B is the bandwidth. The B(s) ρ(s) − 2 − maximum ripple is given by 1/(1 + ε ). Kn and fc are ZL(s) + ZL( s) proportionality constants so that 0 G(ω2) 1 for all rL(s) = − (8) ≤ ≤ 2 frequencies. Cn(x) are the Chebychev polynomials of the ρ(jω) 2 = 1 G(ω2) (9) first kind : | | − 2 For ρ(s) to be real, it is necessary that 0 G(ω ) 1. T0(x) = 1 (15) Once G(ω2) is given, ρ(s) can be determined≤ by spectral≤ T1(x) = x (16) factorisation (and using analytic continuation) : 2 T2(x) = 2x 1 (17) 2 − 2 N(s ) ρ(s)ρ( s) = 1 G( s ) = 2 (10) The equivalent input network of the transistor consists − − − M(s ) of a series RC-network. This means that, using the termi- nology of section II-A, N(s2) and M(s2) are respectively the numerator and the 2 denominator of G(s ), and they both can be decomposed 1 1 + sRCi as : ZL = Ri + = (18) sCi Ci N(s2) = n(s)n( s) (11) For the EE217 transistor at high frequencies : − M(s2) = m(s)m( s) (12) − Ri = RI + RS = 11.25 Ω (19) These n(s) and m(s) are formed by the left half-plane Ci = CGS = 0.31 pF (20) zeros of respectively N(s) and M(s). Therefore : Using the specifications in table I and going through the n(s) steps described in section II-A, Z2(s) turns out to be : ρ(s) = (13) ±m(s) 2s4 + 2.71s3 + 8.75s2 + 3.16s + 2 Z2(s) = (21) So, given G(ω2), ρ(s) can be determined by spectral fac- 0.630s3 + 0.283s2 + 0.179s torisation. If also Z (s) is given, then Z (s) can be deter- 11.2 1 L 2 = 3.17s + + (22) mined by using equation (8). Under certain conditions[2] s 0.156 1 for ρ(s), a passive network can be derived that implements s + 1.82 s + 2.87 Z2(s). This is a second order chebychev bandpass filter with a B. Input lossless matching 6 dB/octave roll-up over the passband. All the numbers Examining the unilateral figure of merit u for the EE217 are normalized to a center pulsation ω0 of 1 rad/s. The transistor (figure 6), this transistor can be considered corresponding ciruit is given in figure 2 and the element highly non-unilateral (or bilateral). This means first of all values are given in table II. Note that CGS fullfills the that there is a risk of making the transistor unstable. Fur- function of C1, R1 is the input resistance Ri of the transis- thermore the input and ouput matching networks cannot tor. R2 is the source resistance. be designed independently. The input matching network expects a source resistance The reason that u is so high for this transistor, is that R2 of 32.3 Ω. This can be converted to 50 Ω by an ideal S11 is so close to 1. This also means that we can get a transformer. The ideal transformer can be removed by in- considerable gain from the input network. Taking all this troducing an extra element (L2) and changing the other into account, we decided to add only an input match, that element values. Table III gives the final input matching 3 (a) (b) Fig. 2. Second order chebychev bandpass filter with a 6 dB/octave Fig. 3. General form of a 2-element L-match (a) and π-match (b) roll-up over the passband. networks. C1 310 fF L1 1.42 nH L12 2.86 nH C2 1.95 pF L2 0 nH R2 32.3 Ω TABLE II Broadband matching network. (a) (b) network. This network can be obtained by equating the Z-matrix of the network in table II with an ideal trans- Fig. 4. Acheivable impedances of two inductor L-match (a) and former and the Z-matrix of a similar network without an CL π-match (b). The shaded regions correspond to unattainable impedances. ideal transformer but with an additional inductor L2. The final circuit, including the transistor, is shows in figure 7. Figure 8 shows the simulated results this circuit to provide exact gain compensation at the band edges; a and confirms the specifications given in table I. byproduct of this process is a flattened gain response over the bandwidth of interest. C. Conclusion A. Topology Selection Network synthesis of sloped bandpass filters is an inter- esting technique to compensate for the 6 dB/octave roll- The circuit topology used in the mathematical derivation off of the transistor.
Load more

Recommended publications
  • Theory and Techniques of Network Sensitivity Applied to Electrical Device Modelling and Circuit Design
    r THEORY AND TECHNIQUES OF NETWORK SENSITIVITY APPLIED TO ELECTRICAL DEVICE MODELLING AND CIRCUIT DESIGN • A thesis submitted for the degree of Doctor of Philosophy, in the Faculty of Engineering, University of London by Pedro Antonio Villalaz Communications Section, Department of Electrical Engineering Imperial College of Science and Technology, University of London September 1972 SUMMARY Chapter 1 is meant to provide a review of modelling as used in computer aided circuit design. Different types of model are distinguished according to their form or their application, and different levels of modelling are compared. Finally a scheme is described whereby models are considered as both isolated objects, and as objects embedded in their circuit environment. Chapter 2 deals with the optimization of linear equivalent circuit models. After some general considerations on the nature of the field of optimization, providing a limited survey, one particular optimization algorithm, the 'steepest descent method' is explained. A computer program has been written (in Fortran IV), using this method in an iterative process which allows to optimize the element values as well as (within certain limits) the topology of the models. Two different methods for the computation of the gradi- ent, which are employed in the program, are discussed in connection with their application. To terminate Chapter 2 some further details relevant to the optimization procedure are pointed out, and some computed examples illustrate the performance of the program. The next chapter can be regarded as a preparation for Chapters 4 and 5. An efficient method for the computation of large, change network sensitivity is described. A change in a network or equivalent circuit model element is simulated by means of an addi- tional current source introduced across that element.
    [Show full text]
  • Synthesis of Multiterminal RC Networks with the Aid of a Matrix
    SNTHES IS OF MULT ITER? INAL R C ETWO RKS WITH TIIF OF A I'.'ATRIX TRANSFOiATIO by 1-CHENG CHAG A THESIS submitted to OREGO STATF COLLEOEt in partial fulfillment of the requirements for the degree of !1ASTER OF SCIENCE Jurie 1961 APPROVED: Redacted for privacy Associate Professor of' Electrical Erigineerthg In Charge of Major Re6acted for privacy Head of the Department of Electrical Engineering Redacted for privacy Chairman of School Graduate Committee / Redacted for_privacy________ Dean of Graduate School Date thesis is presented August 9, 1960 Tyred by J nette Crane A CKNOWLEDGMENT This the3ls was accomplished under the supervision cf Associate professor, Hendrick Oorthuys. The author wishos to exnress his heartfelt thanks to Professor )orthuys for his ardent help and constant encourap;oment. TABL1 OF CONTENTS page Introductior , . i E. A &eneral ranfrnat1on Theory for Network Synthesis . 3 II. Synthesis of Multitermin.. al RC etworks from a rescribec Oren- Circuit Iì'ipedance atrix . 9 A. Open-Circuit Impedance latrix . 10 B. Node-Admittance 1atries . 11 C, Synthesis Procedure ....... 16 III. RC Ladder Synthesis . 23 Iv. Conclusion ....... 32 V. ii11io;raphy ...... * . 35 Apoendices ....... 37 LIST OF FIGURES Fig. Page 1. fetwork ytheszing Zm(s). Eq. (2.13) . 22 2 Alternato Realization of Z,"'). 22 Eq. (2.13) .......... ietwor1?. , A Ladder ........ 31 4. RC Ladder Realization of Z(s). r' L) .Lq. \*)...J.......... s s . s s S1TTHES I S OF ULT ITERM INAL R C NETWORKS WITH THE AID OF A MATRIX TRANSFOMATIO11 L'TRODUCT ION in the synthesis of passive networks, one of the most Imoortant problems is to determine realizability concU- tions.
    [Show full text]
  • Multi-Pole Bandwidth Enhancement Technique for Transimpedance
    Multi-Pole Bandwidth Enhancement Technique for Transimpedance Amplifiers Behnam Analui and Ali Hajimiri California Institute of Technology, Pasadena, CA 91125 USA Email: [email protected] Abstract quencies. Capacitive peaking [3] is a variation of the A new technique for bandwidth enhancement of ampli- same idea that can improve the bandwidth. fiers is developed. Adding several passive networks, A more exotic approach to solving the problem was which can be designed independently, enables the control proposed by Ginzton et al using distributed amplification of transfer function and frequency response behavior. [4]. Here, the gain stages are separated with transmission Parasitic capacitances of cascaded gain stages are iso- lines. Although the gain contributions of the several lated from each other and absorbed into passive net- stages are added together, the parasitic capacitors can be works. A simplified design procedure, using well-known absorbed into the transmission lines contributing to its filter component values is introduced. To demonstrate the real part of the characteristic impedance. Ideally, the feasibility of the method, a CMOS transimpedance ampli- number of stages can be increased indefinitely, achieving fier is implemented in 0.18mm BiCMOS technology. It an unlimited gain bandwidth product. In practice, this achieves 9.2GHz bandwidth in the presence of 0.5pF will be limited to the loss of the transmission line. Hence, photo diode capacitance and a trans-resistance gain of the design of distributed amplifiers requires careful elec- 0.6kW, while drawing 55mA from a 2.5V supply. tromagnetic simulations and very accurate modeling of transistor parasitics. Recently, a CMOS distributed 1. Introduction amplifier was presented [7] with unity-gain bandwidth of The ever-growing demand for higher information trans- 5.5 GHz.
    [Show full text]
  • A Review and Modern Approach to LC Ladder Synthesis
    J. Low Power Electron. Appl. 2011, 1, 20-44; doi:10.3390/jlpea1010020 OPEN ACCESS Journal of Low Power Electronics and Applications ISSN 2079-9268 www.mdpi.com/journal/jlpea Review A Review and Modern Approach to LC Ladder Synthesis Alexander J. Casson ? and Esther Rodriguez-Villegas Circuits and Systems Research Group, Electrical and Electronic Engineering Department, Imperial College London, SW7 2AZ, UK; E-Mail: [email protected] ? Author to whom correspondence should be addressed; E-Mail: [email protected]; Tel.: +44(0)20-7594-6297; Fax: +44(0)20-7581-4419. Received: 19 November 2010; in revised form: 14 January 2011 / Accepted: 22 January 2011 / Published: 28 January 2011 Abstract: Ultra low power circuits require robust and reliable operation despite the unavoidable use of low currents and the weak inversion transistor operation region. For analogue domain filtering doubly terminated LC ladder based filter topologies are thus highly desirable as they have very low sensitivities to component values: non-exact component values have a minimal effect on the realised transfer function. However, not all transfer functions are suitable for implementation via a LC ladder prototype, and even when the transfer function is suitable the synthesis procedure is not trivial. The modern circuit designer can thus benefit from an updated treatment of this synthesis procedure. This paper presents a methodology for the design of doubly terminated LC ladder structures making use of the symbolic maths engines in programs such as MATLAB and MAPLE. The methodology is explained through the detailed synthesis of an example 7th order bandpass filter transfer function for use in electroencephalogram (EEG) analysis.
    [Show full text]
  • Network Synthesis Using Nullators and Nora.Tors
    NETWORK SYNTHESIS USING NULLATORS AND NORA.TORS By FUN YE I/ Bachelor of Science National Taiwan University Taipei, Taiwan 1964 Master of Science Oklahoma State University Stillwater, Oklahoma 1968 Submitted to the Faculty of the Graduate College of the Oklahoma State University in partial fulfillment of the requirements for the Degree of DOCTOR OF PHILOSOPHY May, 1972 c-~/~,o Jq7~0 Y3 7 w ttop~ . .i .. ' r l ' ' ,. : , ..... OKLAHOMA STATE UNIVERSITY LIBRARY AUG 16 1973 NETWORK SYNTHESIS USING NULLATORS AND NORA:TORS Thesis Approved: Dean of the Graduate College ACKNOWLEDGMENTS First of all, I would like to express my sincere gratitude to Dr. Rao Yarlagadda, my thesis adviser, for his guidance and contribu­ tions without which this thesis would not have been possible. I appreciate the assistance and help of Dr .• Daniel D. Lingelbach, the chairman of my committee. I also appreciate the assistance and encouragement of the other members of my committee, 1Dr. Charles M. Bacon and Dr. Joe L. Howard. I owe a special thanks to Mr. Andrew Y. Lee for his interest and suggestions. I would like to appreciate the encouragement of my father, and the understanding and patience of my wife, Lily, during the writing of this thesis. Finally, I gratefully acknowledge the financial support from the National Science Foundation under Projects GK-1722 and GU-3160 during 1my doctoral studies. TABLE OF CONTENTS Chapter Page I. INTRODUCTION 1 1.1 Statement of the Problem. 1 1.2 Review of the Literature 3 1.3 Technical Approach ••• 4 1.4 Organization of the Thesis. 7 II.
    [Show full text]
  • Circuit Analysis and Synthesis Telecommunication Engineering
    Circuit Analysis and Synthesis Telecommunication Engineering Course Program CIRCUIT ANALYSIS AND SYNTHESIS Telecommunication Engineering (3rd Year ) Fall Term 2004/05 Departamento de Electrónica y Electromagnetismo Escuela Superior de Ingenieros. Universidad de Sevilla A ) Instructors: Group I: Óscar Guerra Vinuesa <[email protected]> Room: E2-SO-EE-08 (ESI) Tel.: 954-487378 Group II: Ricardo Carmona Galán <[email protected]> Room: E2-SO-EE-08 (ESI) Tel.: 954-487380 Group III: Rafael Domínguez Castro <[email protected]> Room: E2-SO-EE-08 (ESI) Tel.: 954-487379 Class hours: Group I: Tue. 15:30-17:00 / Thu. 17:45-18:45 / Fri. 19:30-21:00 (Lectures in Spanish) Group II: Tue. 17:15-18:45 / Wed. 19:30-20:30 / Fri. 15:30-17:00 (Lectures in English) Group III: Mon. 15:30-17:00 / Wed. 17:45-18:45 / Thu. 15:30-17:00 (Lectures in Spanish) Office hours: Group I: Tue. 9:00-12:00 / Thu. 9:00-12:00 Group II: Tue. 9:00-12:00 / Wed. 16:30-19:30 Group III: Mon. 16:00-19:00 / Tue. 16:00-19:00 B) Web page http://www.imse.cnm.es/elec_esi/asignat/ASC/index_en.html C) Objectives Learning to analyze and design electronic circuits with passive and active elements. Mastering the realization of continuous-time analog filters. D) Lectures 1. Continuous-time LTI circuit response and representation 1.1 Circuit analysis and synthesis 1.2 Classification 1.3 I/O representation in LTI systems 1.4 Zero-input and zero-state responses 1.5 Natural and forced responses 1.6 Poles and zeros of the transfer function.
    [Show full text]
  • Synthesis of Filters for Digital Wireless Communications
    Synthesis of Filters for Digital Wireless Communications Evaristo Musonda Submitted in accordance with the requirements for the degree of Doctor of Philosophy The University of Leeds Institute of Microwave and Photonics School of Electronic and Electrical Engineering December, 2015 i The candidate confirms that the work submitted is his own, except where work which has formed part of jointly-authored publications has been included. The contribution of the candidate and the other authors to this work has been explicitly indicated below. The candidate confirms that appropriate credit has been given within the report where reference has been made to the work of others. Chapter 2 to Chapter 6 are partly based on the following two papers: Musonda, E. and Hunter, I.C., Synthesis of general Chebyshev characteristic function for dual (single) bandpass filters. In Microwave Symposium (IMS), 2015 IEEE MTT-S International. 2015. Snyder, R.V., et al., Present and Future Trends in Filters and Multiplexers. Microwave Theory and Techniques, IEEE Transactions on, 2015. 63(10): p. 3324- 3360 E. Musonda developed the synthesis technique and wrote the first paper and section IV of the second invited paper. Professor Ian Hunter provided useful editorial comments, suggestions and corrections to the work. Chapter 3 is based on the following two papers: Musonda, E. and Hunter I.C., Design of generalised Chebyshev lowpass filters using coupled line/stub sections. In Microwave Symposium (IMS), 2015 IEEE MTT- S International. 2015. Musonda, E. and I.C. Hunter, Exact Design of a New Class of Generalised Chebyshev Low-Pass Filters Using Coupled Line/Stub Sections.
    [Show full text]
  • Active Network Synthesis Using Operational Amplifiers
    AN ABSTRACT OF THE THESIS OF Ching Hwa Chiang for the Master of Science in (Name) (Degree) Electrical Engineering presented on L 7, ) & 7 (Major) (Date) Title ACTIVE NETWORK SYNTHESIS USING OPERATIONAL AMPLIFIERS Abstract approved Leland . Jensen (Major, rofessor) Three synthesis methods for the realization of the voltage transfer function by means of RC elements and three different active devices are presented. These three devices are a high -gain amplifier, a voltage con- trolled voltage source (VCVS) and a negative immittance converter (NIC). The VCVS and NIC as well as the high - gain amplifier are realized by an operational amplifier. The properties of the operational amplifier are stated. The matrix representation which describes the electrical behavior of this device is defined. The realizations of VCVS and NIC using an operational ampli- fier are derived. Synthesis techniques for these network configurations are developed and investigated. Examples are given for each case followed by experimental results. A Butterworth low -pass function is selected for all three synthesis examples. The actual networks are built. The experimental results of actual networks are analyzed and compared with the theoretical results. A general com- parison of these three different synthesis methods is discussed in the conclusion. ACTIVE NETWORK SYNTHESIS USING OPERATIONAL AMPLIFIERS by Ching Hwa Chiang A THESIS submitted to Oregon State University in partial fulfillment of the requirements for the degree of Master of Science June 1968 APPROVED: ciate Professor fThepartment of Electrical and Elec onics Engineering in charge of major Had of Department of Electrical and Electronics Engineering MEWDean of Graduate School Date thesis is presented ¿2-tz 7 / , G "7 Typed by Erma McClanathan ACKNOWLEDGMENT The author wishes to express his sincere apprecia- tion and gratitude to Professor Leland C.
    [Show full text]
  • Ultra-Wideband Bias-Tee Design Using Distributed Network Synthesis
    This article has been accepted and published on J-STAGE in advance of copyediting. Content is final as presented. IEICE Electronics Express, Vol.* No.*,*-* Ultra-wideband bias-tee design using distributed network synthesis Nam-Tae Kima) Department of Electronic Engineering, Inje University, Gimhae 621-749, Korea a) [email protected] Abstract: This paper presents a design methodology for ultra-wideband bias tees, using a distributed network synthesis considering both RF and DC performance. For the design of bias tees, transfer functions of distributed circuits are offered using equal ripple approximation, and DC current-handling capacity is incorporated into the network synthesis by calculating capacity in terms of the characteristic impedance of a transmission line. A bias-tee circuit with the desired characteristics can be synthesized by properly adjusting the minimum insertion loss (MIL) and ripple of the transfer function with reference to the required performance. As an example, a distributed network synthesis is applied to design a bias tee for ultra-wideband applications. Keywords: Bias tee; network synthesis; ultra-wideband Classification: Microwave and millimeter wave devices, circuits, and systems References [1] G. Aiello and G. Rogerson, “Ultra-wideband wireless systems,” IEEE Microwave Mag., vol. 4, pp.36-47, pp. 36-47, Jun. 2003. [2] B. Minnis, “Decade Bandwidth bias T’s for MIC applications up to 50GHz,” IEEE Trans. Microwave Theory Tech., vol. 35, pp. 597-600, Jun. 1987. [3] P. Bell, N. Hoivik, V. Bright, and Z. Popovic, “Micro-bias-tees using micromachined flip-chip inductors,” IEEE MTT-S Int. Microwave Symp. Dig., Philadelphia, U.S.A., pp.
    [Show full text]
  • ELE 215.3 Network Theory (3-1-2)
    ELE 215.3 Network Theory (3-1-2) Theory Practical Total Sessional 30 20 50 Final 50 - 50 Total 80 20 100 Course Objectives; 1. To provided the basis for formula and solution of network equations. 2. To understand the behavior of network. 3. To develop one – port and two port networks with given network functions Course Contents: 1. Review of Network Analysis (2hrs) Mesh and Nodal-pair ( 2. Circuit Differential Equations (6 hrs) (formulations and solutions) The differential operator, Operational impedance, Formulation of circuit differential equations, Complete response (transient and steady state) of first order differential equations with or without initial conditions, Use of software in solving network different equations 3. Circuit Dynamics (6 hrs) First order RL and RC circuits, Complete response of RL and RC circuit to sinusoidal input, RLC circuit, Step response of RLC circui9t, Response of RLC circuit to sinusoidal inputs, Resonance, Damping factors and Q-factor. 4. Review of Laplace Transform (6 hrs) Definition and properties, Laplace transform of common forcing functions, Initial and final value theorem, Inverse Laplace transform, Partial fraction expansion, Solutions of first order and second order system, RL and RC circuit, RLC circuit, Transient and steady-state responses of network to unit step, unit impulse, ramp and sinusoidal forcing functions. 5. Transfer Functions (3 hrs) Transfer functions of Network system, Poles and Zeros, Time- domain behavior from pole-zero locations, Stability and Routh’s Criteria, Network stability. 6. Fourier Series and Transform (3 hrs) Evaluation of Fourier coefficients for periodic non-sinusoidal waveforms, Fourier Transform, Application of Fourier transforms for non-periodic waveforms.
    [Show full text]
  • A Study of the Synthesis of 3-Port Electrical Filters with Chebyshev Or Elliptic Response Characteristics Bruce Vaughn Smith Iowa State University
    Iowa State University Capstones, Theses and Retrospective Theses and Dissertations Dissertations 1991 A study of the synthesis of 3-port electrical filters with Chebyshev or elliptic response characteristics Bruce Vaughn Smith Iowa State University Follow this and additional works at: https://lib.dr.iastate.edu/rtd Part of the Electrical and Electronics Commons Recommended Citation Smith, Bruce Vaughn, "A study of the synthesis of 3-port electrical filters with Chebyshev or elliptic response characteristics " (1991). Retrospective Theses and Dissertations. 9582. https://lib.dr.iastate.edu/rtd/9582 This Dissertation is brought to you for free and open access by the Iowa State University Capstones, Theses and Dissertations at Iowa State University Digital Repository. It has been accepted for inclusion in Retrospective Theses and Dissertations by an authorized administrator of Iowa State University Digital Repository. For more information, please contact [email protected]. INFORMATION TO USERS This manuscript has been reproduced from the microfilm master. UMI films the text directly from the original or copy submitted. Thus, some thesis and dissertation copies are in typewriter face, while others may be from any type of computer printer. The quality of this reproduction is dependent upon the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleedthrough, substandard margins, and improper alignment can adversely affect reproduction. In the unlikely event that the author did not send UMI a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyright material had to be removed, a note will indicate the deletion. Oversize materials (e.g., maps, drawings, charts) are reproduced by sectioning the original, beginning at the upper left-hand corner and continuing from left to right in equal sections with small overlaps.
    [Show full text]
  • S Reported in Last Year's Research Objectives Is Being Explored in Greater Detail
    XXXI. NETWORK SYNTHESIS Prof. E. A. Guillemin R. O. Duda H. B. Lee, Jr. S. G. Chamberlain A. I. Grayzel W. C. Schwab RESEARCH OBJECTIVES The effectiveness of methods of approach to the synthesis problem as reported in last year's research objectives is being explored in greater detail. The detailed reports given below are specific steps in this evaluation process. The further development of an approach and its implementation will absorb our efforts for some time to come; and it is our expectation that many collateral problems will be generated in the process. Already the results of this work have clarified aspects of network theory which repre- sent gaps in classical linear dynamics. The development of network theory seems to be on the threshold of a new phase that promises to be at least as significant as the one that yielded our present state of accomplishment in synthesis. E. A. Guillemin A. A NORMAL FORM FOR A MATRIX PERTINENT TO RLC NETWORKS WITHOUT MUTUAL INDUCTANCE Guillemin1 has shown how the problem of finding the normal coordinate transforma- tion for a network with an arbitrary loss function can be reduced to that of simultane- ously diagonalizing two matrices, and has indicated the value of this result for a more general approach to network synthesis. Desoer pointed out that the equations for any linear circuit can always be cast in the Peano-Baker form y = Ay + f (1) and showed how the eigenvectors of the matrix A can be identified with modal behavior. Another formulation of the problem, which possesses certain advantages for synthe- sis applications, can be obtained from a combination of these methods.
    [Show full text]