DOCSLIB.ORG

Synthesis Techniques for Active RC Filters Using Operational Amplifiers

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text

Load more

SYNTHESIS TECHNIQUES FOR ACTIVE RC FILTERS USING OPERATIONAL AMPLIFIERS by He man i Mationg Jov_e\r United States Naval Postgraduate School 4 2 V 2 THESIS SYNTHESIS TECHNIQUES FOR ACTIVE RC FILTERS USING OPERATIONAL AMPLIFIERS by Hernani Mationg Jover June 1970 Tkl& document k<u bzzn appnjovtd ^on pabtic <*e- lexuz and 6aZz; lti> (tu&vLbution ii> unturuXzd. T136104 Synthesis Techniques for Active RC Filters Using Operational Amplifiers by Hernani Mationg Jover Lieutenant, Philippine Navy B.S., Philippine Military Academy, 1962 Submitted in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE IN ELECTRICAL ENGINEERING from the NAVAL POSTGRADUATE SCHOOL June 1970 I 'OSTGRADUATE SCHOOL 3Y, CALIF. 93940 ABSTRACT The stimulus provided by the trend towards microminiaturization has generated considerable interest in active RC filters utilizing operational amplifiers. A comprehensive and unified presentation of the many different techniques to synthesize such filters is made along the lines of modern filter theory in this thesis. TABLE OF CONTENTS I. INTRODUCTION 15 A. DISADVANTAGES OF INDUCTORS 15 B. DEFECTS OF PASSIVE RC FILTERS 16 C. EVOLUTION OF THE ACTIVE RC FILTER 16 D. ADVANTAGES OF THE OPERATIONAL AMPLIFIER 17 E. PREVIEW AND PURPOSE 18 II. MODERN FILTER THEORY 19 A. HISTORY AND EVOLUTION 19 B. TYPES OF FILTERS 2 C. THE FILTER DESIGN PROBLEM 21 D. FILTER CHARACTERISTICS 24 1. Butterworth Class 2 5 2. Chebyshev Class 26 3. Bessel Class 33 4. Comparison of Classes 34 E. FREQUENCY TRANSFORMATIONS 34 F. FREQUENCY SCALING 39 G. THE FILTER DESIGN PROCEDURE 39 H. EXAMPLES 42 III. THE OPERATIONAL AMPLIFIER 53 A. DEFINITION 53 B. ANALYSIS 55 C. NATHAN'S MATRIX ANALYSIS 60 IV. INFINITE -GAIN SINGLE -FEEDBACK REALIZATIONS 61 A. THEORETICAL DEVELOPMENT 61 B. BRADLEY AND McCOY [1952] 66 C. MATHEWS AND SEIFERT [1955] 70 D. PAUL [1963] 81 E. HAKIM [1964] 92 F. MUIR AND ROBINSON [1968] 102 G. ADVANTAGES AND DISADVANTAGES 105 V. INFINITE -GAIN MULTIPLE -FEEDBACK REALIZATIONS 107 A. THEORETICAL DEVELOPMENT 107 B. RAUCH AND NICHOLS [1956] 110 C. BRIDG MAN AND BREN NAN [195 7] 112 D. WADHWA [19,62] 116 E. FOSTER [1965] 121 F. HOLT AND SEWELL [1965] 126 G. ADVANTAGES AND DISADVANTAGES 132 VI. INFINITE -GAIN GENERAL REALIZATION TECHNIQUES 136 A. LOVERING [1965] 136 B. BRUGLER [1966] 142 C. ADVANTAGES AND DISADVANTAGES 148 VII. INFINITE-GAIN STATE-SPACE REALIZATIONS 150 A. THEORETICAL DEVELOPMENT 150 B. KERWIN, HUELSMAN, AND NEWCOMB [1967] 155 C. HOLLENBECK [1969] 162 D. SALERNO [1969] 167 E. TOW [1969] 173 F. ADVANTAGES AND DISADVANTAGES 184 VIII. CONCLUSION 185 APPENDIX A. TOW'S FREQUENCY TRANSFORMATION PROCEDURE 187 APPENDIX B. COMPUTER PROGRAM 1 190 APPENDIX C. NATHAN'S METHOD OF MATRLX ANALYSIS 192 BIBLIOGRAPHY 195 INITIAL DISTRIBUTION LIST 199 FORM DD 1473 20 1 LIST OF TABLES I. Table 2-1. The Butterworth Polynomials 2 7 II. Table 2-2. Roots of the Butterworth Polynomials 2 7 III. Table 2-3. Polynomials for Chebyshev Filters 30 IV. Table 2-4. Roots of Chebyshev-derived Polynomials 31 V. Table 2-5. The Bessel Polynomials 35 VI. Table 2-6. Roots of the Bessel Polynomials 35 VII. Table 2-7. Percentage Overshoot and Rise Time of the 37 Three Filter Classes VIII. Table 4-1. Some Transfer Functions Realizable by 84 Figure 4-13 DC. Table 4-2. Transfer Admittance Relationship of the 84 Three Type 1 T-Networks X. Table 5-1. Normalized Capacitor Values for Butterworth 125 Filter LIST OF ILLUSTRATIONS 1. Figure 2-1. Ideal magnitude and phase characteristics of 22 the four different filter types 2. Figure 2-2. Attenuation characteristics of the four filter 23 types 3. Figure 2-3. Butterworth low-pass amplitude responses for 28 various values of n 4. Figure 2-4. A fifth-order Chebyshev approximation to a 32 low-pass filter 5. Figure 2-5. Normalized magnitude responses of various 36 fifth-order filters 6. Figure 2-6. Magnitude vs Frequency Plot of Filter 43 Transfer Function of Example 2-1 7. Figure 2-7. Magnitude vs Frequency Plot of Filter 45 Transfer Function of Example 2-2 8. Figure 2-8. Magnitude vs Frequency Plot of Filter 47 Transfer Function of Example 2-3 9. Figure 2-9. Magnitude vs Frequency Plot of Filter 48 Transfer Function of Example 2-4 10. Figure 2-10. Magnitude vs Frequency Plot of Filter 50 Transfer Function of Example 2-5 11. Figure 2-11. Magnitude vs Frequency Plot of Filter 52 Transfer Function of Example 2-6 12. Figure 3-1. Circuit model for the differential-input 54 type of operational amplifier 13. Figure 3-2. Idealized model of the differential-input 54 type of operational amplifier 14. Figure 3-3. Common circuit symbols for the 56 operational amplifier 15. Figure 3-4. Fundamental inverting amplifier circuit 56 16. Figure 3-5. Complex linear feedback circuit 59 9 Z 17. Figure 3-6. Feedback circuit with neither input to the 59 operational amplifier grounded 18. Figure 4-1. Basic single-feedback active filter 62 configuration 19. Figure 4-2 . Differential-input operational amplifier 62 using resistors for input and feedback elements 20. Figure 4-3. Single-ended operational amplifier in 65 basic single-feedback configuration 21. Figure 4-4. Active network configuration of Bradley 65 and McCoy 22. Figure 4-5. Transfer impedance networks from the table 69 of Bradley and McCoy 23. Figure 4-6. Circuit realization of Example 4-1 71 24. Figure 4-7. Active network configuration of Mathews 71 and Seifert 25. Figure 4-8. Location of poles and zeros for 2-terminal 73 RC network configuration 26. Figure 4-9. Second Foster form realization of an RC 73 admittance function 27. Figure 4-10. Circuit realization of y (s) and y (s) 78 1 2, Bl 1 IB 1 ?8 28. Figure 4-11. Circuit realization of y (s) and y 11DO (s) 1 dZ 1 IB/ 29. Figure 4-12. Circuit realization of Example 4-2 80 30. Figure 4-13. Paul's active network configuration 82 31. Figure 4-14. Type 1 T-Networks for Paul's configuration 83 32. Figure 4-15. Type 2 T-Network for Paul's configuration 87 33. Figure 4-16. Type 3 Network for Paul's configuration 87 34. Figure 4-17. Paul's circuit to simulate 89 - V (s)A.(s) = 1/(1 + s T ) o 1 10 35. Figure 4-18. Paul's circuit to simulate 89 2 2 - V (s)A, (s) = 1/(1 + k 2s T + s T ) o 1 1 36. Figure 4-19. Circuit realization of Example 4-3 91 37. Figure 4-20. Hakim's active network configuration 97 4-21. 99 38. Figure Circuit realization of y (s) and y, , D1 (s) IZdI 1 Id 1 39. Figure 4-22. Circuit realization of y (s) and y (s) 99 1 2 B2 1 1B2 40. Figure 4-23. Circuit realization of Example 4-4 101 41. Figure 4-24. Active network configuration of Muir and 103 Robinson 42. Figure 4-2 5. Basic circuit block used in triple amplifier 103 realization of transfer functions 43. Figure 4-26. Circuit realization of Example 4-5 106 44. Figure 5-1. General infinite-gain multiple-feedback 108 configuration 45. Figure 5-2. Second-order prototype of multiple- 109 feedback configuration * 46. Figure 5-3. Second-order low-pass filter network of 109 Rauch and Nichols 47. Figure 5-4. Circuit realization of Example 5-1 113 48. Figure 5-5. High-pass active network configuration 113 of Bridgman and Brennan 49. Figure 5-6. Bandpass active network configurations of 115 Bridgman and Brennan 50. Figure 5-7. Wadhwa's third-order active network 117 configuration 51. Figure 5-8. Wadhwa's configuration to simulate 119 3 2 H(s) = - a /(b s +b s +b s + 1) Q 3 2 x 52. Figure 5-9. Wadhwa's active network configuration 12 3 2 to simulate H(s) = - a,s/(b s + b s + b.s + 1) 11 53. Figure 5-10. Wadhwa's active network configuration 120 2 3 2 to simulate H(s) = - as /(b s + b s + b s + 1) c» O c* X 54. Figure 5-11. Third-order Rauch active filter 123 123 55. Figure 5-12 . Circuit realization of Example 5-3 56. Figure 5-13. Configuration of Holt and Sewell 12 7 57. Figure 5-14. Active section of Holt and Sewell 127 58. Figure 5-15. Active network of Holt and Sewell to 127 2 2 realize H(s) = (s + A s + A )/(s +bs+b) 59. Figure 5-16. Network realization of passive section 133 60. Figure 5-17. Circuit realization of Example 5-4 134 61. Figure 6-1. Lovering's active network configuration 137 62. Figure 6-2. Circuit realization of Example 6-1 141 63. Figure 6-3. Circuit realization of Example 6-2 141 64. Figure 6-4. Brugler's active network configuration 143 65. Figure 6-5. Circuit realization of Example 6-3 146 66. Figure 6-6. Circuit realization of Example 6-4 146 67. Figure 7-1. Signal flow graph of general n -order 153 open-circuit voltage transfer function 68. Figure 7-2. A summer and an integrator 154 69. Figure 7-3. Signal flow graph of general second-order 157 open-circuit voltage transfer function 70. Figure 7-4. Second-order building-block network 158 of Kerwin, Huelsman, and Newcomb 71. Figure 7-5. First-order lag and lead networks 163 72. Figure 7-6. A universal hybrid active filter 164 12 73. Figure 7-7. Schematic representation of Salerno's 169 realization of the general second-order transfer function 74.
Recommended publications
  • Experiment 5 Resonant Circuits and Active Filters

    Experiment 5 Resonant Circuits and Active Filters

    Introductory Electronics Laboratory Experiment 5 Resonant circuits and active filters Now we return to the realm of linear analog circuit design to consider the final op-amp circuit topic of the term: resonant circuits and active filters. Two-port networks in this category have transfer functions which are described by linear, second-order differential equations. First we investigate how a bit of positive feedback may be added to our repertory of linear op-amp circuit design techniques. We consider a negative impedance circuit which employs positive feedback in conjunction with negative feedback. This sort of circuit is found in a wide variety of linear op-amp applications including amplifiers, gyrators (inductance emulators), current sources, and, in particular, resonant circuits and sinusoidal oscillators. Next we switch topics to consider the archetypal resonant circuit: the LC resonator (inductor + capacitor). We use this circuit to define the resonant frequency and quality factor for a second-order system, and we investigate the frequency and transient responses of a high-Q, tuned circuit. We then introduce the general topic of second-order filters: resonant circuits with quality factors of around 1. We describe the behavior of second-order low-pass, high- pass, and band-pass filters. Finally, we implement such filters using linear op-amp circuits containing only RC combinations in their feedback networks, eliminating the need for costly and hard-to-find inductors. The filters’ circuitry will employ positive as well as negative feedback to accomplish this feat. We discuss some of the tradeoffs when selecting the Q to use in a second-order filter, and look at Bessel and Butterworth designs in particular.
  • Theory and Techniques of Network Sensitivity Applied to Electrical Device Modelling and Circuit Design

    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.
  • 6 Ghz RF CMOS Active Inductor Band Pass Filter Design and Process Variation Detection

    6 Ghz RF CMOS Active Inductor Band Pass Filter Design and Process Variation Detection

    Wright State University CORE Scholar Browse all Theses and Dissertations Theses and Dissertations 2014 6 GHz RF CMOS Active Inductor Band Pass Filter Design and Process Variation Detection Shuo Li Wright State University Follow this and additional works at: https://corescholar.libraries.wright.edu/etd_all Part of the Electrical and Computer Engineering Commons Repository Citation Li, Shuo, "6 GHz RF CMOS Active Inductor Band Pass Filter Design and Process Variation Detection" (2014). Browse all Theses and Dissertations. 1386. https://corescholar.libraries.wright.edu/etd_all/1386 This Thesis is brought to you for free and open access by the Theses and Dissertations at CORE Scholar. It has been accepted for inclusion in Browse all Theses and Dissertations by an authorized administrator of CORE Scholar. For more information, please contact [email protected]. 6 GHz RF CMOS Active Inductor Band Pass Filter Design and Process Variation Detection A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in Engineering By SHUO LI B.S., Dalian Jiaotong University, China, 2012 2014 WRIGHT STATE UNIVERSITY WRIGHT STATE UNIVERSITY GRADUATE SCHOOL July 1, 2013 I HEREBY RECOMMEND THAT THE THESIS PREPARED UNDER MY SUPERVISION BY Shuo Li ENTITLED “6 GHz RF CMOS Active Inductor Band Pass Filter Design and Process Variation Detection” BE ACCEPTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF Master of Science in Engineering ___________________________ Saiyu Ren, Ph.D. Thesis Director ___________________________ Brian D. Rigling, Ph.D. Chair, Department of Electrical Engineering Committee on Final Examination ___________________________ Saiyu Ren, Ph.D. ___________________________ Raymond Siferd, Ph.D.
  • Synthesis of Multiterminal RC Networks with the Aid of a Matrix

    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.
  • Multi-Pole Bandwidth Enhancement Technique for Transimpedance

    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.
  • Chapter 15: Active Filter Circuits

    Chapter 15: Active Filter Circuits

    CHAPTER 15: ACTIVE FILTER CIRCUITS 1 Contents 15.1 First-Order Low-Pass and High-Pass Filters 15.2 Scaling 15.3 Op Amp Bandpass and Bandreject Filters 15.4 High Order Op Amp Filters 15.5 Narrowband Bandpass and Bandreject Filters Electronic Circuits, Tenth Edition J ames W. Nilsson | Susan A. Riedel 2 15.1 1st-Order Low-Pass and High-Pass Filters • Active filters consist of op amps, resistors, and capacitors. • They overcome many of the disadvantages associated with passive filters. A first-order low-pass filter. A first-order low-pass filter. A general op amp circuit. • At very low frequencies, the capacitor acts like an open circuit, and the op amp circuit acts like an amplifier with a gain. • At very high frequencies, the capacitor acts like a short circuit, thereby connecting the output of the op amp circuit to ground. Electronic Circuits, Tenth Edition J ames W. Nilsson | Susan A. Riedel 3 15.1 1st-Order Low-Pass and High-Pass Filters Transfer function for the circuit 1 ‖ Where and = The gain in the passband, K, is set by the ratio R2/R1. The op amp low-pass filter thus permits the passband gain and the cutoff frequency to be specified independently. Electronic Circuits, Tenth Edition J ames W. Nilsson | Susan A. Riedel 4 15.1 1st-Order Low-Pass and High-Pass Filters • Bode plot (1) uses a logarithmic axis, instead of using a linear axis for the frequency values (2) plotted in decibels (dB), instead of plo tting the absolute magnitude of the tra nsfer function vs.
  • Active Damping of Oscillations in LC-Filter for Line Connected, Current Controlled, PWM Voltage Source Converters HERNES Magnar

    Active Damping of Oscillations in LC-Filter for Line Connected, Current Controlled, PWM Voltage Source Converters HERNES Magnar

    Active damping of oscillations in LC-filter for line connected, current controlled, PWM voltage source converters HERNES Magnar Active damping of oscillations in LC-filter for line connected, current controlled, PWM voltage source converters Olve Mo, Magnar Hernes, Kjell Ljøkelsøy SINTEF ENERGY RESEARCH Sem Sælands vei 11 7465 Trondheim, Norway Phone: +47 73 59 72 00 [email protected] [email protected] [email protected] http://www.energy.sintef.no/ Keywords Converter control, Power Quality Abstract Presented is a method for active damping of oscillations between line reactance and filter capacitors in LC-filter for line connected current controlled pulse width modulated (PWM) voltage source converters. The idea is to include closed loop feedback control that controls the capacitor voltage oscillations to zero by adding damping components to the current references. The voltage oscillations are calculated from manipulated measured filter capacitor voltages (using phase locked loop (PLL), Park- and inverse Park-transformation, low pass filtering and summation). The advantage of such an approach is that the higher oscillation frequency components can be controlled independently of remaining converter control. It is only the higher frequency components that are controlled by this additional closed loop voltage control. Further, additional measurements and increased converter rating are not required. Simulations and measurements presented in this paper show that the method works as intended. If active damping is implemented, then the voltage quality at the point of converter connection is maintained also in cases were filter oscillations is to be expected when the LC-filter is introduced. Introduction The basis for the discussion is a current controlled, line connected, PWM voltage source converter as shown in Figure 1 (used for instance as active rectifier / inverter, STATCOM or active filter).
  • A Review and Modern Approach to LC Ladder Synthesis

    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.
  • Network Synthesis Using Nullators and Nora.Tors

    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.
  • Circuit Analysis and Synthesis Telecommunication Engineering

    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.
  • Synthesis of Filters for Digital Wireless Communications

    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.
  • Active Network Synthesis Using Operational Amplifiers

    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.