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Inductance Simulation for Microelectronics and Transistorized Loy

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Inductance Simulation for Microelectronics and Transistorized Loy INDUCTANCE SIMULATION FOR MICROELECTRONICS AND TRANSISTORIZED LOY-FREQUENCY ACTIVE GIRATORS by KENNETH RAOUL MORIN B.Sc., Queen's University, Kingston, Ontario, 1961 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE r > . in the Department of Electrical Engineering ¥e accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA October, 1963 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that per• mission for extensive copying of this, thesis for scholarly purposes may be granted by the Head of my Department or by his representatives,, "it is understood that copying, or publi• cation of this thesis for financial gain shall not be allowed without my written permission. Department of Electrical Engineering The University of British Columbia,. Vancouver 8, Canada. Date October 25, 1963 ABSTRACT An inductance can be simulated for microelectronics applications using semiconductor elements (e.g., the "inductance diode"), using circuits containing amplifiers, or using gyrators. The last two methods are considered in this thesis. Several "amplifier methods" have appeared in the literature; these methods are classified into integrating- or differentiatiiig- type circuits, and a differentiating-type circuit is proposed which is believed to be new. Gyrator realization methods are tabulated and compared. An "active gyrator" ("AG") is proposed as a circuit element (it has unequal gyration resistances). The AG behaves much like a gyrator; it can be used to simulate inductance, and an analysis shows that it can be used to make isolators and circulators with a power gain. Methods of realizing an AG with amplifiers are investigated, and an analysis leads to seven 2-amplifier circuits. One of these AG circuits appears "best" for inductance simulation, and this one is investigated experimentally using a transistor circuit. An extensive bibliography of the inductance simulation and gyrator literature is presented. ACKNOWLEDGEMENT The author is indebted to Dr. M.P. Beddoes, the supervising professor of this project, for his help and guidance throughout the course of the project. Thanks are also given to those prof• essors and graduate students who provided helpful discussion, and in particular, to CR. James, for his thorough proof-reading. Acknowledgement is gratefully g^iven to the National Research Council of Canada for the assistance received through a Bursary and a Studentship held by the author during his studies. The work described in this thesis was supported by the Nat-. ional Research Council under Grant BT-68. ix TABLE OP CONTENTS ACKNOWLEDGEMENT ix 1. INTRODUCTION .. ...... c 1 2. INDUCTANCE SIMULATION 5 2.1 Methods for Eliminating, Miniaturizing, and Simulat• ing Inductors . 5 2.2 Classification of the Various "Amplifier Methods" of Inductance Simulation 7 .1 Integrating circuit ..............»•«.<>.. 7 .2 Differentiating circuit 12 2.3 Relationship Between the Various "Amplifier Methods" of Inductance Simulation,and the AG ...... .......... 15 3. GYRATOR AND ACTIVE GYRATOR THEORY AND APPLICATIONS ..... 17 3.1 Survey of Gyrator Literature .«.......<> . 17 3.2 Gyrator Symbols 20 3.3 Definition of an Active Gyrator 24 3.4 The Activity of the Active Gyrator 25 3.5 Applications of the AG 26 .1 Simulation of inductance 26 .2 The AG used as an isolator 27 .3 The AG used as a circulator 29 a) Introduction 29 b) Conditions for circulation , 30 c) Matching 34 d) Power Gains 36 Page 4. CIRCUITS FOB REALIZING ACTIVE GTRATORS 39 4.1 Introduction .*•...........................«««•••..« 39 4.2 Effects of the 2 Types of Circuit Components on the I Matrix . 41 .1 Input conductance ............. 41 .2 Output connections 42 • 3 Negative resistance ..............43 4.3 Design of a 3-^Amplifier AG 43 4.4 Clue for Designing 2-Amplifier AGs 46 4.5 Classification and Preliminary Screening of 2-Amplifier AGs ...... 48 4.6 Results of the Analyses of the 16 Configurations ... 49 5. EXPERIMENTAL RESULTS 52 5.1 Allowance for the Finite Output Impedance of the Amplifiers 52 5.2 Circuit Diagrams for the Prototype AG 55 5.3 Experimental Results 57 .1 Preliminary adjustment of the AG ................. 57 a) Adjustment for Y-^ & 0 ......................... 58 b) Adjustment for Y22 ~ 0 59 .2 Inversion of resistance .....•...«......•••««•.«•« 60 .3 Simulation of inductance ........................ 60 6. CONCLUSION 64 7. BIBLIOGRAPHY ..... 66 7.1 Subject Index to Bibliography ............. ........ 66 7.2 References 68 Page APPENDIX 81 A.l The 4 Possible output Connections for Each Configuration 81 k»2 A Systematic Method of Analysis ........ 82 .1 The first step 84 .2 The second step ................................... 87 LIST OF ILLUSTRATIONS Figure Page 1.1 - Definition of an ideal gyrator ................«... • 1 2.1 - (a) The simple R-C integrator; (b) the operational amplifier integrator 8 2.2 - '•. Simulated inductance using a simple R-C integrating circuit and a pentode tube (grid-leak resistor omitted) .•.«.•.*..........................•«.•.«•»• 8 2.3 - Stern's circuit for a simulated inductance .««•««••. 9 2.4 - Basic circuit used by Holbrook and McKeown. (a) actual circuit; (b) approximate equivalent circuit 10 2.5 - Midgley and Stewart's simulated inductance circuit 12 2.6 - (a) The simple R-C differentiator, and (b) the operational amplifier differentiator, shown with a small resistor R^ connected (to produce v^ ' from "the current x ^) +oeoo<>eoo**w*0*Qoooo»ot>***»+4ri*<t-6-a«-4+ 13 2.7 - Diagram of Towner's artificial inductor .......... 14 2.8 - An inductance simulation circuit which uses the operational amplifier differentiator of Figure 2.6(b) 14 2.9 - Classification of simulated inductances which use amplifier me"fcho.cLs +ooco*e*ioooa9ot>» + Qo«o9904i** + «<> + <r*e- 15 3»1 —• Representative cross section of a field effect tetrode ^ ^ ^ ^ ^ « ^ ^0 « ^ a m o • ^ o ^ o o c« c « o o 0 a « « « » » 0 • * ^ ^ ^ ^ ^ ^ ^ ^ 20 3.2 - Comparison of gyrator realization methods .«...„..«« 21 3.3 - Tellegen's symbol for the ideal gyrator. Sometimes one of the semicircles is omitted (e.g., st57c) «... 22 3.4 - Gyrator symbol proposed by Feldkeller .............. 22 3.5 - Shekel's symbol for the 3-terminal gyrator •»«.«.«.. 23 3.6 - Hogan's symbol for the (microwave) gyrator ......... 24 3.7 — Circuit symbol and equations for the AG ............ 25 3.8 - The AG as an isolator: (a) parallel connected^ and (b) series vi Figure Page 3.9 - Equivalent circuit for the isolator of Figure 3.8(a) 3.10 - A 3-port network made from a 3-terminal device ..... 29 3«11 - The two basic circulator configurations: (a) voltage sources, and (b) current sources ..... » ........•• «.« 31 3012 •=- The first step in deriving the matrix defined in 3.13 - (a) and (b) Input admittances to the circulator shown in Figure 3.11(b); (c) and (d) values of input admittance obtained when an AG is used. The direction of circulation is indicated by the arrow.. 35 3.14 - An application of a circulator. The circle represents a 3-port circulator ........ <» o.......... 37 3.15 - The product Gm "GT ^, as a function of G_/G_ ... 38 ia->c c—>b n m 4.1 - The two components which will be used to build AGss (a) conductance, and (b) ideali'zed voltage amplifier, which has A realj positive or negative 39 4 = 2 •=- Skeleton of the. AG- starting point for each AG design 40 4.3 =• Successive steps taken in the analysis of AG 4.4 - Illustrating the effect of output connections ...... 42 4.5 - Negative resistances using voltage amplifiers .«»«•« 43 4.6 - The start of D 4 o 7 3 ™*CHT1J) X i f X G I* AG!" • ^aa«««-«0*«*»*0e*a«0a««0o4>aA0 4»«a«^i0*« 43 4.8 - Obtaining the voltages +V^+V"2 from the port voltages 46 4.9 => Changing the skeleton of an AG circuit .......»oo.«. 47 4.10 - Summary of 2-amplifier AG circuits ......a... 50 5.1 = The output connections for an amplifier with finite output conductance, G : (a) actual circuit; (b) approximate -equivalent when G^rvG^«Go ......... 52 5.2 - Design sheet for configuration number 8, using the approximation given in Figure 5.1(b) ............... 54 5.3 - Circuit diagram of the Q amplifier ................• 55 vii Figure Page 5.4 - Circuit diagram of the P. amplifier ...........»«•».. 56 5.5 — Schematic diagram of the AG prototype .............. 56 5.6 - Artwork for the printed circuit board (actual size) 57 5.7 - The AG used to invert an impedance Z-^: experimental apparatus 58 5.8 - Experimental results, inversion of resistance ...... 61 5.9 - Experimental results, simulation of inductance; (a) low frequency measurements, Z- ; (b) high frequency measurements, 62 5.10 - Approximate equivalent circuit for the simulated inductance (losses are neglected) 63 A.l - Design sheet used for the investigation of AG circuits 83 A.2 - Design sheet for configuration number 8, D-l- ...... 85 A.3 - Equivalent circuit for finding-1;the "intrinsic terms" • for the configuration D-l- 86 A.4 - Equivalent circuits for finding some of the "amplifier terms" for the configuration D-1-. T matrices are given ................................. 87 A.5 - Design sheet for configuration number 5, D+1+ ...... 90 A.6 - Design sheet for configuration number 6, D+l- ...... 91 A.7 - Design sheet for configuration number 11, D-2+ ..... 92 viii 1. INTRODUCTION There is currently much interest in the making of tiny electronic assemblies. Both resistors and capacitors have quite successfully been miniaturized; however, inductors have not been miniaturized so successfully. Initially, an attempt was made to develop miniature inductances by circuit techniques; but as the work progressed, emphasis shifted to the synthesizing of^ gyrator circuits. Techniques have been described which eliminate the need for inductors by redesign of circuits. Other approaches deal with making miniature inductors* for instance by winding fine wire on a tiny ferrite core.
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