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Shults Robert D 196308 Ms 10 AN INVESTIGATION OF THE INFLUENCE OF CIRCUIT PARAMETERS ON THE OUTPUT WAVESHAPE OF A TUNNEL DIODE OSCILLATOR A THESIS Presented to The Faculty of the Graduate Division by Robert David Shults In Partial Fulfillment of the Requirements for the Degree Master of Science in Electrical Engineering Georgia Institute of Technology June, I963 AN INVESTIGATION OF THE INFLUENCE OF CIRCUIT PARAMETERS ON THE OUTPUT WAVESHAPE OF A TUNNEL DIODE OSCILLATOR Approved: —VY -w/T //'- Dr. W. B.l/Jonesj UJr. (Chairman) _A a t~l — Dry 3* L. Hammond, Jr. V ^^ __—^ '-" ^^ *• Br> J. T. Wang * Date Approved by Chairman: //l&U (A* l/j^Z) In presenting the dissertation as a partial, fulfillment of the requirements for an advanced degree from the Georgia Institute of Technology, I agree that the Library of the Institution shall make it available for inspection and circulation in accordance witn its regulations governing materials of this type. I agree -chat permission to copy from, or to publish from, this dissertation may be granted by the professor under whose direction it was written^ or, in his absence, by the dean of the Graduate Division when luch copying or publication is solely for scholarly purposes ftad does not involve potential financial gain. It is under­ stood that any copying from, or publication of, this disser­ tation which involves potential financial gain will not be allowed without written permission. _/2^ d- ii ACKNOWLEDGMEBTTS The author wishes to thank his thesis advisor, Dr. W. B„ Jones, Jr., for his suggestion of the problem and for his continued guidance and encouragement during the course of the investigation. At the same time, special, thanks are due to the other members of the reading committee3 Drc J. Lo Hammond and Dr. J. T. Wang, for their constructive criticisms in the preparation of the manuscript. Appreciation is also expressed to Mr. R» So Johnson for his advice and suggestions in the preparation of the analog computer program. TABLE OF CONTENTS Pag ACKNOWLEDGMENTS . ii LIST OF ILLUSTRATIONS v SUMMARY ............... ... ix CHAPTER I. INTRODUCTION ......... 1 II.. TUNNEL DIODE OSCILLATOR THEORY ............. k Basic Oscillator Circuits Linear Methods of Analysis Linear Analysis in the Complex Frequency Plane Linear Differential Equation Analysis Alternate Quasi-Linear Analysis Nonlinear Analysis Nonlinear Considerations Graphical Solution- Method of Isoclines and Phase-Plane Analysis III. INSTRUMENTATION AND PROCEDURE ............... ^0 Approach to the Problem Method of Solution Function Generator Computer Solution Final Machine Equation Method of Recording Computer Data Definition of Circuit Parameters Variation of the Circuit Parameters IV. EXPERIMENTAL RESULTS ................... k$ Near-Sinusoidal Oscillations General Approach Quasi-Linear Considerations Impedance Level Variable, Q and Bias Fixed Q Variable, Bias and "Impedance Level Fixed Bias'Variable, Impedance Level and Q Fixed Overall Effect of the Circuit Parameters Relaxation Oscillations iv TABLE OF CONTENTS (Continued) Page CHAPTER V0 SUMMARY AND CONCLUSIONS . 79 APPENDICES ............... .... 82 A. TYPICAL DIODE PARAMETERS (GE Type 1N29^0) ......... 83 B. SCALING PROCEDURE FOR EQUATION (73) ........... 8k Choice of Base Parameter Values Time Scaling Amplitude Scaling Changing the Problem Variables BIBLIOGRAPHY ............... ..... 95 LIST OF ILLUSTRATIONS Figure Page 1(a)« General Characteristic of the Tetrode Vacuum Tube . 2 1(b). Polynomial Representation About the Center of the Negative Resistance Region Used by Van der Pol .... 2 1(c). Tunnel Diode Static Terminal Volt-Ampere Characteristic 2 2. Equivalent Circuit of the Tunnel Diode when Biased in the Region of Negative Resistance k 3(a)* Simple Oscillator Circuit ...... .... 5 3(b). Incremental Equivalent Circuit of Figure 3(a) ..... 5 k(a.). Basic Oscillator Circuit 6 Mb). Incremental Equivalent Circuit of Figure k(a.) ..... 6 5- Practical Oscillator Circuit ............. 6 6° Suitable DC Load Line 7 7» Unsuitable DC Load Lines 7 8. Simplified Equivalent Circuit ............. 8 9. Basic Oscillator Circuit ...«,... = ....... 11 10. Equivalent Tank Circuit ................ Ik 11. Alternate Equivalent Basic Oscillator Circuit . Ik 12. Dynamic Load Line Conducive to Growing Oscillations . 16 13. Influence of Circuit Parameters on the Modes of Circuit Operation (After Strauss) ............... 17 Ik. Basic Oscillator Circuit ............... 19 15. Diode Characteristic Used to Represent the Nonlinear Function f(e) ............ ... 20 l6o Simplified Construction of Arbitrary Solution Curve Using the Method of Isoclines . 2k Figure Page 17(a), Numerical Evaluation of f(e) for Use in Equation (50) . 27 cl f 17(b). Numerical Use of the Graphical Construction for (-=—) . 27 18. Example of a Phase Trajectory ...*»...„...... 28 19« Basic Function Generator . 31 20. Equivalent Circuit of Parallel Combination ....... 32 21. Stabilized E-I Characteristic of the Parallel Combination .»..»» ........ ......... 32 22. Modified Function Generator ............... 3^ 23. Output of the Function Generator ............ 36 2k. Derivation of the Function f(e) ............ 37 25. True Function Generator 38 26. Unsealed Computer Solution of Equation (61) ....... 39 27(a). Computer Solution for the Phase Trajectory ....... kl 27(b). Computer Solution for the Instantaneous Waveform .... kl 28. Tank Circuit ...................... k2 29• Three Dimensional Model Used to Systematize Taking Data .......................... hk 30. Allowable Range of Variation in External Tank Conductance for Near-Sinusoidal Oscillations ...... ^7 31(a). Phase Trajectory for Kz = 1, Kr = 2, (Q = 1/2 tL ) and Bias = 125 mv ............. kg 31(b). Instantaneous Waveform for K = 1, K = 2, (Q = 1/2 a ) and Bias = 125 mv ............. kg 31(c). Output of Prototype Oscillator for K = 1, K = 2, (Q = l/2 QL) and Bias = 125 mv >.?... * . .... kg 32(a). Phase Trajectory for K = 1/2, K = 1^ (Q = l/2 0^) and Bias = 125 mv • • • 50 32(b). Instantaneous Waveform for K = 1/27 K. = 1^ (Q =1/2 0^) and Bias = 125 mv • • • * ........ 50 Vll Figure Page 32(c). Output of Prototype Oscillator for Kz = 1/2, Kr =1, (Q * 1/2 Qfc)) and Bias = 125 mv . , . 50 33* Effect of Kz on Dynamic Load Line for Fixed Bias and Constant Q ................... 51 3^(a). Phase Trajectory for Kz = 1, Kr = 1, (Q = 0 ) and Bias = 125 mv ............... 53 3^(b). Instantaneous Waveform for Kr = 1, K = 1, Z r (Q = Qb) and Bias = 125 mv . 53 35(a). Phase Trajectory for K = 1, K = 50, (Q = 1/50 Q^), and. Bia§ = 125 mv ............ $k 35(b)» Instantaneous Waveform for L = 1, L « 50, (Q = 1/5O Qb), and Bias = 12$ mv ............ 5^ 36. Effect of Circuit Q on Dynamic Load Line for FLxed Bias and Impedance Level .............. 55 3T« Variation of Incremental Diode Conductance ........ 56 38. Allowable Range of Bias Points for Various Combinations of K and K . 58 z r y 39• Various Bias Points for a Given Dynamic Load Line .... 59 k0„ Equivalent Oscillator Circuit .............. 60 kl» Composite Volt-Ampere Characteristic . 60 k-2. Piecewise-Linear Composite Characteristic 61 43. Skew Distortion of Output Waveshape ........... 63 kk(a). Phase Trajectory for Kz = l/2, Kr = 10, and Bias Point A = 100 mv .................. 68 ^4(b). Instantaneous Waveform for K - 1/2, K = 10, and Bias Point A= 100 mv . .Z. ,r......... 68 ^5(a). Phase Trajectory for K = l/2, K - 10, and Bias Point B = 180 mv Z r. 69 ^5(b). Instantaneous Waveform for K = l/2, K = 10, and Bias Point B = 180 mv . /". ... ,r. ........ 69 k6('&). Phase Trajectory for K = l/2, K = 10, and Bias Point C = 250 mv Z. ... .r. ........... 70 ^6(b). Instantaneous Waveform for K7 = 1/2, K = 10, and Bias Point C = 250 mv ..."..../......... 70 ^7(a). Phase Trajectory for Kz = 1/2, K = 10, and Bias Point D = 300 mv . .r. 71 viii Figure Page 47(b). Instantaneous Waveform for K = l/2, K = 10, and Bias Point D = 300 mv ,..?... ? . 71 48(a). Phase Trajectory for K = 1, K = 56, and Bias = 125 m ..?... r. ....... .... 0 74 48(b). Instantaneous Waveform for K = 1, K = 56, and Bias = 125 mv ...... ? . T ........ 74 ^9(a). Phase Trajectory for K = 1/4, K = 3.5, and Bifcs = 125 mv . ... Z. .... r. 75 49(b). Instantaneous Waveform for K = l/4, K =3.5, and Bias = 125 ny . .. ... Z. .... r. ....... 75 50(a). Phase Trajectory for K = J, K = I35, and Bias = 125 mv ....?... T ........... 76 50(b). Instantaneous Waveform for K = 3, K = I35, and Bias = 125 mv ... ... z ... * ........ 76 51. Relaxation Oscillation ..... ...... 78 Al. Typical Static Characteristic Curve and Equivalent Circuit ...... ............. 83 Bl. Scaled Computer Program for Equation (Bl8) for K = 1, K = 1 .................... 92 z ' r «• ix SUMMARY A detailed analysis of a tunnel diode oscillator inevitably requires the solution of a nonlinear differential equation describing its operation. In the past, the volt-ampere characteristic of a device which displays negative dynamic resistance in a reasonably symmetrical N-type curve has been described by a simple third order polynomial. For example, the characteristic of the tetrode vacuum tube is usually des- 3 cribed by the simple expression i = - ae + be . Because of the simpli­ city of the approximating polynomial used to describe the tetrode, van der Pol was able to solve the nonlinear differential equation which des­ cribes the tetrode oscillator. The original work published by van der Pol in 193^+ bas long since become a classic in the field and has been the inspiration for numerous researches on nonlinear oscillations» The analysis of a tunnel diode oscillator is complicated by the fact that the volt-ampere characteristic of a tunnel diode is grossly asymmetrical about the region of negative dynamic resistance and cannot be approximated by a simple polynomial. It has been the purpose of this investigation to obtain, without the use of an approximating poly­ nomial, the solution to the nonlinear differential equation which des­ cribes a tunnel diode oscillator. The characteristic of the solution which has been of primary interest is the waveshape of the steady-state output and how it is influenced by the different circuit parameters.
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