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A Tunnel Diode Parametric Down Converter

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A Tunnel Diode Parametric Down Converter Scholars' Mine Masters Theses Student Theses and Dissertations 1962 A tunnel diode parametric down converter Leland Lovell Long Follow this and additional works at: https://scholarsmine.mst.edu/masters_theses Part of the Electrical and Computer Engineering Commons Department: Recommended Citation Long, Leland Lovell, "A tunnel diode parametric down converter" (1962). Masters Theses. 2721. https://scholarsmine.mst.edu/masters_theses/2721 This thesis is brought to you by Scholars' Mine, a service of the Missouri S&T Library and Learning Resources. This work is protected by U. S. Copyright Law. Unauthorized use including reproduction for redistribution requires the permission of the copyright holder. For more information, please contact [email protected]. A TUNNEL DIODE PARAMETRIC DOWN CONVERTER BY LELAND L. .LONG A THESIS submitted to the facility of the SCHOOL OF MINES AND METALLURGY OF THE UNIVERSITY OF MISSOURI in partial fulfillment of the work required for the Degree of ii ABSTRACT The problem, as presented, is to derive analytical expressions for the conversion gain, bandwidth, and noise figure of a self excited tunnel diode converter and to verify, if possible, the validity of these express- ions by building such a converter. These analytical results are presented and discussed. The converter circuit is shown along with the resulting intermediate frequency output. Gain and bandwidth measurements are also given. It is concluded that the self excited converter could very defin­ itely be of value as a low noise pre-amplifying device in the ultra-high frequency and microwave frequency ranges. iii ACKNOWLEDGEMENTS The author wishes to thank Prof. G. G, Skitek for many helpful suggestions regarding the thesis proper. Discussions with Dr. R. C. Harden and Prof. F. L. Grismore were also very enlightening with respect to circuit analysis techniques and tunnel diode applications. iv TABLE OF CONTENTS Page LIST OF FIGURES...................................................... vi LIST OF SYMBOLS..................................................... vtii CHAPTER I. INTRODUCTION......................................... 1 A. Statement of the Problem. ............................ 1 B. Significance of the Study.............. 1 C. Reasons for the Investigation........................ 4 CHAPTER II.. REVIEW OF THE LITERATURE............................. 5 CHAPTER III. THE TUNNEL DIODE..................................... 7 A. Theory................. 7 B. Ratings and Specifications............................15 CHAPTER IV. ANALYTICAL RESULTS.................................... 19 A. Development of Current-Voltage Relationship for the Parametric Down Converter......... ......... 19 B. Derivation of Tunnel Diode Impedance Matrix........ 24 C. Conversion Gain. ................ 28 D. Bandwidth............... 32 E. Noise Figure.................. 37 Definition....... 37 Thermal Noise in Resistors........................33 Noise Equivalent of the Tunnel Diode.. ............ 39 Input Noise Power......... 39 Output Noise Power................................42 Amplifier Noise Figure............................45 CHAPTER V. EXPERIMENTAL PROCEDURE AND RESULTS.................... 47 A. Procedure.......... 47 Introduction............. 47 Local Oscillator Design..................... 47 V Page Coupling Circuits. ........... 53 Converter Circuit....... ................. 54 Gain and Bandwidth ............ 57 CHAPTER VI. CONCLUSIONS AND RECOMMENDATIONS........... 58 A. Conclusions......................... 58 8. Recommendations...... .............. 58 BIBLIOGRAPHY............................................................59 VITA....................................................................60 vi LIST OF FIGURES Figure Page 1. (a) Volt ampere characteristic of a p-n junction detector diode*.*...... ................................. 3 (b) Volt ampere characteristic of a tunnel diode..... .......... 3 2. Tunnel diode p-n junction energy level diagrams......... ........ 8 (a) Zero bias condition........................................ 8 (b) Forward^bias condition for maximum current I p ............ 8 (c) Forward bias condition for current approaching Iv ....... 9 (d) Forward bias condition for increasing current................ 9 3. Tunnel diode volt-ampere characteristic showing positions corresponding to junction energy level diagrams of Figure 2*...«........ *.................... 10 4. Semiconductor energy level diagrams for various stages of doping........... ................................ 11 (a) Intrinsic semiconductor at 0° K ...... .................... 11 (b) P-type and n-type semiconductors with normal rectifier doping levels assumed............. ........... 11 (c) P-type and n-type semiconductors used in tunnel diodes......... ......... ....... ............. ......... 12 5. Small signal equivalent circuit of the tunnel diode .......... 18 6. Dynamic resistance of the tunnel diode as a function of voltage. The resulting resistance is plotted as a time varying function of the local oscillator frequency........................... 20 7* A-C equivalent circuit of the converter analyzed............. 23 8. A-C equivalent circuit of the converter with the tunnel diode replaced by its equivalent non-linear two port...... 27 9. (a) Converter input loop with the tunnel diode replaced by its equivalent impedance.............. ............ ..... 29 (b) Converter output loop with the tunnel diode replaced by its equivalent impedance.........................29 10. Plot of ^ co(db) vs. A 33 vii Figure Page 11. Converter normalized bandwidth as a function of gain factor A with C = 1 ............ ................ 36 12. Voltage source equivalent of a resistor shown as a noise voltage generator. ............................ 40 13* (a) Current source equivalent of a tunnel diode shorn as a noise current generator.... ............... ...... 41 (b) Voltage source equivalent of a tunnel diode shown as a noise voltage generator.......................... 41 14. Block diagram of the converter showing input generator replaced by its noise voltage generator......... 42 15* (a) Converter input loop used for noise figure calculations.................. 43 (b) Converter output loop used for noise figure calculations........ 43 16. Local oscillator circuit used showing 30 me output wave form which appeared across the tunnel diode............ 50 17. A-C equivalent of the local oscillator circuit................. • 51 18. D-C equivalent of the local oscillator circuit..... ............ 52 19. Completed converter circuit..................................... 55 20. (a) Wave form across the tunnel diode with unmodulated carrier impressed............................... 56 (b) Wave form across the tuned plate of the IF amplifier with unmodulated carrier impressed......... 56 (c) Wave form across the tuned plate of the IF amplifier with 1000 cps modulating the BF carrier...........56 21. Local oscillator with D. C. supply isolated by L^ ............... 56b LIST OF SYMBOLS Ls -— Tunnel diode parasitic inductance, CD - Tunnel diode parasitic shunt capacitance, R s - Tunnel diode parasitic loss resistance. R(t) -Tunnel diode resistance as time function, R 0 - Tunnel diode quiescent resistance. rA ~— First order resistive term appearing in fourier series approximation of R(t), Ip ---Tunnel diode peak current. Iv -- Tunnel diode valley current. Vp ---Tunnel diode peak voltage. Vv --- Tunnel diode valley voltage. i(t) ---Sum of RF and IF currents flowing through tunnel diode. v(t) -— Total voltage drop across tunnel diode. i A(t) ---RF current. i z{t) ---IF current. v^(t) — RF voltage drop across tunnel diode. v 2(t) --- IF voltage drop across tunnel diode. '1/^ ---Instantaneous value of pump voltage. 11 -— Peak RF current. I jL *— Peak IF current. V_£* ---Peak RF voltage drop across tunnel diode. V^1 ---Peak IF voltage drop across tunnel diode. V3 — Peak value of pump voltage. V g ---Peak value of RF generator voltage. Q± ---Phase difference between i±(t) and Qz --- Phase difference between iz(t) and output loop voltage drops. ix 1 1 — I Z — i*' ej9i ___ ii e >e>* ____ x , ' ^ ? 2 V ± ---- V i ' 6 ' V V* ---- H — Generator — Input loop loss resistance, R i_---- Load resistance. V -— - Output loop loss resistance. L ± ----Input loop tank circuit inductance. C i - — Input loop tank circuit capacitance. L 2 -— - Output loop tank circuit inductance. C * ~ Output loop tank circuit capacitance. ■fl — - Signal frequency. f 2 — — Intermediate frequency. +3 ~ — Local oscillator frequency. 2TT-fA . OJz ---- 2 Trfc. LJ, — 2Trf3. £ ----Exponential. ----Tunnel diode impedance at f ± • Z z ---- Tunnel diode impedance at f 2 • ---- Conversion power gain. P u ----AC power developed in R . P ,N ---- Maximum available input power from HF generator. — - Total series resistance in input loop. X r 2 — - Total series resistance in output loop, Xx - - Total series reactance in input loop. x 4 - - Total series reactance in output loop. -i x* V * - tan r , V° ~— Normalized conversion gain at center frequency. \ -— Gain factor. Y - — Normalized conversion gain at off resonant frequency. B -— Amplifier bandwidth. S -— Normalized amplifier bandwidth. Q jl - — Input circuit loaded Q. Qz —— Output circuit loaded Q. C ~— Amplifier Q factor. N. n — Noise input power. N out — Noise output power. F — Amplifier noise figure. 2 2 c « — Mean squared value of resistor noise voltage. K — Boltzman’s constant. T — Absolute temperature. A f — Arbitrary noise bandwidth. io — Mean squared value of tunnel diode noise current.
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