THEORY, DESIGN,

AND SOME APPLICATIONS OF

TUNNEL DIODE TRIGGERS

Shanti Lal Sarnot

Thesis submitted to

Indian Institute of Technology Delhi

for partial fulfilment of the degree of

Doctor of Philosophy in Physics

January 1971

ACKNOWLEDGEMENTS

I wish to express my hearfelt thanks to

Dr. A.B.Bhattacharyya, who initiated and supervised

the programme of the present thesis.' I owe so much

to him for providing the necessary guidance, inspiration

and stimulating discussions in this work.

I am also thankful to my friends; both at TIT

and elsewhere for their encouragement and help. My

special thanks are due to Dr. Prabhat K. Dubey for his

generous help and useful suggestions.

This work was carried out under the financial

support of the Council of Scientific and Industrial

Research, India.

Skate.-LL L Same±

INTRODUCTION AND SCOPE OF THE THESIS

Introduction

The tunnel diode1 is recognized as one of the fastest

switching device presently available. The switching time of

a typical tunnel diode circuit is within a fraction of a

nanosecond2, with operating frequencies of, usually, hundreds

of megacycles. Due to the negative resistance it is suitable

for compact and high speed pulse circuits3,4. Such circuits

are presently extensively used in the field of instrumentation,

nuclear electronics5 and computer technology6 for finding

solutions of the problems where transistors have shown limita-

tions.

Due to recent progress in the development of high-speed

transistors, the switching circuits can operate well in the

frequency region of the order of 10 Mc7. Therefore, the

advantage of tunnel diode lies in its application at frequencies

above this (i.e., from a few tens of megacycles to several

hundreds of megacycles); experiments with pulse circuits in

this range are very important. For ultra-high computation,

tunnel diode offers a speed which cannot be duplicated in any

other semiconductor device. Also, the tunnel diode circuits,

as a rule, contain two to three times less components in

comparison to analogous transistor circuits. This large

reduction of the number of components results in an increase

of the operating speed and reduction of the multi-component

unreliability.

2

Short Review

The digital circuits using tunnel diodes can have two

particularly attractive features: high speed and a well-

defined triggering threshold8. A. trigger with one tunnel

diode is simplest to conceive and can be designed with one

or two stable states3,9. In the simplest form, tunnel diode

triggers are used for information storage10

and logic

operations11 '12 . In the counting mode, it is used at first 13

instance for frequency division and pulse counting As a

threshold device14

1 having high sensitivity to the signals 15

of nanosecond duration, the trigger is used for pulse selection 1

as coincidence circuit16

1 for realizing AND, OR logic opera-

tions17

1 indicating initial level18-201

and so on21.

It is necessary to recognize that the resetting of the

trigger in the initial state is usually accomplished by delayed

external pulse of opposite polarity, which in many cases

introduces circuit complexity. Hence in a typical discrimina-

tor circuit22

for example, a solution was suggested in which

the load line is practically horizontal and intersects the

tunnel diode characteristic at one point. Thus the return

of the circuit in the original state takes place automatically

with the withdrawal of the pulse.

When the bistable circuits operate in counting mode, it

is necessary to obtain bipolar pulses which complicates the

circuit operation23. In addition, the voltage swing, obtained

across the tunnel diode, differs in magnitude and duration

3

and is governed by the circuit conditions. Nevertheless, the

high switching speed unables the formation of fast pulses from

slowly varying input pulses .

Tunnel diodes when connected in pair, popularly known

as Goto pair25, have proved to be extremely useful and are

used extensively10'26/27. The tunnel diode pair circuits are,

by nature, more critical to dispersions in tunnel diode para-

meters compared to the circuits with single tunnel diodes28,

though the latter do not have the advantage of isolated

input-output system and resetting possibility with only one

type of pulse. In any case, the understanding of the

characteristic of tunnel diode pair circuits must be preceeded

by a thorough investigation of single tunnel diode circuits;

the former case is only a smart extension of single tunnel

diode characteristic. Circuits with series-cascaded tunnel

diodes29130

, which show the potentialities of counting

pulses in a remarkably simple way and have no transistor

analogue, are of definite practical interest.

As it stands, the circuits are little understood mostly

because of the fact that in the early progress in the field of

tunnel diodes, many arm-chair analyses were put forward and

one develops a feeling that the tunnel diode circuits are

basically designed arbitrarily.

Problems in the Theory, Design, and Applications of Tunnel

Diode Triggers

The characteristic of the tunnel diode, a two pole

device, is so specific, and altogether different in nature

than that of a transistor or vacuum tube, that the circuits

with tunnel diodes cannot be designed in a conventional way.

The difficulties in designing tunnel diode circuits become

more apparent when we reconcile that the previously available

two pole devices (e.g. gas tubes) were only operable in a

very narrow sphere due to their limited speed and stability

(which is even lesser than that of the transistor or vacuum

tube), and therefore the difficulties for very high speed

circuits were not recognizable for two pole devices.

To mark out specific problems in the theory, design,

and applications of tunnel diode triggers, we discuss them

separately.

Theory: From the survey of the existing literature

on tunnel diode triggers, it is found that most of the works

deal with only specific circuits and their experimental

performance; the emphasis on the necessary theory was rather

not paid. However, where the theoretical predictions are

made, the approaches fail to cover relatively wide range of

problems encountered by a circuit designer. Nonetheless,

the applications of tunnel diode triggers in logic and

memory circuits are theoretically understood through computer

solutions for specific problems. Therefore a definite need

for analytical generalization of the circuit problems, for

the evaluation and design of these circuits, always existed.

Owing to nonlinearities in the diode characteristic,

the dynamic behaviour of the tunnel diode triggers is described

by first and second order nonlinear equations. The general

solutions of such equations do not exist for all cases that

might be encountered while dealing with various circuits. In

the earlier work, to simplify the analysis, linear piecewise

approximation for the tunnel diode characteristic is widely

used10. The results thus obtainedl 'at best, be considered

to yield preliminary information and for a precise assessment

of these circuits this approximation is found to be in-

adequate4. To improve the results, for a few specific cases,

analytical32 and computer solutions33'34 employing some

curve fitting expressions for the characteristic are suggested.

However, the methods are not versatile in character and, as

they stand, cannot be readily used for practical purposes.

Moreover, the earlier studies on the transient response are

in general superficial and scant consideration is given to

the determination of delay, overdrive, etc. as a function of

the circuit parameters. It is further noted that no analyti-

cal work is done on the nonlinear biasing of the trigger

circuits and other information available is also meagre.

Thus it is imperative to give analytical treatments for the

dynamic performance of tunnel diode triggers under a variety

of input pulses. It is particularly important because in

many applications, the error in the dynamic threshold is

governed by the input current leakage to the junction

capacitance which should be controlled with a high degree of

accuracy (upto 1% - 5%).

6

Design: In the design of triggers, the starting point

is the static design procedure. Also, it is essential to have

a knowledge of the circuit parameters such as the storage

current, input sensitivity, temperature stability and their

dependence on the variation of device parameters. However,

complete information is yet not available. The analysis of

the static design of logic circuits351 two tunnel diodes28,

and transistor-tunnel diode composite system is not directly

applicable to the design of single tunnel diode triggers.

In tunnel diodes, when operated near threshold, the

problem of stability and reliability assumes significant

importance and it is difficult to predict the state of

operation.

A. common difficulty in designing single tunnel diode

triggers is the isolation between the input and output36

Since the tunnel diode is a two terminal device, same pair of

terminals must be used for both input and output, and thus

the output signal of a logic circuit can affect the circuit

which supplies the input signal. An ideal coupling element

to provide directionality and input-output isolation is the

backward diode36. For understanding the effect of the

isolating element on the trigger design and performance, a

study of the various aspects of the backward diode is

essential.

The cascading of successive trigger stages is also a

problem associated with these circuits3738. The solution

7

lies, in general, on the type of applications and merits

investigations whenever more than one stage is involved.

Some of these difficulties are removed in the tunnel

diode-transistor hybrid circuits22 but they are not of concern

in the present thesis.

Applications: Out of numerous uses of tunnel diode

triggers, our chief interest has been in counting circuits.

When the trigger is used for counting purposes, its dynamic

behaviour is determined by the internal storage element, and

thus significantly differs from the behaviour of ordinary set-

reset triggers1039. The transient analysis for such a case

has not been given. The counting speed of the circuits is

experimentally obtained for circuits13

, quite arbitrarily

designed. Some reports deal with qualitative aspects of

the triggers without serious considerations of the design

aspects4o. Thus, it is important to understand the transient

process, when the trigger operates in the counting mode, to

establish the conditions of counting, the speed of operation,

and finally to give an optimum design procedure. Without

solving these problems, an assessment of the virtues of tunnel

diodes in counting mode would be only superficial.

We wish to mention at this stage that, though tunnel

diodes have received considerable attention in advanced

countries like U.S.A.10141, U.S.S.R.4,6,22,421and

Japan 44

little effort seems to have been made in our country to

develop experience, and if necessary, an expertise in the

8

branch. This work was initiated and undertaken, in addition

to many academic points of interest, in the background of

recommendations of Bhabha Commission45

and Education

Commission46 to strengthen the applied work and to develop

our own knowhow to meet the national requirements.

In the present thesis, we are concerned with single

tunnel diode triggers only. The main objective is to provide

analytical foundation to various dynamic processes, and to

use these results in designing a binary counting stage. The

study also ambraces backward diode, which is frequently used

in tunnel diode circuits.

Summary of the Work

Chapter 1 begins with a brief discussion of the tunnel

diode static parameters and their dispersions due to

manufacturing tolerance, temperature variation, and degrada-

tion. A curve-tracer is described for displaying the v-i

characteristic on the oscilloscope, and a simple method for

obtaining peak and valley parameters is also given. For

representing the static characteristic by some functions,

some curve fitting approximations are mentioned and a

particular approximation, due to Kononov and Sidorov24 i 1 is

discussed in detail.

In chapter 2, study of the worst case circuit

performance of a single tunnel diode bistable trigger is made

taking into account the tolerance of the device parameters

and circuit components with special reference to the input

characteristics and storage current. A procedure for

9

obtaining the optimum load and bias voltage is outlined. It

is shown that the scattering in various parameters puts

certain limitations on the design and performance of such

circuits and that a critical selection of operating conditions

and components is necessary for reliable opei.ation.

In chapter 3 the step response of a bistable trigger

is studied. Both the idealized case of voltage switching

mode and the practical case of current switching mode are

considered and a general analytical method for switching time

calculations is given. In the latter case, the analytic

closed-form expressions, for both forward and reverse

switching, are derived considering the voltage dependence of

the junction capacitance and a small inductance. The contri-

bution due to the capacitance variation and that due to,the

inductance are expressed by separate terms added in the

usual switching time expressions. The conditions of effective

switching are also obtained from analytical considerations

and the influence of overdrive is studied. The analysis

shows that the switching time depends on the average resistance

of various segments and that the magnitude of negative

resistance is of no consequence in determining the switching

speed.

Chapter 4 comprises the study of transient response

for time-dependent signals. The forward transient

characteristics of a practical trigger for ramp pulses are

studied. The cases of trapezoidal and triangular pulses

1.0

are investigated in detail. The numerical results for a wide

range of slope of trigger pulses are compared under different

circuit conditions and the error in the results due to a

straight-line approximation is estimated. From these general

results, the results for an open load condition follow

immediately. Further investigations are carried out on the

forward and reverse nonregenerative delays for a wide range

of form and duration of input pulses and the results are

obtained in terms of certain parameters which describe all

types of practical pulses. Specific examples of a linear

pulse and a pulse coinciding the form of the diode current

is discussed in detail.

In chapter 5 the switching time of backward diodes and

some of their uses are discussed. An approximation for the

backward diode reverse characteristic is suggested which is

used in deriving expressions for its switching time. Owing

to extremely low junction capacitance it has an exceptionally

high switching speed. This approximation, in conjunction

with Kononovts power functions are used in deriving the

transient characteristics of a tunnel diode with a backward

diode as nonlinear load. The backward diode is also used in

parallel with tunnel diode to improve the top of output wave-

form. It was earlier believed that such a combination

improves the transient response47

However the results of

the present study contradict it. The use of nonlinear element

is further considered and, in contradiction to earlier views,

it is shown that its use in tunnel diode trigger circuits does

not accelerate the transient process; it serves mainly to

increase the stability and sensitivity of the trigger.

Chapter 6 is devoted to the study of the dynamic

performance of a monostable circuit for linear as well as

nonlinear biasing. For relatively large inductancel the pulse

width and recovery time are the most important parameters of

the output pulse which are computed using straight-line and

power function approximations. It is found that the two

results differ appreciably; the latter results are in good

agreement with the experimental observations. Corresponding

to these approximations, the shape of the output pulse is

also computed. The former approximation gives a concave top

whereas the latter gives a slightly convex top which conforms

to the experimental pulse shape. The pulse width and recovery

time are found to vary linearly with inductance. It is

further noted that, as compared to linear biasing, the

recovery time is drastically reduced in nonlinear biasing,

and the pulse width can be controlled by suitably adjusting

the backward diode bias voltage.

In the last chapter a practical single tunnel diode

binary is studied and an attempt is made to obtain an

optimum dynamic performance. The conditions of counting mode

operation are established and a relation between various

parameters, viz. circuit inductance, repetition period of the

input pulse, pulse width, overdrive,etc. and the frequency of

12

operation is obtained. These are basically a consequence

of the study of an important dynamic parameter - the storage

current. The proposed binary is essentially a bistable

circuit coupled with a monostable one. The monostable circuit

with nonlinear biasing gives bipolarity pulses to trigger the

bistable stage; their period can be controlled by inductance,

and the amplitude by suitably biasing the nonlinear element.

For better sensitivity and stability of the bistable circuit,

it is also biased nonlinearly.

CONTENTS

Index of Symbols

(1)

INTRODUCTION AND SCOPE OF THE THESIS

1

CHAPTER

1 Static Characteristics of Tunnel Diodes 18

2 Static Design of a Tunnel Diode 40

Bistable Trigger

3 Step Response of Tunnel Diode 60

Bistable Triggers

4 Transient Characteristics of a Tunnel Diode 106

for Time-Dependent Signals

5 Backward Diodes in Tunnel Diode 146

Trigger Circuits

6 Dynamic Behaviour of Tunnel Diode 178

Monostable Circuits

7 Single Tunnel Diode Binary Counter 208

CONCLUSIONS 233

LIST OF PUBLICATIONS 238

Relevant Reprints