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