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Masters Theses Student Theses and Dissertations

1969

Tunnel diode models for electronic circuit analysis program Tunnel diode models for electronic circuit analysis program

(ECAP) (ECAP)

Carmon Dale Thiems

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Recommended Citation Recommended Citation Thiems, Carmon Dale, "Tunnel diode models for electronic circuit analysis program (ECAP)" (1969). Masters Theses. 7002. https://scholarsmine.mst.edu/masters_theses/7002

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TUNNEL DIODE MODELS FOR

ELECTRONIC CIRCUIT ANALYSIS PROGRAM (ECAP)

BY :;4 I

CARMON DALE THIEMS , 1938-

A

THESIS

s ubmitted to the faculty o f

THE UNIVERSITY OF MISSOU.I - R J~LA

in part ial f ulfil lmen t of the requirement~ for t

Degree of

MASTER OF SC IENCE IN ELECTRICAL ENGI~EE I .J

Rolla, Hissouri

1969

Approved by

T. 2274 ~

68 pages

TABLE OF CONTENTS

LIST OF FIGURES . ....•••..•.••.•.•...•...••..•....•....... LIST OF PHOTOGRAPHS ••••••••••••••••••••••••••••••••••••••

LIST OF TABLES . ..•.••.•.•...•••.••..•••.••..••.•••.•.••.•

I. INTRODUCTION • •..•.••••.•••••.••.••.•••...•..•...

II. MODELS Ah~ CURRENT-VOLTAGE CHARACTERISTICS .•.•••

III. MODELS IN CIRCUIT APPLICATIONS •.•••••••.••...••.

IV. CONCLUSIONS ..•..•.•..•.............•.•••...•....

APPENDIX I-SUXMARY OF MODELING OF ACTIVE DEVICES FOR COMPUTER-AIDED CIRCUIT DESIGN •.•••••.•.•..•.

REFERENCES . ....•...•.•.••.•...•......••..•.•...•

i-.??S:DIX II-ANALYSIS, CALCULXi'ION M~D SEL:C:CTlOJ.\ OF PA1\fu'1ETERS FOR TUNNEL DIODE HODELS .•.•..•....

BIBLIOGRAP11Y ............... g •••••••••••••••••••••

'i IT!...,. • •••••••••••••••••••••••••••••••••••••••••••

iii v

vi

.1

4

30

J4

43

45

59

LIST OF FIGURES

Figur~ 1 Tunnel Diode Current-Voltage Characteristics

Figure 2 Model 1 Current-Voltage Characteristics

Figu-re 3 Hodel 1

Figure 4 Model 1 Current-Voltage Curve

Figure 5 Model 2 Current-Voltage Characteristic

Figure 6 Model 2

Figure 7 Hodel 2 Current-Voltage Curve

Figure 8 Model 3 Current-Voltage Characteristic

Figure 9 Model 3

Figure 10 Model 3 Current-Voltage Curve

Figure 11 Relaxation Oscillator

Figure 12 Astable Multivibrator

Figure 13 Model 1 Oscillator Output \vaveform

Figure 14 Model 2 Oscillator Output tvaveform

Figure 15 Model 3 Oscillator Output Waveform

Figure 16 Model 1 Multivibrator Output tvaveform

Figure 17 Hodel 2 Mul tivibrator Output t.Javeform

F::.gure I-1 Diode Current-Voltage Characteristic

Figu::..::: I-2 D::.ode Models

F~gure I-3 Ebers-Noll Hodel

'io':..gure I-4 Beaufoy-Sparks Charge Control Model

·?::..gur~ I-S Linvill Lumped Model

7::.gu-:.-.: 1-6 Zener Diode Model

iii

Page 1

4

6

7

8

11

12

13

16

17

19

21

23

25

27

~ r .JO

37

3S

39

39

40

iv

Figure I-7 Tunnel Diode Model 4l

Figure II-1 Tunnel Diode Current-Voltage Characteristic 47

Figure II-2 Model 1 48

Figure 11-3 Three Section Piecewise Linear Current Voltage Curve 49

Figure II-4 Model 2 52

Figure 11.;..5 Five Section Piecewise Linear Current Voltage Curve 53

Figure 11-6 Hodel 3 56

Figure I1-7 Model 3 Current-Voltage Characteristic 57

v

LIST OF PHOTOGRAPHS

Page Photograph l TD-19 Current-Voltage Curve 2

Photograph 2 TD-13 Current-Voltage Curve 2

Photograph 3 Oscillator Output Voltage Waveform::. 18

Photograph 4 Multivibrator Output Voltage Waveform 18

vi

LIST OF TABLES

P<:.ge TABLE I Model 1 ECAP Data 5

TABLE II Model 2 ECAP Data 10

TABLE III Model 3 ECAP Data 15

TABLE IV Model 1 Oscillator ECAP Data 20

TABLE v Hodel 2 Oscillator ECAP Data 22

TABLE VI Hodel 3 Oscillator ECAP Data 24

TABLE VII Model 1 Multi vibrator ECAP Data 26

TABLE VIII Model 2 Multi vibrator ECAP Data 26

TABLE II-1 Data From G.E. Data Sheet 46

TABLE II-2 Model 1 Parameter Values so

TABLE II-3 Model 2 Parameter Values 55

TABLE II-4 Model 3 Parameter Values 58

1

I. INTRODUCTION

In this paper ECAP models for the tunnel diode are pre-

sented. Results showing the model, the current-voltage charateris-

tics are discussed. Operation in typical circuits is presented.

A summary of the current state of the art in modeling appears in

Appendix I.

Since ECAP is only structured to accept piecewise-linear

models of these devices, that type of model is presented here.

All of the models are developed to approximate the typical tunnel

diode current-voltage characteristic shown in Figure 1 and also

in Photographs 1 and 2. In Figure 1, peak current (Ip) and peak

voltage (Vp) identifies the point on the curve where the negative

portion of the V-I curve begins and valley current and valley

voltage identifies the point where the negative portion of the V-I

curve ends. These models use controlled current sources to

I

~ Ip il.) i-1 CJ C'~ ;:: r~

'T"i ....... ....... ..... s -

v VOLTAGE (millivolts)

Figure. 1 Tunnel Diode Current-Voltage Characteristics

o_

u

2

! !/ v I I

I I I )

I I I 1/ I

if - V1

Photograph 1 (traced) TD-19 Current Voltage Curve

CURRENT-2ma/cm VOLTAGE-O.OSv/cm

/'/ I I

I I

\ i I II

I

I I I I I I

I I

J I l

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Photograph 2 (traced) TD-13 Current Voltage Curve

CURRENT-0.2ma/cm VOLTAGE-O.OSv/cm

3

realize the negative slope portion of these curves rather than

the negative resistors used by other tunnel diode models.

The models shown in Figure 3, 6 and 9 use all of the

available ECAP stored elements; resistors, inductors, capacitors,

voltage sources, dependent current sources, and independent

current sources. The method used to select the element values for

a particular tunnel diode is discussed in Appendix II.

II. MODELS AND CURRENT-VOLTAGE CHARACTERISTICS

The first model shown in Figure 3 and its current-voltage

curve in Figure 2 represent the simpliest meaningful straight

line approximation of the current voltage curve of the actual

I ~

~ Ip ~ ~ ~ ~ 8 ~ ~ ~ ~ ~

E '-'

~ z ~

~ ~ u

Iv

device.

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VOLTAGE (millivolts)

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Figure 2 Model 1 Current-Voltage Characteristics

The conductance G1 shown in Figure 3 is the element which

accounts for the positive slope line from (0,0) to (Vp,Ip).

4

At that point the controlled current source with -GX1 and control-

led by current in R3 is switched in the circuit S2 and provides

the negative slope line from (Vp,Ip) to (Vv,Iv). Then the control-

led current source with GM1 controlled by current in Rz and current

source -I1 are switched in for the remaining positive slope

The model is discussed in more detail in Appendix ~I.

5

'Ilk ECAP data in TABLE I describes the model of Figure 3

approximating TD-19 General Electric tunnel diode.

TABLE I Model 1 ECAP Data

Transient Analysis Bl N(l,2), R=(lOE7,0.36) E2 N(2,0), G~(0.154,0.058), E•(0,-0.355), I•(0,-0.00095) B3 N(2,0), R=lOES B4 N(2,3), R=l0E8 B5 N(3,0), R=O.OOl, E=-0.065 B6 N(2,0), R=l0E8, E-0.355 B7 N(2,0), C=l7E-!l BS N(4,1), L=O.SE-Y B9 N(2,3), R=l0E8 c ******************************************************* C These three cards describe the voltage generator to C give the voltage sweep for determining the model V-A C characteristic. BlO N(0,4), R=30, E=(l.5,0) Bll N(4,0), C=O.OSE-6 Bl2 N(4,0), R=l0E8, E=(-0.45,0) c ******************************************************* Tl B(9,2), GM=(0,0.185) T2 B(4,3), GM=(0,-0.185) Sl E=l, (l) , OFF 52 B=S, (3,4), OFF S3 B==6, (2,9), OFF S4 B=l2, (10,12), OFF

W!1en determining the current-voltage characteristic of the

model, B7 and B8 should be changed to the following:

37 N(2,0), R=l0E8 B8 N(4,1), R=O.OOl

This is required because the energy stored in the capacitor and

inductor are of the same order of magnitude as the energy cissi-

pated in the other elements and changing the direction of the

voltage and current cause the capacitor and inductor to reverse

bias the model. \\fhen used in a circuit these effects are normal

and ~ccount for the internal inductance capacitance. The

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VOLTAGE (VOLTS)

Figun• ( H-c1~1 1 Cun·cnt-Vo1t<Jg,' Curve

8

results of the ECAP program using this data are shown in Figure 4.

The results verify that the desired curve has been generated. How-

ever when compared with the actual device current-voltage curve

of Photograph 1, the model is seen to represent the actual device

rather inaccurately as expected.

The second model shown in Figure 6 with the current-voltage

curve in Figure 5 represents a modified straight line approxi-

mation of the current-voltage curve of the actual device which

will give a more exact approximation of the actual device charac-

teristic.

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Figure 5 Model 2 Current-Voltage Characteristic

The conductance G1 shown in Figure 6 provides the positive

slope line from (0,0), to (Vl,Ip)• Switch S2 changes Gl and

switches in the current source -II to provide the constant current

line from (V1 ,Ip) to (V2,Ip)• Switch S3 then turns on the con-

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10E7,R5

R9

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Figure 6 Hodel 2

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trolled current source -GM1 controlled by current in R4. This

provides the negative slope line from (V2 ,IP) to (V 3,IP). The

constant current line for (VJ,Iv) to (V4,lv) is generated with

10

GM1 controlled current source controlled by R3 current, and current

source Iz being turned on by switch S4. The conductance G2 turned

on by switch SS generates the positive slope line from (V4,Iv).

The model is discussed in more detail in Appendix II.

The ECAP data in TABLE II describes the model of Figure 6.

TABLE II Model 2 ECAP Data

Transient Analysis Bl N(l,2), R=(l0E7,0.36) B2 N(2,0), G=(O.l61,1E-8) B3 N(2,0), R=l0E8, E•-0.0618, I•(0,-0.01) B4 N(2,3), R=l0E8 BS N(3,0), R=O.OOl, E•-0.0682 E6 N(2,0), R=l0E8 B7 N(2,4), R=l0E8 BS N(4,0), R:O.OOl, E=-0.249 B9 N(2,0), R=l0E8, !•(0,0.00905) BlO N(2,0), G=(lE-8,0.0887), E•-0.408 Bll ~(2,0), C=27E-12 Bl2 N(S,l), L=O.SE-9 Bl3 N(2,3), R=l0E8 c ****************************************************** C These three cards describe the voltage generator to C give the voltage sweep for determining the model V-A C characteristic. Bl4 N(O,S), R=30, E=(l.S,O) Bl5 N(S,O), C=O.OSE-6 Bl6 N(5,0), R=l0E8, E=(-0.45,0) c ****************************************************** Tl B(4,6), GM=(0,-0.0492) T2 B(l3,9), GX=(0,0.0492) Sl B=l, (1), OFF S2 B=3, (2,3), OFF 53 B=S, (4,6), OFF S4 B=8, (9,13), OFF SS B=lO, (10), OFF S6 B-16, (14,16), OFF

When determining the current-voltage characteristic of this

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VOLTAGE (VOLTS)

.-

..... .....

model as with the first model, the capacitor and inductor must be

rc~oved and replaced with an open and short respectively. Bll

and Bl2 should be changed as follows:

Bll N(2,0), R=l0E8 Bl2 N(S,l), R=O.OOl

The results of the ECAP program using the second model are

shown in Figure 7. The results verify that the desired curve

has been generated. In comparison with Photograph 1, the current-

voltage curve of the actual device, it is evident that this rrodel

does give a more exact approximation of the actual device character-

is tic.

A third model is shown in Figure 9 and its current-voltage

curve in Figure 8 uses resistor-capacitor time constant effects

to eliminate the straight lines and sharp corners of the other

two w~dels.

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Figure 8 Model 3 Current-Voltage Characteristic

12

,

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---------------------, ,. ' ----- - ~/- ..... -- - - -- - - - - - - - - - - - - _,_ ... "<""- - -

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Figure 9 Model 3

Gz

..... lo)

The conductance c1 provides the curve from (0,0) to {Vp.Ip).

The negative slope portion of the characteristic from {Vp,Ip) to

(Vv,Iv) is generated when Sl turns on the -BETA controlled cur-

rent source, controlled by current in G2, switch S2 turns off

Rg to provide the remainder of the curve from {Vv,Iv)• This

completes the characteristic for increasing voltage. However

this model unlike Models 1 and 2, uses a different portion of

the circuit for decreasing voltage. S4 and SS turned on during

increasing voltage but are used for the decreasing portion of the

curve. ~~en the voltage reaches the maximum and starts to decrease

switch S3 turns off. C2 is allowed to charge up again increasing

current in G2,decreasing it in controlled current source. When

switch SS turns off as the voltage decreases the C2 capacitor stops

charging up discharge reducing current in G2 and increasing current in

c1 . This action is what gives the characteristic its premature

rise of current. This will be discussed in greater detail in

Appendix II.

The ECAP coding of TABLE III describes the model of Figure 9.

The results of ECAP program using the third model are shown

in Figure 10. This model for increasing voltage duplicates the

actcal device closely, however, there is a large discrepancy on

retracing the curve for falling voltage.

The first two models shown use the same components to approxi­

mate the tunnel diode during the rising and falling of voltages.

The third model, however, uses part of its elements during rising

voltages and part during falling voltage. In selecting one of

these models, the desired accuracy is the basic criterion.

14

15

TABLE III Model 3 ECAP Data

Tra~sient Analysis El N(l,2), L=0.8E-9 E2 N(2,3), R=0.36 B3 N(3,0), G=0.154 B4 N(3,0), R=l0E8, E=(-0.355,0) B5 N(3,0), R=l0E8, E~(-0.065,0) B6 N(3,0), C=27E-l2 B7 N(3,0), R=l0E8, E=-0.355 B8 N(3,0), R=l0E8, E=(-0.408,0) B9 N(3,8), R=(O.Ol,lOES), E=(0,-0.45) BlO N(S,O), C~2E-12 Bll N(0,4), R=(lO,lOE8), Ec(l.5,0) Bl2 N(4,5), R=(lOES,O.l) Bl3 N(5,6), R=(0.1,10E8) Bl4 N(7,6), R=(lOO,O.Ol) Bl5 N(9,7), R=(l0E8,0.01) Bl6 N(0,9), R=(lOE8,19), E=(0,0.875) Bl7 N(6,0), C=O,OSE-6 BlS N(6,0), G=0.308 c ****************************************************** C These three cards describe the voltage generator to C give the voltage sweep for determining the model V-A C characteristic. El9 N(O,l), R=(l0,10E8), E=(l.S,O) B20 N(l,O), C=O,OSE-6 B2l N(l,O), R=l0E8, E=(-0,45,0) c ****************************************************** Tl B(l8,3), BETA=(0,-0.8) Sl B~S, (3,5,12,18), OFF S2 B=4, (4,11,13), OFF S3 B=lO, (9,16), ON S4 B=S, (8,15), OFF S5 B=7, (14), OFF S6 B=21, (19,21), OFF

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'---------., ___________________________ , _ t ________ t __ ______j__ _____ L ____ _______~ _ .__ ___ ,L_ ___ ___j__ ___ ,L ____ j____ __ ___,c__ L_ ___ t__ __ __._ __

.03 . 06 .09 • 12 .15 .18 .21 • 211 .n • 30 .33 • 36 • 39 .42

VOLTACE (VOLTS) Figure JD }·lfldel 3 Cttncrll -Voltar,e CuJ:VQ

_l_ __ _

.45 .'J8

..... 0'\

17

III. MODELS IN CIRCUIT APPLICATIONS

All three models were tested in various tunnel diode

circuits. A relaxation oscillator circuit Figure 11 and astable

multivibrator circuit Figure 12 were used •

301

.l

5.9 ~

. OOOSE-6 I 1-----...,

TD r---..... ~----1

TD-19

22 .OOOSE-6

Figure 11 Relaxation Oscillator

jlE-3

In the operation of the relaxation oscillator the output

volta6C initi8lly jumps to a level of approxim~tely .4 volts.

The voltage decays during which time the tunnel diode voltage is

increasing. ~1en the tunnel diode voltage reaches peak volt

the output voltage goes negative due to the effect of the capacitor

inductor circuit. At the same time the tunnel diode voltage has

increased to greater than valley voltage (Vv). The output voltage

decays and when the tunnel diode voltage decays to valley voltage

the output voltage jumps positive and repeats. This circuit

output voltage is shown in Photograph 3.

0

18

~ I

"~ \ I 1

v \

Photograph 3 (traced) Oscillator Output Voltage Waveform

VOLTAGE-0.2v/cm TIME-20u sec/em

l \

l

I \ - --~

I .

'

I I

~-~

T I 1

I -.J

I

~I I ~ .. ---

Photograph 4 (traced) Hul ti vibrator Output Vol ta~;e I.Javeforn

VOLTAGE-O.Sv/cm TTI1E-2u sec/ em

25.5 lE-3

.26

TD

D-13

19

Figure 12 Astable Xultivibrator

In the operation of the astable multivibrc::.tor the outp~t

voltage is zero volts to start out. It stays low until this

tunnel diode voltage reaches peak voltage (Vp) then the o~tput

voltage goes straight up past valley voltage (Vv) due to inductor

actio~. The voltage stays high until it has decayed to Vv then

the voltage drops down to zero and it repeats. The waveform for

this circuit output voltage shown on Photograph 4.

The ECAP aata for Model 1 is shown in TABLE IV. The output

wav~fot'"m for the oscillator circuit, the voltage versus tix:1c c::.t

node 6, is shown in Figure 13.

?he output waveform in Figure 13 approximates the actual

device output voltage at the beginning but failed to go into

oscillation.

The ECAP dat::a for Model 2 is show-n in TABLE V. The output

waveform for the oscillutor circuit, the voltage versus tirce ut

node 6 is shown in Figure 14.

20

TABLE IV Model 1 Oscillator ECAP Data

Transient An.:llysis Bl !.'1(1,2), R=(l0E7 ,0,36) E2 N(2,6), G=(O.l54,0.058), E=(0,-0.355), I= (0,-0. 00095) E3 I\(2,6), R==l0E8 B4 N(2,3), R=l0E8 ES N(3,6), R=O.OOl, E=-0.065 B6 N(2,6), R=lOES, E-0. 355 B7 N(2,6), C=27E-12 BS N(4,1), L=0,8E-9 B9 N(2,3), R==l0E8 rno N(4,0), R=22 Ell N(5 ,4), R=30l Bl2 N(0,5), R=O.l, E=5.9 Bl3 N(L;,6), C=O.OOOSE-6 Bl4 N(6,0), C=0,0005E-6 3:!.5 N(6,0), L=lE-3 Tl B(9,2), GH=(O,O.l85) ~') .1._ B(Ll,3), GM=(0,-0.185) Sl B=l, (1), OFF S2 B=5, (3,4)' OFF S3 B=6, (2, 9) ' OFF

The output waveform of Figure 14 approximates the actual

device output until the first diode switch tries to turn on at

p.:ak voltage (Vp)· Then the switch oscillates for the remainder

of the test.

The ECA? data for Hodel 3 is shown in TABLE VI. The

output wavcfo::r:. for the oscillator circuit, voltage versus

timz at node 10, is shown in Figure 15.

-tf)

~ ~ -~ ~

.s

.4

• 3

• 2

.1

'-··

" . .

'

. .. . ' ·'-

··. . '

1

'• ··. '@...._

j

'l ..

.. .. ~

,. .. ....... .....

I -' - .; ' ! .

3 4 Ot f----f

-.1

-.2

-.3

-.4

-.5

Figure 1~ Model 1 OGciJl;

~

5 6

I . i

i j

j ..

i .. I ..

~

,, ! ' I

i j i -- ... ;· ··-·

9 lO

c: - ( ·:c· :;· L~ ~- (~ ·;~ ~~ :-:. :~- ;1

,.~~(.; !: t:

' ~ i ,_ .

' '0 ... -I

I ·-·-· i i

11 12 1

Gi.tCL:i.t d~:::;..:

I I

L I r· i

,_ i

-+--

H

--<.::>

1---+ I --+S -1---. -{-------. : "l •••• •' ................. . I i I . • • ··C'···· .... '

r J •• ,.~•·••••• ... .... ..... •"" ..

' ... . ··

/.

i/

i -/cr"' . !/

/,

TlHE (lo-5 seconds) Output Havcfon11

../

.......

I ...0""

/

N .......

B2

36 E7 .. 'If"'\

.JO

B9 BlO

Bl2 El3 Bl4 Bl5 51.6 Bl7

Dl9

T2 Sl

S3 S4 S5

TABLE V Hodel 2 Oscillator ECAP Data

Transient A;.1alysis N(l,2), R=(l0£7,0.36) K(2,6), G=(0.161,1E-8) K(2,6), R=lOES, E=-0.0618 N(2,3), R=l0E8 N(3,6), R=O.OOl, E=-0.0682 N(2,6), R=l0E8 K(2,L;), R::::lOE8 N(4,6), R~O.OOl, E=-0.249 N(2,6), R=lOES, 1=(0,0.00905) N(2,6), G=(lE-8,0.0887), E=-0.408 N(2,6), C=27E-12 N(S,l), L=0.8E-9 N(2,3), R=l0E8 N(7,5), R=30l N(5,0), R=22 ~(0,7), R=O.l, E=5.6 N(5,6), C=O.OOOSE-6 N(6,0), C::::O.OOOSE-6 N(o,O), L=lE-3 B(4,6), GH=(0,-0.0492) B(l3,9), GN=(0,0.0492) B=l, (l), OFF B=3, (2,3), OFF B=5, (4,6), OFF B=B, (9,13), OFF E==lO, (10), OFF

22

The output waveform in Figure 15 approximates the actual

circuit waveform. The difference in amplitude and frequency is

due to the different source voltage used in the ECAP model

~nd the &ctual circuit.

The ECAP data for Xode1 1 is shown in TABLE VII. The

output w~veform for the multivibrator circuit, voltage versus

time at node 6 is shown in Figure 16.

-tl)

H t-1 0 :> ........

. _';

• I}

.3

.2

• 1

·. . ' ..

" "

. . . ' "

.. ··. . '0 ..._

.. .. .. • • a I ··... r .. ---. ... ,/:_ '

--. .-..... --v

r

' f

I '

! l i i I ! : ~ -· --I I

s~,..i 1~ch :2 ()n.t.i.ll.t:d"';:''-l (}:\

Vo)· Pc·;t;"dt~tk1." Of l'(':;i:.: .

~-i ' I

I J

'r. " ' ~ '.·1 t .-,:

r

_:ct::t _C:!:rc~·;i,t

~ -1 --·­! !

' ! 1-- " • .. ,! "i

dt.t;~

~~! ~d Off . '0_

.......; - ....... - --:--0 L

I......,_

·l 1

I l

n (.!.i

0 1-----~-- .. l-----1---f-- ~-<" I -1--------~- .. --+---+·--._ ... J

f (.; . 1 :,::.. . -

-.2

-.3

-.4

-.5

::, "! .l I~

,. _l 7 ~

I I ;

1/

i i/

,/ --:-

0/ / '

/ /

/ /

/

c{

i TIME (lo-5 seconds)

Figure 1~ Mod0l 2 Oscill~tor Outpvt Waveform

J (, I J • 1 ·:; J -~ :I 1. •• "

i ,.....&

J 'r J ,. :) ~ ,

N w

,,-

B3 _, D'-}

BS

B7 BS B9 BlO Ell Bl2 :213

Bli' :2.:~ 8 :::::.9 320 E2l E22 B23 324 Tl Sl. S2 S3 S4 S5

:'AELE VI Hodel 3 Oscillator ECAP Data

Tr;::.sient .\nalysis N(l,2), L=0.8E-9 N(2,3), R==0.36 ~(3,10), G=0.154 N(3,0), R=l0E8, E=(-0.355,0) N(3,0), R=l0E8, E=(-0.065,0) K(3,10), C=27E-12 K(3,10), R=l0E8, E=-0.355 N(3,0), R=l0E8, E=(-0.408,0) N(3,S), R=(O.Ol,lOES), E=(0,-0.45) K(3,l0), C~2E-12 N(l0,4), R~10,10~3), E~(l.5,0) ~(4,5), R=(lOE8,0.1) K(5,6), R=(O.l,lOES) N(7,6), R=(lOO,O.Ol) N(9,7), R=(lOES,O.Ol) N(l0,9), R=(lOI::8,10), E=(0,0.875) N(6,10), C=O.OSE-6 N(6,10), G=O.JOS N(l ,0), R==22 N(ll,l), R=501 i\(0,1:!.), R=O.l,E-5.9 N(l,lO), C=O.OOOSE-6 :~(10,0), C=O.OOOSE-6 K(lO,O), L=lE-3 3(13,3), E~TA~(0,-0.8) B=5, (3,5,12,18), OFF 3=4, (!>,11,13), OFF B""lO, (9,16), ON n~S, (3,15), OFF B""7, (14), OFF

The ou'::put ~·;<:vefoi'ill in F::.gu:-e 16 approximates the actual

d~vice ou~put voltage very closely.

The ECAP dat<:! for }loC:.::!l 2 is shown in TABLE VIII.

output waveform for the nultivibrator, voltage versus time at

node 5 is shown in Figure 17.

24

-tl:l f-4 .... , 0 :> ._, w L~

~ ... ~ p ~

5 ·-

4

.'\

' ' '

,. '

i G

' I. ' I '-.

;:t._." [·.~~-!~ .1.

i ....... : Tcr.~·. Cl::r_.~_:.~ L r'::

' l ! .

........

' ' ... ' ' i ....... _

(.:) ··~ -...

1 --..;_

h •:;

-- -... . .---·_ ... ::::J

I I ,.. I

!

.. !

-'

. )

0 t _; ____ ;:_ ___ _j _____ --11-------- I I

~~ L J c 7 !-----~--: -~---·---!-·-~·

B ~? H• --+---+qr-----4

l 'l .....

-1

-3

-4

-5

J

/ /

..

' / /

/

/ /'

/ /

_,.")­

//

TIME (lo-S seconds) Figure 15 Hodel 3 Osd J ];>Lor Oul)1Ul t·!;.-..-~- fon1

,. I I

........... t\>..__

:

........._ i-.....--.. ! -~ .. ----·-.. -0

1? 13 J_{; 1~, J{:' --l-----1·---1---·1-----

N V•

Tl.;.):E VII ~1odel 1 Multivibrator ECAP Data

Tr~~sient Analysis 31 N(l,2), R=(lOE7,1.7) 32 N(2,0), G~(O.Ol54,0.0058), E=(0,-0.355), I=(0,-0.000095) S~ N(2,0), R~lOES 34 N(2,3), R=l023 BS ~(3,0), ~=0.001, E=-0.065 36 N(2,0), R=l0E8, E=-0.355 57 N(2,0), C=3.5E-12 ES N(4,1), L=O.SE-9 [g ~(2,3), R=lOES B:J N(5,4), L=lE-3 Ell N(6,5), R=25.5 Bl2 :~(0,6), R==O.Ol,E==0.26 Tl B(9,2), G}l=(O,O.Ol85) 'I'2 B(4,3), GH=(0,-0.0185) s: B~l, (1), OFF S2 E:::5, (3,4), OFF 53 B=6, (2,9), OFF

TABLE VIII Model 2 Multivibrator ECAP Data

El B2 33

E5 B5

Tra:.:.sient ;:-.!(1,2), N(2,0), )1(2,0), N ( ? -) _,j '

N(3,0), N(2,0),

Analysis R= (lOE7, 1. 7) G:::(O.Ol61,1E-8) R=l0E8, E=-0.0618, R""l0E8 R=O,OOl, E=-0.0682 R""lOES

37 N(2,4), R=lOES :.:-3 , r-:(L,,O), R::..:O.OOl, E=-0.249

I= (0 ,-0. 001)

:)9 :,(2,0), R::.:lOES, !=(0,0.000905) ;~::.0 :H2,0), G=(lS-3,0.00887), E::o-0.408 ~~l ~(2,0), C=3.5S-12 ~l2 ~(S,:), L=0.8S-9

015 ::C.l6

S3 S4 S5

N\2,3), :\.::..:1028 ::\(6,5), !...=lE-3 v17 6) R""25.5 ... \ ' 5I

N, .,7), ~=O.Ol,E~0.26 .• ~L;,6), GN=(0,-0.00492) DC3,9), GA:-:(0,0.00492) I3z:o l , (l ) , 0 FF D=3, (2~3), OF::' B= 5 , (Lf • 6 ) , 0 YF :S""-3, (9, 1.3), OFF E=lO, (10), OFF

26

I I

.. . . '·

/ /

-I

I I

.· . . :

.. / . .

j )U

I I

/

.. /

: :

:

. / 0

/

: . .

: . . /

-• .1_

.• -··

':. . ':. . • .

~ \ \ \ •' . . :

\ \ ·. \ L.7

. .

... ! I I j l ! I ..; '

·. '

\ . . ...

.... , . I "l I _! j l '

\ I

c -: l

\ j

\I ... l I l I ~

··~ i C· ._

\': I •.

\ : . \ : \ .... l _, ' I I I \ ·..

: . ...

\..._

!'

\ ·. ' ".1

---·-·------------------~~----------------~~----------------~~-----------------l------------------~\0 0

(SJ.10A)

~:)V~'IOA

0 ..... 0

~ ....

i 0 ' (.

/ / /

f\' .· : : I I

. . I .. :

4 . . . / :

/ /

/

'···

(""; N

(SJ.'1CA

) 3::)V

.L10A

0 \

/':

/

·. \

. _

,/

: ,..-

·. \ \

28

·::;

.)

u-. i ! .....

I -l ~

l ..... I j

("")

.....

~ <"'-;

-.... --0 .....

\ ...J

c-

\ \ ~

c.:;

\ : ,; \~

1'

! -; ..0

! I -· ""'

-1 ..::-

-....... \ : \ · •. \ -~

-N

\

,. \ : \

~.

\:. ,.....

. \ \ . I • 0

.... 0

..0

I c

~~

0

29

The output w.:veiorm in Figure 17 ap?ro::drr.atcs t:•e actu;:;l

C.cvic.a ou-cput voltage, however, like l·!o~cl 2 on the osci.llutor

circuit, the first switch at tunnel diode peak voltage oscill~ted

for approximately half of the program before continuing.

IV. CGXCLUSIOl\S

These thre.:! rr:oclcls are simila~ in th~:t they all cha:tge

current lev~ls to simulate the tu~nel diode curve. They are

riifferent in complexity and also in the type of elements used to

ch~nge the current.

Hodel 1, the three section piecewise-linear model, is the

sir:1pliest of the three. The eleme:1t used in generating the

c~~ren~-volt~ge curve is the dependent current source. The curve

is generated by switching in or out the proper dependent current

element. The clata plotted in Figure 4 shows that the rr.odel

dis?lays the negative resista~ce regie~ and accurately follows

specif~ed path for increasing and decreasing voltage.

}:odel 2, tue five section piecewise-linear model, is similar

:.:o I·:oC:cl 1 using straight 1::.~'1es, although, it more closely

3L~:...::i3teci the actual tunnel diode current-voltage characteristic.

Eoc;~l 2 switc~es both dependent &nd independent current sources in

o-:: Ol't or tl-;e ci:::cuit to generate its curr~:J.t-volt.:ge curve. The

c~t~ plvtted i~ Figure 7 shows th~t the ffiOdel d~?licates the desired

curv.:; for bo·.:::h incrcasir.g and deere.:;:; ing vol ta:;cs.

'!-~odel 3 has C! sn.ooth current-voltage curve .:s o·?;:;os..:;d to

ou: current g2ncratcd from an RC circuit. The CC!ta plo:t~J i:l.

r:..zt.re lO shm.;s the r.1odel ~s simulating a portion of the d.:;sired

c~::vc for volt.;::ge up to valley voltage then the model deviates

:Zror" ;;he desired curve, althout;h, it still looks like a tunnel

31

diode for increasing voltage. The model can simulate a device

~..r.1.:;::.-e the dec::ea::;ing voltage is not ~sed. The characteristic for

~~creasing voltage looks like a tunnel diode curve but again

differs considerably from the desired c~rve. The reason for

the difference is due to the met~od of selecting the parameters.

C~ t~is rr~del it was done by a t::.-ial and error rr£thod. Parameter

selection is covered in more detail in Appendix II.

To verify the operation of the ~odels in circuits, data

~•.:.s ;:a:(en on Hodels 1, 2 and 3 in a relaxi!tion oscillator and

H.::ccls 1 .:.~1d 2 in an astable multivibrator. Due to the method

of switching in and out the curreat in Hodel 1 and 2, the tir.1.e

step must be selected in relationship to the sr.~allest tir;:c

co~st~r.t of the circuit. If the tir.~e step is too large the

s\o.r:..::ch will oscillate. This problem existed on Hodels 1 and 2

~,;.'-1til the ti:.1.:; step was select~d in the range of lE-9 to

l.2-l.l. J:'~1is grea·::ly extei.1ds the cooputer time reGuiring c.n

I-:0t..:.:- ;:a ~~:.1 .:1 ?ro;:;r.:;m of 10-100 micros..::conds. Eodcl 3 using

cu-.:~·"-::.t ge:ner.:ltccl in a::1 RC ci:::-cuit does not have the s.:.r::e pro~ l~r.:

_;: ~~c switches, sine~ tho nature of RC ci:::-cuits is a ~ore gradual

c~~~~c, this a~lows Xodel 3 to use a large ti~e step, ~n the

~an~c o£ 2.53-6 a~d thereby reduce the corr.pute:::- time requi::~c.

7~c ~~ta plotted for Xodcl 1 in the oscillator circuit,

~igurc 13 s:;o'"'"' t!1e out:;...;t voltage as st.:trting as the actual

ciJ:c~it ?hotor_;rapi"! 3 however, it does not go into oscillatio:-t.

~he voltaze used in the ECAP program is 5.9 volts which i» the

32

a~cu&l ci~cuit was at upper threshold of oscilla~ion. The ~o~cl

s2~r.:~ to be f.n.;r£crt.1ing as expcct..;d, und if t:~e circuit wa5 r2Tu:1.

using a lom::r v.:>ltagc such as 5.6 or 5.3 volts the output voltagC!

~ould oscillate similar to the actual device volta~e.

Th~ data plotted in Figure 16 for Model 1 in the nultivibrator

c::. :.:-.::cit s::,J';vs the r:.odel performing as expected. Cor:tparing tr.e

plotted results to Photograph 4, Model 1 doE:s simulate the tunr.el

diode, in the nultivibrator circuit.

T~e data plotted in Figure 14 for Model 2 in the oscillator

c~rcuit shows that the nodel goes ~nto switch oscillatio~ at

·.::.:.:-.::cl diode peak voltage the first switching of a current

.;;lc~.:.::.nt. and does<•' t get past the switcr .• The data plotted for Nodzl 2

..... I:',ultivibrator circuit shown in Figu.:-e 17 sho\.JS tha SO.lT.e preble:::

as t:1.;;: osc!.llation circuit. In the r.ml ti vibrator circuit the

s-v;,::.tch S2 .:>;;;cillatecl until. the current in the tunnel diode in-

~~~~sed enough to supply the current source and the re~aining

c:c~2~t~. Then ~h~ program procced~d. After that point the c~del

s!~ul~t~3 th~ first portion of the actual waveform in Photogr~~h 4.

:s b~:~~ cliv~ded with other ~lcm~nts. The current availa~!e f~o~

L~~ v0~ta~c source is lc~3 than required by the currc~t source

~cc with the series inductance in the circuit, the capacitor is

::-,c only e lcmcnt that the current source can draw the current

.... ·, ~ . -.)

L ',.___

i::.:.:t:.ctot· is rc:-.:ovcd f::-or.1 th.:! circ ·.;it tb.: c~.;rrcnt sou::-ce cc"Jlc

r~ceive ~ll its current fron the volt~gc source 3r1d sho~.;ld ~ot c.:.::

switch osc~ll~tion.

M0J2l 3 w~s only tested in the oscill~tor circuit bccau~c

t~~ ~od~l ~~s only set up for the ~J-19 ci::-cuit. T~e cethod of

The dat& plotted in Figure 15 shows th~t

t~~t ci=cuit Yill oscill~te and ::-c?r.:.:scnts the actual diode &s shown

circuit voltage used en the circuit.

:iocicl l si:.:1ulates the tur.nel diode in t he ci::-cui:s te s ted.

T~·, .:; ;·:.o.::.e.:.. is sir.~ple c.lthough, it required considcr.::ble cc:-::puter

ti;-;:e to run each circuit.

~oci~l 2 ~id co: give accc?t~blc results, .::lthough, wich

- . - . . ~·.:o c.~:.:. c~ ~ :.ci-:s it coulJ ope~.::te .::s i:1tcndcd.

:-::cC:.ific~tion is to re::-.ove the s;:;rics inductor (L ;:; )

..... ~· _ .., .., • l - · ... ... .__ .. ~.,...~...;._ ... .

. -. -· -~,.... -· , -lt,..--l.... .......... ~o.o.

, • • ,.... _l . ' .... V\..'-- to scl(;ct

calcula~ing time versus cocputer tirr.e.

? a r z. r.:e ~ c r s .

o.-.c possible

A??ENDIX I

SL~~RY OF MODELING OF ACTIVE DEVICES

FOR COXPUTER-AIDED CIRCUIT DESIGN

34

35

Cor:<putcr-Aided Ci::-cuit Ar.alysis is one of the f&st cx·?;:.;-,ciir.g

L~CS Of the COmputers of today. X~ny progra~S ~~Ve been written

to analyze or design electronic circuits. Many were designed

<=.-. ·-~=· f , r ~ ~,-,. · Fil r~l ~v~ one spec~~~c purpose; or exam?~e, ~ow-l'ass ~~~l?tlc · tcrl-'.

Band Pass Ladder Crystal Filter Dcsign[4], Poles and Zeros of

k~plifier Transfer Functionsf4,ll], Flip Flo? Worst Case Dcsign[3l,

Ir:.vertcr \cJorst Case Design(3], Envior:-;;ental Resistance Inherent

L'- Equipr.:.:::nt [ L,] and m..:rr:"'rous others.

S..::;;ne p::-ograms of a more general n.:1ture have been developed

that c.::n be used to analyze many kinds of circuits, sor::e such

progr.:.;:·.s arc Transistor Circuit Analysb (NET-1) [4,10], System

for Circuit Evaluation and Prediction of Transient Radiation Ei~cct

(;;CE?'.:X:.::) (13], Electronic Circuit Analysis of Electronic Circuits

Ali of ~he p~obrams, Doth S?~cific and ge~er~l, nust in so~~

0i. ~~s~lts of ~~y of these progr~~3 and the e:::fi.cie::;:c use of

c~2:~c~crist~cs. The ~odcls for resistors, capacitors, inducc0rs,

v0lta~c sources, and current sources are generally included as

36

stored models of the programs. Models for diodes, transistors

and other active devices are non-linear type. NET-1, SCEPTRE

and CI~CUS have some of these models stored in their programs.

Some programs, ECAP in particular requires the user to supply the

~odels. ECAP, while not handling the non-linear models, can still

approximate non-linear devices with piecewise-linear models.

Regardless of \vhich program is used, the models must be developed

~o simul~te these devices. A number of models have been developed

for the the diode. The primary difference in these various

~odels is the differe~t elements used to simulate the device

~nd the para~cters used for these various elements. These dif­

ferenc.:!s arise from linearity or non-linearity of the uodel and the

accuracy re~uirc~. Diode current-voltage curves simulated by

various models are shown in Figure I-1.

I

-----.-----v A

A) Ideal

:B

B) Piecewise-Linear

I

=========..:!""'----- v

c C) Non-Linear

Figure I-1 Diode Current-Voltage Characteristic

37

The simple linear switching diode model[6J Figure I-2A

with large resistaace when the current is in the reverse direction

a~d small resistance when the current is in the forward direction

a?p~oximates the current-voltage curve of Figure I-lA. The more

corr:plex modcl[l] Figure I-2B which takes into account transi.tion

cavacitance diffusion capacitance, bulk, and leakage resistances,

and current source approximates the current-voltage curve of

Figure I-lB or I-lC. This model can be linear or non-linear

dcpendi~g on the values of the elements of the model. The more

coillplcx the model the more parameters must be supplied to simulate

a device.

A B

cd

~------~: (~------

1 I ,,.._, -----< ~----t

I (---Q

t~.--~i----ll c

Figure I-2 Diode Models

7te number and type of elem2n~s used in a model is a function

of tl:e a?proach taken to simulate the current-voltage relationship.

Gne approach is to use conventional elements to develo~ tte required

curren~-voltage curve without using the device parameters. An

alteraate approach is to use conventional elements to develop the

required current-voltage curve but use the device parameters plus

38

acditio:-.al measurements. This approach is used with the Ebers-H'oll

rnodelt4] Figure I-3.

Cse+cte etc

I j I

0 6 ' E c

__.,.. -<-

IE Ic

B

Figure I-3 Ebers-Moll Model

A thirci a?proach used in the developm~nt of the Beaufoy-Sparks

Ch~rgc Control model[4) Figure I-4 and the Linvill Lumped

rs 9 '4'J rr.ccielL • ,~ Figure I-5 is to approximate the current-voltag~

c-.;rvc by using conventional elements and by creating new elcn;;:nts

~s ~cquired. The new elements are used to simulate an internal

pi1ysical phcno;.:~enon. Beauioy-Spark.;; Charge Control model intra-

C:uccd the base store Sb element. Linvill Lu.'1lped model introduced

~:h:::-~e new ele::.1cnts' stor.::tnce se' diffusancc zd and combinance ••e·

The Linvill r.-:odel n:ost closely rcp:::-csents the physical device

phcno;~:.:!non, however the Ebe:;:s-Noll rr.odel is used most widely

:.-ccause r.o r.c\J circuit clements are required. This is an adv.o.:1tage

since the ele~ent values can be determined by measuring a typical

39

i.:nit or assured from the manufacturer's sheet.

.,.. Vn.,. OB/tc

.c. )>--+<r 8 ('

0

r r <> 0

I I I I I I

cbrco _L <:: 't:h~ etc.::: - ¢QB c ~c -.- ""Be---

' ~t -sc• ta l

l 1 I tB

I j

1 rbb

B Figure I-4 Beaufoy-Sparks Charge Control Model

~r -·or-----~Ill~-----~ ........L-

c

n(o) He

B

Figure I-5 Linvill Lumped Model

t,O

hrork has been done on a Zener Diode model [ 1 l fi rrure r-r.-~- v

by :.~.:>drfying Ebers-Xoll diode topology of Figu:::-e I-2B. This

mociel c~~ be linear or non-linear depending on the values of Ll

c ... ...

Fig~re I-6 Zener Diode ~odcl

Some work has been dor.e uith negative resist.:mce devices,

r • , D~~iclsl~J put forth several curve fitting methods for tunnel

d~cd~s by fitting the entire function with I(v) = Ave-ab +

··.~,·',::. .. ~1V - eb?vJ' + t'(eCV-1). Th" · · h f ~ - - - ~ LS equatLon lS t e su~ o the

t~~~cling curre~t, the d~ffusion current, and the excess curre~t,

::-cspi.O!ctivcly. Another method of representing the V-I charact~ristic

i~ to divi~c it into several zones and fitting the cu;:ve with a

'I'h.;:; A0 , A1, A2 •••• A11 are oi:ltained fron r::easured data.

I<.. H. Je>.J.sen and M.D. Liebcr:nann[7] in their book IE:-~

Elc:::tronic Circuit Analvsis P:--c..;:;r.::m T2chnigues and Applications

show a turned diode modeJ, for ECAP. See Figure I-7.

The n~del uses negative resistors to provide the negative

sl~:~.:;. T'!-.c capacitor is added to prevent the model from lockir.g

I

.. I

I --I s;~~

i ! -'- _._

41

I I I :

-,, T I '-· ---->----~------~-· ------<lo---.....J

! c

Figure I-7 Tunnel Diod8 }~odel

up. Lock U? can o.:.cur \vh.::n th.; model is switching to the ::cgativc

rcs:.:.sta:1ce at V,...., ao.:d C.ecrcasiag voltar~c causes the currcnt­r'

volt~gc curve to follow a decreasing voltage and increasing

current path instead of the desired curve. The cap3citor pre-

c

42

vents the voltage from decreasing .:;t VP point. This co::C:itio.:1

rcqui res that c.:;:re be taken in selecting the value for s:-:ur.t

c.::p.aci~or.

k1 ~dd~tional restriction i~ the selection of the ti~c-

s::ep. :'he parasitic ele~ncnts arc very l.n:J?ortant when conside-::-ing

the transie~t response of the model. The time-step oust be in

the range of the parasitic element time constant.

r ·:P L-J

D .. \l~:.EL> 2·~.E. (1957) D.:;\r~:lc:::~::::.-::t o~ l,~~t!1c~::.-'"~~t::cc::.. :-:vC:cla oi Scmiccnductor Davic~s foe Co~pu~er­Aided Circ~it D~si~n, Prccecdi~g of I~EE, vol. 55 no. 11, Novc;:i0er, p. 1913-1920.

::Ji~i·~~l Compt:t..::r P::o:Jr.2.:a. for Tr.c..1~sient l.r~ol:.lsis of E2:.c:c·:::ro"i1ics Ci::cuit (CI~1.CUS) (3/vS-1) Es2ris Gu!~e, S2=~tlc~ Washington, Roc~ns Co~?any, 1967.

--n. (196~) Co:~-;?-;;·~~r Prozr~r . .-:3 for C::::cuit DcsiGl1, Elcct::o-Tcch:.-"olo::,-y,. '\lOl. 73 no. 3, ::~.:n:ch,

p. 101-103, 162, 164.

(~.] l:"".~.l~:z, r~I. (1965) Co::~)t:tei..'" Pro~rL..:::s ~or Circuit Design,

r• ...... i '-~:I .i

"'"''. 1 ...... ~.~"':-':V)t'l', ...:~--.. .... :~l:..V~L:· .. .L 7

Elcctro-Tectillolcgy, vol. 77 no. 6, Jcnc, p. 54-57.

c.o. D:;i::tz a i'-:oC.cl J-ob, 2lectronics, ~o. 2, Jnnucry 23, ?· 82-87.

Pz.rt 5: vol. 40

Elect::c .. :'.!lc Ci::cuit li!!.:!l}?Si.s ?:-c:;r.:::·=-~ (2Ci,:..1?) {'\· ~~l"'JQ-17',-?_n~.''.?) 'uT,•!"'.· . ...,.v- ~·..-,·----u-···l r .... , J... ..,.... .. , - '""'- ./6-J.-J v........ v~"""' ::.> ...... ._..... '"'"""', t.\:.:.1.1. L...J J! .ta:tnz,

I~J "'Y., In-:2~".t1~tic·ncl Dusi:r!eGs l{~~:1.i-ries

Cm .. ')J. , 1%.5.

"). _... ¥:"1 •. i"J. • ...).

Ci::ct::lt !:.::~1.:;/s~~~ :.)~ogr.::::t Tcc:c"<_:liqucs t-..-pplic~:~ic:1s? E::glc~;ovd Cl::..f:2s, Nev.// Prcuticc-li~ll, IA-'"lc., Pot lOS-154.

~· .. ~c.

Jc::cey,

·_.,,-_ . .-,·.r.--::r.., Jo7-.-."' r:. (~r.':;·.~:"' -;-,._ ... ,_ a1 -,._· .... ,,,,~ o·:: T•··'~'"'<:>""o'"''"' ..._ ,v___ ·-J. - -·,i._Jiu, .....,,_.,. ... ~~--- .. _.._.,_.._.._...~ - 4"--L ... w-.::J"- _...,

·~ ·-_~ ... ., .... 7 .... -,- .,.. .!..,~\\, -~.;..,,

~:1d ~icd.t.:-!s, P::occcd:L::~; vf the I::\.E, ~--ol.

no. 6~ June, p.ll4l-ll52.

Juh.n. G. (1953) :·:~d2ls o= •:tr:l: .. sistors ~::d Dioclc~, :~(:W Yo::::, l·1cG:r ... ~:.J-~~ill, Inc.

L .. \-312.9, La<:; l~l~rr.~s S(:i(;~1tific L~b·orato~-y,

7C90/94 V~~G~oa, A~~~st.

43

44

[12] Revised SCEPTRE User's i:L:.~--.u.:1l: Vol, 1, (AFWL-T~-67-124),

Kirtland ~ir Fore~ B~sc, X0~ ~exico, Intcr~~tio~~l

I Business r.:c.:.ch:r..::s Corp. , April 1962.

[13] SCHEERER, W.G. (1968) Sclectin:~ Device Hodcls for Co:::~.mter­~idcd Design, Elc~tro-Tcchnology, vol. 81, no. 55, May, p. 43-48

45

APPENDIX II

/J/:l~LYSIS, CALCU'..:..ATION Al\fv SELECTION

OF PAIWfE'!'ER FOR TtJ1"NEL DIODE HODELS

46

All of t~~ ~odcls have several elements, lar3c rcsist~ncc

103 oh~::.s, end z:r,;:ll : . .-~s::.stancc C. 001 ohr.1, which are used ;.iS

cur::-2nt sensing clerr:.:.:nts and ar-e the sam;; for ::ny tu:1ncl ciioC:c

series inductance, series resistance and tcr~inal capacitance

resp~ctively. The value for these cl;;rncnts can be obtained fro~

t:i:e r::.:mufacturer' s data sheet. See TABLE II-1. Figure Il-l

::.~ . .Jws rel.:ltionship of parameters in TABLE I to current-vel ::age

curve.

TAB:..E II-1

DATA FROM G.E. DATA SHEET

Vall~y Poi~t Voltage

7ermin2l Capacitance

l\ega-::i v.: Terminal Co:J.ductanc.:

Ip

Iv

vP

Vv

Vr

Vfp

Ls

Rs

•G

TD-19

10.00 rna

.95 rna

65 mv ·

355 nw

20 mv

510 U'.V

0.8 nh

0.36 ohms

27 pf

85xlo-3 mho

TTJ-l3

.095 :aa

65 I:\V

355 -::.v

20 mv

510 -..:.v

O.S n!"l

l. 7 oh::-.s

3.5 p:.::

S.Sxl0-3 r.1r.o

I

Ip

lvl ~--~-------------------~--=========~----------~~----VOLTAGE (millivolts)

47

Figure II-1 Tunnel Diode Current-Voltage Characteristic

Hodel 1 shown in Figure II-2 is a three section piecewise-

linear model. The elements simulate the three straight lines

depending on the terminal voltage. Sl turns the diode off when the

diode is back bias. When the voltage is between 0 and peak voltage

the model consists of Ls, Rs in series with G1 and c1 in parallel.

~fuen looking at the current-voltage characteristic this beco~es the

slo?e as~ociatcd with the line from (0,0) to (VPIP). l.Jhen peak

voltage level is reached, switch S2 is activated and turns on a

depe~dent current in R3. The current source has a -GM1 and is

puting current into the model thereby reducing the diode current

with increasing voltage. This is the negative resistance line

and it consists of the sum of G1 line and the -GM1 line to give the

desired negative resistance to the ~~del. When valley voltage level

Ls 10E7,R5

O,GHd. f )

I ~

G1,G~

I

I

I

o,v2 -=..

," 7

( t )

--- .... ----------- ----..,.---- --I

I

I

,

R3

- -' \

0,-GHJ

10E8 I ) LH SJ " ;

R4 , ,

I

I >10E8 :' 0.001 > r ~ I

' ' Rs ' I

' ...... .l - - .- __ I S2

cl

vl-=- - v2

Figu1T II-2 Nodd 1 ,p.. OJ

49

is reached, S3 switches G1 to G2, turns on a controlled current

source GM1 controlled by R2 to cancel the -GM. S3 also turns on I1

to control the current level at Vv the point where the third

section starts. For decreasing voltage the diode retraces the same

path.

Model 1 shown in Figure II-2 has elements Ls, G1, Gz, Vl,

Vz, GM1, I1, and C1 which must be specified from data of the

particular tunnel diode.

Selecting values for these elements depend on how the current-

voltage characteristic is to be approximated. Figure II-3 shows

the tunnel diode current-voltage characteristic and three ways to

select and approximation to the curves. Of the three shown, they

all have about the same amount of error when compared with the

actual model curve. The first curve using the (VP,IP) and (Vv,Iv)

points was selected in this paper. Using this curve as the approxi-

mation v1 and v2 are VP and Vv respectively.

,.... (/) I <l) f.< Ip <l)

fr I ~ til ~'~ ~

,,, ....... ',_, .-I •.-4 '\. ',' s - '' I ~ I z I !:<J c:G I ' ' c:G

~ ' :;::l I u I I -----1

lvf -- -2 -3

v v p v

v

VOLTAGE (millivolts)

Figure II-3 Three Section Piecewise-Linear Current-Voltage Curve

50

vl - v p

v2 • Vv

Gl, G2, GM1 and I1 are obtained from the following relationships:

VvGl-Iv G!11 •

Vv - Vp

Il • Iv

Gl • Ip

v p

G2 .. If - IV

vt - vv

For If • Ip:

I - Iv G2 • p

v f- Vv

The specific values for Model 1 representing TD-19 and TD-13

are shown in TABLE II-2.

TABLE II-2

MODEL 1 PARA.'1ETER VALUES

Par.:i::leter TD-19 TD-13

vl 0.065 0.065 volts

v2 0.355 0.355 volts

Gl 0.154 0.0154 ~.ho

G2 0.058 0.0058 mho

GM1 0.185 0.0185

Il 0.00095 0.000095 amp

51

Model 2 shown in Figure II-4 is a five section piecewise­

linear model. When the voltage is between 0 and the diode peak

voltage, G1 element provides the first line from 0 to v1 • At v1

the switch S2 turns on. It changes G1 to an open circuit and

turns on an independent current source -11 which draws current

from the device and maintains the current level constant at I1

from V1 to V2, At V2 switch S3 turns on a controlled current

source -GM1 which is controlled by R4. This source removes

sufficient current to generate the negative resistance portion

of the curve from v2 to v3• At V3 switch S4 turns on a controlled

current source GM1 which is controlled by R3 and cancel the effect

of the -GM1 of switch S3. S4 also turns on an independent current

source I2 which supplies current to the device to maintain the

current level constant at 12 from V3 to V4. At V4 switch S5

turns on and G2 is then in the circuit and is the element which

generates the line from V4 to Vfp• For decreasing voltage the

diode retraces the same path.

Sl turns the diode on if the diode is forward bias and off

if the dJode is reverse bias.

The elements simulate the five straight lines depending on

the terminal voltage.

Model 2 shown in Figure II-4 has elements Ls, Cl, Gl, G2, VI,

v2, V3, V4, GMI, 11, and 12 which must be specified from data of

the particular device.

The selection of values for these elements depend on the

S! .. I ~

· 10E7, Rs

A

c

,.-• S2

., -""t ~ '\. ( I I

I

~

Gl, lE-8

R2 lOEB

vl-=-

0,-Il

"' -- -- -- ---..L-

" / ,/

J:f • '>..

~E8 > ~

\

\ . y- - - \

531--' CD ·~R6 0,-GM1 lOEB

(_ I Rs

.001

v2 V3-

Figure II-4 Hodel 2

........

' \

\

\ I + I

VI ~

53

current-voltage characteristic shown in Figure II-5.

This curve is a better approximation to the actual device then

the Model 1 curve. The voltage ratios selected are dependent on

the shape of the current-voltage characteristic and for tunnel

diodes with a curve proportioned differently, the voltage would

be different.

-tl) Q)

'"' Q)

~ Ill ~ ,.-j ,.-j

~

s -E-1 z ~ ~ ~ :;J (J

I

Ip

Iv ' ..... -.-::-=------=

v3

VOLTAGE (millivolts)

Figure II-5 Five Section Piecewise-Linear Current-Voltage Curve

The yoltage V1, V2, V3 and V4 are the following:

v1 - .95Vp

V2 • 1.05Vp

VJ • .70Vv

V4 • 1.15Vv

54

Gl, Gz' GM, 11 and Iz are obtained from the following relationship:

GM1 • Ip - Iv

v3 - vP

ll - Ip

12 - Ip - I v

Gl • Ip

vl

Gz -If - IV

Vf - v4

For If • Ip:

Gz • IP - Iv

vf - v4

The specific values for Model 2 representing TD-19 and TD-13

are shown in TABLE II-3.

Model 3 shown in Figure II-6 is a smooth curve model. The

elements simulate the model so there are no sharp corners. The

curve, like the other models, is made up of pieces. The elements

Ls in series Rs in parallel with G1 and Cl provide the waveform

from 0 to Vp• At Vp, Sl turns on a controlled current source -BETA

which is controlled by Gz. Sl also closes the open resistor R6 to

allow the capacitor C2 to change up and supply current to Gz. This

develops the negative resistance portion of the curve by sub­

tracting BETA times the G2 current from the initial waveform,

which continues from Vp to Vv• At Vv the switch S2 turns on and

opens resistor R7. This removes the voltage source from Cz it

55

discharges, increasing current in G1 and generating the portion of

the curve that goes from Vv up. At the same time S4 and S5 have

turned on setting up the circuitry, R9 , R10 , R11 and 0.875 voltage

generator, for decreasing voltage. S4 shorts R9 and S5 shorts Rlo•

When the voltage starts down capacitor C3 (also S3) senses the

change and R11 is reduced to 10 ohms. Cz is charged up causing

the current in G1 to decrease and generate the curve down to Vv·

At that time S4 turns off, opening R9 causing c2 to discharge

through G2 increasing diode current. After Cz is completely

discharged, the voltage continues to decrease and the current and

voltage decreases back to 0.

Model 3 shown in Figure II-6 like the previous models has

elements v1 , v2 , v3 , v4 , Ls, Rs, c1, G1 , G2 , and BETA which need

to be specified for each particular device.

Parameter

vl

Vz

VJ

v4

Gl

Gz

GMl

Il

12

TABLE II-3

MODEL 2 PARAMETER VALUES

TD-19 TD-13

0.0618 0.0618

0.0682 0.0682

0.249 0.249

0.408 0.408

0.161 0.0161

0.0887 0.000887

0.0492 o:oo492

0.01 0.001

0.00905 0.000905

volts

volts

volts

volts

mho

mho

amp

amp

A

c

~

I I I

o~ 1 1

-BETA~~

~

Gl

v2 ,o

.. - -- - - -- ---:,- -- -~---- -' '

;------­- --,---------------

,_-­\

' -~

' j!

Sl R2 I lOE8-c1

v1 ,o _

ss

V2..=_

' \ ....

' '--\...---' ---- I \

-~

·~-1 S4 I

\.

R4 10E8

Rs 0 01 t1

lOEB ., ~

\ \ \ .. I

R3 10E8

--, j_ \ I

I

~O,V.s...=.. I

v4,o-=- I

I

S31- ..L

I

I I I

'

C3 2E-12

I I I

Rs

.......

~

'

) l ! ! ~ ~ J I

Figure II-6 Model 3

-------,

' '

'

-=-.875

\

\

\

\ I

\ I

\

c2 ' .OSE'f

-6 G2

\..n 0\

-Cl)

G) .... CIJ

~ Ill

o.-4 ...... ...... o.-4 a ........

~ p:; p:; ::;:, u

I

Ip

Iv

Vz VOLTAGE {millivolts)

I /

I I

I I

I

I I

Figure II-7 Model 3 Current-Volta~e Characteristic

v3 - .95Vp

v4 • 1.15Vv

57

a2 and BETAare interrelated in this model by the following

equation: Iv .11-expafC--l • BETA [1-exp-{t*;~P)J vl L Rl J ~2.-

where:

Iv • valley current

v1 • Charging Voltage • 1.5 volts

Rl • Rs +-1-

C • O.OSE-~2

tp • R C ln [Rlip vl

The unknown quantities are:

BETA

• Time to Reach Peak Point

tv • Time to Reach Valley Point

58

tv is approximately a constant for a range of BETA's and G2's,

therefore, to obtain an acceptable tv set BETA•l and G2 • 2Gl

and run ECAP for the current-voltage. tv is the time that

52 turned on. Then by picking values of BETA and solving

for G2 all the parameters for the model will be selected for

Model 3 representing TD-19 are shown in TABLE II-4.

TABLE II-4

MODEL 3 PARA.'ffiTER VALUES

Parameter TD-19

vl 0.065 volts

v2 0.355 volts

V3 0.0618 volts

v4 0.408 volts

v5 0.510 volts

Gl 0.154 tr.hos

G2 0.308 mhos

BETA -0.8

59

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60

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61

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62

VJ..TA

The author, Carmon Dale Thiems, was born January 14, 1938,

in Highland, Illinois. He received his primary and secondary

education in Highland, Illinois. He received his college education

from the University of Illinois in Urbana, Illinois. He re-

ceived a Bachelor of Science Degree in Electrical Engineering

from the University of Illinois in June. 1964.

He has been enrolled in the Graduate School of the University

of Missouri - St. Louis since September of 1965.