Title: Low frequency noise sources in bipolar junction transistors
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Title: Low frequency noise sources in bipolar junction transistors
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Language: English
Creator: Jaeger, Richard Charles, 1944-
Copyright Date: 1969
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Volume ID: VID00001
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LOW FREQUENCY NOISE SOURCES IN

BIPOLAR JUNCTION TRANSISTORS












By
RICHARD CHARLES JAEGER


A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF
THE UNIVERSITY OF FLORIDA
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE
DEGREE OF DOCTOR OF PHILOSOPHY


UNIVERSITY OF FLORIDA
1969













ACKN OLEDGEMENTS


The author wishes to express his appreciation to the members of

his supervisory canmittee for their advice and cooperation. In

particular, the author wishes to thank both Dr. A. J. Brodersen and

Dr. E. R. Chenette for their guidance and helpful suggestions through-

out the course of this research.

The author is also indebted to the University of Florida Department

of Electrical Engineering for the use of the microelectronics

facilities there.

Special appreciation is due Gert Choate, whose assistance in

the preparation of the devices constructed for this study was

invaluable.

This investigation was supported by the Advanced Research

Projects Agency, U. S. Department of Defense and monitored by the

Air Force Cambridge Research Laboratories under Contract No. F19628-

68-C-0058.

The author is very grateful for the financial support provided

by his NDEA Title IV fellowship.














TABLE OF CONTENTS


Page

ACKNOVLEDGEMENTS.............................................. iii

LIST OF TABLES.................................................. v

LIST OF FIGURES................................................. vi

ABSTRACT........................................................ ix

CHAPTER

ONE. INTRODUCTION............................................ 1
Historical Background ............................... 1
Low Frequency Noise Model of the Transistor .......... 4
Summary............................................... 7

TWO. 1/f NOISE SOURCES IN BIPOLAR JUNCTION TRANSISTORS...... 10
Noise Figure and Equivalent Noise Resistance.......... 10
Low Frequency Noise Performance of the Transistor
as Predicted by the Existing Noise Model............ 15
Breakdown of the Existing Noise Model................ 19
An Improved Noise Model Including Two 1/f
Generators......................................... 22
Separate Dominance of the Two 1/f Noise Generators... 29

THREE. BURST NOISE............................................ 34
Introduction......................................... 34
Burst Noise Model and Spectral Representation........ 34
Functional Dependence of Burst Noise.................. 42
Combined Spectral Effects of Burst and 1/f Noise..... 51

FOUR. LOW NOISE AMPLIFIERS.................. ................ 55

FIVE. CONCLUSIONS AND RECOMMENDATIONS ........................ 66

APPENDIX. MEASUREMENT SYSTEMS AND METHODS..................... 71

BIBLIOGRAPHY.................................................... 86














LIST OF TABLES


Page

TABLE

4-1. GAIN AND BANDWIDTH OF THE LOW NOISE AMPLIFIER ........... 61















LIST OF FIGURES


Page

FIGURE

1-1. Basic transistor noise model.............................. 2

1-2. lybrid-Pi small signal model of the transistor............ 5

1-3. Noise model employing the Hybrid-Pi model of the
trans istor............................................ 6

1-4. Simpl ified l a frequency noise model of the transistor.... 8

2-1. Representation of a noisy twoport......................... 11

2-2. Basic noise measurement system ............................ 13

2-3. System for measuring equivalent noise resistance.......... 14

2-4. Simplified low frequency noise model of the transistor.... 16

2-5. Noise model for determination of accuracy of base
resistance measurements............................... 18

2-6. Noise figure versus source resistance For CA-3018 876...... 20

2-7. Noise Figure versus source resistance for unit Z.......... 21

2-8. Tetrode transistor structure............................. 23

2-9. Noise resistance versus frequency with gate voltage as
a parameter for device /l 195.......................... 24

2-10. Noise figure versus source resistance with gate voltage
as a parameter for device / 195....................... 25

2-11. Improved loa- frequency noise itodel for the 1/f noise
region.................................... ........... 26

2-12. Transistor structure showing two components of the
base resistance of a transistor ....................... 28

2-13. Noise resistance versus frequency for device / 147........ 31







LIST OF FIGURES (continued)
Page
FIGURE

2-14. Noise figure versus source resistance for device
/ 147.............................................. 32

3-1. Burst noise waveforms................................. 35

3-2. Burst noise model .................................... 37

3-3. Equivalent burst voltage versus source resistance...... 39

3-4. Random telegraph wave spectrum......................... 40

3-5. Burst noise spectrum.................................. 41

3-6. Two level burst noise spectrum ......................... 43

3-7. Multi-level burst noise model .......................... 44

3-8. Equivalent burst voltage versus temperature with
collector current constant......................... 45

3-9. Equivalent burst voltage versus collector current
at constant temperature............................. 46

3-10. Average burst rate versus collector current at
constant temperature.............................. 47

3-11. Equivalent burst voltage versus temperature with
constant emitter-base voltage..................... 49

3-12. Collector current versus gate voltage showing
presence of burst noise............................ 50

3-13. Noise model including 1/f surface noise and burst
noise generators................................... 52

3-14. Structured spectrum predicted by model including
burst noise and 1/f noise......................... 53

3-15. Noise figure versus frequency showing structured
spectrum .......................................... 54

4-1. Transistor differential amplifier and small signal
equivalent circuit................................. 56

4-2. Equivalent noise resistance versus frequency of the
differential amplifier............................. 58

vii








LIST OF FIGURES (continued)
Page
FIGURE

4-3. Lcw noise amplifier configuration................... 59

4-4. Small signal model of the low noise amplifier........... 60

4-5. Theoretical and experimental burst noise reduction
using the low noise amplifier....................... 63

4-6. Noise figure reduction using the low noise amplifier... 64

4-7. Noise figure versus collector current for low
noise ampl ifier.................................... 65

5-1. Improved low frequency noise model including two
1/f noise generators and the burst noise
generator.......................................... 67

5-2. Low noise amplifier configuration ...................... 69

A-1. Basic noise measurement system......................... 72

A-2. Actual noise measurement system ........................ 73

A-3. Transistor test jig.................................... 76

A-4. Burst noise measurement system......................... 77

A-5. Burst rate measurement system.......................... 79

A-6. The infinite limiter ................................... 80

A-7. Methods of Beta measurement............................ 81

A-8. Test jig for h. measurement ........................... 83
le
A-9. Differential amplifier test jig........................ 84

A-10. Low noise amplifier .................................... 85








Abstract of Dissertation Presented to the Graduate Council
in Partial Fulfillment of the Requirements for the Degree of
Doctor of Philosophy


LOW FREQUENCY NOISE SOURCES IN
BIPOLAR JUNCTION TRANSISTORS

By

Richard Charles Jaeger

June 1969


Chairman: E. R. Chenette
Co-chairman: A. J. Brodersen
Major Department: Electrical Engineering


This dissertation is concerned with the sources of low frequency

noise in bipolar junction transistors. Noise measurements on silicon

planar diffused transistors indicate that the present noise model

inadequately represents the noise performance of modern transistors.

An improved noise model is presented which includes three distinct

excess noise sources. Two of the noise sources have a 1/f noise

spectrum. One represents noise generated at the surface of the

transistor; the other represents noise generated in the emitter-base

space charge region. The importance of the third source of 1nC

frequency noise, burst noise, has only been recognized recently since

the advent of monolithic integrated circuits. Burst noise consists

of sudden discrete shifts in the dc collector current of the transistor.

The erratic behavior of this noise can severely impair the performance

of high gain integrated amplifiers. The electrical behavior of burst

noise is experimentally investigated and a phenomenological noise

generator is developed.








A transistor amplifier configuration utilizing two transistors and

a dc current source is analyzed using this improved noise model. Both

the analytical and experimental results shew that this configuration

is capable of dramatically reducing the effects of the lcw frequency

noise sources of bipolar junction transistors.













CHAPTER ONE


INTRODUCTION



Historical Background


Theory of the low frequency noise performance of the bipolar

junction transistor has existed for many years and has remained

essentially unchanged since its inception (1, 2, 3). The essence of

the shot and thermal noise performance of the transistor is shown in

Fig. 1-la. The shot noise of the intrinsic transistor may be repre-

sented by a shot noise generator ib in parallel with the base-

emitter junction and a shot noise generator i in parallel with the

collector-emitter terminals of the transistor. Also shown in Fig. 1-la

is the thermal noise generator eb associated with the extrinsic base

resistance of the device. The low frequency 1/f noise of the

transistor may be represented by a flicker noise generator in parallel

with the emitter-base junction of the transistor as developed by

Fonger (4). The basic low frequency noise performance of the transistor

is represented in the model of Fig. 1-lb.

The source of the 1/f noise represented by the above noise

generator has been a source of considerable conjecture. Fonger

originally associated 1/f noise with fluctuations in current recombining

at the base surfaces. More recently Sah (5) and others (6) have shawn





















































+ rx


(b)



Fig. 1-1. Basic transistor noise model.


- +







more experimental evidence supporting the surface noise theory.

Gibbons (7) has suggested that the source of 1/f noise in la noise

transistors is the emitter-base transition region rather than the sur-

faces of the device. Knott (8) recently concluded that there is 1/f

noise originating within the transistor. Investigation is clearly

needed to determine whether more than one 1/f noise generator exists

in the transistor and to determine the proper location in a transistor

noise model of the generators which are found to exist.

Another noise phenomenon, burst noise, has been entirely neglected

in the transistor noise model. Originally noticed in carbon resistors

and reverse-biased p-n junctions, burst noise has only recently been

recognized as a problem in transistors (9, 10). With the advent of

integrated circuits, and their associated yield problems, the luxury

of ignoring or disposing of bursting units can no longer be afforded.

One can no longer select special low noise units with which low noise

amplifiers may be constructed, but must accept the performance of the

transistors comprising the integrated amplifier. Thus burst noise

cannot be tolerated in low noise integrated amplifiers. The breadth

of this problem and lack of available information about burst noise

indicate that a study of this phenomenon is needed. This noise form

is neglected in the noise model of Fig. 1-1, and a generator character-

izing the effects of burst noise should be included in any complete low

frequency noise model of the transistor.

Both burst noise and 1/f noise reduce the sensitivity of amplifiers

at low frequencies. The present method of controlling 1/f noise is

to attempt to produce transistors having "clean" surfaces and oxides








by careful process control. At this time there is no known method of

controlling burst noise. Investigation is needed to determine if

circuit techniques exist through which the 1/f and burst noises may

be controlled.



Low Frequency Noise Model of the Transistor


The Hybrid-Pi small signal model of the transistor was chosen as

the transistor model to be used in this study (11). The above model

was chosen because it provides both an accurate description of the

performance of the transistor over a wide frequency range and insight

into the physical processes which occur in the transistor. The

Hybrid-Pi model of the transistor is shown in Fig. 1-2. A noise model

of the transistor is easily generated by superimposing the four noise

generators discussed earlier on the model of Fig. 1-2. The resulting

noise model of the transistor is shown in Fig. 1-3. The two current

generators ib and ic are noise generators showing the full shot noise

of the base and collector currents respectively. The generator if is

a phenomenological noise generator which describes the noise performance

of the transistor in the 1/f noise region. The noise emf eb is a

generator which represents the full thermal noise of the base

resistance rx. The above generators can be described by the formula-

tion below (12).



The model of Fig. 1-3 tacitly assumes that the transistor bias
currents are much greater than its leakage currents and that the
transistor has reasonably high beta.

























00

























4-


4,



4-,
i--------


























0



0














L,
o,
e-





0,













I--
.0 1 a




















O






^ O


0
U)
C























-z
4-J





,



o-






,-&
-o










0 E








Sa,





. I


*-
J3Z








ib = 2ql Cdf (1.1)

.2 2qI df (1.2)
c B

e = 4kTr df (1.3)
b x

f KI df/f (1.4)

For low frequencies the model of Fig. 1-3 may be considerably

simplified. At las frequencies the effects of C and Cu are unimport-

ant, and these capacitors may be deleted from the model. The resistor

ru affects the gain of the transistor only when the device is operated

under conditions of high voltage gain and may also be neglected.

The result of these simplifications is the model of Fig. 1-4. The

model of Fig. 1-4 will be the low frequency noise model used throughout

this noise study.



Summary


The purpose of this work as developed above is twofold. First

the 1/f and burst noise phenomenon are to be studied and modeled, and

then methods of controlling these two noise forms are to be investi-

gated.

Chapter Two presents the results of an experimental study of 1/f

noise beginning with the above low frequency noise model and resulting

in the development of an improved noise model which more fully explains

the noise performance of the transistor in the 1/f noise region.

Chapter Three presents the results of a study of burst noise

including modeling of burst noise by a burst current generator,

determination of the functional dependence of this generator, and

qualitative ideas as to the origin of the burst noise phenomenon.

























C-




9

A low noise amplifier configuration is presented in Chapter Four.

This amplifier should provide a method of realizing lao frequency low

noise amplifiers whose noise resistance is basically limited by the

thermal noise of the base resistances of the transistors comprising

the amplifier and by the shot noise of the collector current of the

second transistor of the amplifier configuration. This amplifier

also provides a method of effective control of burst noise.

Results of this study and recommendations for further work

indicated by this study are presented in Chapter Five.















CHAPTER TWO


1/f NOISE SOURCES IN BIPOLAR JUNCTION TRANSISTORS



Noise Figure and Equivalent Noise Resistance


In any noise study it is necessary to have a noise measure which

may be used to compare the noise performance of various noisy devices.

Two common and convenient measures are equivalent noise resistance R
n
and noise figure F. Equivalent noise resistance and noise figure,

developed below, will be used to characterize the noise performance of

devices throughout this thesis.

The noise of a twoport may be conveniently represented by two

noise sources as shown in Fig. 2-la (13, 14). For a given input

termination Rs, the equivalent circuit of the twoport may be further

reduced to the circuit of Fig. 2-lb in which the noise source et is

given by

e = e + iR (2.1)

The total mean square noise voltage e2 at the input of the twoport
n
may be computed with the aid of Nyquist's theorem (15),
2
e = e2 + 4kTR df (2.2)
n t s
and can be represented by the equivalent circuit of Fig. 2-1c in which

R is now a noiseless resistor. The noise emf e may be expressed as an

equivalent noise resistance defined by












































eN

NOISELESS
'S TWOPORT
S OISELESS TWOPOT






(c)


Fig. 2-1. Representation of a noisy twoport.








R = e lkTdf .(2.3)
n n
In this form, the equivalent noise resistance Rn is a convenient

quantity by which various noisy devices may be compared. Noise figure

F may be defined in terms of the equivalent noise resistance R and is
n

given by the formula belao (16).

F = R /R (2.4)
n s
Thus equivalent noise resistance R provides both an effective method

of comparing the noise performance of various devices and a method of

determining the corresponding noise figure F.

Measurement of equivalent noise resistance R can be accomplished

using a sinusoidal comparison technique (17). Figure 2-2 shows the basic

measuring system consisting of the device under test, a sinusoidal

calibrating signal, a noiseless variable gain amplifier, a filter, and

a quadratic detector.

The device under test may be represented by an equivalent noise

resistance followed by a noiseless twoport having a gain A as shown in

Fig. 2-3. The equivalent noise resistance R may be determined using the

following procedure. With the switch in position one, the reading Ml of

the detector will be

Ml = (4kTRndf)1/2 Al AVI (2.5)

With the switch in position two and with the amplifier gain set to the

second gain setting, the detector reading M2 is obtained.

M2 = (e 2 + 4kTR df)12 Al AV2 (2.6)
cal n
Choosing the calibrating signal such that M2 = Ml:

(eca2 + 4kTRndf)A12AV22/(4kTR df)Al2AVI2 = 1. (2.7)
cal n n
This may be easily solved for noise resistance Rn yielding

Rn = cal /(4kTdf) (AVI/AV2) (I-(AV2/AVI)) (2.8)





13







I- 0
a= C,3 &3 L
-a 1- LU



















































E






in
(=r rr







































0=0


























U
~oo_
















uLu
cro











wi


--
U LU
cn sLL i
K -- -- =* >*









1/







vll

4-
C
--* ------ -- d


8L

s~a





1m


u 0 r


<_ U I








14





<_3













4~00













CD U


I- CC














01
c











IC
LUU
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~IOPI
4'V1


















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'U
IIU,
LI


0'
c-
















01
r-------I--------- (U




31
v- CT
<-'

4 Z
=3 Ifl.
LU I






i-J


L_-___. _ _~_-- _..__

OC


0
r^








The value of noise resistance R is determined using the above
n
equation.



Low Frequency Noise Performance of the Transistor
as Predicted by the Existing Noise Model


The low frequency noise model of Chapter One is shown in Fig. 2-4.

The noise figure of the transistor obtained from this model is

F = 1 + r/R + gm(R +r) 2/2hFER +m(R,+rx o m 2/2Rs 2

+ if(R+r ) 2/4kTRsdf .(2.9)

The above expression may be simplified by considering two noise

regions; a region in which the I/f noise generator dominates the

transistor noise performance, and a region in which shot and thermal

noise generators are dominant. The resulting expression for noise figure

in the shot noise region is

F = + rx/Rs + g(Rs+r) 2/2hFERs + gm(Rs+rx+ o/gm) 2/2Rs 82.

(2. 10)

This expression for the noise figure in the shot noise region has a

minimum value F given below (18).

F min + g (r +Rs in)/ E (2.11)

Rsmin [(hFE( + 2r + (gmr) 2/hFE))]/2/g (2.12)
The noise figure of the transistor may be minimized by the proper

selection of source resistance R For a given value of r the noise

figure may be computed in the shot noise region, and the model of

Fig. 2-4 may be verified for the shot noise region.

In the 1/f noise region the I/f noise generator dominates the noise

performance, and the noise figure expression of Eqn. 2.9 reduces to the

express ion

















c-







F = 1 + i(R+r) /4kTRdf (2.13)
f xs
This expression may also be minimized by proper choice of source

resistance R .

Fmn = 1 + if(r /kTdf) for (2.14)
mm f x
R = r (2.15)
smin x
Noise figure measurements in the 1/f noise region may thus be used to

determine the value of the base resistance r of the model of Fig. 2-4.

The noise figure in the 1/f noise region must be of a sufficient

magnitude to insure accuracy of the measurements of rx using the above

method. The sufficient magnitude is determined below. For the model

of Fig. 2-5, the noise figure is easily determined to be

F = + r /R + M(R +r) 2/R M = i/4kTdf + -J
x s s x s 2hFE
(2.16)

which has a minimum for

Rsmin = (r2 + r /M)12 (2.17)

Manipulation yields

r2 = R2/ [1 + 4F /(F. -1)2] (2.18)
x s main min
Thus for r to be determined within one percent, F in the I/f noise
x man
region must be at least 202. A minimum noise figure of 20 is required

if r is to be determined within ten percent.

Measurements of noise figure versus source resistance in the 1/f

noise region can be used to help characterize the model of Fig. 2-4.

The base resistance r may be easily determined by noise measurement in

the 1/f noise region. Then, knowing rx, the minimum noise figure and

source resistance corresponding to this minimum may be calculated for

the shot noise region. Measurements in the shot noise region may then

be used to check the validity of the noise model of Fig. 2-4.




























































Fig. 2-5. Noise model for determination of accuracy of base resistance
measurements.





19

The apparent validity of the preceding noise theory is demonstrated

by unit CA-3018-876. Measurements of noise figure versus source

resistance in the 1/f noise region yield a value of r = 560 ohms as

indicated in Fig. 2-6, Measurements of F versus R in the shot noise
s
region yield values of F .i and R of 1.26 and 5 kohms respectively,
min smin
also shown in Fig. 2-6. Values of R and F 5.6 kohms and 1.24
smin mmn
respectively, predicted using Eqns. 2.11 and 2.12 with the above

valuesof rx,show excellent agreement with the above measurements. Small

signal measurements yield a value of r = 545 ohms. Thus the noise

model of Fig. 2-4 correctly predicts the low frequency noise performance

of the transistor tested, and the I/f noise generator sees the same

base resistance as the base current shot noise generator.



Breakdown of the Ixistino Noise Model


The transistor discussed above demonstrated very good agreement

with the accepted noise model and its theory. However, low frequency

noise measurements upnn other transistors have sh-own little agreement

with the above theory. The 1/f noise generator above sees the total

base resistance rx, and the minimum noise figure in the 1/f noise

region should occur for a source resistance R equal to the base

resistance r In most cases, as shown by the typical unit of Fig. 2-7,

the value of r obtained by small signal measurements disagrees greatly
x
with that obtained from noise measurements in the 1/f noise region.

Unit Z has a base resistance value of 7.8 kohms determined by small

signal measurements, but the indicated value of r determined from
Fig. 2-7 is 27 ms
Fig. 2-7 is 2.7 kohms.










1000-

UNIT CA-301B-B76
I = 100pa


300-
1 HZ




100-


] o


10 HZ
5 30-

















U0

SI I

100 300 Ik 3k 10k 30k
SOURCE RESISTANCE (ohms)


Fig. 2-6. Noise figure versus source resistance for CA-3018-876.










UNIT Z
IC =50Oia
F = 45HZ


4000
SOURCE


6000
RESISTANCE


Fig. 2-7. Noise figure versus source resistance for unit Z.


_I ------,





22

The origin of this discrepancy was studied further by producing special

four terminal devices, tetrode transistors, in the Microelectronics

Laboratory of the University of Florida. The geometry of the tetrodes is

shown in Fig. 2-8. The fourth electrode consists of a field plate or

gate physically located over the emitter-base junction of the transistor.

By applying a potential to the gate the carrier densities at the surface

of the transistor under the gate can be altered, and any mobile ions in

the oxide under the gate may be affected. It is also knain that a

potential on this gate will affect the 1/f surface noise of the device

(19, 20).

Measurements of noise figure versus frequency for device #195 are

shown in Fig. 2-9. As the gate voltage is increased, the 1/f noise of

the device increases greatly as expected. Measurements of noise figure

versus source resistance for device /195 are shown in Fig. 2-10. The

value of R smin of these figures varies widely as the gate potential and

hence 1/f surface noise varies. The variations above may be accounted

for through the model developed below.



An Improved Noise Model ncludin Two 1/f Noise Generators


Consider the noise model of Fig. 2-11 in which two 1/f noise

generators are sho.n. The noise figure in the 1/f noise region is found

to be

F = 1 + i(R +r) 2/4kTR df + 2 (R +r )2/4kTR df. (2.19)
f I s a s f2 s x s
Again the expression for noise figure may be minimized through the

proper choice of R .
[2 + 2 ]1/2 .2 (2.20)
Rsmin = [(r +Ex/( + E] = f2/f (2.20)



















1 MIL
-k --


EfAI TTER
\\
CNA OEI NGS
\\1 1






\N s

N
\\ ^
V V
CONAs VPEN \>


Fig. 2-8. Tetrode transistor structure,








UNIT #195
IC = 100pa
R, = 510


VY = +52V


I I I 1
20 50 100 200
FREQUENCY


Fig. 2-9. Noise resistance versus frequency with
parameter for device # 195.


I I00 50I0
I000 2000 5000


gate voltage as a


I U, .


,w























in


a~~~ i -I s

II et
f a \ 4
C, en*
I-- II 4.o
S II
0 44

0 ,



o




C~c)

to L



Coa en C r


\ \- LU

C)
en \ \ 17)















a L~a
\~ ~ \T T t/



I I I I I0
\ 3 I / V








C to LvI
UI rQ S 0OM
/II / L+

/ / IU S>
/ / 11 -Le
// '
B'/ -0 0






Q~~~~~- O a ca isc^ -
Q ~ ~~ ~ 10cO -

aynoij asi





26



















10




0







0
/ .-










4-1
0









c


E
SaC














-4-
0







Two cases of Eqn. 2.19 emerge, depending upon the dominance of

either irl or if2 as shown below.

For insufficiently large,
2
R = r and F = + i r /kTdf (2.21)
smin a man fl a
For if2sufficiently large,
2
R = r and F = 1 + i2r /kTdf (2.22)
smin x min f2 x
As the ratio of the two noise sources, E varies, R varies
smin
between the values r and r The values of r and r may be deter-
a x x a
mined as discussed below.

Earl ier measurements have confirmed the validity of the model of

Fig. 2-4 for some transistors. In that model it was seen that the 1/f

noise generator and the shot noise generator shared the same position

in the model. This generator should then be associated with the active

base region of the device. As discussed in Chapter Qne, the existence of

a generator in this location has been alluded to in the past. Other

measurements have associated 1/f noise with the transistor surfaces,

particularly near the surface of the emitter-base junction. The

approximate position of the above generators can be determined from the

device geometry as shown in Fig. 2-12. The total base resistance r
x
of a transistor may be divided into two parts: a portion due to the

inactive base region between the base contacts and the edges of the

emitter and a portion corresponding to the active base region under the

emitter of the transistor as shao.n in Fig. 2-12 (21). A noise generator

associated with the surface of the maitter-base junction should see only

a portion of the base resistance corresponding to the inactive base

region rather than the total base resistance of the device. On the other





















































Fig. 2-12. Transistor structure showing two components of the
base resistance of a transistor.


\ 7 EMITTER


2ra 2r



2rb 2rb
*1 BASE







hand a noise generator associated with the active base region would see

the total base resistance of the device.

The base resistances of Fig. 2-11 can nov be determined. The

resistance ra is approximately the base resistance due to the inactive

base region, and the sum ra + rb is equivalent to the total base

resistance of the device so that

r = ra + b (2.23)

Measurements upon device /'195 determine the values of ra and rb

of the model of Fig. 2-11. The geometry of the tetrode transistor

indicates that there is 1/18square of material in the inactive base

region. Sheet resistivity measurements for device /195 yield a value

of 180 ohms per square for this region and hence a value of 10 ohms

for the value of ra. Small signal input impedance measurements indicate

a value of 650 ohms for the total base resistance r yielding a value

of 630 ohms for rb. The measurements given in Fig. 2-10 clearly show

values of Rin which fall within the range of 20-650 ohms. This
smin
performance is predicted by the model of Fig. 2-11 and the ratio e of

Eqn. 2.20 is effectively varied by varying the value of the gate

potential on the tetrode.



Separate D ominncof tho r _Twqo f_ fo_ Generators


The noise figure in the 1/f noise region for the improved noise

model of Fig. 2-11 was given in Eqn. 2.19. If the noise generator if2

is sufficiently dominant, the noise figure would be given by Eqn. 2.22.

This was the case of the CA-3018 of Fig. 2-6. The case of dominance of

the generator ifl was developed in Eqn. 2.21, and is demonstrated belcw.








Device A147 was a specially treated device in which I/f surface

noise could be made the dominant noise form. Before metalization the

oxide over the surface of the above transistor was contaminated with

sodium ions by heating the transistor in a saturated salt solution at

950C for twenty minutes. This treatment introduces mobile sodium ions

into the oxide which may be later influenced by the potential on the

gate electrode (22, 23). The completed transistor was subjected to heat

treatment at a temperature of 200 C For fifteen minutes with the gate

biased at first to plus fifty volts and then later at minus fifty volts

with respect to the other electrodes. The heat treatment with the gate

positive causes the mobile ions to drift toward the silicon-sil icon

dioxide interface, and with the gate negative the ions drift toward

the gate electrode. The results of noise measurements upon the transistor

with the ions drifted both toward and away from the transistor surface

are shawn in Fig. 2-13. With the ions drifted toward the gate electrode

a structured spectrum was obtained. This will be discussed later. With

the ions drifted toward the surface of the trans istor, I/f noise enhanced

the noise spectrum by almost 20 db. Since the I/f noise here was

greatly influenced by the ions in the oxide under the gate the dominant

source of this 1/f noise is the surfaces near the base-emitter junction

of the transistor. Measurements of noise figure versus source resistance

with the ions drifted toward the transistor surface are given in Fig. 2-14,

and the indicated value of r of the model of Fig. 2-9 is 22 ohms. Sheet

resistivity measurements yield a value of 10 ohms for the bulk material

of the inactive base region for this device.

The above measurements show the existence of the two 1/f noise

generators of Fig. 2-10 in which r is the resistance of the inactive
a








UNIT #147
RS = 3k
iO = 50pa
HEAT TREATMENT
15 MINUTES AT 2000C AND
S- Vg = +4gV

- Vg = -40V


FREQUENCY (HZ)

Fig. 2-13. Noise resistance versus frequency for device f 147.


109








108









E
107



C-3




106








105








104







32

























O1


o-3

a)

^CC -o
Co^ U



E.





Co 0
4-c












I m
^^ "S
I I ]

Co
wcoCo Co: Co C
C- -_ 0)





\ C-
* I- I I C o

- II1 3'Co \_
Coc 5C Co US C' -
C- IC C 3 Co in




0)U




cn 0)
_____^ oI 0

C* o cCi Co Co ^r
II II O Z 3: / s











S Co* Co Co- C= /o
CO C3- S













~UflW 31011 a
-a

a)
i-








-o


3~n3 1j3SIIl
Ln





33
base region, and the total base resistance of the transistor is given

by

r =r + r (2.24)
rx ra b













CHAPTER THREE


BURST NOISE



_Itroduct ion


Typical burst noise waveforms are shaon in Fig. 3-1. The waveforms

sho.n are of collector current versus time and consist of sudden discrete

shifts in the de collector current of the transistor. The above

phenomenon has long been observed in resistors and reverse-biased p-n

junctions, and recently burst noise has been observed in the transistor.

Burst noise has become a major problem in transistors only

recently. In the past, one could select acceptable quiet devices

with which lew noise amplifiers could be constructed. In today's

integrated circuit technology this procedure is no longer economically

feasible, and burst noise has become a problem causing reduction of the

yield of acceptable functioning integrated circuits.

The results of a study of the burst noise phenomenon are presented

bel o'.



Jiu-stlcDise Model and Sectral Representation


Burst noise has been shown to be a function of temperature, collector

current, and source resistance,and to be independent of collector-base

voltage (24, 25). The bursts are associated with the base-emitter
















o











(a) 50 msec/cm












U










E










(C) 5 msec/cm


Fig. 3-1. Burst noise waveforms.






36

junction of the transistor, and the burst magnitude as measured at the

collector of the transistor increases with increasing source resistance.

The above knowledge leads to the modeling of burst noise by a burst

current generator as shown in Fig. 3-2a. The functional dependence

of this burst current generator will be discussed later. The current

generator generates current pulses in the form of a random telegraph

wave, and it sees some portion r of the total base resistance r .
c x

The functional dependence of the burst generator, iBB, the value of

the resistance r and hence the location of the burst generator, and

the statistical representation of burst noise by a random telegraph

wave are studied and determined below.

For a given operating point, the value of rc may easily be

determined. Taking a Thevenin equivalent of the generator iBB and

resistors R and r of Fig. 3-2a, the equivalent circuit of Fig. 3-2b

is obtained in which an equivalent burst voltage generator e B,

referred to the input of the transistor, is defined.

eBB = iBB(Rs+r) (3.1)

Extrapolation of measurements of eBB versus RS will intersect the

R axis at

R = r (3.2)

The position of the burst current generator can thereby be determined,

as demonstrated belcw for unit #147.

Unit #147 was the treated unit discussed earlier. With the ions

in the oxide drifted taoard the gate electrode burst noise was very

evident. Measurements of equivalent burst voltage yield a value of

eight ohms for the resistor r of the noise model of Fig. 3-2b as
c











b rc rd C







8 8
Ry V 0





e e
rc + rd = rx

(a)




rx C




Rs v

+ v rtv vm




e

egB iBB (Rs + rc)

(b)


Fig. 3-2. Burst noise model.








demonstrated in Fig. 3-3. As discussed earlier, the 1/f surface noise

generator of this transistor saw a base resistance of approximately

22 ohms. Thus, within experimental error, both the burst noise and

surface 1/f noise generators are located in approximately the same

region near the surface of the emitter-base junction, and these two

noise generators see approximately the same portion of the total base

resistance of the device.

As mentioned earlier, burst noise may be modeled by a random

telegraph wave as discussed below. Since the measuring apparatus removes

the average value of the noise, the burst noise may be conveniently

modeled by a random telegraph wave whose normal ized power spectrum is

given by

S(w) = 1/( + (Tf/2a)) (3.3)

in which a is the average number of bursts per second (26). The above

power spectrum is shown in Fig. 3-4, and it has a value of one-half for

w = 2a/ n. The power spectrum of burst noise may be measured, and the

results correlated with measurements of the average burst rate in

order to confirm the supposition that burst noise can be represented

by a random telegraph wave.

Verification of the random telegraph character of burst noise is

demonstrated by device CA-3018-R-543. The low frequency noise of this

device was dominated by burst noise, and the average burst rate was

determined to be 369 bursts per second. The normalized noise spectrum

of the burst noise should have a value of one-half for a frequency of

238 Hz. The measured power spectrum of the burst noise is presented in

Fig. 3-5 and has the predicted shape and a half power frequency of





39



















\ 0o





m
@














\ r
o
6" \






\ f
ul
\- C


-L \ i 0






I--- i, ii'
cj L




Ijl. \ u LU 14
cc

'ino in





SC U


















o_ "
L(. CO CiO \ n=*

3I \n 00 i
-n I II en




,- C I 1 CO3 tD -42

n C' l CO 0n 0
in) -- C C )
C% a ll

CN P 1-.




\I-o
r in


\ C





\ cr
>

\ r^1









in C i C i T i in - C,






(A901) 3U3V1OA ISu9na ii!31iVAhln33












S(f) = /[1 + (nf/2a)2]
a = AVERAGE BURST RATE


I I I I I I f
a/nt 2a/w 3a/ 7 4a/7r 5a/wT 6a/F

FREQUENCY


Fig. 3-4. Random telegraph wave spectrum.








CA-301B-543-R
RS = lOOkO
IC = 500A
RN = 6.5 X 1010 X Tin
AVERAGE BURST RATE
a = 369 BURSTS/SECOND


I I I
100 200 300
FREQUENCY (HZ)


I I
400 500 600


Fig. 3-5. Burst noise spectrum.


0.2 -
C-








255 Hz, well within experimental accuracy. Burst noise is well

represented by a random telegraph wave.

Burst noise may also have multiple levels as depicted in Fig. 3-la.

For a device in which two levels of burst noise are present, the power

spectrum should show the presence of both levels. Figure 3-6 shows

the power spectrum of device #123 which had two dominant burst levels.

The spectrum is the superposition of two burst noise spectra of Fig. 3-4.

Multiple level burst noise may be modeled as shown in Fig. 3-7 in

which there is a burst noise generator for each burst level.


Functional Dependence of Burst Noise


Experimental measurements have been made to characterize the

functional dependence of burst noise. Equivalent input burst voltage

eBB is found to have the functional dependence given below.

1. eBB is independent of collector-base voltage when the
transistor is in the forward active operating region;

2. Fig. 3-8 shows the variation of eBB as a function of
temperature with I constant. The functional depen-
dence is found to be

egg = kl exp (-T/To ); (3.4)

3. With temperature constant, equivalent burst voltage is
related to collector current by

egg = k2 (c ) n 1/2 (3.5)

as indicated in Fig. 3-9.

4. Fig. 3-10 demonstrates that the average burst rate
is linearly dependent upon collector current when
the temperature is constant.
ABR = k c (3.6)
Combining Eqns. 3.4 and 3.5, the overall functional dependence of

equivalent burst voltage upon temperature, collector current, and base-

emitter voltage is determined (27).




43





























II II




N







LU C C
- C CO














2











a
o 0














LU C
%



II























L ) S S I
CU




oLU






) S I
I~ u







/~ ln
// '" S C






/ I)













~ cn






(sluiij) 33NY.lSlS3a 3SION









T44











































O
E
&a



















ra)
I















----- 0
(-*










0,
^> s ^










#89
RS = 50kO
IC = 100,a
5 BB EOB T/To
To =260K


3



2 -





10-3





0 5




3



2


C


10-4 I I I I I I
-60 -40 -20 0 20 40 60
TEMPERATURE (C)


Fig. 3-8. Equivalent burst voltage versus
collector current constant.


temperature with

















UNIT #89


SI [ I
100 400 900 1600
COLLECTOR CURRENT (pa)


2














30




20




10-


I I I
100 400 900
COLLECTOR CURRENT (pa)


Fig. 3-9. Equivalent burst voltage versus collector current at
constant temperature.


UNIT #126














700
UNIT #226
T = 270C








500













l00












0


0 100 500 1000
COLLECTOR CURRENT (pa)




Fig. 3-10. Average burst rate versus collector current at constant
temperature.
u-l





me



!0



















tempe ratu re.







eBB = kT3/2exp(-(E -qVbe)/2kT) exp(-T/To) for n = 1/2 (3.7)

The above expression may be verified by measuring the dependence of

eBB upon temperature with base-emitter voltage constant. The expected

variation of Eqn. 3.7 on a normalized basis is shown in Fig. 3-11a

for typical values of T and E as determined by computer analysis.

Measured results are given in Fig. 3-11b shaving good agreement with

Eqn. 2.27.

Further study of burst noise was undertaken using the tetrode

transistors discussed earlier. By varying the gate potential the

carrier concentrations under the gate may be changed. As the gate

potential is made more positive the base region near the surface of

an npn transistor becomes more and more depleted of majority carriers.

This is evidenced by a fall off in the collector current of the

device (28). The units described by Fig. 3-12 had no evident burst

noise until the base region of the device was sufficiently depleted.

After the appearance of the burst noise, the bursts remained essentially

unchanged until the surface of the base region began to invert, and

then the bursts generally disappeared at this time. Burst noise

appears to be intimately associated with depletion of the base region

near the base-emitter junction.

Drift experiments also indicate a relationship between surface

conditions and burst noise. An untreated device, unit #91, showed

no bursting with the ions in the oxide drifted toward the gate. With

the ions drifted to the surface, burst noise appeared. The burst

noise again disappeared upon drifting the ions back to the gate.




49


COMPUTED FROM EuQ. 3.7
Eg = 1.1 ev. To =30K, K4 = 10

20


10- ---- BE = E .70Y


5-
_VBE VB 65


2-



1 I i I I
-30 -20 -10 0 10 20 30
TEMPERATURE (C)


(a)

MEASURE UNIT #22
10 -
VBE = .73Y


SVBE = .69V



2-


I I I I I I
-30 -20 -10 0 10 20 30
TEMPERATURE (CC)
(b)
Fig. 3-11. Equivalent burst voltage versus temperature with constant
emitter-base voltage.












UNIT W





BURSTING
t- --- >4


1000 -



500 -




200 -



100



1000



500




200



100




1000



500


GATE VOLTAGE (volts)


UNIT J


BURSTING


Iuu I -,- I,
30 60 90 120 150
GATE VOLTAGE (volts)



Fig. 3-12. Collector current versus gate voltage shaking presence of
burst noise.


60
GATE VOLTAGE (volts)


1


I I


I







Combined Spectral Effects of Burst and 1/f Noise


A model of transistor noise including a burst generator and a 1/f

noise generator may be used to further explain observed noise spectra.

Using the model of Fig. 3-13, the noise figure may be computed to be

F = 1 + kfc/f + k2/(1 + (mf/2a)2) (3.8)

For the proper relationship between constants k1 and k2, the noise

figure spectrum of Fig. 3-14 may be obtained. The burst and 1/f noise

regions are clearly defined. The above effect is demonstrated in

the spectrum presented in Fig. 3-15. The spectrum of device 2N930-54

shows first a burst noise character and then a 1/f noise character as

frequency is decreased. Many transistors show the presence of signifi-

cant components of both 1/f noise and burst noise, and the spectrum of

Fig. 2-28 can often occur.






















U,



0)







U,

r0
a0)


ME 0)
'V 01

U)
0

0)





U,











r U
rC

0)
-u
o0









Ic-






53






















to c

C)





U






O



C C



L 3





-u-






-D-
= C0
a





















j -
L0
:3



o C U
o Q




C-
3 U
^ -
4-










) u-





54


















o



O
T 0 -- C4-
































--f
22 ^L




























0
as- C)

























1 I I I I

























380013 BSION
JJ in






L 4-


I In
/ C(


/ L.
/ I 3I









c~i <3 cs ira 10
10 c~l ,
3mi3U 3SIO
















CHAPTER FOUR


LOA NOISE AMPLIFIERS


Any noise source associated with an amplifier may reduce the

sensitivity of that amplifier. At low frequencies, burst noise and

1/f noise are most significant in reducing the sensitivity of an

amplifier. Methods of controlling burst and 1/f noise are discussed

below, and a new low noise amplifier is proposed.

Because of the proximity of devices in integrated circuits,

thermal coupling between devices has been postulated as a possible

source of correlation of the I/f noise sources in adjacent transistors

in integrated circuits (29). The differential amplifier of Fig. 4-la

is ideal for studying the possible correlation of 1/f noise sources

in devices. Using the small signal equivalent circuit of Fig. 4-1b,

the differential output noise is found to be

2 2 2 2
Vd (BoRLR' /(Rsr ))(ifl + '- f2 fllf2) (4.1)

Positive correlation could improve the noise performance of the

transistor differential amplifier. If no correlation is present,

other amplifier configurations must be studied in order to find a

method of controlling noise.






























U


U

.
CU

CU


cU

CU
Co












-o r

L.






E
CU



CU


L
C)
4-













rC
LC


L.
Hr






Fig. 4-2 shcws the noise spectra of two matched transistors of

the transistor array CA-3018-G. The lower spectral curves are of

transistors 345 and 678 of the above array operated separately in the

common emitter connection. The upper spectrum is of the same

transistors operated in the differential amplifier configuration.

Close examination shows that the upper curve is the sum of the lower

two, indicating that the noise of the two transistors in the

differential amplifier adds quadratically. Thus no correlation is

present in these transistors throughout the spectrum measured.

The transistor amplifier of Fig. 4-3 provides an amplifier

in which 1/f, burst, and shot noise can be controlled. The small signal

model of Fig. 4-4 is used to analyze the noise performance of this

stage. The generators inl and in2 can represent either 1/f, shot,

or burst noise generators depending upon the choice of the base

resistors ra, rb, rc, and rd. The components of load current caused

by the noise generators inl and in2 are given belcw.

i /ni = 6o(R +ra+r 2+rx+ o(R +r a)-r-r )
2 x2 s a (4.2)
Rs +xl +l +(6+)(rx2+r2 )

i /i = ( ( +l)rc -R -r +r +r, r )
n2 o o s xl ( 2 d ) (4.3)
R + rxl + rl + (+1) (r 2 + r 2)
s xl 0 0 x2 ?2

For the proper choice of the collector current ratio

Icl/ Ic2 = 2 / r for o constant (4.4)

the load current component caused by inI or in2 may be set to zero.


iI / inl = 0 for

c2/ cl +(( +1) (Rs+r) rb + ra)/r 2
c2 cl o 'se )/ra


(4.5)





58










CC
4- --





uur


m0
E






a)



















U
C





















I









C;
7-
3 I 3aa




















4--
I I I t U



(sugo)o CI >

( o 3 I- LU U 1>









U








C

'4--- r
U-




















S(suquo) 33HiSIS3a 3SIO
































3
N


T-i~-


m


N


Y3






60


































v----- viA-- ----

























.---
SE










0.

('3





_



























Cn
-3












U)







L-f






i] / n2 = 0 for

C2/ Il = I + orc /r2 -(Rs+r -xr x)/r (4.6)

The current source of Fig. 4-3 may be adjusted for the desired collector

current ratio required to remove the desired noise component from the

output current of the amplifier. This technique may be used to

remove burst noise, I/f noise, and shot noise components of load

current. The noise resistance of this amplifier is then basically

limited by the thermal noise of the base resistances rx1 and rx2 plus

the shot noise of the collector current Ic2 since the noise of these

generators cannot be affected in this configuration. The voltage

gain of the configuration of Fig. 4-3 is found to be

Av = o (B +2)R I/(Rs + r r + (B+l) (r2 +r )) (4.7)

which is approximately equivalent to that of a common emitter amplifier

stage operating with a small source resistance. Analysis of the

frequency response of the amplifier of Fig. 4-3 finds that it is

comparable to that of the common eaitter stage also as shown in Table 4-1.


TABLE 4-1

GAIN AND BANDWIDTH OF THE LOW NOISE AMPLIFIER


R = .01 R = .1
s s
Gain Bandwidth Gain Bandwidth

C-E 189 .406 161 .127

Multiple Transistor 98 .44 98 .2
Ampl ifier








The amplifier of Fig. 4-3 can provide excellent noise performance at

low frequencies in trade for a loss of gain without sacrificing band-

width performance as compared to a common emitter stage operating under

equivalent conditions.

The use of the amplifier to control burst noise is demonstrated

in Fig. 4-5. The theoretical and measured curves of burst noise load

current versus collector current Icl are shown in this figure for the

cases in which transistor TI is bursting and then in which T2 is

bursting. The results show that the burst noise may be eliminated by

proper selection of the collector current Icl.

The same amplifier configuration should provide effective control

of 1/f and shot noise also. Dramatic evidence of this is presented

in Fig. 4-6. The noise spectrum of the amplifier is shown for various

values of collector current Icl. By adjusting Icl for a noise minimum,

a reduction of noise figure from 1040 to 6 is obtained at a frequency

of 20 Hz. The breadth of this null is shown in Fig. 4-3 indicating

that adjustment of Icl is not extremely critical. The results above

indicate that the transistor amplifier of Fig. 4-7 may be used to

produce very low noise amplifiers for low frequencies through proper

amplifier adjustment and transistor matching and selection.










730 72.5
I 2 =95a
RS = 10oo

o lil/i0B1
\ i1/iBB21
0
















/BD







.001 --- ---i------ ^----1 ---------
0

.0 1 I lllI







0 30 60 90 120 150
COLLECTOR CURIiEINT ICI (pa)

Fig. 4-5. Theoretical and experimental burst noise reduction using
the lao noise amplifier.











IC1

C2
2000-

\ RS R
1000- RS R


500- -
02 89/0a
SR = 1000on

200 -
*

S100- 0, = O.86a
(IS 0)





20 -


10- \ IC1 = 150a


5-


IC1 = 6pa
2-


1 I I I III I

20 50 100 200 500 1000 2000 5000
FREQUENCY (HZ)


Fig. 4-6. Noise figure reduction using the low noise amplifier.





65











N* s












.4- 'S1\-.





I C ,
Is I \








E
i C~ a \

Coo









= II C 4






II 0 -
C








S/ a)





I I I I 0










0 i 0 i i -





l 3.
1! / >" f



LLr / in

aa
NL

3
en



a,



rn^






3Un31J 3StON jr

or














CHAPTER FIVE


CONCLUSIONS AND RECOMMENDATIONS


The preceding work has produced several results which are

discussed bela .

1. Burst noise has been studied and the phenomenon characterized.

Burst noise in bipolar junction transistors has been shown to be

associated predominantly with the base-emitter junction and with the

depletion of the surface of the base region near this junction.

2. The existence of two 1/f noise generators has been demonstrated.

One noise generator has been shown to be associated with the surface

noise of the emitter-base junction of lhe transistor. The second I/f

noise generator is associated with the active base region of the

transistor. The presence of the second I/F noise generator as

speculated by Gibbons has been shown to exist.

3. An improved model of the lao frequency noise of the bipolar

junction transistor has been developed and is illustrated in Fig. 5-1.

The model includes the shot and thermal noise generators plus two I/f

noise generators and the burst noise generator discussed above. The

sum of the resistances r and rb of Lhe model of Fig. 5-1 represents

the total base resistance of the transistor in question, and the

resistor r is the resistance of the material of the inactive base

region of the transistor.























r x=r, + rb


i2 = 2qlcd

ib2 =2qIdf


if2 .-[K IB'df/f"2
if22 -=[K2 1 07Y2d[ /f2


eb2 = 4kTrdf

igB2 = K3 df/[1 + (7f/2a)2]








Fig. 5-1. Improved low frequency noise model including two
1/f noise generators and the burst noise generator.








4. A low frequency low noise amplifier configuration has been

demonstrated. Effective control of burst noise is possible through the

use of the amplifier of Fig. 5-2. The same amplifier configuration

can be used to realize amplifiers having very low equivalent noise

resistances at low frequencies. The noise resistance of the above

amplifier is basically limited by only the base resistances of the

transistors used to build the amplifier and by the shot noise of the

collector current of the transistor T2 of Fig. 5-2.

5. The improved noise model has been used to predict and explain

the existence of structuring of noise spectra which have been observed

but have remained unexplained until this time.

Several areas which deserve further study have originated as a

result of this research and are discussed below.

1. The preceding work has demonstrated the existence of a

1/f noise source associated with the active base region of bipolar

junction transistors. The origin of this 1/f noise source needs to

be determined.

2. Further study of burst noise is indicated. The physical

cause of burst noise deserves investigation with the hope that this

will lead to methods of process oriented control of the burst noise

phenomenon.

3. The low noise amplifier developed in Chapter Four deserves

further study. The possibility of realizing a very lao noise amplifier

at lao frequencies is most stimulating. The configuration appears to

be amenable to integration, and in fact much of its performance is due

to the matching which can be obtained between devices in integrated





69















o0






































CC












C)




---
c
o







L)





5-j
CI

-0














1 ..




70



circuits. It is recommended that this ampl ifier configuration be

exhaustively studied.














APPENDIX


MEASUREMENT SYSTEMS AND METHODS


The results of Chapters Two, Three, and Four were obtained using

the systems described in this Appendix. Two major systems are

described which can be used to determine noise resistance, noise

figure, and equivalent burst noise voltage. Other minor systems are

described, and methods of measuring transistor parameters developed.

The system used to measure noise resistance was described in Chapter Two.

The block diagram of this system is shavn in Fig. A-1.

The actual measurement system is shown in Fig. A-2. A Hewlett-

Packard HP-II1 oscilloscope is used as the system's variable gain

amplifier and to monitor the noise output of the device under test.

Follaoing this amplifier is a monitor oscilloscope which is used to

insure that no clipping of the noise occurs in the main amplifier.

The filter and quadratic detector are contained in a Quan-Tech wave

analyzer. This wave analyzer tunes from I Hz to 5 kHz with bandwidths

of I Hz, 10 Hz,and 100 Hz with a full scale sensitivity of 30 V to 100

volts rms. The wave analyzer permits the selection of four meter time

constants of 0.1, 1, 10 and 100 seconds, providing excellent averaging

capability. A dc analog recorder output drives a chart recorder which

is used to provide accurate determination of a given meter level. The

calibration signal is derived from the BFO output of the wave analyzer

















































































































































-C,





73







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and is set to one volt rms. This signal is monitored on a voltmeter

and oscilloscope, and it is followed by variable attenuation to provide

an adjustable calibrating signal.

Use of the system is as follows. With the calibrating switch open,

the noise in a particular frequency range is measured with a given

amplifier gain setting, and the detector reading is recorded. The main

amplifier gain is then reduced by an arbitrary factor (100 times for

example). The calibrating signal is introduced by closing the

calibrating switch, and the attenuator is adjusted until the original

detector level is attained as monitored on the recorder. The equivalent

noise resistance is then given by:

R = I/[(-.(AV2/AVl) (4kTdf) (antilog(total system

attenuation in db/10))] (A.I)

In the above expression, AVI/AV2 is the ratio of the main amplifier gain

settings, and the total system attenuation also incorporates this

figure. An accurate knowledge of the effective noise bandwidth df is

necessary to provide accurate measurement of noise resistance using the

above system. The filter characteristics of the wave analyzer were

experimentally measured, and the effective noise bandwidth was deter-

mined by numerical integration. The results of this process yielded

effective noise bandwidths ofl.2Hz,12.5 Hz, and 125 Hz, for the 1 Hz,

10 Hz, and 100 Hz bandwidth settings of the wave analyzer respectively.

Also affecting the accuracy of the system is the background noise of the

main amplifier and wave analyzer. Therefore, continual checks must be

made in order to insure that the background noise of the systan is

negligible with respect to the output noise of the device under test.







This is accomplished by connecting a resistor, equivalent to the output

resistance of the transistor under test, across the input of the main

amplifier. As long as the rms value of the noise voltage measured under

these test conditions is less than one-tenth of that during the measure-

ment of the transistor under test, then the error in measurement of the

equivalent noise resistance Rn, introduced by system noise, will be less

than one percent.

The transistor under test is mounted in the test jig of Fig. A-3.

The circuit consists of a fixed attenuator and transistor biasing circuitry.

The source resistance of the transistor is easily controlled in this

circuit, and the attenuator circuit provides both attenuation and

matching for the variable attenuator. Also the value of the biasing

resistor RB may be varied between wide limits without affecting either

the value of source resistance R as seen by the transistor or the

precision of the fixed attenuator.

The second measurement system is the system of Fig. A-4 which is

used to measure equivalent b'Jrst voltage eBB. The system consists of

the transistor under test, the HP-141 oscilloscope and a calibrating

signal. The oscilloscope is again used as a variable gain amplifier,

and the storage capability is used to measure burst amplitude. The

calibrating signal consists of a signal source adjusted to yield a

one volt peak-to-peak amplitude followed by a variable attenuator.

The test jig is the same as that of Fig. A-3 which provides attenuation,

matching for the variable attenuator and biasing.

With the calibrating signal off, the burst amplitude at the output

of the transistor under test is stored and its amplitude determined. The






76






















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system gain is then reduced by a convenient factor (100 for example),

and the calibrating signal is adjusted to provide a signal of the same

ampl itude at the output of the transistor under test. The equivalent

input burst voltage eBB is given by:

eBB = 1/[antilog(total system attenuation in db/20)] .

(A. 2)

Again the total system attenuation includes the ratio of thi amplifier

gains.

The above two systems may be used to provide measurements of

equivalent noise resistance versus source resistance and frequency,

and measurements of equivalent burst voltage as a function of source

resistance, temperature, and operating point.

Measurement of the average burst rate utilizes the system of Fig.

A-5. The burst output of the transistor under test is amplified and

passed through the infinite limiter which removes the background

noise from the bursts. The clean bursts are then counted by the

counter, and the average burst rate determined. The infinite limiter

is real ized using an analog computer and the circuit of Fig. A-6.

Measurcment of B is accomplished using the circuit of Fig. A-7.

With a small signal applied from the source, the adjustable resistance

R is varied to yield a null on the detector. When the null is reached,

0 is given by

o = (R1 he)/R (A.3)

Precision potentiometers are used to provide accurate measurement of 6 ,

and a wave analyzer is used to provide a signal source and detection.

In order to help characterize the small signal models developed

in Chapter Two, the las frequency short circuit input impedance






79





























































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h. = r + r (A.4)
ie x ii
must be determined. The impedance h. is measured using a Wayne-Kerr
i0
B-601 bridge utilizing the test jig of Fig. A-8. The cla frequency

short circuit current gain S of the transistor and the transistor base

resistance rx may then be determined using this value.

The standard emitter coupled pair connection of transistors is

used to measure the noise of the differential amplifier. The noise

measurement system of Fig. A-1 is used except that the scope amplifier

is now used in its differential input mode. The equivalent noise

resistance of the emitter coupled pair is then referred to the input of

one of the transistors of the pair as shown in Fig. A-9. The noise of

each transistor is measured separately in the common emitter connection

using the measurement system of Fig. A-1 and the test jig of Fig. A-3.

The burst noise and noise resistance of the compound Darlington

connection of transistors are measured using the circuitry of

Fig. A-10. The collector current ratio is varied by varying the

current source current control resistor R. The variation of burst

noise output current and amplifier noise resistance as a function of

current are determined using the two major systems described earlier.

The measurement systems of this chapter provide the instrumentation

necessary to verify the theory presented in Chaptes Two, Three, and

Four.


















CT





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BIBLIOGRAPHY


1. A. van der Zell, "Noise in junction transistors," Proc. IRE,
vol. 46, pp. 1019-1038, June 1958.

2. L. J. Giacoletto, "The noise factor of junction transistors,"
in Transistors I, pp. 296-308, Princeton: RCA Laboratories, 1956.

3. W. Guggenguehl, and M. J. 0. Strutt, "Theory and experiments of
shot noise in semiconductor diodes and transistors," gBc, 1E,
vol. 45, pp. 839-857, June 1957.

4. W. H. Fonger, "A determination of I/f noise sources in semi-
conductor diodes and triodes','inTransistors I, pp. 239-295,
Princeton: RCA Laboratories, i956.

5. C. T. Sah and F. H. Hielscher, "Evidence of the surface origin
of the 1/f noise," Physical Review Letters vol. 17, pp. 956-958,
October 1966.

6. G. Abowitz, E. Arnold, E. A. Leventhal, "Surface states and 1/f
noise in mos transistors," IEEE Trans. Electron Devices, vol. ED-14,
pp. 375-379, November 1967.

7. J. F. Gibbons, "Lo~ frequency noise figure and its application to
the measurement of certain transistor parameters," IRE Trans.
Electron Devices, vol. ED-9, pp. 308-315, May 1962.

8. K. F. Knott, "1/f voltage noise in silicon planar bipolar
transistors," Electronics Letters, vol. 4, pp. 555-556,
13 December 1968.

9. W. H. Card and P. K. Chaudhari, "Characteristics of burst noise,"
EPrf .IEEL, vol. 53, pp. 652-653, June 1965.

10. G. Giralt, J. C. Martin, F. X. Nateu-Perez, "Sur un phenomena
de bruit dan las transistors, caracterise par des creneaux de
coupant d'amplitude constante" C. R. Acad. Sc. Paris, vol. 261,
pp. 5350-5353, 1965.

11. P. E. Gray, D. Devitt, A. R. Boothboyd, J. F. Gibbons, Physical
FlstLnisL c _and Circuit Models of Tasistos, Chapter 4,
John Wiley and Sons, Inc., New York, 1964.







12. E. R. Chenette, "Noise in semiconductor devices," Adyances n
EljtrQonics, vol. 23, L. Martin, ed., Academic Press, 1967.

13. H. A. Haus _t al., "IRE standards on methods of measuring noise
in linear twoports," Proc. IRE, vol. 48, pp. 60-68, January 1960.

14. H. Rothe and W. Dahlke, "Theory of noisy fourpoles," Pro. IRE,
vol. 44, pp. 811-818, June 1956.

15. D. K. C. MacDonald, Noise and Fluctuations: An Introduction,
pp. 34-37, John Wiley & Sons, Inc., New York, 1962.

16. H. A. Haus t al., "Representation of noise in linear twoports,"
Eroc._jRE, vol. 48, pp. 69-74, January 1960.

17. R. D. Thornton .at alI., Handbook of Basic Transistor Circuits and
easurienents_, Chapter 9, John Wiley and Sons, Inc., New York, 1966.

18. E. R. Chenette, "Low noise transistor amplifiers," Solid State
Design, pp. 27-30, February 1964.

19. C. T. Sah, "A new semiconductor tetrode -- the surface-potential
controlled transistor," Eroc_.RE_, vol. 99, pp. 1623-1634,
November 1961.

20. F. Levenberger, "1/f noise in gate-controlled planar silicon
diodes," fjlectronicsLetters, vol. 4, p. 280, June 1968.

21. R. D. Thornton, 0. Dewitt, E. R. Chenette, P. E. Gray, Characteristics
and Limiations of Transistors, Chapter 4, John Wiley and Sons, Inc.,
New York, 1966.

22. S. R. Hofstein, "Proton and sodium transport in SiO, films,"
IELEET I ranrl._ElsoLalDLei, vol. 55, pp. 749-759, November 1967.

23.. E. Snow .eL al., "Ion transport phenomena in insulating films,"
J. Applied Physics, vol. 36, pp. 1669-1673, May 1965.

24. D. Wolf and E. Holler, "Bistable current fluctuations in
reverse biased p-n junctions of germanium," J. Applied Physics,
vol. 38, pp. 189-192, January 1967.

25. G. Giralt, J. C. Martin, F. X. Nateu-Perez, "Le bruit en
crenaux des transistors plans au silicium," Electronics Letters,
vol. 2, pp. 228-230, June 1966.

26. A. Papoulis, Probabil ity, Random Variables and Stochastic Processes,
Chapters 9 and 10, McGraw-Hill, Inc., New York, 1965.





88

27. P. E. Gray, D. Dewitt, A. R. Boothroyd, J. F. Gibions, Physical
lJ_!;_rius and Circuit Modls of Transistors, Chapter 3, John
Wiley and Sons, Inc., New York, 1964.

28. V. G. K. Reddi, "Influence of surface conditions on silicon
planar transistor current gain," Solid State Electronics, vol. 10,
pp. 305-334, 1967.

29. 0. Mueller, "Thermal feedback and 1/f flicker noise in semi-
conductor devices," General Electric Technical Information Series,
No. R64-CPD-12, November 20, 1964.













BIOGRAPHICAL SKETCH


Richard Charles Jaeger was born on September 2, 1944, in New

York, New York. He completed his secondary education in Fort

Lauderdale, Florida, in June, 1962, and entered the University of

Florida in September, 1962. He received the degree of Bachelor of

Electrical Engineering with High Honors in April, 1966. Upon

receiving an NDEA Title !V graduate felloship, he entered the

Graduate School of the University of Florida and was awarded the

degree of Master of Engineering.in December, 1966. Since that time

he has pursued studies leading to the degree of Doctor of Philosophy.

Richard Charles Jaeger is married to the Former Joan Carol

Hill, and they have a son, Peter Charles Jaeger. He is a member of

Phi Kappi Phi, Tau Beta Pi, Eta Kappa Nu, Sigma Tau, the Institute

of Electrical and Electronics Engineers, and Kappa Sigma social

fraternity.









This dissertation was prepared under the direction of the chairman

of the candidate's supervisory committee and has been approved by all

members of that committee. It was submitted to the Dean of the College

of Engineering and to the Graduate Council, and was approved as partial

fulfillment of the requirements for the degree of Doctor of Philosophy.


June 1969






Dean, College of Engineering




Dean, Graduate School






Supervisory Committee



Ch,_. an,



I / '






1' lU_




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