Frequency variations of transistor parameters

Item Type text; Thesis-Reproduction (electronic)

Authors Latorre, Victor Robert, 1931-

Publisher The University of Arizona.

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FREQUENCY VARIATIONS OF THAIS IS TOR PARAI-ETERS

by

V icto r Re Latorre

A Thesis

submitted to the facu lty of the

Department of E le c tr ic a l Engineering

in p a r t ia l fu lfillm en t of the requirements fo r the degree of

MASTER OF SCIENCE

in the Graduate College, U niversity of Arizona

1956

Approved:D irec to r of Thesis ^ ( / Date r

7 7 ^ 6 -77

This th e s is has been submitted in p a r t ia l fu lf illm e n t of req u ire ­

ments fo r an advanced degree a t the U n iversity of Arizona and is

deposited in the Library to be made availab le to borrowers under

ru les of the L ibrary a B rie f quotations from th is th es is are

a llw a b le i'Jithout. special: permission# provided th a t accurate

acknowledgment of source i s made* Requests fo r permission fo r

extended quotation from or reproduction of th is manuscript in

whole or in p art may be granted by the head of the major depart— ‘

ment or the dean of the Graduate College when in th e i r judgment

th e proposed use of the m ateria l is in the in te re s ts of scholar^

■Ship* In a l l o ther instances# however# perm ission must be obtained

from the author*

.s im m s ;

flie author ivlshes to express h is apprecia tion fo r the a s s is ­

tance and encouragement of Dr«. fhom s. Le Martin^ J r . , head of the

Department of E le c tr ic a l Engineering* Valuable assis tance was

a lso received from Mr. A. H* Perkins and Ifr* D» J . Sakrison of

the Department of E le c tr ic a l Engineering. The author also wishes

to express h is g ra titu d e to h is w ife, Haney, who typed the f in a l

manuscripfco. •

fhe fin a n c ia l a ssis tan ce supplied by the Anry E lectron ics

Fhoving Grounds a t Fort Huachuca through the Department of E lec­

t r i c a l Engineering i s hereby g ra te fu lly acknowledged e

f ABXS OF COEMrs:

In troduction .

Ohapber .1 % e Common E m itter Equivalent C ircu it

1-1 In troduction

1-2 D efin ition of “A11 Parameters

1-3 Development of The Comaon E m itter Hybrid Para-

> meter Equivalent G lrouit For C irc u it Design

Chapter 2 S ta tic \¥ a lu e s of Parameters and Independence

Of Frequency of and ' P :_ - '"-"P-"'.■|;,fi'Ti«»'ni>«... ■ inf ii irriiin • '• ' " "

■ r":'P2-l In troduction - ■ '"P '■ ■

2-2 Static'Measurements, of./Parameters 1

2-3 E ffect of Frequency"of 1 and

Chapter 3, The V aria tion q1 $ With F requency

3—1 In troduction • • . -

3-2 ... T heore tica l E aslsrgor She AC. Measurement of

3-3 - Experimental R esults - Comparison of AC and DC

^ ValUes of ^ ■ .

Chapter 4 The V aria tion of A ^ With "Fr equency / .

4-1 In troduction

• 4-2. . • D erivation o£ L ^ From The Input C irc u it •„ :CW.-S, I r„ :i in-rmui.iiiriwi; ... . w. ,T « ,rm r f 'K r n r u ii Ti f - . t -r V.. rz:- .

, ‘ - ' , ' , . : . . " '

4“3 The' E ffec t of A ^ on The Upper Cutoff Frequency

of The T ran s is to r .

Chapter $ M odification of The Common E m itter Hybrid A P a ra - ..

met e r Sduivalent C ircu it

I»ge

1

. 1

: ' . 3 'r

10

10

13

14

14

- IS

23

23

27

5-1 IQitroduGtlon .

5-2 ffae E ffec t of The Bas©Spreading Resistance

on, dev io u s R esults . .

Chapter 6 Bandpass - T ran sis to r Amplifiers

6-1 In troduction

6-2 D erivation of The Expression For The Gain ^ ..

'= of Tuned T ransis to r Amplifiers •' . ' . .

6-3 Center Frequency of Tuned T ran sis to r Am plifiers ■

6-4 Proposed Method of Design For luned T ransis to r

6-5 N eu tra liza tion of funed T ran sis to r Amplifiers

6-6 C h a rac te ris tic s of An Experimental funed gran—

-s i s t o r 'Am plifier

page31

31

34

35

40

44

53

58

ILIalBTRATIOm

1-1 Gpnmioii Hybrid Parainete.g;.EgniYalen t C ircu it

1-2 Change in Nomenclature j Goromon E iiiitter5 Hybrid

Parameter Equivalent C ircu it ‘ .

1—3 Equivalent C ircu it With Connected Load

1-4 S im plified Equivalent:. C ircu it ' -

1-5 F in a l Equivalent C i r c u it ' .

g f l l^ p p t_ r;-C h a ra c te ris tic s i

2-2 Output C h a rac te ris tic s

3-3- Girfeult IJsed to Measure As A Function of F re-

;.-4 - mehWrl: - ' i v - - ; - -V ■.:

3-2 Olass.' A‘Equivalent C ircu it of Figure 3-1

%-“% % f la t io n of With Frequency . ;

3-4 C irc u it Used to Determine Frequency Response of $

3.^5: Va ria tio n o f $ With Frequency"

4-1 C ircu it Used to Determine The E ffect o f Frequency

• ;■ \ ; '' - .■ . ,v >: ;4-2 C la s s ii Equivalent Input C ircu it -

4-3 ; ihe V a ria tio n . of With Frequency : ' •, ■

4-4 Ih q ;E iieGi °1 A^o on She Upper Cutoff Frequency,

5-1 Correc t. Form of She' Common E m itter Efcrbrid A Param eter; ,.

■ ? - Equivalent C ircu it v .

6-1 Equivalent C ircu it For A Tuned T ransis to r A m plifier

page2

4

5:

B

9

11

12

15

16

19

21 22

25

26

28

30

32

{(One E tage) 36

6—2 C ircu it Used to B61>e rid.ne the C eaier Frequencypage

• of Tuned I ra n s is to r Am plifiers 42

^-3 A lterna te Form of F igure (6*2) . 42

6-4 Location of Poles and Zeroes y Actual G lro u lt: ' ' 46

6-5 Location of Poles- and Zeroes - E ffec tiv e Equivalent

C ireu it ' : . ' - ' 47

6-6 . Bffec tiv e Equiv a len t C ircu it - Grounded E m itter ;

. ; Amplifier ’ . ■ 48 ‘

6-7 C ircuit Used to Determine E ffec tive ¥alues of Para—

i meters - . '. " ■ 49

6-6 Erequency Response of The ■ Input C ircu it 51 .

; 6-9 _31nmt':&%pacltameuyat,'%6%ageC8aln 52

6-10 One Stage T ran sis to r Amplifier With funed Input

and:;Output C ircu its ' 54

6-11 " N eutralised . Grounded Em itter .funed Am plifier ' 55

6-12 Equivalent C irc u it of -A N eutralized Grounded E m itter

■i Amplifier ■ ■■ " ■ ' . 56

6-13 Grounded-Emitter Tuned T ran sis to r Amplifier • . 60

6 -I4 Frequency Response of A Grounded Em itter Tuned

"Eraasistor Am plifier, . : . 61,

IfflRQBUCTICM

As th is paper i s concerned w ith the t r a n s is to r as a c ir c n it

element, i t i s apparent th a t frequency e ffe c ts are im portant, and

th a t we must know these e ffe c ts a In the design of p ra c tic a lly any

e lec tro n ic c i r c u i t , the frequency response of the system i s of v i t a l

in te re s t * I h e 'usual design requirements specify the desired frequency

response of ’ the system and, from these and other requirem ents, the

system can be designed i f the parameters o f. the ac tive elements o f

the system are known,

Thus, i t i s necessary th a t the e ffec ts of frequency on the para­

meters of the t r a n s is to r must be estab lished before any good design

can be developed«, I ;.' : 'I;.,1 v :'l> '

1

Chapter 1

THE COMMON EMITTER EQUIVALENT CIRCUIT

(1 .1 ) Introduction

The common em itter equivalent c ir c u it was developed to fa c i l i t a t e

design of tra n sis to r c ir c u its • I t i s true th at the common base hybrid

(or “h”) parameter equivalent c ircu it i s more widely used, but the

author f e e ls that i t possesses a disadvantage that n ecess ita tes the

development of a d ifferen t form of equivalent c ir c u it . This disad­

vantage becomes apparent from a consideration of most e lectron ic c ir ­

c u it s . Nearly a l l conventional tra n sis to r c ircu its arc designed for

the common emitter connection, not for the common base connection from

which the h-parameter equivalent c ir c u it was designed.

(1 .2 ) D efin ition of "A" parameters

The c ir c u it diagram of the common em itter hybrid parameter equiva­

len t c ir c u it i s shown in Figure ( l . l ) . The four hybrid parameters

are defined as fo llo w s:

A^i i s the input resista n ce with the co llec to r shorted to the

em itter.

1 . The o r ig in a l d e fin it io n s of the hybrid A parameters were made by Dr. Thomas L. 1-fe.rtin, Josef Gartner, and Aladdin Perkins at the U niversity of Arizona in December, 1954*

d . i )

f/G . ( / - / ) Common Etn/£tc.r j tfybnc/P A r A M c X ^ r E & u iv » /e y > r C trcu /C

A^2 i s the output admittance with the base an open c ir c u it .

j (1*2)" h . - . o

Al2 v°l^ aSe feedback factor w ith the base an open c ir cu it •

‘ tv; 4nt' - (1 -3)

A ^ i s the r a tio of the c o lle c to r current to the base current

w ith the co lle c to r shorted to the em itter.

A,, = _&5_ = .^ 5 /

The factor A ^ , which i s defined as the current am plification

fa c to r , i s more commonly id en tif ied by the symbol-^ • Therefore,

the equivalent c ir c u it assumes the form shown in Figure (1 .2 )•

(1 .3 ) Development of The Common Emitter Hybrid Parameter Equivalent C ircu it For C ircu it Design

The equivalent c ir c u it drawn in Figure (1 .2 ) i s not su ited to

a stra igh t forward c ir c u it design . This seems to be a disadvantage

common to a l l two-generator equivalent c ir c u i t s . This c ir c u it can

be further sim p lified by evaluating the voltage generator in the input

c ir c u it . This i s the generator narked A^Vc in Figure (1 .2 ) .

Assume that the tr a n s is to r has some arbitrary three-term inal

load connected as shown in Figure (1 .3 )• Three new terms are defined

as fo llow s:

u

a

+

F ^ /G . ( / - 2 ) C tf/M & e f n n o m e n c l a t u r e ;

C o m m o n B r n t t t e r , H y b n J

Parameter fciu/vaknt Circuit"

5

3o-

+

Q(hn

cTc

z z Vc

V

m ’ T r ~ b

f~/Gr. ( /~3) E quivalent C ir c u tt IV/thConnec.tecf Z<?a</

■= Input, impedance of the connected load c ir c u it .

Zq =z Input impedance o f the entire passive co llec to r c ir c u it .

Zj.j = Mutual impedance of the en tire passive c o lle c to r c ir c u it •

These terms are indicated in Figure (1 .3 )•

From the c ir c u it , i t can be seen th at th e co lle c to r voltage Vq i s

Now, define a new parameter so that the c ir c u it can be further

sim p lified in to a more u se fu l form. This parameter, A^., i s the

voltage am p lification , measured from the base to the c o lle c to r , and

i s given by:

This ra tio i s u su a lly a negative, complex number for the common

em itter c ir c u it .

given by:

(1 .5)

Therefore,

(1 .6)

(1 .7 )

From the equivalent c ir cu it of Figure (1 .3 ) , and from the equations

previously developed, the voltage gain parameter i s :

(1.8)

Thus, the negative component of the input impedance becomes:

- * • ^ - A ^ ( 1 .3 , ,

Because the base to co lle c to r gain, A c , i s normally negative.

th is i s a negative impedance. Therefore, the to ta l input impedance

of the c ir c u it i s :

= A,, - A,z 0z* a .n)or-7 _ /ft/2C,ZZ/ (1.12)

And the equivalent c ir c u it assumes the form shown in Figure (1 ,4 )•

Because the operation of a tra n sis to r changes with changes in

s ig n a l frequency, the equivalent c ir c u it must in d icate the cause of

the changes, I t was assumed that the frequency changes were the resu lt

of reactive components a c tu a lly associated with the tr a n s is to r . This

w il l be discussed in more d e ta il la te r : at th is p oin t, the f in a l equi­

valent c ir c u it i s assumed to have the form shown in Figure (1*5) •

8

72

E E

jF/G* ( Si mp/ / / t ec/ £<yutvf>/ent Circuit

F/G-. (1-5) f /naf £qu/vakvt C/rco<£

vo

10

Shapber 2

STATIC VALUES OF PAEAmEHS AICl Iffl38FBE)EHDl OF FRiQCBffil OF Ay AHD

(2ol) In irodystlon

I t - 2 3 necessary to-Mow- th e s ta t i c c h ay ae ta ris tie s of the tran-= .

s i s to r before th e e ffec ts of freqmeney can be deterainecL . $he s ta t i c

or d ire c t cu rren t values fo r the previously defined parameters were

deteraiined by ordinary methods,, described b r ie f ly in the paragraphs

th a t follow* ' , _

• (2q2) S ta t ic Jfeasurements of Param eters

' #he input mad output c h a ra c te r is tic curves fo r the t r a n s is to rs

were obtained. w ith a Libraseope X-Y p lo tte ro For th e output character-”

3 s t ie s 9 the t r a n s is to r was operated a t d iffe re n t parametric values

of ' base currentg and the 'c o lle c to r voltage v a ried from zero v o lts to

th e aagtmom allowable vo ltage without exceeding the znaximum. c o lle c to r

dissapationo , The p lo t te r recorded a continuous curve showing c o lle c to r

curren t as. a function of c o lle c to r voltage fo r each param etric value

of base current® - .

/ fhe input c h a ra c te r is tic s Were obtained in a s im ila r irnnner^ th e ;

c o lle c to r voltage serving as the fam ily parameter<. Shus^ fo r each value

of c o lle c t or voltage^, th e base voltage was varied from zero, v o lts up . '

to the maximum allow able;value, and th e p lo tte r recorded a continuous

( * * > j .^ 3 y / t e h /d

t - H

/C

— 6 -t— ■ I 8 L-i.-l VZ--L4 _ |_ 4 :. SL4_ ^ „ |_ ^ 6 4

1 . i L------i.—| . —•"'V' V o * 7 1 0 j—• 1 -• i— j— | _j .!.!

: I I | ; : | f i ; : , : I J I , I I

curve of th e base cu rren t as a function of the base v o ltag e» Figures

(2ol) and (2 ©2) show sample c h a ra c te r is tic curves fo r both the input

and output, c ir c u i ts of the tra n s is to r ,. From the previous d e fin itio n s

of th e .hybrid param eters, i t is c lea r th a t they can be determined

d ire c tly from th ese curves * ..

(2*3) E ffec t of Frequency on A- -, And Aqq

The dynamic or a lte rn a tin g current values of and AP? were

determined from measurements made by Kf*®. David 1© Sakrison of th e

E le c tr ic a l Engineering department a t th e U niversity of Arizona, and .

th e values obtained are in a,greement (w ith in 10 fa) w ith the s ta t ic

values© Therefore, from these r e s u l ts , i t can be sa id th a t A and

A__ are constant w ith frequency©. This i s in accordance w ith the equ i-

.valent c irc u it shown in Figure (1*5)« From th is you can see th a t

th e changes in input and output impedance are accounted fo r by the

capacitances present in these c irc u its 6 The voltage feedback fa c to r ,

a lso has an e f fe c t upon the input impedance© This w il l be d is ­

cussed in more d e ta i l in a l a t e r chapter©

14

Chapter 3

THE VARIATION OF f WITH FREQUEICY

(3 #l) Introduction

In Chapter two, i t was noted that the value of the current ampli­

f ic a t io n factor f , equal to was determined from the s ta t ic

ch a ra cter istic curves. The purpose of th is chapter i s to show, theo­

r e t ic a l ly , that ^ i s independent of frequency and, then to v e r ify

th is theory by experiment. This assumption that ^ i s not frequency

dependent disagrees with the generally accepted theory which assumes

frequency dependence# However, i t i s f e l t that the approach presented

in th is chapter merely depends upon a simpler d e fin it io n of the base

current, 1^. S p e c if ic a l ly , in the theory proposed, the base current

i s assumed to be only in the impedance designated as •

In the more common theory of frequency dependence of ^ , the base current

i s assumed to be a l l of the current in to the base term inals# I t should

be clear from the equivalent c ir c u it shown in Figure (l#5) that th is

new notion greatly f a c i l i t a t e s the design of a multitude of e lectron ic

c ir c u its using tra n sis to rs •

(3 .2 ) T heoretical Basis For The AC Measurement of $

The c ircu it used for determining the AC value of @ i s shown in

Figure (3 .1 ) . The operation o f the c ir c u it i s best understood from

15

cc

/ r/£ . (3- / ) (/sc</ ta T/Peazure*P 3 s 3 F u n c T /o /7 o f F r e q u e n c y

16

it*

+

Vc

Fitn —/ •/ A 2-i /fL

6 3 - 2 ) C / 3 5 5 /4 EQutVA/eut C i r c u i t

o f . /v s - t/rc ( 3 - i )

17

th e Class A equivalent c i r c u i t in Figure (3 .2 ) . A ctually , the c ir c u it

i s e sse n tia lly a bridge c i r c u i t . and Cx are ad justed to produce

a n u ll de tecto r reading a t a number of d iffe re n t s ig n a l frequencies

provided by the s ig n a l source V. The c o lle c to r s ig n a l voltage i s mon­

ito re d with a Cathode Ray Oscilloscope a t a l l times to assure th a t th e

condition of C lass A operation always e x is ts .

Now, a t bridge balance:

(3-1)

Hence,

(3 .2)

The loop equation around the input c ir c u i t i s :

(3 .3 )

Or:

(3 .4 )

S u b s titu te equation (3*2).

(3 .5 )

Cancel 1^, rep lace with R% The

re s u lt i s :

(3 .6)

Where:I

' A„ C/A/ (3 .7 )

In the steady s t a t e , equation (3 .6) reduces to :

r = A , t R M a - j (3 ‘10)

This equation provides the experimental basis fo r estab lish in g

the frequency v a ria tio n ^ *

(3 *3) Experimental R e su lts - Comparison of AC And DC Values of

From the c ir c u it presented in the previous sec tion , data were

taken fo r a number of t r a n s is to r s . Plots were then made of ^ as a

function of frequency. These curves are shown in Figure (3 .3 ) .

From Figure (3 .3 ) , i t i s evident th a t ^ is independent of frequency.

However, to more firm ly e s ta b lish these r e s u l ts , another method was

used, as described below.

I f the output c ir c u i t of the t r a n s is to r is broad-banded (R^

made very sm all) and a constant value of s ig n a l base curren t m aintained,

i t is possible to determine the frequency response of a new parameter,

ft • The d ifference in and l ie s in the assumption of the path

fo r the base c u rre n t. In Figure (1 .5 ), the base current i s shown only

in the impedance 9 the parameter a p p lie s .

By defining the base cu rren t as the current in to the input term inals

0 0

2 A/ * 96

— W

| —|- |

n 6

m - : - ;

11

ill;.!'!*4—• — i * —|- -

e m ^ / . i ; \ r ' « * s > s )VftftatfonF(&. (3-3)

1 [_ J L

20

of the t r a n s is to r , we must use another parameter to represent the cur­

ren t am plification fa c to r . This parameter i s .

The c ir c u i t used to determine f t* as a function of frequency is

given in Figure (3.4)* Because R2 i s very sm all, i t i s v a lid to assume

th a t the output c irc u it i s sh o r t-c irc u ite d , was determined fo r

numerous values of s ig n a l frequency from the following expression:

(3*11)

Now, because the output c ir c u i t was sh o r t-c irc u ite d , the r o l l - o f f

of the frequency response curve i s caused so le ly by the input c i r c u i t .

The frequency response c h a ra c te r is tic of the input c ir c u i t was d e te r­

mined th e o re tic a l ly . Figure (3*5) shows the curves fo r each of the

above-mentioned se ts of d a ta . These curves are in close agreement

and, th e re fo re , i t can be sa id th a t the apparent change in f t w ith

frequency can be a ttr ib u te d to the input c irc u it and th a t f t i s

constant with frequency.

21

R t

V 7x - v r v n ^

zv) V:— V,bk

VTVAJ

cT - V"

/V(z. (3 -^ ) CtrcutC Usee/ to fietermmQf r e q u e n c y R e s p o n s e o f p

23

Chapter 4

THE VARIATION OF A_ ICTH FREQUENCY

(4#1) In troduction

The voltage feedback fa c to r , A ^ , i s th e most d i f f ic u l t of the

hybrid A parameters to measure. I t i s possible to determine the s ta t i c

value of A ^ from the s t a t i c input c h a ra c te r is tic curves, but th is is

extremely d i f f ic u l t because of the very c lose spacing of th e curves.

However, the approximate average value of A ^ fo r some 40 d iffe ren t

junction t ra n s is to rs i s Q.5 x 10"^. This value i s assumed to be accu­

ra te w ith in an order of m gn itude . This might seem to be a ra th e r

poor apiiroximation. However, i t should be noted th a t A ^ is a very

small quan tity and, as w i l l be shown in subsequent paragraphs, i t

can usually be neglected.

The dynamic values of A-^ were determined a t various frequen­

c ie s . The techniques used in measuring A ^ and the conclusions drawn

from these measurements a re discussed in th e remainder of th is chapter.

(4*2) D erivation of A ^ From The Input C irc u it

A12 was previously defined as the r a t io of the base voltage to

the c o lle c to r voltage w ith the base an open c irc u it ( equation 1.3 ) .

From th is d e fin itio n , i t seems lo g ica l to apply a constant s ig n a l

vo ltag e♦ to the c o lle c to r and measure the re su ltin g open-c ircu it

base voltage# The c i r c u i t used is shown in Figure (4#l) • The

A equivalent c irc u it of the input c i r c u i t of the t r a n s is to r is

in Figure (4 ,2 ) . From Figure (4*2), i t i s e a s ily seen th a t :

R earrang ing term s:

Vb[$u + /s c ^ - K [ '/sc,*,J

And:

/ ! V t U , f

Hence:

Vb/ h z = (> + r f t 'S C / A , ) ^

In a more convenient form:

A >t = + ~ jtc 7 A ,) '4 ,lC /A / \In the s te a d y -s ta te . Equation (4*5) becomes:

^ " Q" c'~ -&

24

Class

shown

(4 .1)

(4 .2)

(4.3)

(4.4)

(4.5)

(4 . 6)

25

cc

/~/&. { V'/) Circuit L/seo/ to DcCermmt.Jhc e f fe c t o f fpexfutncy on A /z

26

FIG. ( Y-2) C/3SS /I £Qui\/a/cnt —

Tnput C/rcutt

27

From Equation (4 .6 ) , i t i s apparent th a t A-^ i s frequency depen­

den t, I t i s in te re s tin g to note th a t the curve of as a function

of frequency would follow the rec ip roca l of the curve of th e base to

c o lle c to r voltage gain as a function of frequency fo r the lower values

of frequency. This can be seen more c le a r ly from Equation (4 .4 ) .

As th e frequency of operation i s fu r th e r increased , the fac to r

which appears in Equation (4 .6 ) , becomes more im portant. Figure

(4.3) i s a p lot of Equation (4 .6) and in d ica tes the v a ria tio n of A ^

with frequency.

(4.3) The E ffec t of A ^ on The Upper Cutoff Frequency of The T ransis to r

c u to ff frequency of the t r a n s is to r i s i l lu s t r a te d by the curve of

Figure (4 .4) • The base to co llec to r voltage gain was computed theore­

t i c a l l y by assuming the cu to ff frequency was con tro lled e n tire ly by

the input c ir c u it parameters and was neglected . These assumptions

a re v a lid fo r rqbher low-gain c i r c u i t s .

The curve of th e r a t io of the c o llec to r voltage to the base voltage

as a function of frequency is also shown in Figure (4 .4 ) . The cu to ff

frequency of the ac tu a l curve is seen to be lower than th a t of the

th e o re tic a l curve,,and i t can be assumed th a t A ^ does lower the upper

cu to ff frequency. Figure (4.4) i s a rep resen ta tive curve fo r one par­

t ic u la r type of t r a n s is to r , the B ell 2N-27. However, s im ila r curves

c (4.7)

The e ffe c t of the vo ltage feedback fa c to r , A , on th e upper

. . 1 _! L I 14

j:!ra-r-w-, rri ■

.1 .

!- ITF

z . cn «xj nc *.5 ^r I I I !

r M4—,• I '!" ! 1

I ' 1 f * *— ,

‘ ! 1 i ■ ■ 4 j- -L-r"

j .:

j.iLjiir■iii' ir: | .

4 -

",4

:u:'iir 4.11:. j -

to -E» U1 CTl « l 00 to >-•

■ l : I" | , - I I ; I . . I , ! ! ' ! f i ' l l 11' 1 ' !'. |" ■ i] ■ |T

I ! i 1 ■ .—i—^-|-j-- ■

r h t 7!

I !

I 1 I

•i ii ’ 11 * I i

T' - t I i :| j

Ml ; i4 —rr-?—4r y—‘h 'T-! I! 4- I -

:j t :

i - ;"4

Tl

4 !

-44—I I !

J - L h i X : - L . _ .r

j f ' j

TT

Ti4l

-• »+- ♦—«X -

i .

' r 7' \ i 'T

r -t i n

44;" i : .

-

i I i14!. i.

1" r4 -4

L - J . -h -

- f -

1- -i

4~L |-

T

1 .

/■/&■ f f . j ; Me. .

rr

■! -f| <X>,

L _ i . .ij» * | ) ! :: j 4 4 , j 1 - ^ 4 r l 4 - j - W [ -

i

“ J T

i ■ —i~!- ~f'

, u J I

i.. i

were obtained fo r th e Sylvan!* 2Eh35 and th e Tezas Instrument type

903«, and the r e s u l ts were in accordance w ith re s u l ts presented here®

1 i s seen to reduce the upper cu to ff frequency of the t r a n s is - ■ 12 -

t o r but* as ean.be seen from Figure (4e4)s i t i s a very sm a ll,reduo-

tlo iio Therefore d i t i s generally safe to neglect th i s e ffec t in

design work o

QJI C l "vj *—• c n -s j c r

w * ,Z%

a » m-i—J __ L l - i . . ;.i i

3 1

- . ' Shapfcer 5 - ;

MODIFICATION OF THE COBMOH EMTTTER HYBRID A PlRiFETER EQUIFAISl® CIRCUIT

(5®l) I n t roduction

The fo m of th e cofimion em itter hybrid A parameter eqx&ralent c i r ­

c u i t th a t has been used in the previous chapters i s not e n tire ly co rrec t 6

I t can be seen from Figure (1*5) th a t the input c ir c u it was assumed •

to consist of a r e s i s to r s A._> in p a ra l le l w ith a cap ac ito r5 0 . >' ; U , o ; . . ■ 321 :

The a c tu a l c ir c u i t c o n s is ts of these two elements in p a ra l le l plus an

a d d itio n a l re s is ta n c e 5 r ^ $ in se rie s w ith th e base of th e tra n s is to ro

This new res is tan ce is termed the Fbase spreading re s is tan ce^ ”." and

i t s usual value i s about one-fourth th e value of A ^o The c irc u it w i l l

simply be presented in th is chapter* and no d e ta ile d analysis w i l l be

performed9 For a fu r th e r study of th is form of th e equivalent c irc u it*

r e f e r to. “Development of a Grounded Em itter Equivalent C ircu it f o r The

Junction Trans is t o r*11 by Mr® David J» Sakrison* Department of Elec­

t r i c a l Engineerings U niversity of Arizona» The co rrec t form, of the ■

common em itter hybrid A parameter equivalent c ir c u i t i s shorn i n .

F igure (5@l)* - . . : "

, (5o2) The E ffe c t:o f The Base Spreading Resistance on Previota R esults

: • Chapters 3 and 4 d ea lt w ith the frequency v a ria tio n of th e cu rren t

am plification factor* M * and of th e voltage feedback factor* A^gi

32

So vAA'V'

r„

z

/C

c IN ' « (b ^ ^ z z

Z f z F

FlGr. C-5 ' / ) C orrect Form o f The Common?£ w etter ftybrto/ F Fa ra m e te r Equ/vajent C ircu it

33

The re s u lts presented in these chapters were obtained through the use

of the common em itter hybrid A parameter equivalent c irc u it w ith the

base-spreading res is tan ce neglected . The e ffe c t of th is omission

on the re s u lts of chapters 3 and 4 w il l be discussed in th is section

from a q u a lita tiv e standpo in t.

In chapter 3 , the curren t am plification fa c to r f t was shown to

be constant w ith frequency. The basis fo r th is conclusion was shown

to l i e in the d e f in itio n of the current L as being only in the impe-

dance designated as A c • Therefore, even with the addi­

tio n of the base-spreading re s is tan c e , i t can be seen th a t , since

is not the curren t in to the base te rm in a ls , f t is independent of

frequency.

Chapter 4 was concerned with the e ffe c ts of frequency on the

voltage feedback fa c to r , In th is case, the base spreading r e s is ­

tance would simply in troduce a constant term in the expression for

A1? ( Equation 4*6 ) , and th e frequency e ffe c ts would not be a lte re d .

Therefore, the conclusion th a t A^> is frequency dependent i s v a lid

fo r the complete common em itte r hybrid A parameter equivalent c i r c u i t .

3 4

G ha#er 6 .

MSDPiSS W$B3BT0B 4MBIF3EBS;

(6 o3.) In troduction

In th e previous chap ters, the common em itte r , hybrid A parameter

equivalent c i r c u i t was presented, and the frequency v a ria tio n s of i t s

parameters were in v es tig a te d « The remainder of th is paper w il l deal

w ith the design and operation of some bandpass t r a n s is to r am plifiers

in the megacycle rangeo The equivalent c ir c u i t discussed in Ohapber

5 w il l be in v estig a ted in so f a r as i t s usefulness in the design of

tuned am plifiers i s concernedo

The m ajority of the previous re s u lts were obtained w ith junction

tra n s is to rs ., although some surface b a rr ie rs were used^ . ::HtMevers._,in •

th e higher range o f frequencies, th e su rface b a r r ie r t ra n s is to rs were

used almost exclusively® ' ' ;

: t pr TheCwidth of th e base region and the in te re le c tro d e capacitanCes

t f th e surface b a r r ie r t r a n s is to r s are very much sm aller than those

of th e -ju n c tio n tra n s is to rs * For these two reasons, which impose the

upper lim it on the frequency of operation of . t r a n s is to r s ^ , t h e :surface

b a r r ie r t r a n s is to r s were used* ' Vrv '

- B= Bradley, and o th e rs , S h e Surface B a rrie r T ran s is to rs 11 ■ ;‘ Broc*, IE®», ¥ o l0 hlo ppo 1702 - 1720, December, 1953® ■; '

35

(6 .2) D erivation of The Expression For The Gain of Tuned T ran sis to r Am plifiers

The expression fo r the gain of one sing le-tuned stage w i l l be

developed f i r s t . Then, th is derivation w i l l be extended to include

the input coupling c i r c u i t , and then, fo r f,nn id e n tic a l stages in cas- *

cade. The equivalent c i r c u i t presented in Chapter 5 s h a ll be used

fo r these d e riv a tio n s•

The equivalent c ir c u i t fo r one tuned s ta te assures the form

shown in Figure (6 .1 ) . The gain of one stage s h a ll be considered

as being from to B^ ' . This d e fin itio n of stage gain provides

a basis fo r the development of design equations fo r any number of cas­

caded s tag es , and is ra th e r s im ila r to the procedure used w ith vacuum

tu b es•

Consider th e equivalent c ir c u it shown in Figure (6 .1 ) . The nodal

equations fo r the output c ir c u it are :

(6.1)

(6 .2)

Or:

(6 .3 )

W V ^ vez b; ■I

A /W

'IN ^c. ■"c_ _ _

/ - / & . (6~. J ) £:Qu!va/en£ Circuit for 9 Tuned Thi/isistbr

/ ^ m f / z / z e r ( O n e 5 1 a & e ) .

V)O

6G3

So that;

e3 * r „ e < ,(s c ,„ + - j L )

37

(6 .4 )

S u b stitu te equation (6 .4 ) in to equation (6 .1 ) .

-Ph=*'ei[sc'"+£; ]b > + ih

Or;

- P h -- e i [ r " * s i ) ~ - k ]

Now, from, the input c ir c u i t ;

Substitu te equation (6 .7 ) in to equation (6 .6 ) .

'^Ir “ ^ 'rO&'+k +&) ~ i ]Tiie gain for one stage was defined as;

* > - f f -Therefore;

- f— r .

a &•* - A + & ) & * yt l

(6 .5 )

(6.6)

(6 .7 )

(6 .8)

(6 .9 )

(6 .10)

38

Let

J- + J- = —/Zr /Tr /?, (6.11)

And

^ + (6.12)

Therefore, equation (6.10) becomes

yf a i7 i ( s c w *-fc)(sc0 + j£ + £ ) - £ % - ] (6.13)

Rearranging term s, equation (6.13) can be expressed as

-VAf)) = (6.14)[r„r,t CoCM( s + - f c -N ) p Gl J

The term ^ s calcu lated and found to be around 3* This

term , upon expansion of th e denominator, w i l l be part of th e co e ffi­

c ie n t of the "s" term in the cubic equation . The other components

of th is c o e ffic ien t were determined to be about 115. Therefore, the

*''*'/Y\% term m y be neg lected .

The expression fo r the gain becomes

/iw . c ™ £ . 7t e ) ( j % * 5 < 6 J 5 )

Consider th e coupling c ir c u it in the input of the am p lifie r.

The nodal equations are

I ® = e / * s r ) + ( 6 ,1 6 )

39

r„Hence

epL = e2 (5C/W ^ ^ )* II

And

£ ie,r', ( s c '« + - k ; + ~ k i )

Also

^ Cs^ +-fc )(sc°+«;+£)-% ]

For the input s ig n a l

(6.17)

(6.18)

(6.19)

(6.20)

Ts = -|i- (6.21)Z<J

Therefore

a . /

e ‘ " ' A ) - f - <6-22)

The term in th is expression can be neglected as the ra tio

of th is term to the other terms in the c o e ff ic ie n t of "s’* i s about

3 to 115• Therefore, the expression for the gain becomes

r 7 L - ) « ■ » >

40

To determine the o v era ll voltage gain o f a cascade o f "n" id en ti­

c a l tuned sta g es , i t i s necessary to consider only the output or c o lle c ­

to r c ir c u it of the la s t s ta g e . The output voltage w i l l appear at the

c o lle c to r terminals of the la s t stage, and the ra tio o f th is voltage

to the input s ig n a l vo ltage w il l be^the overa ll voltage gain of the

cascade•

From the i n i t i a l d e f in it io n i t i s c lea r that the vo ltage gain of

the la s t stage w i l l be

- / j

Therefore, the overa ll voltage gain of "n" id e n tic a l tuned stages

in cascade is

A( i ) _ ___________________________ n H ______________

A j c o (s1* n3 c7

The sign ifican ce o f th is resu lt s h a ll be discussed la te r in th is

chapter,

(6 .3) Center Frequency o f Tuned Transistor Amplifiers

One of the most important design considerations for bandpass

am plifiers i s the center or resonant frequency of the am p lifier .

The expression for the center frequency o f one stage of a tuned tran­

s is to r am plifier sh a ll be derived.

The c ir c u it diagram i s shown in Figure (6 .2 ) The c ir c u it can

a

a lso be expressed in the form of Figure ( 6 .3 ) . From Figures (6 .2 )

and (6.3) , i t i s immediately obvious that

Y, = &> +j w < :/ J Z J T

Y2 = G , y- J w C

x --

(6 .26)

(6.27)

(6 .28)

The t o ta l admittance i s given by

y - Y +> Y*~ V 2 + y 3 (6 .29)

Su b stitu te for Y, , ^ , and ^

(MO)

M ultiply through by the denominator

Yr z C) CS 00 C? f (93 - t J U J Cz (?jJ u > C z + & t + G 3 (6e31)

Let 6-2 •fS'j - Gry . Equation (6.31) becomes

Yr r (<** + )*>€, + 7 ZL. + G * ' ) + GrzGs -tJcoCz G j (6 .32)J tti Cf, + Gry

42

D----- -------vWV— ------c^3

)----------

: 4 | C,-ir ch - 4%:

-----------c

F / (S', f"S'- 2 .) Circuit (/sec/ to determineThe. Center Ffervency of Tune/ Tf-Jns/st’or /fmy’/tf/ers

F/6. ( 6'3.) f ) / terna/e Form 0 / fysure. Csi'),

43

R ationalize equation (6.32)

V - f c , t j t ^ C / ) f c y ttoCz )+ {Crzba+ju*CzGj^fcy - j to C i 3* S + * f c ? (6-33)

Nov/, a t resonance, the imaginary part of the previous expression

i s equal to zero . Therefore, the expression is

(jtuC , + j j ^ ) f 6 y f ( u C2 ) +Ju> c2 GyCr? -J & c2 <rz Gj = O ( 6 .34)

Or, in more convenient form

{jLCtfxl+cSl c,c\ -6y +cJl C2GjGry Gj - O .(6.35)

Factor equation (6.35)

j l c fGrf -Cz -ICzG-i r= o (6 .

Divide by L C t C z

36)

V 2 GJ Co

Therefores

c o & = - 6 ^ - A ' - y c (6.38)

Uh

6 ^ i- V 6 ^ — 'V C

Where:

b = ^"3 G-^ _ G-z G-3C l L C , C , C x , ~ C , C Z (6*39)

zr \ _ Gr^yC - - z (6.40)

Hence, the resonant frequency of the c irc u it is

(6 . 41)

The sign ificance of th is expression sh a ll a lso be discussed in

the next paragraph.

(6.4) Proposed Method of Design For Tuned T ran sis to r Am plifiers

The expressions developed fo r the gain and cen ter frequency of

bandpass t r a n s is to r am plifiers are very cumbersome, and th e i r complexity

presents many problems to the c ir c u i t designer. Approximations were

attem pted, but they were found to be in v a lid . For example, the design

procedure could be g re a tly sim plified i f the re a l pole in the complex

s plane could be neglected (the pole-zero diagram fo r equation 6.15

i s shown in Figure 6 .4 )• U nfortunately, the loca tion of the re a l pole,

which i s determined by the physical s tru c tu re of the t r a n s is to r , i s

such th a t i t can not be neglected .

At the present tim e, the most p ra c tic a l so lu tion of th is problem

seems to be the use of an e ffec tive equivalent c i r c u i t . By using

th is method, the pole-zero diagram assumes the form shown in Figure (6 .5 ) .

The r e a l pole i s elim inated by assuming a l l the impedances of the

equivalent c irc u it are in p a ra lle l . I t should be emphasized th a t the

base-spreading re s is ta n c e , r ^ , is not being neglected. This w ill

become more c le a r from the method used to determine the e ffe c tiv e

parameters, which w ill be described below.

The pole-zero diagram of the e ffe c tiv e equivalent c ir c u it i s

p ra c tic a lly of the same form as th a t obtained in vacuum tube c irc u its •

The cen ter frequency and the bandwidth are immediately obvious, and

the design i s , th e re fo re , g rea tly s im p lified . The e ffe c tiv e equivalent

c ir c u it i s assumed to be of the form shown in Figure (6 .6 ) . The v a l­

ues of the e ffec tiv e parameters were determined in the following

manner.

The c irc u it diagram of the c ir c u it used to determine the e ffec­

t iv e values of the parameters in the input c ir c u i t i s shown in Figure

(6.7)# The load res is tan ce in the c o llec to r c ir c u i t i s se t equal to

zero, and the output c i r c u i t is therefo re broadbanded - the base to

c o llec to r voltage gain being equal to zero. A c o il , whose inductance

and res istance is accura tely known, is placed in shunt with the input

c ir c u it of the t r a n s is to r . By changing the sig n a l frequency, a maxi­

mum value of e0 i s found. This maximum occurs a t the resonant f r e - 2 -quency of the input c ir c u it of the t r a n s is to r . The bandwidth of the

input c ir c u it i s then found by varying the frequency on e ith e r side

of the resonant frequency.

The input capacitance, C ^ , is then given by

F/G. C6-Y) Location of Fo/es dnf j?*roes —

A ctu al C/routC

47

j w

F /Gr. {6 .S ) LocaCtor) e)/ Fo/es Zeroes£ - f f e c t /u & £ ^ u o / a / e n £ C / r c o > /£

48

/~/0. CG-&) E ffecttre JrQiftvdtt-nt CircuitGrrovno/ea E m itter Emf/z/zer.

Cc

CE

FIG". ( 6 .7 ) C ircv/t C/ssJ to Determ//je F-ffccJt/us^l/a/ves o t Fardm et'ers.

5

50

The input re s is ta n c e , , is e a s ily calcu lated from:

% = Z - > r 3 C T (6.43)

Where

(6.44)

(6.45)

R being the p a ra l le l res is tan ce a rof the c o il a t th is frequency.

A curve of the input c ir c u it response i s shown in Figure (6 .8 ) .

The value of the input capacitance i s a function of the base to c o lle c ­

to r gain . This is analagous to the M ille r e ffe c t observed in vacuum

capactiance as a function of voltage gain i s shown in Figure (6 .9 )•

A ll the inform ation required to design a tuned t r a n s is to r ampli­

f i e r can be determined in the preceeding manner. This method was

used and an am plifie r constructed in th e labo ra to ry . The character­

i s t i c s of th is am plifie r w i l l be discussed in the next sec tio n .

3 . A. N. Perkins, "A Common Em itter Equivalent C ircu it For T ransisto r Design," (T hesis), U niversity of Arizona, 1955•

tu b es , and the equations are of the same form?. The curve of the input

vl 01 si a (£/1

. : : . I

■ • • r I■ t :

f2/rJrtwencY - tncps _

FIG C6-8) FKavzncy Response 0/ The Input Circuit to r — Pht/co Surtece ~S9rr/€r - -2.p~/2.9

10

(6e5) N eu tra liza tion of Tuned T ransis to r Amplifiers

53

The problem of n e u tra liz a tio n a rise s when using a one stage

am plifier w ith both input and output tuned or when cascading tuned

am plifiers • This can be seen from the c i r c u i t diagram shown in Figure

The base to c o llec to r feedback cap ac ito r, C^c , provides positive

feedback when the input conductance is negative (the input conductance

becomes negative when the impedance in the c o llec to r c ir c u it is induc­

tive* ) I f the positive feedback is of s u f f ic ie n tly large amplitude,

the am plifie r w ill o sc illa te *

The method of n e u tra liz in g th is type of tuned t r a n s is to r ampli­

f i e r i s analogous to the H azeltine system used in grounded cathode

vacuum tube am p lifie rs . The c ir c u it diagram of a ty p ic a l neu tra lized

grounded em itte r am plifier i s shown in Figure (6*11)* The equivalent

c ir c u it of th is am plifier i s shown in Figure (6*12).

The c ir c u i t w il l be neu tra lized when E^e is equal to zero, or:

(6 .10) .

E b t ~ E cat = £ c 6c -f- E t z = O (6 . 46)

Therefore, fo r proper n eu tra liz a tio n

(6.47)

And

(6.48)

54

F/G. { S./o) Ofte StaGe frans/stor rfmj>////erWith 7u/ie</ fr7fe/t dnJ t c/t/ouf Circuits.

/mnm

55

i—ii

Z7G-. C6. / I ) A /eotra//*ec/ G-rouYiJ&J tr/v ttter7une<J rf/n/f/t/zer.

56

C-SC

o —E

E/G*. f 6 - / 2 ) E p u /ra /en t C i r c u i t 0/ a

A /e u tr a /z z c * / G r tr u z jc /^ c /

E m i t t e r f) m ^ /i- /z c r :

I f Ig is much larger than the currents through and

w ill be the same. Tliis i s assumed to be tru e fo r high Q c i r c u i t s .

Then, fo r s tead y -s ta te operation:

Using the above r e s u l t s , a grounded em itte r am plifier was con­

s tru c ted w ith both the input and the output c irc u its tuned to the same

frequency. Without n e u tra liz a tio n , the c i r c u i t immediately burst

in to sustained o sc illa t io n upon the app lica tion of bias p o te n tia ls .

The inductances in both the input and the output c irc u its were varied ,

but with no e f f e c t .

The c i r c u i t was then a lte re d by f i r s t center-tapping the inductor

(6.49)

And

(6 .50)

Also, from equation (6 .49):

(6.51)

S u b s titu te equation (6.51) in to equation (6 . 50)•

- T , 0 'u> /.3 ) j u > C v _

%J CaJ (6.52)

Therefore:

(6.53)*-3

■ ■ ' . : V' V V;- - 58

. g jja th e c o lle c to r e ir c u i t and connecting th e n e u tra liz a tio n capacitor^

- G > from one side of th is c o i l to the base of the transisto r® This• ' ■■■. ■ \ V . . : '' ■■ ' ■ - -

i s the c ir c u i t th a t i s shown in Figure (6*12) * Bias p o ten tia ls were

applied and the c ir c u it no longer o sc illa te d bub operated as an ampli­

f ie r*

(606) C h a rac te ris tic s of I n Experimental Tuned T ran sis to r Am plifier .

The design procedure fo r tuned t r a n s is to r am plifiers was- outlined

in section (6*4)« , Using th is method, a one stage tuned am plifie r

was constructed and i t s c h a ra c te r is t ic s . s tu d ied « The am p lifie r was

designed to have a cen ter frequency of 4 <>3 megacycles s a bandwidth of '

. 200 k ilocycles j, and a gain of a t le a s t 16 0 The c irc u it diagram is

shown in Figure (6S13) e

The th e o re tic a l and. experimental response curves are shown in

Figure (6*14)* -The experimental am plifier had; a cen ter frequency of

4o l megacycles 5 a bandwidth of 240 k ilocycles and a gain of 19*4*

Although the re s u lts are not exactly equal to the calcu lated values s

.they are ra th e r encouraging® ,. -' • ; - ' ‘ , - 6 '

T h eo re tica lly 5 the gain-bandwidth product was 3*2 x 10 cycles

- per seconds while the gam-bandwidth product determined experim entally■' ■■■■ ■' ' ' 6 '' ' '■■■ ■ '' ' ‘ ' was 4*66 x 10 cycles per seconds As in vacuum tube c i r c u i t s 5 the

gain-bandwidth product may be thought of as a fig u re of m erit fo r th e

c irc u it in question* Because the figu re of m erit of the a c tu a l c i r ­

c u it was g rea te r . than the th e o re tic a lly ca lcu la ted "value5 the design

appears to be a ra th e r pessim istic one® Perhaps one of the more

' "■ : ‘ " . ■ . ...■ ; ; 59outstanding reasons fo r th is could be the use of average values fo r the

parameters of the e ffe c tiv e equivalent c i r c u i t <,

The e rro r in th e cen te r frequency, is le s s than 5 This could

be caused by the values of the parameters of the e ffe c tiv e equivalent

c i r c u i t , -which are not accurate to more than 5 % because of in s tru ­

ment a t ion o A lso5 the inductances used were hand-wound on ceramic c o il

forms and i t i s possible th a t the values fo r the inductance and effec­

t iv e re s is tan ce of the c o ils could be s l ig h t ly in erroro

Although th e re s u l ts seem to v a lid a te th e proposed method of

designing tuned t r a n s is to r am plifiers the author fee ls th a t the sub­

je c t bears fu r th e r investigations,

60

bb

/~/G- ( 6 - / 3 ) Grovnc/ec/ JFrntffier Tc/naatTPtins/stor /!ntf////er.

VA

AA

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BIBLlOG-EAHil

ARTICLES

Wo Eo Bradley5 and o thers, "The Surface B arrie r T ra n s is to r , 11 Eroco;, HEoS Volo Al° PP° 1702-1720, December, 1953 =

A ® No Perlsins, !JA Common Em itter Equivalent C ircu it For T ransis to r Design A" (Thesis) s U niversity of Arizona, Tucsdn, 1955«

Do Jo Sakrison^\"Beyelopmeht o f ;A Grounded E m itter Equivalent C ircu it For The Junction T ra n s is to r ,11 (T hesis) , U niversity o f Arizona, 1955<> ' :