View
251
Download
0
Category
Preview:
Citation preview
Synthesis of a transistor blockingoscillator time base generator
Item Type text; Thesis-Reproduction (electronic)
Authors Robb, Harold Griffith, 1932-
Publisher The University of Arizona.
Rights Copyright © is held by the author. Digital access to this materialis made possible by the University Libraries, University of Arizona.Further transmission, reproduction or presentation (such aspublic display or performance) of protected items is prohibitedexcept with permission of the author.
Download date 15/09/2018 06:41:56
Link to Item http://hdl.handle.net/10150/319489
SYNTHESIS
of a
TRANSISTOR BLOCKING OSCILLATOR
TIME BASE GENERATOR
by
Harold G r i f f i t h Robb
A T hesis Submitted to the F acu lty o f the
DEPARTMENT OF ELECTRICAL ENGINEERING
ih P a r t ia l F u lf i l lm e n t o f the Requirements
For the Degree of
MASTER OF SCIENCE
In the Graduate C o llege
of
THE UNitifeRsifY tiF ARiZdNA
STATEMENT BY .AUTHOR
T h is t h e s i s has b e e n s u b m i t t e d i n . p a r t i a l , f u l f i l l
m ent o f r e q u i r e m e n t s f o r a n a d v an ced d e g re e a t t h e U n i v e r s i t y
made a v a i l a b l e to b o r ro w e rs u n d e r r u l e s o f t h e L ib ra ry *
B r i e f q u o t a t i o n s from t h i s t h e s i s a r e a l lo w a b le
w i th o u t s p e c i a l p e r m i s s io n , p r o v id e d t h a t a c c u r a t e acknow
led g e m e n t o f s o u r c e i s made * .Requests-’f o r p e r m is s io n f o r
e x te n d e d q u o t a t i o n from o r r e p r o d u c t i o n o f t h i s m a n u s c r ip t
i n whole o r i n p a r t may b e g r a n t e d by th e h e a d o f t h e .m a j o r
d e p a r tm e n t ,o r t h e Dean o f th e G ra d u a te C o l le g e when i n t h e i r
judgm ent th e p ro p o s e d u se o f th e m a t e r i a l i s i n th e i n t e r e s t s
o f s c h o la r sh ip .* I n a l l o t h e r i n s t a n c e s , h o w e v e r , p e r m is s io n
m ust be o b t a i n e d from t h e a u t h o r . . . .. ..
o f A r iz o n a and i s d e p o s i t e d i n t h e U n i v e r s i t y L i b r a r y t o be
SIGNED:
APPROVAL BY THESIS DIRECTOR
T h is t h e s i s h a s b e en a p p ro v e d on th e d a te shown be low ;
4 \9I»\DR* ROBERT L* WALKER'
P r o f e s s o r o f E l e c t r i c a l E n g in e e f ip g
ACKHO IKIDGBM BNT
The a u t h o r w ish e s t o t a k e t h i s o p p o r t u n i t y to
e x p re s s h i s a p p r e c i a t i o n to D r«, R o b e r t Do W alker u n d e r
whose g u id a n c e t h i s work was acc o m p lish e d o
Thanks a r e a l s o due to th e s t a f f an d members o f
th e Tucson E n g in e e r in g L a b o r a to r y , Hughes A i r c r a f t Company«
T h is work was c a r r i e d o u t w h i l e th e a u th o r was a member o f
th e T e c h n ic a l S t a f f o f th e Hughes A i r c r a f t Company a n d a
h o l d e r . o f t h e Hughes M a s te r o f S c ie n c e F e l lo w sh ip *
IBS-m ACT
A vacuum tu b e b lo c k in g o s c i l l a t o r t im e b a se
g e n e r a t o r i s a n a ly z e d t o e s t a b l i s h th e r e q u i r e d
f u n c t i o n a l c h a r a c t e r i s t i c s o f th e a c t i v e d e v ic e em- ■,
p lo y e d , a n d t o d e v e lo p a m odel c i r c u i t w hich p r o v id e s
t h e b a s i s f o r s y n t h e s i s o f th e t r a n s i s t o r c i r c u i t .
An i d e a l i z e d t r a n s i s t o r i s p r e s e n t e d and a
c i r c u i t c o n f i g u r a t i o n u s in g t h i s t r a n s i s t o r m odel i s
e v o lv e d . The p r o p e r t i e s o f th e r e a l t r a n s i s t o r a r e
e v a l u a t e d and an e q u i v a l e n t c i r c u i t r e p r e s e n t a t i o n
f o r th e t r a n s i s t o r i s d e v e lo p e d .
The t r a n s i s t o r c i r c u i t c o n f i g u r a t i o n i s
a n a ly z e d t o d e te rm in e i t s p e rfo rm a n c e c h a r a c t e r i s t i c s ,
E x p e r im e n ta l e v a l u a t i o n o f t h e t r a n s i s t o r b lo c k in g
o s c i l l a t o r t im e b a s e g e n e r a t o r p r o v id e s v e r i f i c a t i o n •'
o f t h e a n a l y t i c d e s c r i p t i o n a n d e s t a b l i s h e s t h e p e r
fo rm ance c h a r a c t e r i s t i c s o f t h e c i r c u i t .
i l l
TABLE OF CONTENTS
Chapter 1 Page
l el S ig n i f ic a n c e ' l
1*2 N ature o f th e Problem [(.
io3 O b jec tiv e and Scope ij.
1 eIf. Method of Treatm ent 5
C h a p te r 2
2 d l The B lo c k in g O s c i l l a t o r 6
‘I s 2 The Time Base G S S e ra to r ’ 8
2*3 The B lo c k in g O s c i l l a t o r Time Base. G e n e ra to r ' 10
C h a p te r 3
3*1 R e q u i r e d T r a n s i s t o r P r o p e r t i e s 20
3*2 T r a n s i s t o r C i r c u i t C o n f i g u r a t i o n 2i|.
Chapter 4
4*1 Large S ig n a l Behavior 31
4*2 L inear E q u iv a le n t C irc u i ts ' 35
C h a p te r 5
5*1 Blocking O s c i l l a t o r A n a ly s is 40
5*2 B o o ts trap A nalys is 44
5*3 Summary ' 48iv
C h a p te r 6
6„1 P r a c t i c a l C o n s i d e r a t i o n s 51
6*2 E x p e r im e n ta l E v a l u a t i o n 55
6 63' Summary o f R e s u l t s 62
C h a p te r 7
7*1 C om pliance w i th O b j e c t iv e s 6lj.
7*2 S u g g e s t io n s f o r F u r t h e r S tu d y 65
B ib l io g r a p h y 68
%
CHAPTER 1
INTRODUCTION
1 .1 S i g n i f i c a n c e
A c l a s s o f c i r c u i t s g e n e r a l l y r e f e r r e d to as
p u l s e ' a n d d i g i t a l c i r c u i t s i s e x t e n s i v e l y u s e d i n th e
e l e c t r o n i c s i n d u s t r y as b u i l d i n g b lo c k s f o r com plex
■systems su ch a s r a d a r 5 t e l e v i s i o n , d i g i t a l c o m p u te rs ,
n u c l e a r i n s t r u m e n t a t i o n s , a n d p u l s e com m u nica tion n e t
works „ A wide v a r i e t y o f wave s h a p in g c i r c u i t s , u s e d to
g e n e r a t e waveform s w hich i n c l u d e s q u a re w a v es , w ide p u l s e s ,
n a rro w p u l s e s , a n d t im e b a s e s , e x i s t s . . ThC b lo c k in g
o s c i l l a t o r and th e t im e b a se g e n e r a t o r a r e two o f th e s e
p u l s e an d d i g i t a l c i r c u i t s .
The b l o c k i n g o s c i l l a t o r , a r e g e n e r a t i v e c i r c u i t
u s e d p r i m a r i l y t o g e n e r a t e n a r ro w p u l s e s , e x i s t s i n b o th
a s t a b l e an d m o n o s ta b le f o r m s . B a s i c a l l y , t h e b lo c k in g
o s c i l l a t o r , c o n s i s t s o f an a c t i v e d e v ic e w hich f u n c t i o n s
as an a m p l i f i e r , a- p u l s e t r a n s f o r m e r w hich p r o v id e s
c o u p l in g b e tw een th e i n p u t and o u t p u t . o f t h e a c t i v eI
d e v ic e , a n d .a c a p a c i t i v e c h a r g i n g n e tw o rk . O p e r a t i o n o fI !
th e f r e e - r u n n i n g b l o c k in g o s c i l l a t o r i s c h a r a c t e r i z e d by
a p e r i o d o f s h o r t c o n d u c t io n o f th e a c t i v e d e v ic e d u r in g
w hich th e p u l s e d o u t p u t - i s fo rm ed , and a lo n g t im e •
1
i n t e r v a l during which the a c t i v e d e v ic e i s m a in ta in ed in
the OFF s t a t e by a v o l t a g e which i s d ev e lo p ed a c r o ss the
c a p a c a t iv e in p u t network when the a c t i v e d e v ic e i s con
d u c t in g . The p e r io d o f n o n -co n d u ctio n ter m in a tes when the
c a p a c ito r t im in g v o l t a g e decays to a v a lu e which a g a in
p erm its co n d u ct io n o f the a c t i v e d e v ic e . The waveforms
a s s o c i a t e d w ith the c i r c u i t o p e r a t io n are shown in
F ig u re 1 .1 .
/ \ua) Output
b) Timing Waveform
F ig u re 1 .1 B lock in g O s c i l l a t o r Waveforms
The time b ase g e n e r a to r i s a c i r c u i t w hich
g e n e r a te s an outp ut waveform t h a t e x h i b i t s a l i n e a r
v a r ia t i o n o f v o l t a g e or c u r r e n t w ith tim e. T y p ic a l wave
forms o f the v o l t a g e tim e base g e n e r a to r are g iv e n by
3
F ig u re 1 , 2 .
— Ts
a) Sweep V o lta g e
b) Sawtooth V o lta g e
F ig u re 1 ,2 V o lta g e Time Base Waveforms
The p e r io d o f l i n e a r v a r i a t i o n o f v o l t a g e w ith
time i s r e f e r r e d to as the sweep t im e , and th e tim e r e
q u ire d fo r th e c i r c u i t to rec o v er b e fo r e th e i n i t i a t i o n
o f a secon d v o l t a g e i s c a l l e d the r e s t o r a t i o n tim e or the
f ly b a c k t im e . The v o l t a g e time base g e n e r a to r has been
d eve lop ed to a h ig h degree o f p r e c i s i o n . S e v e r a l forms
o f th e c i r c u i t which are in w idesp read u se are the M il le r
I n t e g r a t o r , the B o o ts tr a p Sweep, and the Thyratron Sweep,
1 02 N a tu re o f t h e P rob lem
I n some a p p l i c a t i o n s i t i s n e c e s s a r y to p r o v id e a
t im e b a se waveform, h a v in g a r e s t o r a t i o n t im e my.ch s h o r t e r
t h a n i s o b t a i n a b l e w i th t h e c o n v e n t io n a l t im e b a s e g e n e r a
t o r „ The b lo c k in g o s c i l l a t o r h a s been u s e d i n t h i s
a p p l i c a t i o n by u t i l i z i n g th e t im in g waveform a s t h e c i r c u i t -
o u tp u t* T h e re a r e two o b j e c t i o n s , ' how ever, to th e u s e o f
th e b lo c k in g ' o s c i l l a t o r a s a t im e b a se g e n e r a t o r a F i r s t ,
th e t im in g waveform o f th e b a s i c b lo c k in g o s c i l l a t o r i s
e x p o n e n t i a l i n fo rm r a t h e r t h a n l i n e a r * I n a d d i t i o n , th e
b lo c k in g o s c i l l a t o r i s n o t a p r e c i s i o n d e v i c e 0 The
c h a r a c t e r i s t i c s o f th e c i r c u i t o u t p u t a r e g r e a t l y i n f l u e n c e d
by th e age a n d c o n d i t i o n o f t h e a c t i v e d e v ic e , s u p p ly v o l t - .
age v a r i a t i o n s , an d r e s i d u a l m agn e tism o f th e t r a n s f o r m e r*
1 ,3 O b je c t iv e and Scope
The o b j e c t i v e o f t h i s t h e s i s i s to d e v e lo p a
t r a n s i s t o r b lo c k in g o s c i l l a t o r w hich p o s s e s t h e f o l lo w in g . '
p r o p e r t i e s s
( 1 ) The c i r c u i t t im in g waveform s h a l l e x h i b i t a
d e v i a t i o n from l i n e a r i t y o f no more t h a n f i v e p e r c e n t ,
(2) The p e r i o d o f th e b l o c k in g o s c i l l a t o r s h a l l
be in d e p e n d e n t o f s u p p ly v o l t a g e v a r i a t i o n s o f 25> p e rc e n t*
(3) The c i r c u i t o u t p u t s 1 ( t h e t im in g waveform an d ;
th e p u l s e o u tp u t ) s h a l l n o t be a f f e c t e d i n fo rm o r d u r a t i o n
by c h an g e s o f a c t i v e d e v ic e c h a r a c t e r i s t i c s - u p t o . 30 p e r c e n t .
■ . 5 . ;
I n s h o r t , th e o b j e c t i v e o f t h i s t h e s i s i s to make
th e b lo c k in g o s c i l l a t o r a p r e c i s i o n d e v ic e w h ich can be
u s e d t o p r o v id e a t im e b a se v o l t a g e h a v in g a s h o r t o n - t o -
o f f t im e .
An a d d i t i o n a l o b j e c t i v e i s to p r e s e n t a n a l y s i s a n d
s y n t h e s i s t e c h n iq u e s w hich w i l l make p o s s i b l e " t h e p r e d i c t i o n
o f c i r c u i t "output c h a r a c t e r i s t i c t o w i t h i n 10 p e r c e n t a c
c u r a c y » She a n a l y t i c t e c h n iq u e s w i l l be l i m i t e d to d e s c r i b
in g t h e c i r c u i t b e h a v i o r d u r in g i t s s e v e r a l s t a t e s o f
o p e r a t i o n . C i r c u i t b e h a v io r i n t h e t r a n s l a t i o n be tw een
■ s t a t e s w i l l n o t be c o n s i d e r e d i n t h i s t h e s i s .
I . I 4. Method o f T reatm ent"
A vacuum tu b e b l o c k i n g o s c i l l a t o r w h ich p o s s e s s e s .
. th e p r o p e r t i e s r e q u i r e d h a s b e e n d e s ig n e d . The vacuum tu b e
b l o c k i n g o s c i l l a t o r t im e b a s e g e n e r a t o r c i r c u i t w i l l be p r e
s e n t e d and e v a l u a t e d . An i d e a l c i r c u i t w h ich f u n c t i o n a l l y
r e p r e s e n t s th e vacuum tu b e c i r c u i t w i l l t h e n be e s t a b l i s h . e d .
N e x t , th e p h y s i c a l a t t r i b u t e s demanded * o f t h e t r a n s i s t o r :• •
w i l l be e v a l u a t e d i n te rm s ' o f t h e i d e a l c i r c u i t . A c i r c u i t ". .
c o n f i g u r a t i o n b a s e d on th e assum ed t r a n s i s t o r p r o p e r t i e s
w i l l th e n be d e v e lo p e d . N e x t , an e q u i v a l e n t c i r c u i t b a s e d
on a c t u a l t r a n s i s t o r p r o p e r t i e s w i l l be e v o lv e d f o r th e p u r
pose o f a n a l y t i c d e t e r m i n a t i o n o f c i r c u i t com ponents „ F i n a l l y , •
a c i r c u i t w i l l be b u i l t and t e s t e d to p ro v id e e x p e r im e n ta l
v e r i f i c a t i o n o f t h e d e s ig n t e c h n iq u e s p r e s e n t e d Arid to e v a l - .
u a t e c i r c u i t p e rfo rm a n c e a s a- v o l t a g e t im e b a s e g e n e r a t o r .
CHAPTER 2
DEVELOPMENT OF THE VACUUM TUBE MODEL CIRCUIT
2 .1 The B lo ck in g O s c i l l a t o r
The b lo c k in g o s c i l l a t o r i s a r e g e n e r a t iv e c i r c u i t used
to g e n e r a te p u ls e s o f la r g e m agnitude and sh o r t d u r a t io n . The
c i r c u i t can be u sed to produce p u ls e s p e r i o d i c a l l y ( i n a f r e e
running mode o f o p e r a t io n ) or s i n g l y . A t y p i c a l c i r c u i t
c o n f ig u r a t io n o f the f r e e running b lo c k in g o s c i l l a t o r i s
p r e se n te d in F ig u re 2 . 1 .
E b b
F ig u r e 2 .1 The B lo c k in g O s c i l l a t o r
O peration o f t h i s c i r c u i t can be d e s c r ib e d q u a l i t a t i v e l y
by assuming th a t i n i t i a l l y a n e g a t iv e charge e x i s t s on Cg
7
w hich i s adequate to M a s th e tu b e beyond c u t o f f e The
c a p a c i t o r d i s c h a r g e s th ro u g h th e r e s i s t o r * Eg* u n t i l th e
v o l t a g e a c r o s s Cg i s more p o s i t i v e th a n th e tu b e c u t o f f
v o l t a g e * A t t h i s t im e th e tu b e s t a r t s to c o n d u c t . The
f lo w o f p l a t e c u r r e n t th ro u g h th e p r im a ry w in d in g o f th e
t r a n s f o r m e r ‘ in d u c e s a v o l t a g e i n th e s e c o n d a ry w in d in g o f
a p o l a r i t y su ch t h a t t h e g r i d i s d r i v e n i n t h e p o s i t i v e
d i r e c t i o n * An i n c r e a s e o f th e g r i d v o l t a g e p ro d u c e s a
f u r t h e r i n c r e a s e i n p l a t e c u r r e n t w hich th ro u g h th e c o u p l in g
o f t r a n s f o r m e r d r i v e s t h e g r i d more p o s i t i v e . T h is r e
g e n e r a t i v e a c t i o n c o n t in u e s u n t i l t h e p l a t e c u r r e n t i s
l i m i t e d by t h e n o n l i n e a r i t y o f th e t u b e . When th e p l a t e
c u r r e n t r e a c h e s a maximum v a lu e a n d becomes c o n s t a n t ■
t h e r e i s no to m a i n t a i n a s e c o n d a ry v o l t a g e . The eft
r e g e n e r a t i v e p ro c e s s * t h e r e f o r e * s t o p s .
The p l a t e c u r r e n t c o n t i n u e s t o f lo w a n d re m a in s
r e l a t i v e l y c o n s t a n t u n t i l t h e g r i d v o l t a g e d ecay s s u f f i c i e n t l y
to r e d u c e tu b e c o n d u c t io n * The r e d u c t i o n i n p l a t e c u r r e n t
in d u c e s a v o l t a g e i n t h e t r a n s f o r m e r s e c o n d a ry w in d in g o f
su ch a p o l a r i t y to f u r t h e r r e d u c e th e g r i d v o l t a g e . The
drop i n g r i d v o l t a g e f u r t h e r r e d u c e s th e p l a t e c u r r e n t .
The p r o c e s s i s a g a i n r e g e n e r a t i v e and i n su ch a d i r e c t i o n
t h a t t h e g r i d v o l t a g e i s r a p i d l y d r i v e n f a r b e lo w th e tu b e
c u t o f f v o l t a g e . She c i r c u i t i s a g a i n i n i t s o r i g i n a l s t a t e
w i th a n e g a t i v e v o l t a g e a c r o s s th e c a p a c i t o r an d th e tu b e
8
nonconducting a t th e te r m in a t io n o f th e r e g e n e r a t iv e c y c l e .
The tube rem ains c u t o f f u n t i l th e v o l ta g e a c r o s s th e c a p a c i t o r
decays to a v a lu e more p o s i t i v e than the g r id c u t o f f v o l t a g e ,
when th e e n t i r e o p e r a t io n i s r e p e a te d .
The o p e r a t io n o f th e b lo c k in g o s c i l l a t o r can be
se p a r a te d in t o th e f o l lo w in g p h a ses:
2 .2 The Time Base G enerator
The time base g e n e r a to r i s a c i r c u i t which produces
an outp ut waveform th a t e x h i b i t s a l in e a r v a r ia t i o n o f
v o l t a g e or c u r re n t w ith t im e. The v o l t a g e time base
g e n e ra to r i s the to p ic o f the d i s c u s s io n to f o l l o w . In
elem en tary form , the v o l t a g e time b ase g e n e ra to r i s an
RC i n t e g r a t o r . The outp ut waveform i s taken a c r o ss the
c a p a c i t o r . The output o f the in t e g r a t o r i s g iv e n by
The in h e r e n t d isad v an ta ge o f the s im ple RC in t e g r a t o r i s
th a t fo r an o u tp u t of a g iv e n tim e d u ra tio n th e time
c o n s t a n t , RC, must be much lo n g e r than the r e q u ir e d tim e
i n t e r v a l in order th a t e q u a t io n 2 .1 may be a c c u r a t e ly
r e p r e s e n te d a s 0 Q- 0 , t • This r e q u ir e s th a t the in p u t
(1) r e g e n e r a t iv e turn ON s t a t e
(2) ON s t a t e
(3) r e g e n e r a t iv e c u t - o f f s t a t e , and
(ij.) t im in g s t a t e (OFF s t a t e )
e q u a tio n 2 .1 2.1
RC
v o l t a g e to th e c i r c u i t must be v e ry la r g e to produce a tim e
b ase v o l t a g e o f u s e f u l am plitude* V arious c i r c u i t s have
been d e s ig n e d to overcome t h i s u n d e s ir a b le f e a t u r e ,^
One such c i r c u i t i s r e p r e se n te d by F ig u re 2*2* T h is
^ C
F ig u re 2 ,2 B o o ts tr a p Sweep
c i r c u i t i s r e f e r r e d to as a b o o ts tr a p sweep* O peration o f
the b o o ts tr a p sweep i s e x p la in e d by c o n s id e r in g th a t the
sw itc h i s c lo s e d u n t i l th e i n i t i a l in s ta n t* When th e s w itc h
i s opened, the v o l t a g e a c r o s s th e c a p a c ito r r i s e s from z e r o .
The in c r e a s e in the c a p a c i t o r v o l t a g e i s f e l t by th e tube
grid * C onsider th a t the cathode f o l lo w e r has u n i t y g a in .
The v o l t a g e a c r o ss R%. in c r e a s e s w ith th e in p u t v o l ta g e and
thus m a in ta in s a c o n s ta n t b ia s ; the tube o p e r a te s i n i t s
1 Millman and Taub, P u lse and D i g i t a l C i r c u i t s , McGraw-Hill Book Company, In c * , 195>b, p«202
l lm e a r r e g i o n . The v o l t a g e a c r o s s t h e r e s i s t o r , R , re m a in s
e s s e n t i a l l y c o n s t a n t as and a r e assum ed t o change
e q u a l l y , S in c e th e v o l t a g e a c r o s s R i s e s s e n t i a l l y c o n s t a n t ,
th e c h a r g in g c u r r e n t f o r t h e c a p a c i t o r i s c o n s t a n t , r e s u l t i n g
i n a l i n e a r v o l t a g e s lo p e on t h e c a p a c i t o r ,
2 ,3 The B lo c k in g O s c i l l a t o r Time B ase G e n e ra to r
ThO b l o c k i n g ' o s c i l l a t o r t im e B ase g e n e r a t o r i s a
c i r c u i t - w h ich p o s s e s s e s t h e p r o p e r t i e s o f b o th t h e b lo c k in g
o s c i l l a t o r an d th e t im e b a se g e n e ra to r* ' S p e c i f i c a l l y , th e
© i r 'c u i t w i l l g e n e r a t e b o t h a l i n e a r t im e b a s e v o l t a g e and
a p u l s e of l a r g e a m p l i tu d e a n d ah o r t ’ S u ra t l o h w -Two av en u es
o f a p p ro a c h can be c o S s l f le r e d i n e s t a b l i s h i n g t&d 'c h a r a c t e r - ' '
i s t i c s o f th e b lo c k in g o s c i l l a t o r t im e b a se g e n e r a t o r . F i r s t ,
th e h i r c u l t c an be th o u g ii t o f a s a b lo c k in g o s c i l l a t o r h a v in g
it l i n e a r c h a r g in g c i r c u i t . Which c o n t r o l s ' :t h e t im in g ' s t a t e
by c h a r g in g t h e g r i d c a p a e i t o r a t a c o n s t a n t , r a t e * - # n '
a l t e r n a t e a p p ro a c h i s to t r e a t t h e c i r c u i t - a S a t im e b a se
g e n e r a t o r ' w hich u t i l i z e s ■ th e b l o c k i n g e s o l l l a t O r ' a s '-a lo w
im pedance s w i tc h t o q h i c k l y d i s c h a r g e th e e a p a c i tS r C ; B o th
m ethods w i l l be u s e d io * a n a ly z e th e b l o c k in g o s c i l l a t o r
l im e ' b a se g e n e r a t o r 'as'''m m eans' to" d e v e lo p a -model h i r c u i t
w h ich f u n c t i e n a l l y r e p r e s e n t s t h e a c t u a l c i r c u i t *
The c i r c u i t d iag ra m o f th e b l o c k in g o s c i l l a t o r t im e
base.- g e n e r a t o r ' i s shown i n F i g u r e 2*3 , A n a l y s i s o f t h e
11
A D
F ig u r e 2 .3 The B lo c k in g O s c i l l a t o r Time Base G e n e r a to r
c i r c u i t as a b lo c k in g o s c i l l a t o r w i l l be c o n s id e r e d f i r s t .
The a n a l y s i s w i l l be c o n f in e d to an i n v e s t i g a t i o n o f th e
b lo c k in g o s c i l l a t o r ON tim e . The tu rn -on and t u r n - o f f
s t a t e s w i l l be assumed to tak e p la c e i n s t a n t l y and w i l l
th e r e fo r e be n e g l e c t e d . The t im in g s t a t e o f the b lo c k in g
o s c i l l a t o r w i l l be a n a ly z ed when th e c i r c u i t i s t r e a t e d as
a time base g e n e r a to r .
An e q u iv a le n t c i r c u i t r e p r e s e n t a t io n o f th e b lo c k in g
o s c i l l a t o r i s p r e se n te d i n F ig u r e 2 .^ . The l i n e a r charg in g
c i r c u i t i s r e p r e s e n te d as a v o l t a g e sou rce and a s e r i e s
r e s i s t o r . The tim e d u ra tion o f the tim in g s t a t e i s c o n s id e r e d
to be s h o r t i n com parison w ith th e ch a rg in g c i r c u i t tim e
c o n s ta n t such t h a t the c a p a c ito r i s charged a t a l i n e a r r a t e .
*K
F ig u re 2 e4 B lo ck in g O s c i l l a t o r E q u iv a le n t C ir c u i t
The tran sform er i.s r e p r e s e n te d by an i d e a l tran sform er and
a shunt in d u c ta n ce co rresp o n d in g to the m a g n e t iz in g in d u c t
ance o f the a c t u a l tr a n s fo r m e r » The lea k a g e in d u cta n ce o f
the r e a l tran sform er i s c o n s id e r e d to be n e g l i g i b l e ,
co rresp on d in g to th e assum ption th a t the turn ON i s i n s t a n t
aneous „ The g r id c i r c u i t o f the tube i s r e p r e s e n te d as a
r e s i s t o r i n s e r i e s w ith a diode* The p la t e c i r c u i t c o n s i s t s
o f a sw itc h (which c l o s e s when th e g r id to ca th od e v o l t a g e
r ea c h e s Ec o , g r id c u t o f f v o l t a g e ) a v o l t a g e s o u r c e , and a
s e r i e s r e s i s t o r •
Consider now th a t the sw itc h has c lo s e d by v i r t u e o f
a v o l t a g e in e x c e s s o f Eco and Cg* The p l a t e o f the tube i s
clamped to E^* A c u r r e n t , i ^ , i s f lo w in g in the p la t e
c i r c u i t * A c u r r e n t , i c , i s f lo w in g in the g r id c i r c u i t , and
13
a c u r r e n t , i s f lo w in g through th e d io d e . Current has n o t
y e t had time to b u i l d up in the m a g n et iz in g in d u c ta n c e . &
v o l t a g e appears a c r o ss the tran sform er primary wind
in g . The secondary v o l t a g e i s a l s o - 2% s in c e the id e a l
tra n sform er p a s se s d . c . The secon dary or g r id c u r r e n t i s
equal to and i s a l s o equal to i p . I n i t i a l l y , the d io d e
c u r re n t i s eq u a l to th e d i f f e r e n c e between th e p la t e c u rren t
and the primary c u r r e n t s in c e c u r r e n t has n o t b u i l t up i n the
m a g n etiz in g in d u c ta n c e .
i d - ib “ Ip 2 .2Current b u i ld s up in the in d u c to r as r e q u ir e d by the e q u a t io n
E = Ebb - Eb = L dioo. = L!b 2 .3The assum ption t h a t i s c o n s ta n t im p l ie s th a t e ^ i s
c o n s t a n t . The g r id to cath ode v o l t a g e can remain c o n s ta n t
on ly i f i c i s f i x e d . I t f o l lo w s t h e r e fo r e th a t ip must
remain c o n s ta n t s in c e the ampere turns o f both the primary
and secondary w ind ings o f the i d e a l transform er must remain
c o n s t a n t . As im i n c r e a s e s , i ^ must d ecrea se s in c e a l l o th e r
c u r r e n ts a t the node P are f i x e d . The c u r r e n t , i m, c o n t in u e s
to in c r e a s e u n t i l i t i s equal to th e i n i t i a l v a lu e of i ^ .
When i m i s equal to i ^ the d io d e , D]_, i s r e v e r s e d b ia s e d .
Any a d d i t io n a l in c r e a s e o f i m t h e r e f o r e i s f o r c e d in t o th e
primary o f the i d e a l tran sform er i n a d i r e c t i o n t o oppose
i p . The secondary c u r r e n t , i c , i s in tu rn d ecrea sed
r e s u l t i n g in a reduced g r id to cathode v o l t a g e . The r e
d u c t io n o f egk ca u se s the p la t e c u rren t to d e c r e a s e .
i4
A d ecrea se in f o r c e s a d d i t io n a l m a g n e t iz in g cu rren t
through the transform er prim ary• The e f f e c t i s cu m u la tive
and the tube i s v e ry r a p id ly tu r n e d o f f .
From t h i s d i s c u s s i o n , i t i s se en th a t th e ON tim e o f
the b lo c k in g o s c i l l a t o r i s th e tim e r e q u ir e d fo r the c u rren t
in th e in d u c to r to b u i ld up to a v a lu e equal to th e i n i t i a l
diode c u r r e n t .
V alues o f rg and gm can be determ ined from the p o s i t i v e
g r id c h a r a c t e r i s t i c s o f th e tube in use by the f o l lo w in g
p ro c ed u r e :
(1 ) F in d the p l a t e c u r r e n t and g r id c u r r e n t corresp on d in g to a p la t e v o l t a g e and a g r id v o l t a g e Ebb - Eb ,
(2) C a lc u la te gm from e q u a t io n 2 ,5
(3) C a lc u la te rg from e q u a t io n 2 ,6
The v o l ta g e to which the c a p a c i t o r charges during the
b lo c k in g o s c i l l a t o r ON time can be approxim ated by the
Inn = f E b b - E-bH = ip - ip2 .4
2 .6
Tn = In) (9™ - pig) 2 .7
r e l a t i o n s h i p 2 .8
15
The f i n a l v o l t a g e a c r o ss th e c a p a c i to r a t the end o f th e ON
time i s •co - LcTnC a .
2 . 9
The assum ption t h a t th e tran sform er does not s a t u r a te i s
i m p l i c i t i n the above a n a l y s i s .
#
The b lo c k in g o s c i l l a t o r tim e base g e n e r a to r w i l l n e x t
be t r e a t e d a s a tim e base g e n e r a to r which u ses a b lo c k in g
o s c i l l a t o r t o d isch a rg e the c a p a c i t o r , Cg. The c i r c u i t
diagram i s g iv e n in F ig u re 2*5 . The b lo c k in g o s c i l l a t o r
'b i
E|ob
ii,kcc
.R R
c,\ Th
Ir t4 C 9
F ig u re 2«5 Time Base G enerator w ith B lock in g O s c i l l a t o r S w itch
i s r e p r e s e n te d a s a v o l t a g e so u rc e o f magnitude letc 9
and a sw itc h which c l o s e s f o r Tn seconds a f t e r th e v o l t a g e
on th e c a p a c ito r has been charged to Eco by th e time base
g e n e r a to r .
16
B efore an e q u iv a le n t c i r c u i t fo r the t im e base
g e n e ra to r can be d ev e lo p ed , i t i s n e c e s s a r y to determ ine the
r e g io n o f o p e r a t io n o f th e tu b e . A b r i e f d i s c u s s io n o f th e
c i r c u i t o p e r a t io n w i l l prov ide the n e c e s s a r y i n s i g h t .
Assume t h a t i n i t i a l l y the tube i s con d u ctin g and a v o l t a g e ,
Vkri1Rk i s d eve lop ed a c r o ss th e ca th od e r e s i s t o r . Each time
the s w itc h c l o s e s , th e c a p a c i t o r , Cc , w i l l be charged through
the g r id le a k r e s i s t o r . In th e l i m i t , the v o l t a g e a cro ss
the c a p a c i to r w i l l approach V . and w i l l rem ain c o n s ta n t a t
th a t v a lu e i f i t i s assumed t h a t th e tim e c o n s t a n t Rg Cc i s
la r g e compared w ith the p e r io d o f the b lo c k in g o s c i l l a t o r .
The g r id to ca th od e v o l t a g e of the tube can be determ ined
from the r e l a t i o n s h i p
E = Vk = e gk + j2 R 2 .1 0
The magnitude o f 2 = i s g iv e n by the e q u a tio n
2.11R 4- Rk
Assume now t h a t R^ i s much la r g e r than R. E q u ation 2 .1 1
red uces to E = R » An a d d i t io n a l consequence o f the
above assum ption i s t h a t l2 = Ib • E q u ation 2 .1 0 can be
r e w r i t t e n as !b R = egk + ibR . The g r id to cath ode v o l ta g e
th e r e fo r e i s z e r o . The tube i s o p e r a t in g in i t s a c t i v e or
l i n e a r r e g io n . The o p e r a t in g p o in t o f the tube i s e s s e n t i a l l y
c o n s t a n t , r e s u l t i n g i n a c o n s ta n t p la t e c u r r e n t . I f i t i s
17
assumed th a t = 0 , the c a p a c i t o r i s charged a t a c o n s ta n t
r a t e , g iv in g a v o l t a g e a c r o s s the c a p a c ito r w hich i s a l i n e a r
f u n c t io n o f t im e .
Development o f th e e q u iv a le n t c i r c u i t i s g iv e n in
F ig u re 2 . 6 .
XI (E - if r ) wbb
^ c
A / V
(>U -h )R
C,
A / V
b)
> E
" E t>t>
F ig u re 2 .6 E q u iv a le n t C ir c u i t Development
In F ig u re 2 .6 a the tube i s r e p r e s e n te d by i t s l i n e a r
e q u iv a le n t c i r c u i t . The c a p a c i to r ch arg in g netw ork,
c o n s i s t i n g o f Rg and Cc , i s r e p la c e d by a c o n s ta n t v o l ta g e
E in k eep in g w ith the assum ption th a t the v o l t a g e a c ro ss
18
the c a p a c ito r i s c o n s t a n t . The r e s i s t o r i s r e p la c e d by
an open c i r c u i t by v i r t u e o f th e assum ption t h a t i t i s much
la r g e r than R. The v o l t a g e s o u r c e , -yul^R , can be r e p la c e d
by a r e s i s t o r , yM R , s in c e i s f lo w in g through the
lo o p c o n ta in in g the so u r c e . F ig u re 2 .6b r e s u l t s . The
f o l lo w in g e q u a tio n s are d e r iv e d by e v a lu a t in g the c i r c u i t
o f F igu re 2 .6 b .
e 0 ( t ) = (Ebb . / ( E ) - (Bbb . / I E -VC0 ) e - V C r p .( /U l) lQ C g2.12
e0 ( t ) - ibR +" Gc ( t ) 2 .1 3
Tp = CrD+(yU4.l3R] ^ OLn(Bbb»^B-Vr.ri~) 2 .1 4Ehb4- /^E-£co
M ** i n i t i a l s lo p e = T Xqq. 2 .1 5[r P + (m+i)R] Cg
M = 2 .1 6L1’? +' ( M +T)R]Cg RC,
Model c i r c u i t s have been d ev e lo p ed f o r both the tim e
base g e n e r a to r and the b lo c k in g o s c i l l a t o r . The com posite
model c i r c u i t i s g iv e n by F igu re 2 . 7 .
Lm
bb
F ig u r e 2 .7 B lo ck in g O s c i l l a t o r Time BaseG enerator
CHAPTER 3
DEVELOPMENT OF THE TRANSISTOR CIRCUIT CONFIGURATION
3 »1 R equired T r a n s is to r P r o p e r t ie s
The' vacuum t r io d e has th r e e d i s t i n c t r e g io n s o f
o p era tion * These r e g io n s o f o p e r a t io n are th e c u t o f f
r e g io n , th e l i n e a r r e g io n , and th e s a t u r a t io n r e g io n .
The c u t o f f r e g io n i s one i n which no p la t e c u r r e n t f low s
"by v i r t u e o f a n e g a t iv e g r id to ca th od e v o l t a g e . This
r e g io n o f o p e r a t io n i s r e f e r r e d to as r e g io n I* R egion
I I , th e l in e a r r e g io n , i s one where a c t i v e c o u p l in g e x i s t s
between the g r id and p l a t e c i r c u i t s , and a m p l i f i c a t io n i s
p o s s i b l e . In r e g io n I I I , the g r i d c i r c u i t e f f e c t i v e l y
l o s e s c o n t r o l o f th e p l a t e c i r c u i t . The tube f u n c t io n s a s
a diode i n t h i s s a t u r a t io n r e g io n . O peration i s c h a r a c t e r
i s e d by h ig h g r i d and p l a t e c u r r e n t .
A model c i r c u i t em ploying the vacuum t r io d e as th e
a c t i v e d e v ic e was d e v e lo p ed f o r th e b lo c k in g o s c i l l a t o r
tim e base g e n e ra to r in Chapter 2 . Ah i n v e s t i g a t i o n o f th e
f u n c t io n o f th e vacuum tube i n th e model c i r c u i t w i l l pro
v id e the n e c e s s a r y i n s i g h t to determ ine th e p r o p e r t ie s the
t r a n s i s t o r must e x h i b i t in order t h a t i t may be used as th e
a c t i v e d e v ice i n th e c i r c u i t . When the r e q u ir e d t r a n s i s t o r
p r o p e r t ie s have been e s t a b l i s h e d , a. . c i r c u i t n o n f ig u r a t io n
21
u t i l i z i n g the t r a n s i s t o r ean be devised ,,
I t was e s t a b l i s h e d i n Chapter 2 th a t th e a c t i v e
d e v ic e in th e tim e base p o r t io n o f th e c i r c u i t fu n c t io n s
as a v o l t a g e a m p l i f i e r . The g r id t o ca th o d e v o l t a g e i s
m a in ta in ed a t z ero v o l t s s hence the. in p u t impedance can be
c o n s id e r e d i n f i n i t e , s in c e mo g r id c u r r e n t f l o w s . The
d e v ic e , t h e r e f o r e , f u n c t io n s as a v o l t a g e a m p l i f i e r h a v in g
i n f i n i t e in p u t im pedance„
The a c t i v e d e v ic e i n the b lo c k in g o s c i l l a t o r p o r t io n s
o f th e c i r c u i t o p e r a te s i n both r e g io n s I and I I , The tube
i s h e ld in r e g i o n ' I during the b lo c k in g o s c i l l a t o r t im in g
s t a t e by a n e g a t iv e v o l ta g e on the g r id c a p a c i t o r . When
the v o l t a g e a c r o ss th e c a p a c i t o r ex ceed s the c u t o f f v o l t a g e ,
p l a t e c u r r e n t s t a r t s to f lo w . The d e v ice i s now o p e r a t in g
in r e g io n I I and i s f u n c t io n in g as an a m p l i f i e r . Two modes
o f o p e r a t io n i n r e g io n I I are r e q u ir e d . I n i t i a l l y , When
p l a t e c u r re n t f i r s t s t a r t s to f l o w , th e g r id c i r c u i t in p u t
impsdance i s i n f i n i t e , , The tran sfo rm er c o u p l in g betw een
the g r id and p la t e c i r c u i t , ■ iia c o n ju n c t io n w i t h ' t h e
a m p lify in g p r o p e r t y o f th e d e v ic e , d r iv e s th e g r i d p o s i t i v e
a s • th e p la t e v o l t a g e d rop s . G rid c u r r e n t s t a r t s to f lo w
when th e g r id to cathode v o l t a g e exceed s zero v o l t s , The
in p u t impedance to the g r id c i r c u i t has a - f i n i t e .v a lu e ,
P la t e v o l t a g e c o n t in u e s to drop u n t i l i t i s cau gh t by the
22
c a tc h in g d io d e . O peration in th e l i n e a r r e g io n has s h i f t e d
from near c u t o f f to near s a t u r a t i o n . The p r o p e r t ie s o f the
a c t i v e d e v ic e o f th e b lo c k in g o s c i l l a t o r , th u s , are t h a t o f
a v o l t a g e a c tu a te d sw itc h which fu n c t io n s as an a m p l i f i e r
when th e sw itc h i s c lo s e d .
The r e q u ir e d f u n c t io n s o f the a c t i v e d e v ic e have
now been e s t a b l i s h e d . The n e x t s t e p i s to i n v e s t i g a t e the
p r o p e r t ie s o f an i d e a l i z e d t r a n s i s t o r to s e e i f i t can
f u n c t i o n a l l y r e p la c e th e vacuum tube i n th e model c i r c u i t .
F ig u r e 3 .1 i s an i d e a l i z e d r e p r e s e n t a t io n o f an NPN t r a n s i s t o r .
e
ZS rc
e
F ig u re 3*1 T r a n s is to r C i r c u i t Model
The t r a n s i s t o r c o n s i s t s o f two dioctes "back to back and
a c u r r e n t g e n e r a to r , which sh u n ts the c o l l e c t o r - b a s e d io d e „
The e m it te r base d iod e i s id e a l* The c o l l e c t o r - b a s e d iode
has zero forw ard r e s i s t a n c e and a f i n i t e but l a r g e r e v e r s e
r e s i s t a n c e r c „ The c u r r e n t g e n e r a to r i s a c tu a t e d by a b ase
in p u t c u r r e n t as shown in th e F ig u r e , This t r a n s i s t o r modelH ' ' '
has th r e e r e g io n s o f o p e r a t io n co m p arab le ,to th o s e o f the
vacuum tube* O peration i n r e g io n I r e q u ir e s t h a t the e m i t t e r -
b a se d iode be r e v e r s e b ia s e d such th a t 1 % i s zero.* The
c u r re n t g e n e r a to r t h e r e f o r e has zero m agnitude. The
c o l l e c t o r - b a s e d iode i s r e v e r s e b ia s e d such t h a t the
c o l l e c t o r c i r c u i t i s e s s e n t i a l l y open c ir c u i t e d *
I f a v o l t a g e i s a p p l ie d a c r o s s th e e m it t e r - b a s e
te r m in a ls to forw ard b ia s the e m it t e r -b a s e d io d e , an in p u t
c u r r e n t , f lo w s and th e c u r r e n t g e n e ra to r has a magnitude
p Ty, T his mode o f o p e r a t io n corresp ond s to o p e r a t io n o f
the vacuum tube i n r e g io n II* .Two s i g n i f i c a n t d i f f e r e n c e s
e x i s t however* The f i r s t o f t h e s e d i f f e r e n c e s i s seen in
method o f c o n t r o l l i n g the outp ut current* The output
c u r r e n t o f a vacuum tube i s c o n t r o l l e d by an in p u t v o l t a g e
w h ile w ith th e t r a n s i s t o r an in p u t c u r r e n t e x e r c i s e s c o n t r o l
over th e ou tp u t c u r r e n t . The secon d d i f f e r e n c e , a con
sequence o f th e f i r s t . I s foun d i n th e in p u t impedance l e v e l .
The in p u t impedance o f the i d e a l t r a n s i s t o r i s zero w h ile 1
the Input impedance to the vacuum tube i s i n f i n i t e .
O peration in r e g io n I I I i s i n i t i a t e d by forw ard b i a s
in g b oth th e c o l l e c t o r - b a s e d iod e and the e m it t e r - b a s e d io d e .
In t h i s mode o f o p e r a t io n , the i d e a l t r a n s i s t o r can be r e
p r e se n te d as th ree term in a ls s h o r te d to a common node.
3 .2 T r a n s is to r C ir c u i t C o n f ig u r a t io n
The model c i r c u i t fo r th e b lo c k in g o s c i l l a t o r tim e
base g e n e ra to r i s r e p e a te d i n F ig u re 3*2
Lm
bb
'<3 T
F ig u r e 3*2 B lo ck in g O s c i l l a t o r Time Base G enerator
A t r a n s i s t o r c i r c u i t c o n f ig u r a t io n f o r th e b lo c k in g o s c i l l a t o r
time b ase g e n e ra to r can be d eve lop ed by r e p la c in g the a c t i v e
25
d e v ic e in F ig u re 3*2 w ith th e t r a n s i s t o r model o f F ig u r e 3 . 1 .
C onsider f i r s t th e time base p o r t io n o f the c i r c u i t . F ig u re
3 . 3 a shows the tim e base c i r c u i t w ith the tube r e p la c e d by
the l in e a r v o l t a g e e q u iv a le n t o f the t r a n s i s t o r model.
C
Cp Eb rc
F ig u r e 3*3 T r a n s is to r Time Base E q u iv a le n t C ir c u i t
26
F ig u re 3 .3 b i s d e v e lo p ed by f i r s t w r i t in g the lo o p e q u a tio n
fo r F igu re 3 .3 a and s o l v i n g f o r i b ,
ib — E - fc Re 3 .1Re
The v o l t a g e so u rc es i s (3 ' b = (3 E rc _ ic rc pRe
S in ce l c i s f lo w in g through th e lo o p c o n ta in in g the v o l t a g e
s o u r c e , - i c r c p can be r e p la c e d by a r e s i s t o r h av in g a
magnitude Br c • N ext the c i r c u i t to the r i g h t o f the
ter m in a ls x-x* i s r e p la c e d by i t s T h ev in in e q u iv a le n t ,
g iv in g a v o l t a g e E. F ig u re 3 .3b r e s u l t s . T h is c i r c u i t cans rcbe s i m p l i f i e d by making th e assum ption t h a t p ^ i s
g r e a te r than Ec c -E + Vc o . The s i m p l i f i e d c i r c u i t i s p re
se n te d in F ig u re 3 . 3 c . The ou tp u t a c r o ss the c a p a c i t o r i s
g iv e n by the e q u a t io n
e c «} = P E £ ( W ^ r'c) 3 .2
I f the assum ption i s made th a t (p + 1) rcG i s much g r e a te r
than Tp, E q uation 3 .2 red u ces to
e c ct) = P J ftt = E t 3.3RefP»i)GC R e t
The c i r c u i t o p e r a te s as a l i n e a r charg in g c i r c u i t to the
e x te n t th a t th e above assum ptions are v a l i d .
The vacuum tube tim e base c i r c u i t makes use o f a
g r id le a k r e s i s t o r - c o u p l i n g c a p a c i t o r network to m a in ta in a
c o n s ta n t in p u t v o l t a g e ( s e e F ig u r e 2 . 5 ) • This tech n iq u e
26
F ig u re 3 .3 b i s d ev e lo p ed by f i r s t w r i t in g the lo o p e q u a tio n
fo r F ig u re 3 * 3a and s o l v i n g f o r i b ,
lb — E - icRe 3 .1Re
The v o l t a g e so u rc es i s |3 i p = 3 E rc _ ic rc pRe
S in ce I c i s f lo w in g through the lo o p c o n ta in in g the v o l t a g e
s o u r c e , - i c r c p can be r e p la c e d by a r e s i s t o r h av in g a
m agnitude Br c * N ext the c i r c u i t to the r i g h t o f the
te r m in a ls x - x 1 i s r e p la c e d by i t s T h ev in in e q u iv a le n t ,
g iv in g a v o l t a g e E. F ig u re 3 .3b r e s u l t s . T h is c i r c u i t cans rc
be s i m p l i f i e d by making th e assum ption t h a t p ^ i s
g r e a t e r than Ec c -E + Vc o . The s i m p l i f i e d c i r c u i t i s p re
s e n te d in F ig u re 3 . 3 c . The o u tp u t a c r o ss the c a p a c i to r i s
g iv e n by the e q u a t io n
e c «) = 0 JjjTcfi - 3.2
I f the assum ption i s made t h a t (p f 1) rcG i s much g r e a te r
than Tp, E q uation 3 .2 red u ces to
- f e . 3 - 3
The c i r c u i t o p e r a te s as a l i n e a r charg in g c i r c u i t to th e
e x t e n t t h a t th e above assum ptions are v a l i d .
The vacuum tube tim e base c i r c u i t makes use o f a
g r id le a k r e s i s t o r - c o u p l i n g c a p a c i t o r network to m a in ta in a
c o n s ta n t in p u t v o l t a g e ( s e e F ig u r e 2 . 5 ) • This tec h n iq u e
cannot be used w ith the t r a n s i s t o r * The t r a n s i s t o r i s main
t a in e d i n i t s l i n e a r r e g io n o f o p e r a t io n by a b ia s v o l t a g e
which forward b i a s e s th e e m it t e r - b a s e d iode and ca u ses c u r re n t
to f lo w in to th e base o f th e t r a n s i s t o r . I f a r e s i s t o r were
sh u n ted a c r o ss th e e m it te r base diode to p ro v id e a c u r re n t
path through which a c a p a c i t o r i n the base c i r c u i t c o u ld be
charged , a v o l t a g e would be d ev e lo p ed a c r o ss the r e s i s t o r o f
such a p o l a r i t y as to r e v e r s e b ia s the e m it t e r base d io d e .
O peration would th e r e fo r e be c o n f in e d to r e g io n I . F ig u r e
3 . 4 shows th e t r a n s i s t o r tim e base g e n e r a to r c i r c u i t com p lete
w ith a b i a s in g c i r c u i t arrangem ent w hich c o n f in e s th e
t r a n s i s t o r to o p e r a t io n i n r e g io n I I .
cc
F ig u re 3 .4 T r a n s i s to r Time Base G enerator
28
S u b s t i t u t i o n o f th e model t r a n s i s t o r f o r th e a c t i v e
d e v ic e in th e b lo c k in g o s c i l l a t o r p o r t io n o f F ig u re 3 .2
r e s u l t s i n F ig u re 3«5.
m
c c
C
F ig u re 3«5 T r a n s is to r B lo c k in g O s c i l l a t o r Model
The c i r c u i t i s turned on when the c a p a c ito r v o l t a g e ch arges
to a v a lu e g r e a te r than zero a t which time th e e m it te r -b a s e
ju n c t io n i s forw ard b ia s e d and b ase cu rren t s t a r t s to f l o w .
The su bseq u en t f lo w o f c o l l e c t o r c u r r e n t c a u se s the c o l l e c t o r
v o l t a g e to drop and in d u ces a v o l t a g e in the tran sform er
secon dary w inding which m a in ta in s a p o s i t i v e p o t e n t i a l a c r o s s
the e m it te r -b a s e ju n c t io n . The c o l l e c t o r i s clamped to Ec
by the c a tc h in g d io d e , Dc . i s c o n s ta n t during the ON
29
tim e so lo n g as the e m i t t e r - b a s e ju n c t io n i s forw ard b iased *
Turn OFF i s i n i t i a t e d when th e m a g n et iz in g c u r r e n t equals the
i n i t i a l d iode cu rren t*
Another p o s s i b i l i t y e x i s t s , however* Turn OFF c o u ld
be i n i t i a t e d i f th e v o l t a g e charge a c r o s s th e c a p a c i t o r b e
comes equal to th e ind uced secon dary v o l t a g e b e fo r e the
m a g n etiz in g c u r re n t b u i ld s up to
V m 1. C ifc dt - ^ Tn = %cc " £c 3*4c Jo C b
Under th e s e c o n d i t i o n s , the ON time i s
Tn = C (Bce ~ Bc ) 3 . 5ib b
The ON tim e i s dependent upon th e s i z e o f C and the
m agnitudes of th e supp ly v o l t a g e s .
This u n d e s ir a b le dependance can be e l im in a te d by th e
a d d i t io n o f an e m it t e r r e s i s t o r , R@* The v o l t a g e change
a c r o ss C can be made sm all by r e q u ir in g t h a t R C i s la r g e
compared w ith Tn .
Rj_ = base in p u t r e s i s t a n c e = (p + l)R e 3*6
The base cu rren t i s v e ry n e a r ly c o n s t a n t , hence the ON time
i s the t im e r e q u ir e d f o r the m a g n et iz in g c u r r e n t to change
from 0 to ido«
30
d o * l b ( P "" y ) "
i m = 5cc " E«
3 .7
3 .8
i b = Ecc - Be 3 . 9B R j_
Tn = Lm ~ 3 .1 0b Ri
With the a d d i t io n o f th e e m it te r r e s i s t o r , th e t r a n s i s t o r
b lo c k in g o s c i l l a t o r model c i r c u i t i s f u n c t i o n a l l y e q u iv a le n t
to the vacuum tube c i r c u i t . The com p osite t r a n s i s t o r b lo c k
in g o s c i l l a t o r tim e base g e n e r a to r i s p r e se n te d i n F ig u re 2 . 6 .
cc
F ig u re 3 .6 T r a n s i s to r B lo ck in g O s c i l l a t o r TimeBase G enerator
CHAPTER 4
LARGE SIGNAL TRANSISTOR PROPERTIES
4 -1 Large S ig n a l B ehavior
A t r a n s i s t o r c i r c u i t c o n f ig u r a t io n f o r th e b lo c k in g
o s c i l l a t o r tim e base g e n e r a to r was deve lop ed in Chapter 3•
An i d e a l i z e d t r a n s i s t o r c i r c u i t model was th e b a s i s o f the
developm ent. The to p ic o f t h i s ch ap ter i s the e v a lu a t io n
o f the p r o p e r t ie s o f th e r e a l t r a n s i s t o r . The b e h a v io r o f
the t r a n s i s t o r w i l l be d e s c r ib e d i n terms o f i t s s t a t i c
p r o p e r t i e s .
The d . c . p r o p e r t ie s o f th e t r a n s i s t o r can be r e -2p r e se n te d by th e sym m etrica l c u r re n t- fo rm e q u a t io n s .
I e - I e o ( e q V e b / K T - 1 ) - o q i c lj..l
I c - I Co ( e qVeb/KT - 1 ) - c X n I e 4 - 2
The e m it te r c u r r e n t , d e f in e d by Equation 4*1 ,
c o n s i s t s o f a d iode c u r r e n t , I QO( e ^ 0* ^ ^ - i ) , which
r e s u l t s from an a p p l ie d v o l t a g e a c r o s s the e m it t e r - b a s e
d io d e , and a t r a n s i s t o r cu rren t ,o< ^Ic . cXi^c
f r a c t i o n o f the d iod e c u r r e n t from the c o l l e c t o r - b a s e d iode
which i s c o l l e c t e d by the e m it t e r j u n c t io n . E q uation 4*2
^ J .J . Ebers and J .L . M o ll , " L a reg e -S ig n a l B ehavior o f J u n ctio n T r a n s i s to r s ," P ro ceed in gs o f IRE, i±2, December, 1954* pp. 1761-1772
32
r e p r e s e n t s th e c o l l e c t o r c u r r e n t , I c o ( e ^ 0*5/ ^ _%) i s th e
c o l l e c t o r - b a s e d iod e c u r r e n t , and cXnI e i s th e f r a c t i o n a l
e m it t e r -b a s e diode c u r r e n t c o l l e c t e d by th e c o l l e c t o r j u n c t io n .
E q u ation lj.,3 d e s c r ib e s th e c u r r e n t - v o l t a g e r e l a t i o n
sh ip o f th e p -n ju n c t io n d io d e .
Id = I g ( e qVd/kt - 1 ) 4 -3
I s i s the d iod e r e v e r s e s a t u r a t io n c u r r e n t , i s the v o l t a g e
a c r o ss the ju n c t io n , q i s the e l e c t r o n ch a rge , k i s Boltgm ann’ s
c o n s ta n t , and T i s the ju n c t io n tem perature i n d egrees K e lv in ,
The s i m i l a r i t y o f the d iode e q u a t io n to the d iod e cu rren t
component o f E quations l\.*l and I4 . . 2 s u g g e s t s t h a t a c i r c u i t
app roxim ation o f th e ju n c t io n d iod e w i l l be u s e f u l in
e s t a b l i s h i n g a c i r c u i t r e p r e s e n t a t io n f o r the t r a n s i s t o r , A
p l o t o f the d iod e e q u a t io n i s g iv e n by th e v o lt-a m p ere
c h a r a c t e r i s t i c o f F ig u r e l|_.l.
S\o pe = —
- V
F ig u re lj.,1 J u n c t io n Diode Volt-Ampere C h a r a c t e r i s t i c s
33
When the a p p l ie d j u n c t io n v o l t a g e i s a few v o l t s
p o s i t i v e . E quation 4<3 red uces to
Ip) = I e qV o /k t
s in c e th e e x p o n e n t ia l term d om in atese This c h a r a c t e r i s t i c
i s shown i n th e p o s i t i v e VI p lan e o f F ig u r e l|.»2e Under
^ p o s i t iv e ' b ia s c o n d i t io n s th e diode behaves l i k e a r e s i s t a n c e
in s e r i e s w ith a v o l t a g e sou rces The s i z e , o f t h i s r e s i s t
ance i s eq u a l t o the r e c ip r o c a l s lo p e o f th e VI ' c h a r a c t e r i s t i c s ,
and th e v o l t a g e so u rc es eq u a ls th e s lo p e i n t e r c e p t e A
n e g a t iv e v o l ta g e a c r o s s the J u n etion r e s u l t s i n a n e g a t iv e
e x p o n e n t ia l arguemdnt which r a p id ly approaches zero as a
f u n c t io n o f th e a p p l ie d v o l t a g e . ' 6
The d iod e can be r e p r e s e n te d as. a l a r g e (n ear i n f i n i t e )
r e s i s t a n c e in t h i s mode o f o p e r a t io n . The magnitude o f
the r e s i s t a n c e i n equal to the r e c ip r o c a l o f th e s lo p e
o f the VI c h a r a c t e r i s t i c s i n th e n e g a t iv e p la n e .
A c i r c u i t app rox im ation to the d iod e i s shown in
F ig u r e
^Shea, R .F », e t . a l . , T r a n s i s to r C i r c u i t E n g in e e r in g , John W iley & S o n s , I n c . , 1957s p«30B ............... - ..........
34.
I d e a l
F ig u r e 1^.2 J u n ct io n Diode E q u iv a le n t C ir c u i t
The c i r c u i t c o n s i s t s o f an i d e a l d iode i n s e r i e s w ith a
r e s i s t o r , r ^ , and a r e s i s t o r r p , which shunts th e id e a l
diode and the s e r i e s r e s i s t o r . The r e s i s t o r r^ corresp ond s
to t h e forw ard r e s i s t a n c e o f the r e a l d io d e . The r e v e r s e
r e s i s t a n c e o f the r e a l d iod e i s r e p r e se n te d by r r .
R efer a g a in to th e sym m etrica l c u r re n t- fo rm Equations^
4 .1 and 4 * 2 . The d iode c u rren t component o f each e q u a t io n
can be approxim ated by F ig u re 4 * 2 . The t r a n s i s t o r cu rren t
component can be r e p r e s e n te d by a c u rren t g e n e r a to r .
F ig u re 4*3 r e s u l t s . . A r e s i s t o r r ^ , , i s added i n the base
le a d to accou n t f o r th e f i n i t e r e s i s t a n c e o f th e base
r e g io n . The c i r c u i t o f F ig u r e 4*3 c o n s t i t u t e s a la r g e
s i g n a l e q u iv a le n t c i r c u i t which r e p r e s e n t s th e d . c .
35
F ig u re ij.#3 Large S ig n a l E q u iv a le n t C ir c u i t
b e h a v i o r o f t h e t r a n s i s t o r . T h e c i r c u i t a c c o u n t s f o r t h e
e f f e c t s o f s a t u r a t i o n c u r r e n t a n d r e v e r s e c u r r e n t t r a n s f e r i n
t h e t r a n s i s t o r . T h e c i r c u i t c a n n o t b e u s e d f o r d e t e r m i n i n g
t h e t r a n s i e n t r e s p o n s e o f t h e t r a n s i s t o r . E v a l u a t i o n o f t h e -
t r a n s i e n t b e h a v i o r o f t h e t r a n s i s t o r i s b e y o n d t h e s c o p e o f
t h i s w o r k . ^
1}..2 L i n e a r E q u i v a l e n t C i r c u i t s
T h e l a r g e s i g n a l e q u i v a l e n t c i r c u i t i s s o m e w h a t
u n w i e l d y f o r c i r c u i t a n a l y s i s . I n a d d i t i o n , t h e c i r c u i t
c o m p o n e n t s a r e n o n l i n e a r a n d d e p e n d u p o n t r a n s i s t o r o p e r a t i n g
p o i n t s . I t i s c o n v e n i e n t , t h e r e f o r e , t o d e v e l o p s e v e r a l
l i n e a r c i r c u i t s w h i c h a p p r o x i m a t e t h e t r a n s i s t o r b e h a v i o r
^ J . L . M o l l , * L a r g e S i g n a l T r a n s i e n t R e s p o n s e o f J u n c t i o n T r a n s i s t o r s , " P r o c e e d i n g s o f I R E , I4.2, D e c e m b e r ,1954, PP. 1773-1784
36
o v e r l i m i t e d r e g i o n s o f o p e r a t i o n * C o n s i d e r a b l e u t i l i t y c a n
a l s o b e g a i n e d b y p r e s e n t i n g g r a p h i c a l t e c h n i q u e s f o r e v a l u a t
i n g t h e c i r c u i t p a r a m e t e r s i n t h e s e v e r a l r e g i o n s o f o p e r a t i o n .
P a r a m e t e r e v a l u a t i o n w i l l b e m a d e o n l y f o r t h e c o m m o n - e m i t t e r
c o n n e c t i o n s i n c e t h i s c o n f i g u r a t i o n i s u s e d i n b o t h p o r t i o n s
o f t h e b l o c k i n g o s c i l l a t o r t i m e b a s e g e n e r a t o r *
T h e r e g i o n s w e r e d e f i n e d a c c o r d i n g t o t h e t r a n s i s t o r b i a s
c o n d i t i o n . R e g i o n I i s c h a r a c t e r i z e d b y r e v e r s e b i a s o f
b o t h t h e e m i t t e r - b a s e a n d c o l l e c t o r - b a s e j u n c t i o n s . O p e r a t i o n
i n r e g i o n I I r e q u i r e s f o r w a r d b i a s o f t h e e m i t t e r - b a s e
j u n c t i o n a n d r e v e r s e b i a s o f t h e c o l l e c t o r - b a s e j u n c t i o n .
B o t h j u n c t i o n s a r e f o r w a r d b i a s e d i n r e g i o n I I I . T h e s e
r e g i o n s o f o p e r a t i o n a r e i n d i c a t e d o n t h e c o m m o n - e m i t t e r
o u t p u t c h a r a c t e r i s t i c s a s s h o w n i n F i g u r e
T h r e e r e g i o n s o f o p e r a t i o n w e r e d e f i n e d i n C h a p t e r 3*
R e g i o n U
lb r O
R e g io n %
F i g u r e R e g i o n s o f O p e r a t i o n
37
The boundary o f r e g io n I and r e g io n I I i s the l i n e co rresp o n d
in g to 1^ = 0 e The c i r c u i t o f F ig u re 4«3 can be s i m p l i f i e d
i n r e g io n I , Both ju n c t io n s are r e v e r s e b ia s e d ; th e r e fo r e
the d iod es can be r e p r e s e n te d by open c i r c u i t s * Under
r e v e r s e b ia s c o n d i t io n s , r e v e r s e c u r re n t t r a n s f e r w ith in
the t r a n s i s t o r i s n e g l i g i b l y sm all* cA ^Ic and o( ^l^ can be
om itted* The e q u iv a le n t c i r c u i t f o r the t r a n s i s t o r i n
r e g io n I i s p r e se n te d in F ig u r e Two r e p r e s e n t a t io n s
are shown.
CO
©o
F ig u re 4 -5 T r a n s i s to r E q u iv a le n t C ir c u i t Region I
The c h o ic e o f th e two c i r c u i t s depends upon th e e x te r n a l
c i r c u i t . The r e v e r s e diode r e s i s t a n c e s were in c lu d e d i n
38
F ig u r e 4*3 to a cco u n t fo r th e r e v e r s e s a t u r a t io n c u r r e n t .
I f th e e x te r n a l c i r c u i t c o n ta in s la r g e r e s i s t a n c e s , the
r e v e r s e s a t u r a t io n c u r re n t must be a cco u n ted f o r .
where the curves o f c o n s ta n t 1^ m erge. R egion I I ex ten d s
from th e 1% = 0 l i n e to th e boundary of r e g io n I I I , The
e m it te r -b a s e ju n c t io n i s forw ard b ia s e d w h ile the c o l l e c t o r -
base ju n c t io n i s r e v e r s e b ia s e d . The e m it t e r d iode can be
r e p la c e d by a s h o r t c i r c u i t , cX i^c s ^ a l l compared w ith
the forw ard d iode c u r re n t and can be n e g l e c t e d . The
c o l l e c t o r d iode can be r e p r e s e n te d as an open c i r c u i t . The
l i n e a r e q u iv a le n t c i r c u i t i s g iv e n by F ig u re 4*8* The c i r c u i t
i s shown in the common-emitter form.
The boundary betw een r e g io n I I and I I I i s the l i n e
c c
b
e e
F ig u re 4«8 Region I I E q u iv a le n t C ir c u i t
39
E v a lu a t io n o f the c i r c u i t param eters o f F ig u re lj. , 6 i s
a ccom p lish ed through u se of the common-emitter in p u t and
output s t a t i c c h a r a c t e r i s t i c s . These c h a r a c t e r i s t i c s
appear in F ig u re 4*7•
tc
E 6 E
ATcA l b
F ig u r e 4 -7 R egion I I Parameter E v a lu a t io n
^ P e t t i t , Joseph M ., E le c t r o n ic S w itc h in g , Timing, and P u lse C i r c u i t s , McGraw-Hill Book Company, I n c • , 1959>p. 83
CHAPTER 5
CIRCUIT ANALYSIS
5*1 B lock in g O s c i l l a t o r A n a ly s is
A t r a n s i s t o r v e r s io n o f the b lo c k in g o s c i l l a t o r
time base g e n e r a to r was d eve lop ed i n Chapter 3® A p r e
l im in a r y a n a l y s i s was undertaken to e s t a b l i s h f u n c t io n a l
e q u iv a le n c e between th e vacuum tube c i r c u i t and the
t r a n s i s t o r c i r c u i t . The t r a n s i s t o r was r e p r e s e n te d by an
i d e a l i z e d c i r c u i t m odel. A d e t a i l e d a n a ly s i s o f the b lo c k in g
o s c i l l a t o r tim e base g e n e r a to r w i l l be perform ed in t h i s
c h a p te r . The t r a n s i s t o r e q u iv a le n t c i r c u i t s d ev e lo p ed in
Chapter 4 w i l l be u sed .
The b lo c k in g o s c i l l a t o r tim e base g e n e r a to r i s
r e p r e s e n te d by F ig u re 5*1 .
EbD3
==C,2
F ig u re 5®1 B lo ck in g O s c i l l a t o r Time Base G enerator
4o
A n a ly s is o f th e b lo c k in g o s c i l l a t o r p o r t io n o f th e c i r c u i t
w i l l be c o n s id e r e d f i r s t * For the purpose o f t h i s a n a l y s i s ,
the turn on o f both the tran sform er and the t r a n s i s t o r are
assumed to take p la c e i n s t a n t l y * In a d d i t io n , th e c o l l e c t o r
i s clamped a t some v o l t a g e more p o s i t i v e than th e e m it t e r to
b a se v o l t a g e when th e t r a n s i s t o r i s on. T his assum p tion
c o n f in e s the t r a n s i s t o r to o p e r a t io n in th e l i n e a r r e g io n ;
s a t u r a t io n o f th e t r a n s i s t o r i s a v o id e d . The t r a n s i s t o r
i s th e r e fo r e r e p r e s e n te d by i t s r e g io n I I e q u iv a le n t c i r c u i t .
The tran sform er can be r e p la c e d by an i d e a l tran sform er p lu s
a shunt in d u c ta n c e , L , a c co u n t in g fo r the tran sform er mag
n e t i z i n g in d u c ta n c e . The r e s u l t i n g e q u iv a le n t c i r c u i t i s
shown i n F ig u re 5 o 2 . The d io d e , D3 , i s r e v e r s e b ia s e d
cc.
F ig u re 5»2 B lo ck in g O s c i l l a t o r ON C ir c u i t
4a
during the ON time and i s t h e r e f o r e n e g le c t e d .
The ON c y c le i s i n i t i a t e d when the v o l t a g e a c r o s s the
c a p a c i to r becomes s u f f i c i e n t l y p o s i t i v e to forw ard b ia s the
e m it te r -b a s e ju n c t io n and cause b a se c u r r e n t t o f lo w . As
base c u r r e n t commences to f l o w , th e c o l l e c t o r v o l ta g e drops
to Ec where i t i s clamped by th e d io d e . A v o l t a g e ,
Ec c -Ec , appears a c r o s s the primary winding o f th e transform er,E -EA v o l t a g e o f magnitude — - i s induced i n the tran sform er
secondary w in d in g . (The i d e a l tran sform er p a s se s d . c . )
At the i n i t i a l i n s t a n t o f tu rn ON, c u rren t does n o t f lo w in
the m a g n et iz in g in d u c ta n c e . The cu r re n ts a t the c o l l e c t o r
are r e l a t e d by E quation 5 . 1 .
i d ( o) = p i b - i c = i b (p - i ) 5 .1
The base c u r r e n t i s g iv en by th e eq u a tio n
l b = ( % - Eo K t/RC 5 . 2
where R = rb + (rQ + Re ) (p * 1 ) . I f RC i s la r g e compared
w ith the ON t im e . E quation 5»2 can be approxim ated by
l b - E ° c ~ E C 5 . 3bR
can be c o n s id e r e d c o n s ta n t during the ON t im e , when the
c o n d i t io n s fo r th e app roxim ation are m et. I c i s equal to
1b and i s th e r e f o r e c o n s ta n t f o r the d u r a t io n o f the ONF~c y c l e .
A fter the I n i t i a l i n s t a n t , cu rren t s t a r t s to b u i ld up
i n th e tran sform er m a g n et iz in g in d u c ta n c e . Current b u i ld up
i s d e f in e d by th e E quation
As i m i n c r e a s e s , must d ecrease as a l l o th er c u r r e n ts a t the
c o l l e c t o r node are c o n s t a n t . The m a g n et iz in g c u r r e n t r i s e s
l i n e a r l y as a f u n c t io n o f tim e u n t i l th e d iod e cu rren t i s
reduced to z e r o . At t h i s t im e , i s r e v e r s e b i a s e d . Any
a d d i t io n a l in c r e a s e s i n i are f o r c e d i n t o the primary
w inding in a d i r e c t i o n to oppose i p . This r e s u l t s in a
r e d u c t io n o f and a subsequent d ecrea se o f th e c o l l e c t o r
c u r r e n t , p i^ . The p r o c ess i s r e g e n e r a t iv e , and the
t r a n s i s t o r i s q u ic k ly turned o f f . The ON tim e , t h e r e f o r e ,
i s the tim e r e q u ir e d f o r th e m a g n et iz in g c u r re n t to change
to a v a lu e equal to the i n i t i a l d iode c u r r e n t . ^
i n = (-Ecf ~ E e ) t = i d (o)Jjm
2.7
2.6
k j .G . L i n v i l l and R. H. M attson , 11 J u n c t io n T r a n s i s to r B lo ck in g O s c i l l a t o r s " , P roceed in gs o f IRE, IjJ, November, 1952*pp. 1632-1639
.$W© -o a p a e ite r i s etiarged l a a n e g a t iv e d i r e c t i o n
wltih r e s p e c t to th e base l e a d during the OH phase o f operation®
The v o l t a g e change a c r o s s th e c a p a c i to r i s g iv e n by th e .
'Squat ion,..
V e * f e c T - g e . - ( 1 - c ” T /R C ) 5® 8 '
This e q u a tio n red u ces to
v * gg.c_". & . ’
c bEC
i f T i s much l e s s than EG®
5*2 B o o ts tr a p .A n a lys is
A n a ly s i s o f th e tim e base p o r t io n o f the c i r c u i t
r e q u ir e s a knowledge o f th e r e g io n i n which th e t r a n s i s t o r ,
T^, o p e r a te s .6 The r e g io n o f o p e r a t io n can be determ ined
by e v a lu a t in g the t r a n s i s t o r b i a s i n g network® The b ia s in g
c ircu it: , , which c o n s i s t s o,f a . d io d e , a c a p a c i t o r , Cq 5
and a v o l t a g e so u r c e , i s shown i n f i g u r e 5 ole The
c a p a c ito r i s charged through th e d io d e and the in p u t
c i r c u i t o f th e b lo c k in g o s c i l l a t o r 'w h e n t h e b lo c k in g
o s c i l l a t o r i s eondti©ting.® The c a p a c i t o r ch arges toward a
v o l t a g e , VG = Eb* — The p o l a r i t y o f th e v o l t a g e .
a c r o ss th e c a p a c i t o r i s such t h a t th e e m i t t e r “b a se Ju n ctio n
o f th e tim e base t r a n s i s t o r , T%, i s forward b ia s e d to
e s t a b l i s h o p e r a t io n i n r e g io n I I , Thus, th e in p u t c i r c u i t
o f the tim e b ase g e n e r a to r p r o v id e s a d isch a rg e" p a th fo r th e
c a p a c i t o r during the b lo c k in g o s c i l l a t o r OFF t im e e The d iod e
p r e v e n ts the c a p a c i t o r from d is c h a r g in g t h r o u g h 't h e ' b i a s
v o l t a g e so u rce r e s i s t a n c e . I f th e d is c h a r g in g c i r c u i t tim e
c o n s ta n t i s much g r e a te r than th e ch arg in g c i r c u i t time
c o n s ta n t (B,C>>R.C) and la r g e r than the b lo c k in g o s c i l l a t o r
t im in g p e r io d , th e v o l t a g e a c r o s s the c a p a c ito r can be
c o n s id e r e d co n sta n t* The time b ase g e n e r a to r in p u t c u r r e n t
i s t h e r e f o r e h e ld a t a c o n s ta n t v a lu e .
% 1S b* l h 2 % ^ . 1 0
± Gre f (p f 1 ) (r e Re )
O peration o f th e t r a n s i s t o r , i s m a in ta in ed i n r e g io n I I .
I t was e s t a b l i s h e d in s e c t i o n 5>.l th a t th e b lo c k in g
o s c i l l a t o r 01 s t a t e i s i n i t i a t e d when th e v o l t a g e a cro ss th e
c a p a c i t o r , 0 , r i s e s to "a v a l u e , Vqq,, a t which th e e m it t e r -
base ju n c t io n o f Tg i s forw ard b iased * The b lo c k in g
o s c i l l a t o r con d u cts fo r Tn se co n d s , and th e v o l t a g e change
a c ro ss th e c a p a c i to r a t th e te r m in a t io n o f the 01 s t a t e i s
Ven - ^b2Tn . The b lo c k in g o s c i l l a t o r p o r t io n o f th e
c i r c u i t g iv e n by F ig u r e 2*1 can th e r e fo r e be r e p la c e d by a
sw itc h i n s e r i e s w i t h a v o l t a g e so u r c e , ^b2^ . The sw itc hc
c lo s e s f o r Tn secon ds each tim e the v o l ta g e a c r o s s th e
c a p a c i to r equal The time b a se t r a n s i s t o r i s r e p r e s e n te d
by a r e g io n I I v o l t a g e e q u iv a le n t c i r c u i t , and the b ia s in g
c i r c u i t i s r e p la c e d by a v o l t a g e so u r c e .
F = 2 *,+ ^ p 2 T n - V d 5 . 1 1C
Vd i s the forw ard v o l t a g e drop a c r o ss th e ch arg in g c i r c u i t
d io d e . The e q u iv a le n t c i r c u i t f o r the time b ase g e n e ra to r i s
p r e se n te d in F ig u re 5®3.
cc.
Re,
- -Tn
~ c
F ig u r e 5<>3 Time Base G enerator E q u iv a le n t C ir c u i t
I t i s c o n v e n ie n t to d e s c r ib e the t r a n s i s t o r v o l t a g e ,
p i b l r c , in terms o f the in p u t v o l t a g e . This i s a cco m p lish ed
by s o l v i n g th e lo o p e q u a t io n in d ic a t e d in F ig u r e $ . 3 .
k 7
i _ E - i c l ^ re * Rc ) i b l ■ ---------------------------
Fb + 1*6 + Re
piblrc = prc ____ £ _______ „ c 1 r e +Re )r b -r r-e + Re r b r r e +Fe
5 .1 2
5 .1 3
The seco n d term o f E q uation 5 .1 3 i s r e p la c e d by a r e s i s t a n c e
o f magnitude p r c (r fi + Fe • T his s u b s t i t u t i o n fo l lo w srb+-re+Re
s in c e i c i s f lo w in g in the loop c o n ta in in g the so u r c e .
The c i r c u i t o f F ig u re 5 .3 does n o t r e a d i l y len d i t
s e l f to a n a l y s i s . The c i r c u i t i s th e r e fo r e s i m p l i f i e d by
r e p la c in g the c i r c u i t between th e t e r m in a ls , X-X* by i t s
Thevenin e q u i v a l e n t . The s i m p l i f i e d c i r c u i t appears as
F ig u re 5 .4 »
- A A / ------ \ A / ------WR rcfre+fc yc Rt
lrb+rt4Re
— - Vcocc
F ig u re 5 - 4 S im p l i f i e d E q u iv a le n t C ir c u i t
48
A n a ly s is o f F ig u re 5.[t. i s c o n s id e r e d a t the i n s t a n t the
sw itc h o p en s , The v o l t a g e a c r o s s th e c a p a c i t o r i s
v co ■ Vc t - vnt 5 .1 4
The c a p a c ito r v o l t a g e a s a f u n c t io n o f t im e i s g iv en by th e
E q uation
e C — E-cc ~V B E.H: — E f — Fecc + 3 E. rc — E-j- - cr+Vjrjf'J g ^ ^ * ^ 5n>+re + Re L rb4n?4-Re J
where T - fn> + BfjC£_ijRc + i V c l c . • 5 . l 6L v ne vrt) Ke ' j
The time r e q u ir e d f o r the c a p a c i to r v o l t a g e to r i s e to Vc t
i s g iv en by E q uation 5*17
Tp - T l n f 1 + y 'E c r 4 B E r c — VCT 1 5 - 1 7L L^z rtn-n?4 Re J
The i n i t i a l v o l t a g e s lo p e i s
M = E.cc 4- B E rc - Et -Vco y f r b 4- re 4 VcfR re*i?e n Y l rr + rt> + Re yZ [ v 'J 2
5*3 Summary
The t o t a l b eh av ior o f th e b lo c k in g o s c i l l a t o r has
now been d e s c r ib e d . C o n sid era b le i n s i g h t i n t o c i r c u i t p er
formance can be g a in e d by making some s im p l i f y in g app rox im ations
An app roxim ation to t h e b lo c k in g o s c i l l a t o r ON time can be
made by assum ing t h a t r% + (p + 1 ) ( r Q + Re) i s very n e a r ly
equal to pRe . This assum ption i s v a l i d i f p i s la r g e and
Re i s large compared with r e .
Tn = Lm (P - 1 /b ) = ^b Re"
5 . 1 9bPRe
The s i g n i f i c a n c e o f E quation 5 •1 9 I s t h a t Tn can be made
l a r g e l y ind ep en dent of the t r a n s i s t o r by a proper s e l e c t i o n
o f Re and the t r a n s i s t o r . The v o l t a g e change a c r o s s the
c a p a c i t o r i s h ig h ly dependent upon th e t r a n s i s t o r as i s
i l l u s t r a t e d by E quation 5 .2 0 .
s i m p l i f i e d -by assum ing th a t r Q < r 1;)« R e i . T h is i s a very
good app rox im ation s in c e i s in g e n e r a l s e v e r a l thousand
ohms. A fu r th e r assum ption i s th a t th e t r a n s i s t o r so u r c e ,
P ^ r c i i s much la r g e r than Ecc - E^ - Vc 0 .r 0 + rb ♦ Rei
The i n i t i a l s lo p e on th e c a p a c i t o r i s
The s lo p e of th e time base v o l t a g e i s ind ep en dent o f both
the su pp ly v o l t a g e and the t r a n s i s t o r , T]_, i f p i s l a r g e .
Vcn - l k 2 .In = (Ecc - EpjTn Cz b p Re2Cz
5.20
The eq u a tio n s fo r th e tim e base g e n e r a to r can be
E t Rei Ci
5.21
5o
The b lo c k in g o s c i l l a t o r p e r io d , Tp> i s approxim ate d by
E q uation
Tp — — ibpTn » ^ ejQ _ 5 .2 3E C £t>+tuTn/Ct- ^
Assume now t h a t ^b2^n i s much g r e a t e r than E - V& or th a tc
E = Vd. E q uation 5 .2 2 red u ces to
Tp « ReaCa 5.214-
E q u ation 5 .2 4 p r e d ic t s th a t th e b lo c k in g o s c i l l a t o r p e r io d
i s c o n t r o l l e d o n ly by f i x e d components, a v e r y d e s ir a b le
f e a t u r e . An a d d i t io n a l i n t e r p r e t a t i o n o f E q uation 5 .2 4 i s
th a t i f the v o l t a g e a c r o s s the c a p a c i t o r , C, changes due to
a s h i f t in Pg; the s lo p e o f th e tim e base v o l t a g e w i l l be
changed to compensate e x a c t l y fo r the d e v ia t io n o f Vcn , so
Tp does not c h a n g e 0
The e x te n t to which th e above assum ptions are v a l i d
w i l l be e v a lu a te d in th e f o l lo w in g chapter*
CHAPTER 6
EX PER IM EN TA L EVALUATION
6 ,1 P r a c t i c a l C o n s id e r a t io n s
The outp ut waveforms o f th e b lo c k in g o s c i l l a t o r tim e
base g e n e ra to r are d e s c r ib e d by the f o l lo w in g e q u a t io n s ,
which were d e v e lo p ed in Chapter 5$
Equations 6 ,1 and 6 ,2 d e sc r ib e th e magnitude and d u ra tion o f
the p u lse outp ut; and E quations 6 ,3 and b . k p r e d ic t the
am plitude and p e r io d of the tim e base v o l t a g e . The purpose
o f th e p r e se n t ch a p ter i s t o e s t a b l i s h e x p e r im e n ta l ly the
perform ance c h a r a c t e r i s t i c s o f th e c i r c u i t , and to e v a lu a te
the v a l i d i t y and accu racy of the a n a l y t i c c i r c u i t d e s c r ip t io n .
cc E,c 6.1
b (R i2 +pRe2 ) bFe 2m &m 6.2
|es | —Eg — lb 2 Tn C2
6.3
T 6 . 4
51
52
The diagram o f the experimental c i r c u i t i s shown in
Figure 6 .1 .
2 8 Vcc,
F ig u re 6 .1 E xperim enta l C ir c u i t
The s e l e c t i o n o f th e in d ic a t e d m agnitudes o f c i r c u i t
components i s based on an i n v e s t i g a t i o n o f E q uations 6 .1
through 6 . i | . C onsider th a t a sweep p e r io d of 5 > 00 m icro
seconds i s d e s ir e d . By E quation 6 . 4 the p e r io d i s equal
to ReiCg i f the b ia s v o l t a g e E i s a d ju s te d to equal V#.
For C2 equal to .0 1 m ic r o - fa r a d s , must e q u a l 50 k ohms.
The magnitude o f C2 a f f e c t s th e am plitude o f th e sweep
v o l t a g e as shown by E q uation 6 .3 » In a d d i t io n . E quation
6 .2 i s based on th e assum ption t h a t the product
Cg (R i2 ♦“ Bp e ) i s much g r e a t e r than th e p u lse d u r a t io n . A
f u r th e r r e l a t i o n s h i p r e q u ir e s t h a t Tp » (R^2 *'B2 ^ 6 2
T his i s n e c e s s a r y to in su r e th a t th e b ia s v o l t a g e fo r th e
time b ase p o r t io n o f th e c i r c u i t rem ains a lm o st c o n s ta n t f o r
the d u ra t io n o f the sweep p e r io d . I t i s e s s e n t i a l , t h e r e fo r e
th a t th e t r a n s i s t o r param eters be o b ta in e d t o s e l e c t p r o p e r ly
the rem ain ing c i r c u i t com ponents.
E v a lu a t io n o f the t r a n s i s t o r param eters (p , R^) i s
accom p lish ed through u se o f the t r a n s i s t o r s t a t i c c h a r a c te r
i s t i c s , as d e s c r ib e d in Chapter 1|_* S in ce th e s e param eters
are a f u n c t io n o f th e t r a n s i s t o r o p e r a t in g c o n d i t i o n s , th e
o p e r a t in g p o in t o f each t r a n s i s t o r must be determ ined .
During the b lo c k in g o s c i l l a t o r ON time the c o l l e c t o r (Tg)
i s clamped to Ec ; i n e f f e c t Ec i s the c i r c u i t su p p ly v o l t a g e .
A v o l t a g e , Ecc ~ E c i s a p p l ie d to the c i r c u i t in p u t throughb
the transform er c o u p l in g . The v o l t a g e drop a c r o ss the
e m it te r r e s i s t o r , Rg2> i s v e ry n e a r ly equal to ff-S. ,
s in c e th e v o l ta g e a c r o s s th e e m it te r -b a s e ju n c t io n i s
t y p i c a l l y s e v e r a l t e n th s of a v o l t . The e m it t e r r e s i s t o r
se r v e s as the c i r c u i t lo a d , and the b lo c k in g o s c i l l a t o r
fu n c t io n s as an e m it t e r f o l lo w e r during the con d u ction
p e r io d . A g r a p h ic a l c o n s t r u c t io n to determ ine the c i r c u i t
o p e r a t in g p o in t i s made on th e c o l l e c t o r outp ut c h a r a c te r
i s t i c s o f th e 2N335, as shown i n F igu re b .2 . The t r a n s i s t o r
%
(T^) in th e tim e base p o r t io n o f the c i r c u i t a l s o o p era te s
as an e m it t e r f o l lo w e r ; hence i t s o p e r a t in g p o in t i s
l o c a t e d by s im i la r c o n s t r u c t io n . The nom inal v a lu e s o f
R ei and RQ 2 are 5 0 k ohms and 120 ohms r e s p e c t i v e l y .
6
5
4
OO 3
O 2
040
b Vc t - C O L L E C T O R VOLTAGE— VOLTS
C O M M O N EMITTER OUTPUT CH ARACTERISTICS
F igu re 6 .2 B lo ck in g O s c i l l a t o r O perating P o in t
The t r a n s i s t o r (T]_) o p e r a t in g p o in t must be c o n f in e d
to r e g io n I I during th e b lo c k in g o s c i l l a t o r c o n d u ct io n
p e r io d . T h is i s in su r e d by r e q u ir in g th a t ^cc^~ ^c < Ec .
The tran sform er turns r a t i o n , b , i n th e ex p er im en ta l
c i r c u i t i s 2; t h e r e f o r e , f o r Ecc - 28 v o l t s , Ec must be
g r e a te r than 9*3 v o l t s . Ec i s t h e r e f o r e c h o se n to be
10 v o l t s .
6 .2 E x p er im en ta l E v a lu a t io n
The outp ut waveforms f o r the e x p e r im en ta l c i r c u i t are
p ic tu r e d in F ig u re 6 .3 *
a) Sweep Output
b) P u lse Output
F igu re 6 .3 Output Waveforms
i s a d ju s te d to e q u a l t h e r e fo r e the p r e d ic t e d p er io d
i s 500 m ic r o se c o n d s . The p e r io d o f th e sweep o u tp u t i s
500 m icrosecon ds as shown by F ig u re 6 ,3 a , To p rov id e fu r t h e r
v e r i f i c a t i o n o f E quation 6 , 3 , th e r e s i s t o r was v a r ie d
from 10 to 90kilohms, The r e s u l t s of t h i s e v a lu a t io n are
56
shown in Figure 6.1)..
80
60
R e, 40 io3 ohms
20
O
F ig u r e 6«4 Sweep P e r io d Vs Be ^
The ex p er im en ta l r e s u l t s compare e x a c t ly w ith t h e p r e d ic te d
r e s u l t s o f E quation 6 .4 * I t i s n o te d , how ever, th a t the
accuracy o f measurement fo r sweep p e r io d s up to $00 m icro
seconds was w ith in p lu s or minus 5 m icr o se co n d s , w h ile f o r
sweep p e r io d s g r e a te r than $00 m icrosecon ds the accuracy
o f measurement was p lu s or minus 10 m icr o se co n d s . The
maximum e rro r i s p lu s or minus two p e r c e n t .
F urth er v e r i f i c a t i o n o f E quation 6 . 4 was acco m p lish ed
by k eep in g c o n s ta n t a t $0 k i l ohms and changing the b ia s
v o l t a g e . Eft, from 0 to $ v o l t s . The r e s u l t s o f t h i s t e s t
57
appear in Figure 6 .$ .
o
o t % 3 4 PRF io3 CPS
F ig u r e 6 .5 Sweep P e r io d Vs B ias V o lta g e
The maximum p e r c e n t e r r o r betw een e x p e r im en ta l and a n a l y t i c
cu rves i s 2.5%. The l i n e a r l i t y o f sweep v o l t a g e was
e v a lu a te d through use o f the o s c i l lo g r a m shown i n F ig u re 6 . 6 .
F ig u re 6 .6 Sweep L in e a r i t y
58
D e v ia t io n o f l i n e a r i t y i s d e f in e d by E quation 6 .5*^
d i f f e r e n c e in s lo p e a t b eg in n in g and end o f sweep Eg = i n i t i a l v a lu e o f s lo p e
6 .5
By t h i s d e f i n i t i o n the d e v ia t io n from l i n e a r i t y o f the wave
form shown in F ig u re 6 . 6 . i s two p e r c e n t .
E quation 6 .2 p r e d ic t s the d u r a t io n o f the p u lse
o u tp u t . I t s v a l i d i t y was t e s t e d by m easuring the p u ls e
d u ration f o r s e v e r a l v a lu e s o f Rgj* The ex p er im en ta l
r e s u l t s are shown i n F ig u re 6 .7 •
160
160
HO
100
2xo ?.5" 30 3*5 Tn y -sec.
F ig u r e 6 .7 P u lse D uration
The p u lse d u r a t io n i s c a lu c l a t e d from both forms o f
E quation 6 . 2 , and p l o t t e d i n th e f i g u r e . The maximum
^Miliman and Taub, P u lse and d i g i t a l C i r c u i t s , McGraw-Hill Book Company, I n c . , 1956 , -p. 203
error obta ined w ith the approximate form o f the equation i s
9.9$# I t i s no ted that the error decreases as Eq2 in c r e a s e s .
The approximate form o f the equation i s based on the
assumption th a t p R 2 I s approxim ately equal to r^ r ( r e « '% 2 )P*
This approximation i s in error fo r the va lu es o f Rg2 and
p2 used h ere . However, as Re i s in creased the approximation
becomes b e t t e r . The e f f e c t of changing the supply v o lta g e
fo r the time base t r a n s i s to r i s shown in F igu re 6 . 8 .
r
30
Ecc, 20 :=::::=::T:==0:xVeits
10 I : : : : : : : : " "
0 ».i o-z 0.3 0 .4 0.5 j.6 T(> tm-sec.
Figti^b 6 * 8 Supply V oltage V a r ia t io n
From th is f ig u r e i s seen th a t no chehige in sweep duration
occUi^ fo r supply v o lta g e changes from 3 to 25 v o l t s . As
the supply volt&ge becomes h igh er i t s e f f e c t i s no longer
n e g l i g i b l e in ttib bharging c i r c u i t .
The e f f e c t o f t r a n s i s t o r p change i s shown in
F ig u re 6 . 9 . For p changes from 31*5 to 77 th e maximum
change in sweep p e r io d i s 3 $ .
60
0.1 0.2 o-3 o»4 o-5 0.6 Tp m-sec
F ig u re 6 . 9 T r a n s i s to r Param eters Vs Sweep P er iod
The e f f e c t o f su pp ly v o l t a g e v a r i a t i o n i n the
b lo c k in g o s c i l l a t o r p o r t io n o f the c i r c u i t i s g iv e n by
F ig u re 6 .1 0 .
2
VUi
40
30
20
IO
i i l i i i l l i i l
o o. l 0.2 0 . 3 0.4 0 . 5 c.t- Tjp. m - s e c
F ig u re 6 .1 0 Supply V o lta g e V a r ia t io n
61
From t h i s f ig u r e i t i s seen t h a t a t lower su p p ly v o l t a g e s
c o n s id e r a b le change i n t im in g p e r io d i s o b ta in e d . The i n
put v o l t a g e to the b lo c k in g o s c i l l a t o r during the ON tim e
i s "■ ' 'C' • At lower v a lu e s o f Ec c , the in p u t v o l t a g e
becomes v e ry s m a l l • When th e magnitude o f t h i s v o l t a g e i s
s u f f i c i e n t l y red uced , th e c h a r g in g cu rren t f o r ( i n th e
time base b ia s network) i s d e c r e a se d t o a p o in t t h a t the
d io d e , D]_, i s j u s t con d u ctin g in the forward d i r e c t i o n .
Under t h e s e c o n d i t io n s the d iod e v o l t a g e , V&, i s sm a ller
than normal and i s no lo n g e r equal to E^. The sweep p e r io d
i s t h e r e f o r e red u ced . For f i f t y p e r ce n t change i n supply
v o l t a g e (abou t the nom inal v a lu e o f 28 v o l t s ) a maximum
change i n b lo c k in g o s c i l l a t o r p e r io d o f 8$ i s o b ta in e d .
The d u r a t io n o f the p u lse ou tp ut i s n o t a f f e c t e d over the
e n t i r e range o f su p p ly v o l t a g e v a r i a t i o n .
The e f f e c t o f t r a n s i s t o r parameter v a r ia t i o n s on the
c i r c u i t output waveform i s shown by means o f F ig u re 6 .1 1 .
60
60
Pa
4 0
o 0.1 o.2 o«3 0 .4 0 .5 o .o T p rn- se c .
F ig u re 6 .1 1 T r a n s is to r Parameter V a r ia t io n s
62
p i s changed f rom 38 to 83* The maximum p e r c e n t change i n a
b lo c k in g o s c i l l a t o r . p e r io d i s 2fos and the maximum change i n
p u lse d u ra t io n i s 2*02$ .
6*3 Summary o f R e s u l t s
The b lo c k in g o s c i l l a t o r tim e base g e n e r a to r has been
t e s t e d e x p e r im e n ta lly * The performance c h a r a c t e r i s t i c s o f
the c i r c u i t are shown i n ■figures 6*i|.s 6«5s 6*6$ and 6*7*
The b lo c k in g o s c i l l a t o r sweep p e r io d i s l i n e a r l y r e l a t e d •
to th e c i r c u i t tim e c o n s ta n t The r e p e t i t i o n freq u en cy
o f the b lo c k in g o s c i l l a t o r i s l i n e a r l y r e l a t e d to th e b ia s
v o lta g e * The sweep p e r io d can be made in d ep en dent o f th e
su pp ly v o l t a g e by a d ju s t in g th e b ia s v o l ta g e to be equal
to th e v o l ta g e drop a c r o s s th e b ia s network diode* The
e f f e c t o f su pp ly v o l t a g e v a r ia t i o n on the sweep d u ra tio n
i s o r d i n a r i l y n e g l i g i b l e * &s th e su p p ly v o l t a g e i s i n
c r e a s e d to h ig h v a l u e s , i t s e f f e c t i n f l u e n c e s th e s lo p e e f
the sweep v o l t a g e and hence the period* C h a r a c t e r i s t i c s
o f th e tim e b ase ou tp u t are p r e d ic t e d a n a l y t i c a l l y w i t h in
2 $ , Changes i n p o f th e tim e b a se t r a n s i s t o r o f one
hundred p e r c e n t r e s u l t i n a 2% change in sweep duration*
The p u lse ou tp ut o f th e b lo c k in g o s c i l l a t o r i s
d e f in e d a c c u r a t e ly by E quation 6 * 2 . The d u r a t io n o f the
p u lse o u tp u t was p r e d ic t e d a n a l y t i c a l l y to w i t h i n 2*5$ o f
e x p e r im e n ta l ly o b ta in e d v a lu e s * An approxim ate form o f
t h i s e q u a t io n p r o v id e s p r e d i c t i o n o f th e p u ls e o u tp u t d u r a t io n
to w i t h in 10%, even though i t c o m p le te ly n e g l e c t s ' t h e
param eters o f th e t r a n s i s t o r # The d u ra t io n o f th e p u lse
outp ut has been shown e x p e r im e n ta l ly to be independent o f
th e su pp ly v o lta g e # The b lo c k in g o s c i l l a t o r p e r io d , how
e v e r , shows an Q% change a t a low su p p ly v o l t a g e l e v e l#
This e f f e c t i s ca u sed by red u ced in p u t d r iv e t o th e c i r c u i t #
Changes In the t r a n s i s t o r p o f r e s u l t i n s. 2% change
i n p e r io d and a change i n p u lse du ration # I t i s
con c lu d ed th a t th e b lo c k in g o s c i l l a t o r tim e base g e n e ra to r
i s a p r e c i s i o n d ev ice#
CHAPTER ?
C ONCLUSION S
7 ,1 Compliance w ith O b je c t iv e s
The b lo c k in g o s c i l l a t o r tim e base g e n e r a to r i s a
c i r c u i t which p o s s e s s e s the p r o p e r t ie s o f b o th the b lo c k
in g o s c i l l a t o r and th e tim e base g e n e r a to r ; th e c i r c u i t
w i l l g e n e r a te a l in e a r sweep v o l t a g e and a p u lse o f la r g e
am plitud e and s h o r t d u r a t io n . The o u tp u t waveforms o f
the c i r c u i t are p r e se n te d i n F ig u re 7*1• The t im in g
a) Sweep V o lta g e b) P u lse
F ig u r e 7*1 Output Wavefoims
waveform shown in F ig u re 7 .1 a i s a l i n e a r ramp h av in g a
maximum d e v ia t io n from l i n e a r i t y o f two p e r ce n t* The
p u lse o u tp u t i s shown i n F ig u re 7* l b .
A n a ly t ic te c h n iq u e s w hich make p o s s i b l e the
p r e d ic t io n o f th e s e c i r c u i t o u tp u t c h a r a c t e r i s t i c s
6 4
65
( sweep and p u ls e d u ra t io n ) to w i t h in two and o n e - h a l f p er
c e n t have been d ev e lo p ed and e x p e r im e n ta l ly v e r i f i e d . The
c i r c u i t beh av ior i s l a r g e l y in d ep en d en t o f v a r ia t i o n s in
a c t i v e d e v ic e c h a r a c t e r i s t i c s and su p p ly . .v o l t a g e . E q u a tio n s
which n e g l e c t the t r a n s i s t o r param eters have been d ev e lop ed
1 and e v a lu a te d . The c i r c u i t o u tp u ts can i^e predeterm in ed
w ith th e s e equations, t o an a c cu ra c y o f t e n p e r c e n t . The
b lo c k in g o s c i l l a t o r tim e base g e n e r a to r i s a p r e c i s i o n
c i r c u i t which can be u se d to p ro v id e a tim e b a s e v o l t a g e
h av in g a v ery s h o r t o f f - t o - o n t im e .
7«2 S u g g e s t io n s f o r F u r th er Study
The b lo c k in g o s c i l l a t o r tim e base g e n e r a to r has
fou r d i s t i n c t ph ases o f o p e r a t io n . The OS' tim e and th e
OFF tim e were a n a l y t i c a l l y and e x p e r im e n t a l ly . e v a lu a te d .
F o r ;th e purpose o f t h i s t h e s i s , the t r a n s i s t i o n OS and
t r a n s i t i o n OFF were assumed to ta k e p la c e i n s t a n t l y . That
t h i s i s not t r u e may be v e r i f i e d by an i n v e s t i g a t i o n o f
F ig u re 7 . l b . The sh o r t but f i n i t e tim e i n t e r v a l s r eq u ire d ,
to turn the b lo c k in g o s c i l l a t o r OS and OFF are shown by
' the r i s e tim e and f a l l tim e o f th e p u lse o u tp u t . An
a n a l y s i s o f th e c i r c u i t b eh av ior in t h e s e t r a n s i t i o n
s t a t e s to determ ine th e turn OS time and the tu rn OFF tim e
would be u s e f u l .
66
In some a p p l i c a t io n s , i t i s n e c e s s a r y to provide a
c u r re n t time base r a th e r than a v o l t a g e ramp* A s p e c i f i c
a p p l ic a t io n i s th e m agnetic d e f l e c t i o n o f < th e beam o f a
cathode ray tu b e . I t has been shown th a t to produce a
l in e a r c u r re n t sweep in a d e f l e c t i o n c o i l th e s e components
o f c u r re n t are n e c e s s a r y : an im p u lse , a s t e p , and a
l in e a r r i s e T h e c u r re n t req u irem en ts fo r a p e r io d ic
c u r re n t sweep are shown d ia g r a m a t ic a l ly in F ig u re 7*2.
S+e p
F igu re 7 .2 R equired Current Components
®Miliman and Taub, P u lse and D i g i t a l C i r c u i t s , McGraw-Hill Book Company, I n c . , 1956, p .237« ................
• \ 67
A c lo s e I n v e s t i g a t i o n o f F ig u re 7# l a shows th a t th e
l i n e a r r i s e and a s t e p component o f v o l t a g e are p r e s e n t i n
t h e 'sweep v o l t a g e output.* This s u g g e s t s t h a t th e sw eep"
v o l t a g e ou tp u t can be u se d t o p ro v id e a c u r r e n t time b a s e ,
s in c e the s e r i e s com bination o f a r e s i s t o r and a v o l t a g e
g e n e r a to r i s e q u iv a le n t t o ' a c u r r e n t g e n e r a to r and a shunt
r e s i s t o r * A. means to in tr o d u ce am ap p rox im ation o f th e
r e q u ir e d im pulse component i n th e sweep v o l t a g e output
would p ro v id e a t o p ic f o r fu r t h e r s t u d y 0
BIBLIOGRAPHY
1, E b e r s3 J» J c 9 and M oll , J e L«, “Large S i g n a l Behavior o f J u n ct io n T r a n s i s t o r s ,1* P ro ceed in g s o f IRE, Vol.* l^E,December, 1954# PP« 176l*rl772 0
2 a L l n v i l l , J . G®, and Mattson," R« "He, “J u n ct io n T r a n s i s to r B lo ck in g O s c i l l a t o r s P r o c e e d i n g s o f IRE, V o l0 4 3 , November, 1 9 5 5 , pp. 1632-1639®. . _ _
3 o. Ml lim an and Taub, Puls e and D i g i t a l C i r c u i t s , McGraw- H i l l Book Company, Inc®, 1956 , p„ 202®
4o M o ll , J® L e , “Large S ig n a l T r a n s ie n t Response o f J u n c t io n Trans I s t o r s , lf P roceed in g s o f IRE, Vo I* 4 2 , December, 1954,PP. 1773-1784*
5® P e t t i t , Joseph M», E l e c t r i c a l S w ltc h ln g , Tim ing, and P u lse C i r c u i t s , McGraw-Hill Book Company, Inc®, 1959, :po 83®
6® S h ea , Re p 6 , e t 0 a l e , T r a n s i s to r C ir c u i t E n g in e e r in g ,John W iley & S o n s , Inc®, 1957 , P° 308®
68
Recommended