A TRANSISTORIZED REGULATED POWER SUPPLY
,f
A THESIS
Presented to
the Faculty of the Graduate Division
Georgia Institute of Technology
In Partial Fulfillment
of the Requirement s for the Degree
Master of Science in Electrical Engineering
By
Lincoln PhelpsRice
August 1954
A TRANSISTORIZED REGULATED POWER SUPPLY
Approved:
• / • -
y -
•
—
•-
'
"
•
•
-
~ " "
Date Approved by Chairman: ^0<^ .2.1, /iSJ*
In presenting the dissertation as a partial fulfillment of the requirements for an advanced degree from the
Georgia Institute of Technology, I agree that the Library
of the Institution shall make it available for inspection
and circulation in accordance with its regulations governing
materials of this type.
I agree that permission to copy from,
or to publish from, this dissertation may be granted by the
professor-under whose direction it was written, or, in his
absence, bw the Dean of the Graduate Division when such
copying or publication is solely for scholarly purposes and
does not involve potential financial gain.
It is understood
that any copying from, or publication of, this dissertation >•
which involves potential financial gain will not be allow^dcilf
*».
ACKNOWLEDGMENT
I wish to express my appreciation to Doctor B. J.
Dasher for his suggestion of the subject for this project
and for his invaluable assistance in its prosecution.
TABLE OF CONTENTS
Page
ACKNOWLEDGMENT
ABSTRACT
ii
„
vii
CHAPTER
I.
II.
III.
IV.
V.
VI.
INTRODUCTION
.......
BASIC PRINCIPLES OF TRANSISTOR OPERATION . .
THE TRANSISTOR AS A CIRCUIT ELEMENT
....
1
3
14
DISCUSSION OF THE REGULATED POV7ER SUPPLY . .
29
CONCLUSIONS
61
RECOMMENDATIONS
63
APPENDIX I, DERIVATION OF GROUNDED-EMITTER TRANSISTOR
EQUIVALENT CIRCUIT
APPENDIX II, DERIVATION OF EQUATION (51)
. .
65
68
APPENDIX III, PARAMETERS AND COMPONENT VALUES
71
APPENDIX IV, BRIDGE CIRCUITS
APPENDIX V, OSCILLOGRAPH CIRCUITS
BIBLIOGRAPHY
....
79
....
81
$2
LIST OF TABLES
Table
1.
2*
3.
4.
Page
Values of Stabilizer Parameters
Determined by Various Methods
55
Values of Various Parameters, Components,
and Constants
. . ,
76
Results of Numerical Computations Compared
with Corresponding Experimental Data
77
Point-by-Point Measurements of Stabilizer
Currents and Error-Signal Voltage
73
LIST OF ILLUSTRATIONS
gure
Page
Diagram of pnp Transistor Showing Bias
Batteries
. . . . . . . . .
12
2.
A Two-Terminal Pair . . . . . . . . . . . . . .
15
3.
Static Characteristics of a pnp Junction
Transistor
17
1.
4.
5.
Grounded-Base Equivalent Circuit for a
Transistor
•
19
Grounded-Emitter Equivalent Circuit for a
Transistor .
. . . . . • • • •
20
Schematic of Transistorized Regulated Power
Supoly . . . . . . . . . . • . . . • . . • • •
30
Simplified Schematic of Voltage Stabilizer
. .
31
?*• Generalized Schematic of a Voltage Stabilizer .
35
9.
Equivalent Circuit of Regulated Voltage Supply
37
10.
Equivalent Circuit of Stage One of Voltage
Regulator . „
. . . . . . . . . . . .
39
Equivalent Circuit of Stage Two of Voltage
Regulator • , . • . . . . . . , . . . . . . . . .
39
Equivalent Circuit of Stage Three of Voltage
Regulator for Derivat i on 01 n . . . . . . . . .
41
Equivalent Circuit for Stage Four of Voltage
Regulator for Derivation o f R . . . . . . . .
41
6.
7.
11.
12.
13.
14.
15.
16.
17.
.
Equivalent Circuit of Stage Three of Voltage
Regulator for Derivation of 3
44
Equivalent Circuit of Stage Four of Voltage
Regulator for Derivation of S
44
Oscillogram of Current-Voltage Characteristics
of Silicon Diode D]_ . . . . . . . . . . . . .
51
Oscillogram of the Zener Region of the CurrentVoltage Characteristics of Silicon Diode Dn . .
51
Pag
Modified Error-Detector Circuit with Venier
Control for Varying the Output Voltage . . . .
53
Regulation of Voltage Stabilizer . . . . . . . .
56
Regulation of Voltage Stabilizer on Expanded
Voltage qcale . .
.....
56
Steps in the Derivation of the GroundedEmitter Equivalent Circuit . . . . „ . • • • •
66
Regulation of Rectifier-Filter Unit
73
Rectifier Regulation on Expanded Voltage Scale
74
Error-Signal Voltage Versus Output Current • .
75
Error-Signal Voltage Versus Output Current,
Expanded Voltage Scale . . . . . . . . . . . .
75
Bridge Circuit for Measuring R
. .
SO
Bridge Circuit for Measuring S . . . . . . .
.
SO
Circuit for Obtaining Current-Voltage
Characteristics of Silicon Diode . . . . . .
.
61
Circuit for Obtaining Regulation Curves
...
SI
ABSTRACT
Smaller size, absence of heater elements? resistance
to shock, reduced power requirements and reduced heat generation are among the advantages which a. transistor circuit
enjoys over an electron-tube circuit.
The low power require-
ment of a transistor circuit has made possible the economical
use of a battery as a power source.
In those applications
not suited to the use of batteries, it is desirable to have
a regulated d-c power source which posseses the same attributes with respect to size, heat generation and absence of
heater elements as the circuit it supplies.
The develop-
ment of such a power supply was chosen as the problem for
this Droject.
The supply which was developed consists of a conventional full-wave rectifier using 1N93 diodes and a transistorized stabilizer.
The stabilizer is composed of three
sections, a regulator, a three-stage d-c amplifier, and an
error detector.
The error detector varies the error-signal
voltage across the input terminals of the d-c amplifier
in proportion to the variation in the output voltage of the
stabilizer.
The d-c amplifier converts this error signal
to a current, amplifies it and reverses its phase.
This
current acts as a variable bias for the regulator which
Vlll
consists of a bank of transistors in parallel connected in
series with the output terminal.
The voltage across the
regulator varies in such a manner as to cancel any changes
occurring in the output voltage.
The stabilizer will deliver thirty volts over a
current range of zero to forty milliamperes.
It has an
output resistance of 3.5 ohms and a stability factor of
thirty-five.
The operation of this regulator differs from
that of an electron-tube regulator in two basic ways.
First, the error detector must maintain the correct errorsignal voltage independently of the base current which it
supplies to the first transistor in the d-c amplifier.
Second, the regulator is controlled by a current instead
of a voltage.
The drift inherent in semi-conductors affects the
operation of the stabilizer in two ways.
The drift in the
silicon diode used as the reference element will cause a
direct and equal drift in the output voltage.
The drift
in the transistors will cause a negligible variation in the
output voltage but will change the current limits over which
the regulator will function.
Included in this work are a discussion of basic
transistor principles, the discussion of a. method, of determining stabilizer performance in terms of its stability
factor and output resistance, and the derivation of these
parameters in terms cf the small-signal transistor constants.
CHAPTER I
INTRODUCTION
From their inception transistors have been a potential
solution for many problems in the field of electronics.
Their
advantages over vacuum tubes include their small size, high
efficiency, absence of heater, long life, resistance to shock,
and reduced heat generation.
These are of great importance
to the designer of the miniature and subminiature electronic
equipment required in aircraft, portable, and other mobile
applications.
These favorable characteristics have caused a stampede
to transistorize virtually every known electronic circuit
whose power level was not too large.
The vast majority of
this work is still in the development stage where it is hampered by the present transistor limitations. Foremost among
these are the sensitivity of their parameters to temperature
change and the present lack of uniformity among supposedly
similar transistors.
The latter has made their introduction
into military applications particularly difficult because of
the necessity for readily interchangeable components.
The power source for most transistor circuitry to date
has been the dry cell.
This has been possible because of the
low voltage and low current requirements.
The Bell Telephone
Laboratories are developing a telephone carrier system in which
o
(L-
transistorized components are supplied by batteries which
will require replacement once every five years.
Applications: exist, however, in which it is impractical to supply transistorized circuits from batteries.
Aircraft electronics is a field in which transistors offer
a tremendous advantage ir the saving of weight and space.
This would be largely offset by the bulk and weight of batteries if they were used as sources of power. A subminiature
rectifier-stabilizer which converts the aircraft alternating
current to a regulated d-c voltage is preferable.
This unit should generate as little heat as possible,
since heat dissipation is one of the major problems of subminiaturization.
It should be as light and small as possible
and have regulation characteristics comparable with conventional regulators. A miniature supply using a magnetic
amplifier as a stabilizer has been introduced.
It is believed
that a transistorized circuit to regulate the voltage after
rectification will yield the best regulation characteristics
and equal or exceed the magnetic amplifier in the saving of
space and weight and lack of heat generation.
The development of such a power supply was undertaken
as the project for this thesis to determine the principles
involved.
The succeeding chapters give a discussion of basic
transistor principles followed by a detailed discussion and
analysis of the regulated supply8
CHAPTER II
BASIC PRINCIPLES OF TRANSISTOR OPERATION
Semiconductors.—In order to gain fuller understanding of
the applied operation of transistors, the principles of
operation of semiconductors should be investigated particularly the characteristics that distinguish them from insulating and conducting materials.
In 1897 J. J, Thomson obtained evidence to substantiate
the existence of electrons by determining that the ratio of
charge to mass of a cathode ray is a constant. About this
time scientists had also been observing the various radiation
phenomena and were attempting to ascertain the structure of
an atom.
Thomson and Rutherford each proposed a model con-
sisting of a configuration of positive and negative charges.
Rutherford*s model conformed more closely to existing theory.
The Rutherford atom consisted of a planetary arrangement,
similar to the soler system, in which the positive charge and
most of the mass of the atom were concentrated in a nucleus
at the center with negative charges traveling in orbits around
it.
However, according to current theory, these negative
charges, subjected to a continual centripital acceleration,
would radiate energy causing them to lose their electrostatic
potential and spiral into the nucleus.
This, of course, is
not the observed case and constitutes a defect in the Rutherford atom.
4
In order to explain the spectral series of singleelectron atoms, Niels Bohr introduced two important postulates(l).
The first was that an electron can exist only in
certain stable orbits which satisfy the following quantum
condition
nh
mvr r
2
where n is the quantum number (an integer), m is the electron'
mass, v is the electron's speed, r is the radius of the orbit
corresponding to the quantum number, and h is Planck's constant.
Each value of n leads to a different stable orbit.
The electron will not radiate energy while it remains in one
of these orbits.
The second postulate was that, when the
energy of an atom changes from a value W]_ to a lower value
V*'2, the difference in energy is emitted as a quantum of
radiation given by the Einstein frequency condition
hf = Wi - % 2
where f is the frequency of the emitted radiation.
The con-
clusion to be drawn from the Bohr postulates is that the
electron of a free atom changes levels in discrete jumps.
Methods using quantum mechanics support the Bohr postulates
and are also applicable to multi-electron atoms.
5
This discussion has been confined to free atoms.
When atoms are compressed together into a solid, interaction
occurs between the various electrons.
Pauli's exclusion
principle says that tv/o interacting electrons cannot have
the same set of quantum numbers.
Therefore the energy level
of each of the interacting electrons must be slightly different from the rest and the group of levels farm into bands.
In semiconductors a band of low energy levels occurs which
is filled.
This is called the valence or filled band.
Above
it in energy is an energy region known as the forbidden band
or energy gap to which an electron will not jump.
Still high-
er exists another band of energy levels to which electrons can
be made to jump.
This is called the conduction band.
So far this discussion has assumed that an electron is
a particle or corpuscle.
In 1923 Louis de Broglie(2) conclud-
ed that electrons could be diffracted in a manner similar to
the optical diffraction of light waves.
The deduction made
from de Brogliefs work was that electrons must have the characteristics of waves if they are subject to such diffraction.
This was later demonstrated using a "grating" made of nickel
crystals.
Therefore two concepts of the electron, corpuscular and
wave-like, have been proposed.
It will be convenient to super-
impose the two and consider the electron as being a "wave
packet" consisting of a concentration of waves at a single
point.
6
The electrons in the conduction band possess the most
energy and consequently are the most susceptible to being
removed from the atom.
Electric current flows as a result
of the migration of these free electrons.
Conducting mate-
rials have no energy gap and the conducting band may overlap
the valence band.
The electron migration occurs readily in
these elements with thermal agitation frequently being a
sufficient driving force.
Other elements have an energy gap
of the order of magnitude of one electron volt across which
an electron must cross before it reaches the conduction band.
These elements are called semiconductors.
A third group of
elements have considerably larger energy gaps and are called
insulators.
Germanium is a semiconductor.
of 0.7 electron volts (ev)(3).
It has an energy gap
It has four valence electrons
and forms into face-centered cubic crystals of the diamond
type.
Each atom shares each of its four valence electrons
with an adjacent atom in a covalent structure.
of each atom is called a lattice site.
The location
In this situation
most of the electrons are bound and very few are available
to become carriers of electric current.
In the previous paragraph it was presumed that the
germanium is completely free of impurities.
This is impossible
in practice but the presence of impurities is frequently desirable in semiconductors.
Suppose that a smal 1 portion of melted
arsenic is added to the melted germanium and the mixture
7
allowed to cryatalize.
Arsenic atoms would be found occupy-
ing certain lattice sites in the predominantly germanium
structure.
These arsenic atoms would be bound covalently
to the germanium atoms in the lattice.
However arsenic is
a pentavalent element and only four of its valence electrons
would be engaged in attaching it to the adjacent germanium
atoms.
This leaves an additional electron which can easily
be induced into the conduction band and become a carrier.
It has been found that only 0.05 ev is required for this
electron as opposed to 0.72 ev to force one of the covalent
electrons into the conducting band,
A pentavalent element
added to the germanium is called a donor because it adds
electrons to the semiconductor.
In a similar manner a trivalent element such as
boron will occupy a lattice site and combine covalently
with three adjacent germanium atoms but will lack a valence
electron for the desired fourth bond.
having a positive charge.,
This creates a "hole"
This hole will attract an electron
from a nearby bond and leave a hole at this new location.
Another electron will be attracted to this hole filling it
but creating another.,
In this fashion electrons jumping
successively to nearby holes cause the holes to migrate in
the opposite direction.
A trivalent imparity is called an
acceptor because it creates the holes which accept electrons
from adjacent atoms.
8
Germanium, containing principally donors is called an
n-type semiconductor,, while that containing principally
acceptors is called p-type.
These impurities are deliber-
ately inserted into the germanium until an optimum proportion
is obtained.
The holes and electrons in the semiconductors
are known as "carriers11 of electricity.
In an n-type semi-
conductor there exists an abundance of potentially migratory
electrons due to the presence of the donor impurity.
Traces
of other impurities, which cannot be completely removed, will
create some holes in the semiconductor.
These holes are much
fewer in number than the carrier electrons and are called
minority carriers.
carriers.
The carrier electrons are majority
Similarly, in a p-type semiconductor the electrons
are minority carriers and the holes are majority carriers.
Since holes and electrons are both always present in
a semiconductor the electrons are continually filling the
holes they encounter in a process known as recombination.
The life of a carrier electron from the moment it leaves the
conduction band of its parent atom until it recombines with
a hole is about five to twenty microseconds depending upon
the electron velocity and the relative prevalence of electrons
and holes.
P-N junction.—A p-n junction consists of an n-type semiconductor united to a p-type semiconductor(4). The surface
between the two is the junction.
The bond between the two
cannot be created mechanically because the crystalline
9
structure must be continuous across the junction*
One common
method of forming a junction is to diffuse acceptor impurities
through a portion of a piece of n-type germanium.
That portion
through which the diffusion occurred is thus converted to ptype germanium and a junction is established.
It would seem that an excess of holes on one side of
a junction and an excess of electrons on the other would
cause diffusion in the entire germanium block until the holes
and electrons were uniformly distributed throughout.
How-
ever, at room temperature, the holes in the p region are
prevented from crossing the junction by the donor atoms on
the opposite side.
These atoms have a positive charge which
will repel the holes.
In the same manner electrons attempting
to cross in the opposite direction will be repulsed by the
negatively-charged acceptors in the p layer.
This repelling
charge can be thought of as a potential hill which cannot be
traversed by a majority carrier unless it receives additional
energy from an outside source.
Minority carriers on either
side can easily cross the junction because they are aided by
the potential hill in making their transition.
The current
created in the semiconductors by the transition of minority
carriers is small because they are few in number.
Another
analogy for the potential carrier at the junction is a small
battery with its positive terminal connected to the n-type
and its negative terminal connected to the p-type segment.
Consider a battery to be connected across the p-n
.junction with its positive terminal attached to the n-type
segment.
The potential thus placed across the junction will
aid the potential hill already established by the ionized
atoms at the junction.
This will further prevent crossing
by majority carriers but will cause slight increase in flow
of minority carriers.
This is called the reverse-current or
high resistance condition.
If the reverse potential is in-
creased sufficiently a voltage breakdown, known as the Zener
effect, will occur.
Reversing the battery polarity will give the junction
a low resistance or forward-current bias.
This results
because the battery potential opDoses the potential hill
at the junction and effectively flattens it out. Majority
carriers can now cross the junction barrier freely creating
an electric current.
This current will not be without limit,
however, because, as it begins to flow it creates a potential
drop in the germanium segments themselves due to the resistivity of the germanium.
This drop will tend to counteract
the battery potential and introduce a current-limiting action.
A higher battery potential must then be used to obtain a
current increase.
If the battery potential is made too high
the junction will be damaged due to the heat generated by an
excessive current.
A few tenths of a volt external potential
are sufficient to generate a forward current.
11
Junction transistors.--A junction transistor consists of a
pair of p-n junctions placed "back-to-back".
It can be one
of two types depending upon which type of germanium is
common to both junctions:
pnp or npn*
As its name implies,
a pnp transistor consists of a segment of n-type germanium
flanked on either side by a piece of p-type germanium while
an npn transistor consists of a segment of p-type germanium
between two n-type pieces.
The operation of the two is
almost identical except for the fact that the bias voltages
and the carrier types are reversed.
Therefore, in the
interest of simplicity and clarity, we shall confine ourselves to a study of pnp transistors with the understanding
that the principles involved in the npn type are analogous.
Fig. 1 is a diagram of a pnp junction transistor showing in dashed lines the batteries equivalent to the potential
hills at the junctions.
The block of p-type germanium to
the left is called the emitter, the center segment of the
n-type is the base, and the p-type on the right is the collector.
In the configuration shown the base is grounded and
the emitter and the collector are biased with respect to the
base by the voltages E e and E c respectively.
Note that the
emitter junction is biased in the forward direction while the
collector junction Is biased in the reverse direction.
With an adequate bias, the emitter will become a
source of holes, the carriers in a pnp transistor,
which will cross over into the base.
The number of holes
12
-l\--.
r-»i—I
i
EMITTER
i
_L
BASE
COLLECTOR
*
Pig, 1
Diagram of a pnp transistor showing bias batteries,
13
which will receive sufficient energy to jump into the conduction hand and cross the emitter junction into the base
is determined by the emitter bias.
After the holes have
entered the base they become minority carriers and will recombine with electrons present unless they are first swept
across the collector junction.
The base is made very thin,
about one mil,, in order to increase the probability of a
hole reaching the collector before it recombines.
Since the
collector junction is biased in the reverse direction its
potential hill is enhanced and an electric field is set up
aiding the diffusive migration of minority carriers from the
base to the collector. After entering the collector, the
holes which were minority carriers in the base are once
again majority carriers and support the flow of current to
the collector terminal,
Under these conditions the collector resistance is
very low.
However, as the collector voltage is increased
the holes available from the emitter will increase only
slightly and the collector resistance increases suddenly.
Since some of the holes are lost in the base due to
recombination, the collector current will be less than the
emitter current.
This means that o(; the current gain of a
junction transistor, will be less than unity.
CHAPTER I I I
THE TRANSISTOR AS A CIRCUIT ELEMENT
Open-circuit
p a r a m e t e r s . - - T h e p r e v i o u s c h a p t e r d i s c u s s e d some
of t h e p h y s i c a l
c h a r a c t e r i s t i c s of t r a n s i s t o r s .
ness l i e s in t h e i r
trical
networks.
performance as c i r c u i t
Insight
Their
components i n
usefulelec-
i n t o t h i s b e h a v i o r can b e o b t a i n e d
by u s i n g a t w o - t e r m i n a l - p a i r a n a l y s i s .
This i s t h e
familiar
p r o b l e m of d e t e r m i n i n g the p e r f o r m a n c e o f t h e c o n t e n t s o f a
" b l a c k b o x " by making m e a s u r e m e n t s on i t s f o u r e x t e r n a l
ter-
minals.
The l o o p - b a s i s d i f f e r e n t i a l
pair,
equations
for a two-terminal
shown i n F i g . 2 , a r e
v-, == — i , + _A i 9
1
aix
di2
av2
av2
vP = —
ai-L
I-, + —
(1)
/L
io
(2)
ai2
in which v-,, v 2 , in, and ip represent incremental changes in
V, , Vp, I,, and I ? respectively.
If the frequency is limited
to a range in which the reactive components of the internal
transistor impedances are negligible, and the analysis is
restricted to the linear region of the transistor, the partial
15
_J_I
I
1
'2
i
i
•
•
»-
FiK. 2
A two-terminal pair.
•
16
derivatives in equations (1) and (2) will show little variation and can be regarded as constant resistances.
av 1
3 V1
11
91.
BT2
h
31,
81
2
r
12
y
dv?
21
=
s
i„
1
(3)
r 22
-
The static characteristics of a junction transistor
are shown in Fig. 3.
Inasmuch as V e , Vc, I e , and 1^ are equal
to V-,, Vp, I]_, and 1^ respectively, the open circuit parameters
of this transistor at a given operating point can be found
from the slopes of these characteristics.
The curves are so
steep that an accurate determination of their slopes by
graphical means becomes difficult.
Better results can be
obtained by biasing the transistor to the desired operating
point, applying a small a-c signal at the driving point, and
measuring the a-c response of the transistor.
SheaTs(5)
detailed description of this technique was followed in determining the various transistor parameters listed in Table 2.
Transistors can be connected into a circuit in three
different ways,,
These are designated by the terminal which
is connected to the return paths of both the other terminals.
These configurations are listed below opposite their vacuumtube equivalents.
-20
1
-20
l e constant
-16
-16
2
iz -12 _
-- —
3
>°
|
1
4
>°-B
- "1
5
1
I
1
-4
lc,
3
le,
4
ma
250
\
3*
2
-5
ma
250
200
I*
S"'2
-8
1
l c constant
5
/-3
200
2"
1
/-.
/ - 2
*B0 —
E
> 150
E
100
100
50
50
l e constant
5
lc,
0
l c constant
2
3
le,
ma
Pig. 5
Static characteristics of a pnp junction transistor.
ma
/_4
IS
Transistor
Vacuum Tube
Grounded-base
Grounded-grid
Grounded-emitter
Grounded-cathode
Grounded-collector
Grounded-anode
(cathode-follower
The f i r s t two a r e the mast commonly used connections and w i l l
be studied in g r e a t e r d e t a i l .
Grounded-base connection.—Fig. 4 shows a configuration of
equivalent r e s i s t a n c e s which approximates the
of a grounded-base t r a n s i s t o r .
characteristics
The inclusion of the equiv-
alent voltage generator i n the c o l l e c t o r c i r c u i t i s necessary
because the t r a n s i s t o r i s an active element.
This scheme i s
analogous to the use of an equivalent voltage in vacuum tube
circuit analysis.
The voltage added in the c o l l e c t o r c i r c u i t
by t h i s generator i s a function of the emitter current and a
r e s i s t a n c e , r , called the "mutual r e s i s t a n c e . "
It
can be shewn
r
ll
*
r
21
s
r
b
+
r
b
+ :r
that
e
r
m
r
12
=
r
b
(4)
r
r
22 - b
+
r
c
then the solution for the t r a n s i s t o r parameters i s
r
e ~ r H " r 12
*b
*12
r
r
(5)
r
r
r
m " 2 1 " 12
c
22 "
r
l2
19
^VW
AAAr
o
'm'e
v
Fig. 4
Grounded-baae equivalent circuit for a transistor.
20
With the load, Z^, attached as in Fig. 4
(6)
zx +
Two equations for v
in terms of i
e
v
v
e
e
= (r
~ (r
and i
e
e
+ r,)i
b e
- r )i
e r n e
are
c
+ r,i
be
- (r
c
(7)
+ ZT ) i
L c
(3)
Subtraction of (£} from (7) ^ives
0 = r (i
b e
+ i ) + (r + ZT ) i
c
c
L c
(9)
+ r i
me
from which the collector current i s found to be
-i (r.,+ r )
e b
ra
r
b
+ r
Substitution for i
c
e
=
L
e
\
r
r0.
e 21
22
+
(10)
Z
L
in (7) gives
r
v
+
-i
+ r
e
- r,(r1+ r )
b
b b
m
b
c
L
ID
and so
7 „
^1 ~
(r, + r ) I r + Z_ ) + r ( r
b
e
c
L
b e
—
r, + r + Z_
b
c
L
- r )
m
,—
(12)
I f the open-circuit parameters are inserted into (12) the
result
is
21
z
r
l -
(r
11
r
21
+ Z ) + r ( r
- r )
L_
12 1 1
21
12
f
+
22
Z
L
r Z + r r
- r 2*
11 L
11 22
12 21
Z-, »
r
rnZ
Z,
+
22
Z
+
L
(13)
(14)
L
|r
(15)
F
"
+
22
Z
L
i n which
I 2* I = r
r
I I
1122
This r e s u l t i s
—r
r
12 21
i d e n t i c a l to t h a t obtained for
p o s e d of p a s s i v e ,
linear., b i - l a t e r a l
e x c e p t i o n t h a t r , « i s not equal t o
The t r a n s f e r
impedance i s
Z
=
?l
components w i t h the
r^,.
defined
as
(16)
—
x
a n e t w o r k com-
e
Now
v
= i ZT
c L
c:
and from ( 1 0 ) t h e c o l l e c t o r v o l t a g e
v
c -
Z
(17)
becomes
- i «e ( r Kb + rm
m)
L
r
b
+ r
+ ZT
c
L
(13)
22
Whence
-ZT (r + r )
m
Z9, = L b
^
r + r + Z
b
c
L
(19)
The substitution of open circuit parameters directly into
(19) gives
-7 r
Z21 = _2L±Lr
22
+
(20)
h
which i s again in agreement with the p a s s i v e , l i n e a r ,
bi-
lateral case.
Since a junction t r a n s i s t o r i s p r i m a r i l y a low i n p u t impedance device i t s s h o r t - c i r c u i t current amplification
f a c t o r , «, i s an important index to i t s c h a r a c t e r i s t i c s .
o<
can be derived in terms of the equivalent t r a n s i s t o r r e s i s t ances in the following manner:
I f the c o l l e c t o r i s shorted
as i s i n d i c a t e d by the dashed line i n Fig. !+ i t i s seen t h a t
- 1
ie
v
c
The e x p r e s s i o n for curriait g a i n with a load i s , from e q u a t i o n
(10),
A± .
r, + r
P2
r, + r + ZT
b
c
L
(21)
23
=
ex = A.
b + rm
r
V°
,= a
r,
b
+r
(22
c
r, « r
b m
r « r
b
c
(23
where a is defined a s
a -• r
m
In terms of open-circuit
o< =
(24
IT
c
parameters
21
(25)
r22
Carrier diffusion in the base w i l l limit the value of c*
below unity in a junction t r a n s i s t o r .
Amplification i s
achieved because the c o l l e c t o r current i s delivered a t a
higher impedance l e v e l than the input.
Following i s the
derivation of the voltage gain of a t r a n s i s t o r .
Consider
again the configuration i n F i g . 3 with the load Zj i n s e r t e d
between the c o l l e c t o r and base t e r m i n a l s .
The voltage gain
i s then defined by
A,
The substitution of equations
'21
(26)
(12) and (19) into (26) gives
24
Av =
(r
b
+
-ZL(rb + r m )
r, + r + Z,
5
2
h
,
r } (r
+ Z
+ r (r
r
e
c
L>
b e - m>
r
b
+ r
(27)
c +Z L
-ZT(r. + r )
AV =
L
m
b
( r + r ) (r + Z_ ) + r, (r - r )
b
e
c
L
b e
m
(2S)
In terms of open-circuit parameters the voltage gain becomes
A v - .-
- Z LL
r
h n
T
27\
1
+
(29)
M
To find the open-circuit voltage gain the limit of (29) is
taken as Z^ approaches infinity.
AVQC = lim
ZL^oorn
-r 0 1
AVOC - _
" r 21
- — ^ —
(|r|/Z L )
+
-r, + r
2
r
(30)
^ =_^
r
ll
b
+ r
»
e
ox)
Grounded emitter.--Figure 5 shows the equivalent circuit for
the ^rounded-emitter configuration.
Proof of i t s electrical
equivalence to Fig. 4 is given in Appendix I .
the open-circuit parameters become
In this case
25
r
11
= r
+ r
e
12
b
e
y
21
r
22
r
= r
+ r
e
c
- r
m
=r
e
+ r ( 1 - a)
c
The e x p r e s s i o n s f o r i n p u t and t r a n s f e r
d e r i v e d by t h e
substituticn
(20) r e s p e c t i v e l y
by i n t e r n a l
circuit
S,
(32) i n t o e q u a t i o n s
changes in the
e
"black
ZL + r c [ r e
(15)
and
affected
box."
+ r ) Z
+ r r
+ r (r
+ r
b L
e c
b e
c
_ r
+
Hh <r
m
_, ( r e + r b )
Z.
of
i m p e d a n c e s can be
s i n c e n e i t h e r of t h e l a t t e r i s
(r
1
(32)
- r
e
m
• rb(l
-
r )
m
(33)
a)]
=
ZL
+
rc(l
z
7
L
:=
2\
T-
The c u r r e n t a m p l i f i c a t i o n
c
'21
L^rm "
r r t + vAl
r
e>
== - i ZT
c L
-A
(34)
- a) + Zi
can be d e r i v e d from
OhmT s l a w
v
-a)
(34)
using
26
A/W-
^WVrJI-a)
o
r
t 4
m'b
J -
FI*, 5
Grounded-emitter equivalent circuit for a transietor.
27
-i
Z
r
n
A^_ = _ 2 . = -ii =
Z
-r
iu
b
The s h o r t - c i r c u i t
- r
m
e
r + r - r
+ Le
c
ra
L
L
current; a m p l i f i c a t i o n t h e n
35)
becomes
r
- r
A
=
m e
A
r + r
- r
isc
e
c
m
>
(36)
A, c n = b
.ISC
r
b == _
c
ra
« r
e
m
r « ( r
- r )
e
c
m
where by definition
The v o l t a g e a m p l i f i c a t i o n
(33) and
m
a
l-a
can be d e r i v e d from
(3V
equations
(34)
v
c
=
Z n
21
Z.(r
- r )
L rn
e
Av =
( r + r . )ZT -*- r r
+ r (r + r
e
b L
e c
b e
To f i n d t h e o p e n - c i r c u i t
approach i n f i n i t y
L
voc
(38)
- r )
m
v o l t a g e g a i n Z. i s a l l o w e d
in equation
m
>
to
(3$).
e z.
m
r
+
r
r + r,
e
b
e
b
(39)
0<r>
-co
The t r a n s f e r conductance of the grounded-emitter
configuration
i s defined as
0.r
21
- ^ v
A
Z
l
(40)
l
l
r
n
J
21
(r
+ r, ) ZT
e
b L
- r
m
e
+ r r + r, (r
ec
b e
(41)
+ r
- r )
c
m
By definition
m
,J
21
(42)
zL - o
Then
r - r
m
e
G m
r r + r, (r + r - r )
e c
b e
c
m
G.
m
(43)
m
r
r
e c
+
r
b
(r
(44)
c
r„,)
m;
r <<
r
e
c
<< r
e
m
r
ra
r
e
+r
b^-
a)
r
No attempt has been made to derive or even mention a l l
various types of parameters or methods that have been proposed for t r a n s i s t o r analysis*
The subject of power gain has
not been covered because no significant
the resulting expressions.
insight i s gained from
The limited area t h a t has been
covered was chosen because i t lays a general base for
the
following description of the voltage regulator with a minimum
of extraneous material.
CHAPTER IV
DISCUSSION OF THE REGULATED POl/ER SUPPLY
The power s u p p l y c o n s i s t s o f a r e c t i f i e r
age s t a b i l i z e r .
The r e c t i f i e r
is a conventional
r e c t i f i e r w i t h an R-C f i l t e r .
diodes.
I t u t i l i z e s a p a i r of 1N93
silicon
elements.
The c o m p l e t e s c h e m a t i c of t h e
Fig.
7 is a simplification
s u p p l y i s shown i n F i g .
of F i g . 6 i n which a l l
e l e m e n t s a r e lumped t o g e t h e r and t h e r e c t i f i e r - f i l t e r
r e p r e s e n t e d by a T h e v e n i n g e n e r a t o r ,
E
r a n g e of
l o a d v o l t a g e of t h i r t y v o l t s o v e r a
zero to f o r t y m i l l i a m p e r e s .
can b e a l t e r e d by m e t h o d s t o be shown
The v o l t a g e s t a b i l i z e r
subdivisions:
Error detector.-—The
Zener diode,
section
Any v a r i a t i o n
a d-c
major
amplifier,
sectiai
c o n s i s t s of a
R, ,
inserted
I d e a l l y the
a finite
reverse
i n t h e o u t p u t v o l t a g e must t h e r e f o r e
across the r e s i s t o r .
current
later.
D.. , i n s e r i e s w i t h a r e s i s t o r ,
for
fur-
a s shown.
error-detecting
diode i s constant
unit
specifications
i s composed of t h r e e
a c r o s s t h e output of t h e s t a b i l i z e r .
a c r o s s the
These
an e r r o r - d e t e c t i n g s e c t i o n ,
and a v o l t a g e - r e g u l a t i n g
parallel
and R .
The r e g u l a t e d power s u p p l y h a s b e e n d e s i g n e d t o
n i s h a nominal
volt-
full-wave
The s t a b i l i z e r u t i l i z e s t r a n s i s t o r s and
diodes as i t s non-linear
6.
and a
potential
current.
appear
S i n c e t h e a v e r a g e v o l t a g e a c r o s s R-^
is
50
/
S|
117 v
6 0 cps
g
A/W
-vw
•
=Fc
I
-re-
TR,
C^—0.07 u f d . , 50 v. capacitor
R4—250 ohm resistor
C 2 , Cz—40ufd., 100 v. e l e c t r o - R^—10,000 ohm resistor
l y t i c capacitor
^ a * ^ b * R7a» R7b> ^ c * R7d» R7e»
Dl—50 v. Zener s i l i c o n diode
Rjf, Rg, RQ—47 ohm r e s i s t o r
D2> D*~5 v. Zener s i l i c o n diode S^—S.p.s.t. switch
D4—10 v. Zener s i l i c o n diode
?l* T^a, Tz b —G.P.C. 2517 transistor
T
D^, D5—1N95 diode
2» ? W %h, T4C> T ^ , T ^ , Titf—
R^—12 ohm resistor
Raytheon CK722 transistor
Rg—4^0 ohm resistor
TRi—Power transformer, 50-0-50 v.
Ri—5»050 ohm resistor
at 100 ma.
(All resistors are rated at one third watt.)
Pig. 6
Schematic of transistorized regulated power supply.
Pig. 7
Simplified schematic of voltage stabilizer.
\x
32
is about 0.3 volts, a deviation in output voltage of thirty
millivolts (a 0.1 per cent change in E~) will result in a
ten per cent change in the drop across this resistor.
How-
ever, due to the finite resistance of diode D^, only about
thirty per cent of the total error voltage appears across
R . This voltage increment, e f , is the input signal to the
d-c amplifier.
D-e amplifier.--The d-c amplifier contains three stages in
the following configuration:
npn grounded-emitter, pnp
^rounded-base, nun grounded-emitter using transistors T^,
T , and T respectively. D , D , and D are Zener diodes
~
3
'
2
3
4
used to keep the operating points of T 9 and 'I\ relatively
constant.
If current I -. is zero, T~ will conduct and be limited by the emitter biasing action of resistor R~.
In this
condition the amplifier produces its maximum output current.
An incremental positive increase in the voltage e1
appearing across the input terminals of the direct current
amplifier will be amplified by transistor T-, into an increase
in I C T .
This current flowing through Ro will increase the
bias on T_ decreasing its output current.
cut-off by D
and R
T
is biased to
and will conduct only when driven by
current Ic2
A decrease in I c2
0.
0 causes a decrease in current
I . Thus the d-c amplifier generates a current increment
c3
which is proportional to an input voltage,. This can be expressed mathematically as a transconductance G1
m
33
Gf
m
« —
»»
(45)
from which
if
= G» e ' «= (} e n
rn
(46)
m 0
where ef i s the amplifier input voltage increment, i f i s the
amplifier output current , eQ i s the output voltage of the
s t a b i l i z e r , and, by d e f i n i t i o n
G = G' ( e ' / e ) = G' k.
rn
m
o
(47)
m l
This is the expression for the combined trans conductance of
the d-c amplifier and the error detector.
Regulator.--The regulator section consists of six Raytheon
Type CK722 transistors operating in parallel.
They are
connected directly between the rectifier and the output
terminals in a grounded-emitter configuration and are
driven at their bases by the output current from the d-c
amplifier.
An increase in load voltage has been shown to
be converted by the detector and amplifier stages into a
negative or decreasing increment in the current Ic3»
This
decrease in the; current supplied to the base of the regulator
transistor T, [the group of six being considered as a unit)
causes its operating point to shift closer to cut-off with a
resultant decrease in collector current.
By virtue of Ohmfs
law, this reduction in current supplied to the load lowers
34
the load voltage.
The magnitude of the reduction in load
voltage in the limit will approach the value of the initial
positive change in load voltage.
Regulator parameters.—It has been shown(6) that the operation
of an electronic voltage stabilizer can be defined by a
stability factor, S, and an internal resistance R.
o
(42)
(49)
;r
R + RL
The lower-case characters here represent the partial differentials of the variables denoted by the respective uppercase characters in Fig. £.
the rectifier.
E is the Thevenin voltage of
r
The Thevenin resistance, R , of the rectifier
is included in the stabilizer circuit.
E is a test voltage
inserted in series with the load R_•
From equations (4$) and (49) and the Ohmfs law equation
for the outnut branch.
E.
I0R
E
the following expression for the output voltage has been
derived in the appendix
(50)
55
Fi£. 8
Generalized schematic of a voltage
fltabilizer.
36
E
+ K-,
E„ - _ I
_
-
T
„R
O
(51)
1 + R/RL
Circuit a n a l y s i s . - - T h e parameters R and S for t h i s voltage
r e g u l a t o r are valid only when a l l the t r a n s i s t o r s in the
c i r c u i t are operating in t h e i r l i n e a r region in which case
the e n t i r e c i r c u i t is functioning l i n e a r l y .
This permits
the use of the small-signal techniques discussed in Chapter
I I and the use of an equivalent
circuit.
The r e s i s t a n c e s external to the t r a n s i s t o r s in Fig.
9 are designated by upper-case c h a r a c t e r s .
The i n t e r n a l
t r a n s i s t o r r e s i s t a n c e s are designated by lower-case chara c t e r s and t h e i r l e t t e r s u b s c r i p t s .
Each numerical sub-
s c r i n t a s s o c i a t e s t h a t component with the r e s p e c t i v e l y
numbered t r a n s i s t o r in Fig. 7.
The lower-case e ' s and i ' s
represent changes in voltages and c u r r e n t s .
The non-time -
varying components have been removed by application of the
theorem of superposition.
In solving for i n t e r n a l resistanc e;, R, the chosen
method of attack i s to l e t e
equal zero, to c a l c u l a t e the
amplification in each stage and thus obtain i 0 in terms of
e T , and to eliminate a l l v a r i a b l e s except i
and e.
The
output impedance of each of the f i r s t three stages i s large
in comparison with the input impedance of the following
stage so that the value of the c o l l e c t o r current is v i r t u a l l y independent of the load impedance ( 7 ) .
This permits
<
HWW-AA/VT! X
bl
r ,(i-o,)
Q--
d
r
<rb2
2
92
'cl
..
R
'
r
i — ^ A A ^ _ — < *•
^-r
r
ml'bl
'b3
'C2
VSAr^^-
e2
c2
r
AAA,
r^L*
m2'e2
'b3
-AAAr^Qr
rc 3, d
' - 0 ,3')
t — W V — f
r> <
m3b3
r
'•3
el
'r*
'b4
b4
r
^0'°A)
rm4J b4
K .
Q
• 4
o*S"L
rl_.
STAGE
I
.1
STAGE
2
STAGE
3
J.
STAGE
4
Pig. 9
Equivalent circuit of regulated voltage supply.
^
33
the use of s h o r t - c i r c u i t out, put current
c a l c u l a t i o n s for
these two stages with negligible loss in accuracy.
The f i r s t
stage, shown in Fig. 10, can now be con-
sidered s e p a r a t e l y .
By a p p l i c a t i o n of equation
transconductance of t h i s
(44) the
stage i s determined immediately.
a.
IT
(52)
T
ml
e» ~
The second stage,
" r el
+
r
blU~alT
shown in Fig. 1 1 , may be solved by use of
the c u r r e n t - d i v i s i o n rule snd equations (12) and (22).
-H^i ,
2 cl
e2
R
2
+ 2
(53)
1(2)
2 2 cl
ss «.o< 1
1
c2
^ e2
K
"1(2)
*2R2
1
Cr
2
A . 0 - _ -12
1
cl
2
(54)
lu
2
+
(55)
n(2)
(r
le
b2 + r m2 ) R 2
R~(r, +r ,.)+r ^r +r, (r +r - r J
b2
c2
' e2
b2
eo 9 ~ 9 rr.9
?
1h9
r*9
o 9 c2
r»9
^9
m2
a
A
R
2 2
i2 * 7 R + r
+ -r, 0 ( 1 - a.)
2
e2
b
Similarly the current amplification
for
stage t h r e e
r
is
found bv the a p p l i c a t i o n of equations (33) and (36) to
the c i r c u i t
shown in Fig. 12#
(56)
39
r
r
ci(,-°|)
-AAAr
ibi
-VsAr
'cl
V n
O
6'
PiK. 10
Equivalent circuit of stage one of voltage regulator,
r
r
'(•2
AA/V
-VW'cl
•„.:
'e2
;R2
Z I(2)
c2
C2
—
m2'»2
o
! r b2
Pin. 11
Equivalent oircuit of stage two of voltage regulator.
40
c2 3
R„ + Z.
•3
1(3)
e:J
(57)
c2 i s c 3 3
c3
i s c 3 e3
i3
+
3
c3
-A.
R
isc3 3
c2
R
'13
A
R
3
+
Z
Z
(5B)
K3)
(59)
K3)
-(rm3 " re3)R3
r r 0 +(R. + r , J ( r _ + r _ - r . )
c3 e3
3
b3
e3
c3
m3
>
(60)
—a~ R_
i3
The t o t a l
r . + (R- + r , J ( l
ej
3
b3
t r a n s c o n d u c t a n c e of the
now b e e x p r e s s e d
- a„)
3
d-c a m p l i f i e r ,
G1 , can
as
G*
= G -.A, „A.~.
ra
ml
12
(61)
13
Stage four is analyzed by the simultaneous solution of the
three independent equations fo r the input voltage designated as ei in Fig. 13.
r
3
For ease of manipulation let
= R + r , + r
4
b4
e4
(62)
r. = r . (1 - a. ) + R. + R
4
c4
4
L
r
The voltage equations are
41
r c3 (l-o 3 )
r
m3'b3
Fig. 12
Equivalent circuit of stage three of
voltage regulator for derivation of R.
ir c4 <l-o 4 )
r
ro4 , b4
-AAA/ "KD"1"
AAAr'C3
r
Q
e4
'b4
'
V
Fig. 15
Equivalent circuit of stage four of
voltago regulator for derivation of R.
'04
42
\
=
"ic3(R4 * V
(63)
^4*4
e = ~i R 4 - i ( r + r ) + i ( r + R )
4
c3 r
b4 b4
e4
c4 e4
r
(64)
e=*i(r
+ r ) -i (r - R ) -e
4
b4 b4
m4
c4 4
r
(65)
The solution for i, , from equations (64) and (65) subb4
s t i t u t e d i n t o (63) and ( 6 4 ) , with t h e e l i m i n a t i o n of e
4
y i e l d s the following e x p r e s s i o n i n terms of the v a r i a b l e s
i
, i , and e:
c3
c4
i
+
fh (r
c3 I 4
r
m4
hh [r4r3
+ r
e4
) - R r
r ;3
e4 (R 4
+ r
b4
(66
+
W
]
+ er
3 ° °
I t is seen from F i ^ s . 3 and 7 r e s p e c t i v e l y t h a t
i RT - e
o L
(67
1
-,
c3
=
i1 T
With the a i d of t h e s e e x p r e s s i o n s and e q u a t i o n (46) t h e
s o l u t i o n f o r i -3 becomes
c3
i
= G ( i R - e)
c3
m o L
(62
Without l o s s of accuracy the assumption can. be made t h a t
x
(69)
c 4 * ~1o
Then eouation (65) can be e x p r e s s e d in t e r m s of i
and e
o
43
^ 1GmRL [R4(rm4 " W
- [r4r3
+ r
e4 (R 4
+ r
b4
" Rrr3]
+
(70)
W ] }
+ e [~(1
- GmR4 (rm4 - re 4)]J - 0
m
[_ + a_)ro
J
From equation (49) the expression for R is
(71)
- R,
R =
i0/e
t h e c o m b i n a t i o n of ( 7 0 ) and ( 7 1 ) q;ives
R
+
R
W
L *
^ (r m4 ~ re4} "Vs 3 + V 3
I1 + W r 3
(72)
+ r
(R + r
+ r )
e4 4
b4
m4
~ x R. ( r , - r , )
m4
m4
e4
which r e d u c e s t o
T? «
[R
r
+ r , ( 1 - a ) J r + r , (R, + r . , + r )
c4
4 ^ 3
e4 4
b4
m4 (73)
( 1 + G R ) r „ -G R, ( r ~ - r , )
m r 3 ' m 4 "ni4
e4
The procedure for calculating the stability factor S
is similar to that for R.
In this case e is equal to zero
and e_
r becomes the indeoendent variable and then all variables
are eliminated excent e and e . The evaluation of the first
o
r
two stages i s i d e n t i c a l to t h a t f o r the evaluation of R.
The t h i r d sta^e contains the v a r i a b l e e r in i t s
collector c i r c u i t .
Therefore i t s output current i s a
r
r c5 (l-o 3 )
m3'b3
AM—^y
Fig. 14
Equivalent circuit for stage three of
voltage regulator for derivation of S,
W'V
Fig. 15
Equivalent circuit for stage fcoir of
voltage regulator for derivation of S,
r,n4 b4
'
45
function
of both i
and e .
c2
r
The method c h o s e n t o
solve
t h i s network i s t o w r i t e t h r e e i n d e p e r d e n t e q u a t i o n s
the voltage e'
and t h e n t o e l i m i n a t e i t and
iu_ .
jj
e»
= -i
3
e'
3
e?
,
3
for
D>
R - i R
c2 3
b3 3
(74)
- i,0(r
+ r
) + i r
b3 b3
e3
c3 e3
(7$)
:r
(76)
\, lr o
b3
These e a u a t i o n s
+
bj
r .)
m3
- i
r
(1 - a ) + e
c3 c3
3
r
yield the following
solution
for
ir-i'
(77)
i - * A' „ e + A i
c3
3 r
i 3 c2
where A._ is defined bv eouation (60) and
i3
R
3
+
R
A'
T, r ,o +• (- v o
e3 c3
r
c3 I .i
e3
+ r
b3 *re3
-a) r r o
+
r
o^ 1 ~ a ^)1
b3
3 L e3
R 0 + r. . + r ..
3
b3
G3
+
v
<
R
+
M)
3^ rb3
I1 -
c3
3J
>
(78)
a
3
The fourth stage is solved in a similar manner usin^
Fie:. 15
- -i Q (R + R ) - i,.R + i .R + e
4
c3 3
r
b4 4
c4 r
r
(79)
, = -i 0 R +i. , (r, . +r )+i , (r +R )+e
4
c3 r b4 b4 e4
C4 04 r
r
(SO)
*.,, [,r,
^, , r ,. . ,. - i . fr . (1 - a. ) + R,(£1)
1
eT 4.
, - i,
b4 o4 , + m4
c4 [ c4
4
4J
These equations will -^iv e the following expression in terms
of the three variables i ->, i . , and e :
c3
c4
r
46
- r „,.'
e4 ~Kr{]
"" r 3
r
1
m,
c3- [K4 I m4
+
. [ rr .,.rr.,
*„,.
c4 [ 4
3
++ r r
(62
. (R. ++r w.
r , . + •r x Jj
.
»,.<*,.
mm4
e4 4
b4
+ e r
r 3
" °
i , i s a ^ a i n a p D r o x i m a t e l v e q u a l t o ~ i from w h i c h
c4
'
o
c4 " —
(63)
" "o L
Bv the substitution of equation (46) into (76) it is seen
that
= if
c3
= G e + A' e
m o
3 r
(64
The expression for 3 is finally obtained by the substitution of (?3). and (?4) into (62)
1
0
ra
e0/cr
+ G
i'R, ( r . - r . ) - R r.~
[ 4 m4
e4
r 3_
A'3 [R4(rm4 - r e / f ) -
L Ir4r3
+ r
e4 (R 4
+ r
b4
+
(65)
R ^
W
+ r3
S i
•C- (R . r .-P. r J + ( l / R T ) (V . ( 1 - a . ) r 0 + r , r
L [ c4
4 3 e4 m4
m 4 m4 r 3
A? R r
3 4 m4+r3
Note t h a t 5 i s n o t i n d e p e n d e n t of t h e l o a d
3 becomes i n f i n i t e when t h e o u t p u t t e r m i n a l s a r e
resistance.
short-
c i r c u i t e d and r e d u c e s t o a c o n s t a n t when t h e y a r e o p e n .
former i s t h e o r e t i c a l because t h e d-c a m p l i f i e r
66)
would
The
saturate
47
first and the assumed conditions of linearity, upon which
these derivations are based, would not exist.
Even though S is not independent of the load resistance the expression for E
equation R
in eauation (51) is(6).
In this
appears only in the denominator of the first
Jb
term of the right hand member.
S
1 + R/R
RLS
= S'
(37
R + RL
Sf can be evaluated if equation (&5) is multiplied by R^
and divided bv eouation (72). The result is
51 -
(1 + G R )r, - G R. (r . - r . )
n r 3
m 4 m4
e4
71 - A'TRTr" + A' R (r , ~ r " T
3 r j
3 4 m4
e4
(^ )
which is independent of R-r. The expression for the relation
between the output voltage, output current, and the Thevenin
rectifier voltage in terras of the circuit components can be
obtained by the substitution of equations (73) and {$&) into
(51).
E
°
(E.+KJ
rU-A' R )r, + A' R. (r . -r . )"
1
-1 L
3 r 3
3 4 m4 e4 J
(1+G R )r_
m r 3
-I *R +r . (1-a. )1 r +r (P. +r, +r . )
o _ r c4
4 J 3 e4 4 b4 m4
-G R. (r -r .
m 4 rn4 e4
(39)
1+8
The requirements for EQ to have a minimum of variation are that the coefficients of (E^ + K-^) and I Q , l/ST
and R respectively, be as small as possible.
This means that
a. and G must both be large.
4
m
The parameter a. does not appear directly in l / S 1 . A
large r . is the major factor in making it small.
show a decided increase as a, becomes smaller.
4
R will
Therefore r ,
m4
must approach as close to the value of r , as possible.
is decreased by making A'
as small as possible.
l/S 1
From equa-
tion (7$) i t can be seen that this can be best achieved by
the use of a transistor in sta^e three which has a large
collector resistance.
The two grounded-emitter stages in the d-c amplifier
are the controlling factors in the value of G . These two
m
transistors should also have as large current araplificati on
factors as possible. The amplification through stage two
is less than unity.
I t s purpose i s to increase the range
of control of stage three by supplying i t with an input
current of the correct d-c polarity.
If stage three were
supplied directly from stage one resistor R^ would have to
be connected to the regulated output to provide a d-c return
path for the collector current of stage one.
I t has been
found difficult to drive a transistor to cut-off by this
means whereas positive control is achieved by the utilization
of the additional stage.
R«, R^, and R. each reduces the
2?
y
4
gain of its stage and should be as large as practicable.
49
A practical upper limit is placed on the gain of the
d-c amplifier by the tendency of the entire loop to oscillate
at a frequency near three kilocycles.
This tendency is
caused by the phase shift in the transistors and is minimized
by the insertion of a (3.7 microfarad capacitor C-j connected
from the output of stage three to the input, of stage two.
The resistor values chosen give the greatest gain
through the amplifier and still provide a satisfactory margin
of stability against spurious oscillations over the desired
forty-milliampere current range.
Silicon diodes.---The schematic of the voltage regulator
(Fig. 7) shows that the circuit is designed to utilize four
diodes exclusive of the rectifier.
These are all silicon
diodes with prescribed Zener voltages.
D-. has already been discussed.
The reference diode
D« provides a fixed bias
for the base of To. D^ and D, together prevent the collector voltage of To from exceeding the maximum allowable
limit of thirty volts,, Two diodes were used in series in
order to permit the biasing resistor R~ to be connected
across an optimum negative bias voltage.
Only a few Zener diodes were available for experimentation and their Zener voltages did not all correspond to
the circuit requirements.
Therefore, after it had been as-
certained that the individual stage would function properly,
dry cell batteries were substituted for all diodes except D-j_.
50
The current-voltage characteristics of the reference
diode are shown in Fig. 16.
Fig. 17 shows the Zener region
of the diode characteristics on an expanded voltage scale.
The loop in this trace is caused by either the change in
temperature of the diode during a sweep or the diode capacitance or both.
These oscillograms were photographed with
a sixt3/-eycle sweep frequency.
A few millivolts of noise
are evident at the Zener knee.
This noise does not affect
the normal operation of the detector because the diode
current always exceeds three milliarnperes.
The Zener vcltage(B) is that voltage required to
create an electric field of sufficient intensity through
a p-n junction to cause tunneling between the valence and
conduction bands of the atomic structure.
The factors that
affect the Zener voltage are the barrier width and the
resistivities of the p- and n-type silicon layers. This field
is 2,50,000 volts per centimeter and the resistivity of the
silicon varies, being in the order of magnitude less than
one ohm-cm.
Pearson and Sawyer(9) have shown that the Zener
voltage is a linear function of the junction temperature.
In the example cited this variation was 0.023 volts per
degree centigrade.
A drift of about 0.1 volts was observed
immediately after the load on the regulator was increased
from zero to full.
This caused a six-milliampere drop in
the current through the reference diode which, if its
10
•
•
t
-2
.
>
o a
^ o
©
-M «
og
-2g
-4S«
—
!
-
-6
-10
.50
-20
-10
Volte
Fig. 16
Oecillogram of ourrent-voltage characteristics of silicon diode D^.
-10
.^O.O
-29.5
-29.0
Volts
-28.5
Pig. 17
Oscillogram of the Zener region of the currentvoltage characteristics of silicon diode D]_#
Accuracy of absolute voltage ie about g0«5 volte
vn
52
characteristics are comparable to the example given, reduce
the diode dissipation sufficiently to give a 3.5° drop in
diode temperature.
Altering; the specifications.--The nominal output voltage is
established by the Zener voltage of the reference diode, D-^.
This voltage can be charged in steps by the use of several
diodes or combination of diodes having different Zener
voltages.
These could be inserted one at a time into the
error detector by a wafer switch.
Since this would change
the biases on the transistors in the d-c amplifier, provision
for switching in different biasing resistors and diodes would
be necessary.
The rectifier voltage would also have to be
varied in order to maintain the desired current range without
either driving: the regulator transistors to saturation or
exceeding their maximum voltage rating.
A continuous voltage.
variation between these steps can be achieved with a sacrifice in the regulation characteristics by using the modified
error detector shown in Fig. 1.3. The factor k-, in equation
(47) now becomes a variable dependent on the resistance
between points a and b which will vary with the setting of
the potentiometer.
The maximum output current can be increased by adding
additional transistors in parallel with the regulating
transistors.
The d-c amplifier is considered, adequate to
control an eighty-milliampere regulator because none of
55
-»< R lo
To
transistor
'la
T,
Fig. 18
Modified error-detector circuit with vernier
control for varying the output voltage.
54
the transistors in the d-c amplifier exceed half its maximum
collector current rating at forty milliamperes.
Results.--The numerical values of 3 and R are given in Table 1.
The value of R obtained by measuring the slope of the oscillogram trace in Fig. 19 compares favorably with that obtained
directly using a bridge.
The oscillogram was made with a
sixty-cycle test voltage while the frequency of the a-c
source for the bridge measurement was one thousand cycles.
This frequency difference is a possible cause for the
discrepancy between the two results,
The difference between the value of R calculated from
the measured transistor parameters and component values and
that obtained experimentally is felt to be principally due
to the difficulties involved in making accurate measurements
of the transistor parameters.
Although regarded as constant
these parameters vary with temperature, frequency, and
operating point.
Since none of these can be fixed in a
voltage stabilizer it is to be expected that its internal
resistance and stability factor should vary.
A broad null in the bridge used to determine the
stability factor made an accurate determination difficult
to obtain.
S varied between fourteen and forty-one with
the lower values predominating when large resistances were
used in the bridge arms.
This is equivalent to increasing
the rectifier resistance which will, according to equation
(£5), reduce the stability factor.
The average of the
55
Table 1. Values of Stabilizer Parameters Determined by
Various Methods.
Parameter
Calculated
from
component
values
R
£.9
S
270
Calculated
from static
measurements
on d-c
amplifier
5.0
Determined
by bridge
measurements
3.65
35
Determined
from slope
of oscillo/;ram trace
3.5
5<S
40
1
(0
320*
o
>
10
10
20
Ki H i amperes
50
Pig. 19
Regulation of voltage s t a b i l i z e r .
50.15
50.10
•p
iH
50.05
50.00,
20
Mil Hamper ©a
Fig. 20
Regulation of stabilizer on expanded voltage scale.
Accuracy of absolute voltage is about f0#5 volts.
4C
5?
values obtained using low resistance in the bridge arras was
chosen as the most representative.
The calculated value of stability differs considerably
from the measured value.
It is considered that the methods
used in this calculation should give a result having an
accuracy comparable to that obtained for P.
The problem of drift of the output voltage was mentioned in the discussion of the silicon diodes.
Equipment
limitations precluded quantative measurement of the temperature
characteristics of the stabilizer.
Qualitatively it was
noted that a variation of the temperature of the reference
diode would change directly the average value of the output
voltage with no discernable change in the slope of the
regulation curve.
TV-is indicates that the effect of temper-
ature change on the slope of the current-voltage characteristic of the reference diode operatin : in its Zener region
is negligible.
Therefore kn in equation (47) is essentially
independent of temperature.
No significant change in the
error-signal voltage results from the diode drift.
The drift
in the error detector makes a point-by-point measurement of
the regulation curve meaningless unless sone provision is made
to keep the temperature of the reference diode constant.
In order to observe the characteristics of the stabilizer and exclude the variables introduced by the reference
diode, the error signal , E f , was measured.
This is an
56
i m p o r t a n t parameter because i t s v a r i a t i o n would be i d e n t i c a l
t o t h e v a r i a t i o n i n the output v o l t a g e i f t h e
reference
diode were an i d e a l u n i t t h a t was t e m p e r a t u r e - s t a b l e and had
zero r e s i s t a n c e in t h e Zener r e g i o n .
No d r i f t was observed
in E* a l t h o u g h i t i s f e l t t h a t a small d r i f t
i s p o s s i b l e due
t o t h e i n h e r e n t t e m p e r a t u r e - s e n s i t i v e n e s s of
transistors.
T h i s d r i f t would p r o b a b l y not exceed a few h u n d r e d t h s of a
volt.
The v a r i a t i o n i n E
caused t h e r e b y would be l / k n
o
times as great.
-
l
A drift in E* would ha ve to be caused by
a change in the characteristics of T-, because any drift
caused by transistor T_ or T_ would be counteracted by T
2
3
•* I
b e f o r e i t could reach a s i g n i f i c a n t magnitude.
The o p e r a t i n g p o i n t s of the t r a n s i s t o r s i n the
d-c
a m p l i f i e r have been a d j u s t e d so t h a t T2 and To a r e a p p r o a c h i n g c u t - o f f when the output c u r r e n t i s zero and T^ i s approaching c u t - o f f when the output c u r r e n t is f o r t y m i l l i a r n p e r e s .
A change in o p e r a t i n g point caused by t e m p e r a t u r e
variations
could cause a t r a n s i s t o r to be cut off w i t h i n the r a t e d o u t put c u r r e n t r a n g e , i n which case the v o l t a g e r e g u l a t o r
would not f u n c t i o n .
A change i n the i n p u t v o l t a g e w i l l
l i k e w i s e change the range of r e g u l a t i o n .
If t h e input
v o l t a g e should i n c r e a s e , the range of r e g u l a t i o n would
s t i l l be f o r t y m i l l i a r n p e r e s but would extend between h i g h e r
l i m i t s , e. g. l i v e t o f o r t y - f i v e
arnperes.
or t e n to f i f t y
milli-
I f the i n p u t v o l t a g e should drop, t h e upper l i m i t
of the c u r r e n t r a n g e would be r e d u c e d .
A p r o t e c t i v e device
59
employing relays or warning signals or both should be used
to prevent overloading and to alert the operator when the
limits of regulation have been exceeded,.
This has not been
done here because it is considered to be a special problem
dependent upon the specific application for which the supply
is intended.
A prime advantage which a transistorized supply
enjoys over one employing electron tubes is the absence of
the requirement of a warm-up period.
The unit vail function
the instant the power switch is closed.
With an ideal ref-
erence diode the output voltage would be drift-free immediate
ly.
The diode presently used will allow the output voltage
to drift a few seconds until its temperature becomes stable.
With maximum output current, the ripple on the regulated output voltage is about thirty millivolts peak-topeak.
This is a 0.1 per cent ripple.
Superimposed on the
ripple is a five to ten-millivolt noise which is believed
to be caused by the transistors.
It was noted earlier that capacitor CN was used to
eliminate a three kilocycle oscillation.
It accomplished
this purpose by reducing the gain through the amplifier at
higher frequencies.
The regulator therefore is limited in
its operation to lower frequencies.
This is not considered
a handicap because a capacitor can be placed across the output terminals to insure that the supply presents a low output
impedance to the load at higher frequencies(1). This capacitor would serve two additional purposes.
It would reduce the
60
output noise level to less than one millivolt and it would
provide positive stability against oscillation within the
stabilizer,
C-. would no longer be required.
This capacitor
was not used because it was felt that it would not be an
integral part of an electronic voltage regulator and it was
desired to establish a design for a regulator that would be
inherently stable.
CHAPTER V
CONCLUSION'S
As lias been the usual case in transistor circuit
development work, the stabilizer in a transistorized
rower supply uses current rather than voltage variables.
This nlaces a severe limitation on the error detecting
section in that the error signal, a voltage, is required
to be independent of the transistor currents flowing through
the detector*
Amplification is lost in stages three and four due
to the increase in equivalent emitter resistance caused
by the insertion of the isolation resistors.
The reference diode drift affects the output voltage.
Any transistor drift affects only the current range of the
stabilizer.
Although the internal resistance of this power supply
is not as low as that of a good commercial regulated supply
of conventional design, it has a high stability factor and
its resistance can be decreased by increasing the transconductance of the d-c amplifier.
Perhaps the simplest method
of improvement would be to select transistors having larger
current amplification factors than were available.
62
The purpose of this study, however, was directed
toward discovering the methods and principles involved
in the transistorizing of a regulated supply rather than
merely toward producing a finished model,
CHAPTER VI
RECOMMENDATIONS
A. means of obtaining a continuously variable output
voltage from zero to the desired maximum is necessary to
increase the versatility of this power supply.
A compen-
sator to counteract the change in Zener voltage in the
reference diode due to temperature changes would eliminate
the drift in the output voltage.
These are two avenues
in v;hich further study could be conducted.
A P P E N D I X
APPENDIX I
DERIVATION 0? GROUNDED-EMITTER TRANSISTOR
EQUIVALENT CIRCUIT
Given the grounded-base transistor equivalent circuit
of T^ig. 21(a) , first consider the circuit rearranged with
the emitter grounded as shown in (b). The loop equations
for the grounded-base circuit are
r
, == i ( r , + r ) + i r,
1
e b
e
c b
> (90)
v = i (r + r
2
e b
m
<v
These
+ i (r, + r
c b
c
are valid for both (a) and (b).
With the
application
of Kirchoff's voltage and current laws, (c) is seen to be
eauivalent to (b) with the following
1
V1
= -v
= V
2
-
2
(i
"b
If
-^
e
definitions
» -v1
v
1
V
1
- v'
1
-
+ i )
c
i
= -(i
e
+ i )
b e
(91) is substituted into (90) the r e s u l t
-v 1
V
- v
(ib
+
ic^b
{i
b
+ r
e}
+
i
(91)
is
crb
+ i ) (r + r ) + i (r + r )
c
b
m
c b
e
(92)
(93
A/Wr
AAAr
-vy^
c
-rm(ib*ic)
b
1
< • \
(c)
- ^ v.
AAA/
f
'WV
o
r
i
m't
?..
(b)
Fig. 21
Steps in the derivation of the grounded-emitter equivalent circuit*
*
67
Rearrangement of (92) w i l l give t h e f i r s t loop e q u a t i o n
the g r o u n d e d - e m i t t e r c o n f i g u r a t i o n in ( c ) .
for
The s u b t r a c t i o n
of (92) from (93) and rearrangement w i l l give t h e second.
vT
V
1
= i ( r
b e
S = i J r - rm)
+ r ) + i r
b
c e
I
+
1
r e + r c (1 - a
(94)
APPENDIX II
DERIVATION OF EQUATION (51)
Given the following equations in which the lower-case
characters represent the partial differentials of the variables identified by the upper-case characters in Fig. S
o
(43)
1
(49)
e
r
R +R
L
F, . I RT - E
O
(50)
O L
It is desired to find an expression for the stabilizer outnut voltage, E Q , in terms of the rectifier Thevenin voltage
E r , and the output current, I0(ll).
The solution of the differential equation (4$) for
Eo is
E
SG -
+ F(E)
(95)
in which F(E) is the oonstant of integration, a function of
the voltage E.
to E 2;ives
Differentiation of (95) and (50) with respect
69
f(E)1
o
e
(96)
S
e
1
o _ oR _ j
e~~
e~~ L
(9?
Substitution of (49) into (97) ^ive,
o
e
R
~R
(93
R + RL
R
•»• R ,
From (96) and (93)
(99
f(E) «
R + R,
and so t h e s o l u t i o n
for F(E)
is
-SRE
F(E) - —
+ KR + RL
{ 100
Eouation (95) now becomes
Eo =
Er + K,
1
RE
(101
R + RL
To eliminate E from (101) equation ($0) is utilized.
E + K.
r
1
R(I RT - E )
o L
o
R + RVL
(102
70-
R
E0
(1
E + K,
I L R
r
1 _ o L
S
R + R,
• )
«
R + Ri
From which the d e s i r e d e x p r e s s i o n
E
EQ
. _ r
is
(103)
obtained
+ K,
1 _
1 + (R/R L )
„
I-R
(51)
APPENDIX I I I
PARAMETER APID COMPONENT VALUES
T r a n s i s t o r p a r a m e t e r s . — T h e p a r a m e t e r s of v a r i o u s
were measured by following
by S h e a ( 5 ) .
i n d e t a i l t h e methods
described
Those t r a n s i s t o r s which a r e c o n n e c t e d t o
i n p a r a l l e l w e r e measured, a s a g r o u p w i t h t h e
r e s i s t o r s i n c l u d e d i n the measurement.
isolating resistors
i n the
circuit
in-
analysis.
R - , and R, , w e r e d e t e r m i n e d e x p e r i m e n t a l l y i n t h e
sistor
the
n e c e s s i t y for
B i a s r e s i s t o r s . — T h e v a l u e s of t h e b i a s r e s i s t o r s ,
The f i r s t
operate
isolating
This r e d u c e d
number of m e a s u r e m e n t s and e l i m i n a t e d t h e
c l u d i n g the
transistors
R-j_, Rp>
laboratory.
r e q u i r e m e n t f o r t h e s e v a l u e s w a s t h a t each
tran-
s h o u l d o p e r a t e i n i t s own l i n e a r r e g i o n t h r o u g h o u t
e n t i r e forty-mi11iampere
current range.
t h e s l o p e of the r e g u l a t i o n curve,
s h o u l d be a s s m a l l a s
The second was t h a t
shown i n F i g . 19 a n d 2 0 ,
possible.
Load r e s i s t a n c e . - - 1 0 0 0 ohms was a r b i t r a r i l y
r e s i s t a n c e , R^, for
the
p u r p o s e s of c a l c u l a t i o n .
chosen for
the
The c h o i c e
load
is
immaterial as far as the c a l c u l a t i o n s a r e concerned because
d o e s not a p p e a r i n t h e f i n a l r e s u l t .
d u r i a g t h e b r i d g e m e a s u r e m e n t s for the
T h i s v a l u e was u s e d
stability
was c h o s e n b e c a u s e i t was f e l t t h a t a p e s s i m i s t i c
factor.
result
It
it
72
would be obtained with t h e supply delivering t h i r t y m i l l i amperes to the load without danger of exceeding the maximum
current r a t i n g .
R e c t i f i e r resistance-—The i n t e r n a l r e s i s t a n c e of the r e c t i f i e r f i l t e r unit was obtained from the mean slope of the
r e c t i f i e r regulation curve in the expanded scale in Fig. 23
over the operating range shown.
Ratio of output t o e r r o r - s i g n a l v a r i a t i o n . --This r a t i o , k-, ,
was obtained from the r a t i o of the slope of the e r r o r - s i g n a l
c h a r a c t e r i s t i c s (Fig. 25) to the slope of the r e g u l a t i o n
curve (Fig. 21).
All of the above data i s given in Table 2.
Computation s.—The r e s u l t s of computation of the i n t e r n a l
r e s i s t a n c e , R, and s t a b i l i t y f a c t o r , 3, and the intermediate
constants required for t h e i r computation are l i s t e d in Table
3.
The number of the equation used to obtain each r e s u l t
i s given.
Each use of an approximation i s so designated
and i s included in the equations.
When a r e s u l t has also
been obtained from d i r e c t measurements i t is l i s t e d for
comparison.
The information in the column headed "Point-
by-point measurement" i s based on the data in Table 4.
73
70
60
V
50
40
CQ
-P
o
50
20
10
20
4C
60
Milliamperes
Fig. 22
Regulation of rectifier-filter unit.
80
100
74
Boraal operating ltnH.»
-^
-XV
\ ,
%.
<>
20
40
60
Milliampere8
80
?i|5. 25
Rectifier regulation on expanded voltage scale,
100
75
u.^v
^»^—»^__.____
•
0.25
0.20
So.15
>
0.10
0.05
,
10
20
Milliamperes
40
50
Fig. 24
Error-sigial voltage versus output current.
10
20
Milliamperes
50
40
Fig. 25
Error-si^ial voltage versus output current, expanded voltage s c a l e .
76
Table 2. Values of Various P a r a m e t e r s , Components, and
Constants.
Transistor parameters.
Transistor
number
1
2
3
4
re
(ohms)
b
( ohms)
c
{ohms)
m
(ohms)
3
92
150
94
62
b2
4.9
4.9
0.42
0.42
1.5
1.5
50,000
50,000
d
6,000
6^,000
23,000
23,000
23,500
23,500
45,000
45,000
64,600
64,600
lg,400
IS,400
21,150
21,150
Comnonent s (ohms)
R-p-12
Ri—450
Ro--3050
Rj£—.230
Constants.
P.I--1000 ohms
R P _ _ 3 5 0 ohms
kx—0.256
r
0,9
0.95
0.S
0.9
77
Table 3. Results of Numerical Computations Compared with
Corresponding Experimental Data.
Item
1
Parameter or
constant
°ml
Equa- Computed
tion
value
number
Pointby-point
measureraent
(52)*
0.093
0.075
2
A
i2
(56)#
0.79
0.90
3
A,13
(60)*-
-3.21
-3.04
t
n
(61)
-210
-395
5
Gm
(47)
-67.5
-113
6
A'
f 7^ U
7
R
(73)
(73)
$.9
tf.9
(d5)
270
S*
t
m
\
•
1
-••
Bridge
From oscmeasure- illographic
ment
data
0.0001£3
5.0
5.0
3.65
3.5
35
* Equation -riving an approximate s o l u t i o n was u s e d .
78
Table 4. Point-by-Point Measurements of Stabilizer Currents
and Error-Signal Voltage.
Item
1
2
3
4
5
6
7
g
9
E T (v.) I ,(na.)
cl
0.2rJ
0.28
0.27
0.27
0.26
0.26
0.25
0.2S
0.24
5.0
4.4
4.1
3.?
3.4
3.1
2.7
2.3
2.0
-I 0(raa.)
c2
I -(ma.)
c3
0.5
0.9
1.3
1.5
1.3
2.1
2.5
2.5
3.2
0.9
1.7
2.6
3.7
4.7
5.7
6.8
8.0
9.1
-I .(ma.) I (ma.)
c4
o
25
30
35
41
46
51
56
61
66
0
5
10
15
20
25
30
35
40
APPENDIX IV
BRIDGE CIRCUITS
The b r i d g e c i r c u i t s ( 1 2 )
used f o r t h e d i r e c t
ment of R and 3 a r e shovgn i n F i g s .
former i n a balanced
measure
26 a n d 2 7 . With t h e
condition
R,R T
R =
L L
(104
R2
With the l a t t e r in a balanced condition
v3
t
= _i
R
2
(105
80
OSCILLATOR
I
o
yujL>
1
stfpF^.
Afsfa
m
tt
^^^
DETECTOR
Pig. 26
Bridge c i r c u i t for measuring R.
-^RRr^
r• o
OSCILLATOR
Pig. 27
Bridge olroult for measuring S.
*
APPENDIX V
OSCILLOGRAPH CIRCUITS
CATHODE RAY
OSCILLOSCOPE
OSCILLATOR
Pig. 28
circuit for obtaining current-Voltage
characteristics of silicon diode.
CATHODE RAY
OSCILLOSCOPE
OSCILLATOR
Pig. 29
Olrouit for obtaining regulation curves. Switch S^ is
with S2 open, to obtain the rectifier regulation (Pig.
b. with S2 closed, to obtain the stabilizer regulation
in position o to obtain the error-signal voltage ourve
in position a,
25) j in position
(Pig. 20)j and
(Pig. 2^)«
t3
I
B L I
0 G R A P H Y
Literature Cited
1.
Van Name, F. W. , Jr., Modern Physic: s, New York:
Prentice-Hall, Inc., 1952, P. 9:<?-l3CT.
2.
Hausmann, Erich and Edgar P. Slack, Physics, 3rd
ed. . New York: D. Van Nostrand Company, Inc.,
194?, PP. 759-761.
3.
Coblenz, Abraham and Harry L. Owens, "Transistor
Action in Germanium and Silicon," Electronics, 26
(June, 1953), 166-171.
4.
Coblenz, Abraham and Harry L. Owens, "Point-Contact
Transistor Operation," Electronics, 26 (July, 1953),
15S-160.
5.
Shea, Richard F., editor, Principles of Transistor
Circuits, Hew York: John Wiley and Sons, Inc. ,
1953, 'PP. 4?5-495.
6.
Hunt, F„ V. and R. 17. Hickman, "On Electronic
Voltage Stabilizers," The Review of Scientific
Instruments, 10 (1939), 6-9.
"
7.
Shea, Richard F., editor, Principles of Transistor
Circuits, New York: John V/ilev and Sons, Inc.,
1953, pp. 65, 66.
£.
Pearson, Gerald L. and Baldwin Sawyer, "Silicon P-N
Junction Alloy Diodes," Proceedings of the I. R. E.,
40 (1952), 1349.
9.
Pearson, Gerald L. and Baldwin Sawyer, "Silicon P-N
Junction Allov Diodes," Proceedings of the I. R. E.,
40 (1952) 1350.
10.
Terman, Fredrick Errnions, Radio Engineers1 Handbook,
1st ed., New York: McGraw-Hill Book Company, Inc. ,
1943, r). 615.
11.
Hunt, F. V. and R. W. Hickman, "On Electronic Voltage
Stabilizers," The Review of Scientific Instruments,
10 (1939), 7. "
—
12.
Hunt, F. V. and R. W. Hickman, "On Electronic Voltage
Stabilizers," The Review of Scientific Instruments,
io (1939), 20, ~~?r.
34
Other References
Bardeen, John .and Waiter H. Brattain, "Principles Involved
in Transistor Action," Physical Review, 7$ (1949), 1203-1225.
Conwell, Esther LI. , "Properties of Silicon and Germanium,"
Proceedings of the I. R.'E., 40 (1952), 1327-1337.
Keonjian, Edward, "Temperature-Compensated DC Transistor
Amplifier," Proceedings of the I. R. E. , 42 (1954), 661-671.
Rvder, Robert M. and R. J. Kirch er, "Some Circuit Aspects of
the Transistor," Bell System Technical Journal,
28 (1949),
—
367-400.
"
—~
Schockley, William, "The Theory of p-n Junctions in Semiconductors and p-n Junction Transistors," Bell System
Technical Journal, 2S (1949), 435-4^9.
Shockley, William, "Transistor Electronics: Imperfections,
Unipolar and Analog Transistors," Proceedings of the I. R» £.,
40 (1952), 12.^9-1313.
Shocklev. William, "Transistor Physics," American Scientist,
42 (1954) 41-72.
Shockley, William, M. Sparks, and G. K. Teal, "p-n Junction
Transistors," Physical Review, S3 (1951), 15l-lo2.
Stuetzer, Otmar MI., "Transistors in Airborne Eauipnent,"
Proceedings of the I. R. E., 40 (1952), 1529-1530.
Wallace, Robert Lee and William J. Pietenpol, "Some Circuit
Properties and Applications of n-p-n Transistors," Bell
System Technical^Journal, 30 (1951), 530-563.