DE 2 91966
COMPUTER AIDED STATIC AND TRANSIENT D;ESIGN
OF A CLA$S1OF 1ULTIVIBRATORS:
THE PARALLEL SCHMITT CIRCUIT
by
VICTOR KWOK-KING FUNG
S.B., massachusetts Institute of Technology
(1966)
SUBMITTED IN PARTIAL FULFILLMENT OF THE
REQUIREMENTS FOR THE DEGREE OF
MASTER OF SCIENCE
at the
MASSACHUSETTS
INSTITUTE OF TECHNOLOGY
September, 1966
Signature of Author
Signature Redacted
Departmdnt of Electrical 4igifieerin,
August 22, 166
Signature Redacted
Certified by
A
Thesis SuDervisor
Signature Redacted
Accepted by
Chairman, DepartmentalCoinmittee
on Graduate
Students
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COMPUTER AIDED STATIC AND TRANSIENT DESIGN
OF A CLASS OF MULTIVIBRATORS:
THE PARALLEL SCHMITT CIRCUIT
by
VICTOR KWOK-KING FUNG
Submitted to the Department of. Electrical Engineering on
August 22, 1966 in partial fulfillment of the requirements
for the degree of Master of Science.
ABSTRACT
This thesis is concerned with the static and transient design of the Parallel Schmitt circuit. Particular
emphasis is given to methods which can be developed into
a systematic procudures for the analysis of all classes
of multivibrators and which can be mechanized on the
digital computer.
The static design calcul.tes the value of the four
unknown resistances subject tb four input constraints.
The first two constraints are supplied by analytic expressions for the circuit at its breakpoints, while the
latter two are chosen arbitrarily for their convenience
and usefulness in the transient analysis and the optimization. The correlation between the VF and VK is almost
prefect, showing deviations less than 5% and oftentimes
less than 1%.
The incremental D.C. loop gain is derived and used
to find the conditions for a regenerative circuit. These
are found to be consistent with the conditions obtained
by treating the circuit as a device with a particular
V-I characteristic. The power consumption of the circuit
i investigated and the conditions and proof given for
its minimization.
The system of non-linear first order simultaneous
eqlations used to describe the transient behaviour was
obtained by substituting simple charge control models for
the transistors. Their coefficients, which changed with
current levels, were assumed to be constants in a linear
approximation to the actual solution. Instead of the usual
"IS" shaped curve of output collector current versus time,
the linearized system possesses*'growing exponential* and
(decaying exponential#, which can be neglected. The boundary
conditions are obtained by requiring the collector currents
to be continuous across the origin, t=0. The results
predicted by this linear method are consistently low, as
much of the inertia (base collector capacitance, stray
capacitance) of the circuit has been neglected, but are
mostly within 50% of the measured value.
The final part presents a method for the numerical
integration of the non-linear transient equations. Using
this programtwo ways are suggested for the minimazation
of the power consumption and the hysteresis.
ACKNOWLEDGEMENT
The author wishes to express his gratitude and appreciation to his
thesis advisor at the Massachusetts Institute of Technology, Professor
Paul E. Gray, and his supervisors at General Radio Company, Mr. James K.
Skilling and Mr. Robert E. Owen for their constant guidance and
encouragement.
Table of Contents
PART I
CHAPTER T
I.
II.
INTRODUCTION..................................1
1
1.1
Multivibrators,.....,.................
1.2
A Summary of Each Chapter...............4
1.3
The Parallel Schmitt Circuit ............ S
STATIC ANALYSIS*........... ..
2.1
.....
..
.........
12
Breakpoint analyses of the Parallel.....12
Schmitt Circuit
2.11 Analytis Expression for VF ........ 16
2.12 Analytic Expression for VH ........
2.2
16
iq the Allowable error in firing voltage
for maximium variations in transistor
current gains
2.3
.19
The fourth constraint: emitter current at
firing
III.
.......................
......
2.4
Output Requirements .................... 22
2.5
Solution for Unknowns .................. 24
THE TERMINAL V-I CHARACTERISTIC..............27
oiodes of Operation........27
3.1
The Different
3.2
Waveforms of non-zero rise time...,.....29
3.21 Single lumped reactance outside'....30
the device
3.22 Analysis of the Active Elements
inside the device ------------.
CHAPTER
3.3
IV
.32
The Hysteresis ......................
.35
L OOP GAIN ANALYSIS .............................
4.1
Deriation of the Loop Gain
.35
4.2 -Properties of the Loop Gain
4.3
.35
Relationship of Loop Gain to Other
Circuit Functions .......................
V
P OWER CONSUMPTION ...................
5.1
.42
.....
0
.44
Analytic Expressions for the Power
at the Breakpoints......................... .44
5.2
Power Dissipation in the Circuit
.46
5.3
Minimum Power Conditions .................
.46
PART II
CHAPTER
VI
TRANSIENT ANALYSIS
6.1
,........50
.....................
The Charge Control Theory ................. 50
6.11
Relationships with other transistor
parameters .
6.12
......................
Changes in time constahts with
colletor currents ...................
6.2
.51
52
Derivation of a Set of Simultaneous
Differential Equions......................60
6.3
The Two Methods of Transient Analysis ..... 63
6.31
Analysis involving total variables .. 63
6.32
Analysis involving incremental
quantities .
.
...
6.4
Boundary Conditions.................66
6.5
Transient Solution by Linear Approximation.70
6.6
Stability of the Transient System...73
6.61
Conditions for imaginary roots.74
6.62
Condition for two positive roots....75
6.63
Condition for one positive and
one negative root.............76
6.64
6.7
Condition for two negative roots....76
Numerical Example...................79
CHAPTER
VII THE SPEED UP CAPACITOR.
83
....................
7.1
New Equations including CX**---.-*-'..
7.2
Effects of the Speed Up Capacitor.....86
83
PART III
CHAPTER
VIIILITHEB STATIC SYSTEM..............
.88
8.1
The Static Program........ 000000000 .88
8.2
The Subroutines... . .. 0...
8.:
Verification of D.C. Progranuspredi ct ions
.88
with actual resultsa...... 00 .
THE TRANSIENT SYSTEN............
9.1
General Remarks.. 0. 0 0..0
.
IX
0....
.95
..
........
9.2
The Transient Program.....
.93
.. ...
.. .95
g..
.95
X
XI
THE SYSTEM FOR OPTIMIZATION
Power..........................98
10.1
Minimum
10.2
Minimum Hysteresis.....................99
CONCLUSION.. ...
......
.....
....
. . .........
...
..
..
*.
......
e
102
102
11.1
The Conclusion..**.
11.2
Suggestions for further study.......... 104
APPENDIX 1
Fairchild 2N708 Specifications...... .... 105
APPENDIX 2
Comparison of Errors for
APPENDIX 3
D.C. solution neglecting junction drop..113
APPENDIX 4
D.C. program Results....................114
APPENDIX 5
Computer Programs.......................123
BIBLIOGRAPHY...................
...................
.
112
129
DESCRIPTION OF VARIABLES USED IN SCHMITT CIRCUIT DESIGN PROGRAM
INPUT VARIABLES
VS (Volts)
Supply voltage
VO (Volts)
Ou jatVoltage
VF (Volts)
Firing voltage specifieddby user
VH (Volts)
Holding voltage specified by user
XIL (Ma)
Current drawn by output load
INPUT CONSTANTS
.M*
BETAX
Maximum
C
Betan
Minimum
C
VBEI (Volts)
Base-emitter junction voltage at Cutoff
of Q
VBE2 (Volts)
Base emitter junction voltage at Cutoff
of Q2
VG1 (Volts)
Base emitter junction voltage at Cutin
of Qi
VG2 (Volts)
Taul (nsec)
Base emitter junction voltage at Cutin
of Q2
Base diffusion time constant of Q1
Tau2 (nsec)
Base diffusion time constant of '2
TAUB1 (nsec)
Base recombination time constant of Q
TAUB2 (nsec)
Base recombination time constant of Q2
ERR
% tolerance on resistors
ERV)
% tolerance
on supply voltage VS
SYSTEM VARIABLES
BETAT
Typical
VF1 (Volts)
Voltage on base of Q2 at firing (VF
used by system)
VH1 (Volts)
Voltage on base of Q2 at holding (VH
used by system)
DELTA
Normalized Parameter
ALPHA
Normalized Parameter
SIGMA
Normalized Parameter
Q
Beta quotient
ETA
Allowable variation in Vf as hfe of
Q changes from max to (min
XIEF (mA)
Emitter current at firing
XIEH (mA)
Emitter current at holding
XIE
Change in emitter current
Zs
Transient normalized parameter
Z
Transient normalized parameter
Zi
Transient normalized parameter
G2-
v
OUTPUT VARIABEES
RN (ksLY
Absolute value of Negative resistance
of Schmitt
GMAX
Maximum incremental D.C. loop gain
PF (mW)
Power dissipated at firing
PH (mW)
Power dissipated at holdingri.r
PS (mW)
Power dissipated at saturation
VFA (Volts)
Actual Vf after resistance standardized
VHA (Voh)i)
Actual Vh after resistances standardized
XI1
Collector current of Q2 at which D.C.
open loop gain just becomes greater than
one
(mA)
X12 (mA)
Collector current of Q at which D.C.
open loop gain just begomes less than
one
VFNAX (Volts)
Maximum possible Vf for extreme,.
ance on circuit variables
VFMIN (Volts)
Minimum possible Vf for extreme tolerance on circuit variables
VHMAX ( Volts)
Maximum possible Vh for extreme tolerances on circuit variables
VHMIN (Volts)
Minimum possible Vh for extreme tolerances on circuit variables
UNKNOWS
RE (k Rt)
Emitter resistance
toler-
RX (k -n-)
Collector retistance of Q1
Collector of Q to base of Q
RB (kL)
Base (of Q 2 ) to Ground
RO (k.S)
Output resistance - Collector re-
RC (k SL)
resistance
sistance of Q2
Input transistor current Matrixcollector current of Q as a function
of time
XII (JC)
)
XIO (J
(mA)
Output transistor current Matrix - Col-
lector current of Q2 as a function of
time
T ( J ) (nsec)
Time matrix
-
times at which XII and
XIO are calculated
-1-
PART 1
CHAPTER I
INTRODUCTION
1.1
MULTIVIBRATORS
Multivibrators .are two stage amplifiers in which the
output of the second stage supplies regenerative feed1
The circuit,
back to the input of the first amplifier.
with resistive and reactive elements connecting the amplifier
stages, possesses a number of active and passive states,
between which switching behaviour is possible.
An alternate approach to analyzing the circuit~s operation is to regard it as a two terminal device with a
non-linear V-I characteristics in which there is always a
negative resistance (active) region bounded bygresistance
(passive)
regions.
Using transistors as the amplifier device, there are
four possible configurations in which transistors can be
connected in regenerative feedback.
They are shown in Figs.
1 through 4 together with the resistive circuit representative
of each class.
1.
The V-I characteristics at the terminals
See Reference (1)
-2-
CLASSES OF MJLTIVIBRATORS
CLASS A
CLASS B
Identical pair
Identical pair
C - b,
c -b,
-b
e- e
CLASS C
CLASS D
Complementary pair
Compldmentary pair
SC - b ,
c - b
c-b
,
e - e
-3--
SA'
LES -JORDAN Ckt.
( CLASS A
)
E
A
T
AALEL SCHMITT
Ckt.A( CLASS B
)
A'
A-
SERIEA S CHMIT T
Ckt. ( CLASS C)
A'c
-4-
AA' are either single valued in current (current controlled
devices, Fig. 5) or are single valued in voltage (voltage
controlled devices, Fig. 6).
The object of this thesis is to develop a general method
of analysis for these multivibrators by considering the
Parallel Schmitt circuit of class B as a typical example.
A procedure involving first the static and then the dynamic
design and finally optimization of important circuit functions
is developed and mechanized on the digital computer.
The
two complementary approaches of regarding the multivibrator
as two active devices connected in regenerative feedback
('active device approach') and as a device with a negative
resistance V-I characteristic ('V-I characteristics approach')
is presented and reconciled at each point.
In general, the
former method is employed in the transient analysis of
Part II and the latter is mainly used in the static analysis
of Part I.
1.2
A SUMMARY OF EACH CHAPTER
Part I contains the full static design of the Parallel
Schmitt circuit.
The details of the circuit are presented
in the last section of Chapter I.
In Chapter II four con-
straints for the static design are introduced with the
reasons for their choice.
The unknowns are related to
these constraints by analytic expressions, and finally, a
step by step procedure is presented for their complete
-5-
i'D
N ec~c~1\v~ Re
I
CURRENT CONTROLLED DEVICE
~c~ciVive
i
/
1~
t
U-
I
V
VOLTAGE CONTROLLED DEVICE
c,~wce~
toS c~ve
-6-
solution.
Chapter III treats the Parallel Schmitt circuit
simply as a device with the V-I characteristics of Fig. 7
and considers the behaviour of the circuit under different
The second section presents the
biasing conditions.
different ways in which the "V-I characteristics approach"
and the "active devices approach" account for the 'inertial
of the circuit.
In Chapter IV, the expression for the loop
gain is derived and some of its properties discussed.
Chapter
V presents analytic expressions for the power consumption
and states the conditions and a proof for minimum power
consumption.
Part II deals with the transient response of the circuit.
Chapter VI starts off with a summary of the Charge
Control Theory, presenting the basic charge relationships
used in the analysis.
With this model, a set of non-linear
simultaneous differential equations, with coefficients which
vary with the collector current levels in the transistors,
is found to describe the transient behaviour.
In thefext
setion, an approximate linear solution to these equations
-the
is obtained using boundary conditions derived from eee4
ck't t=0
roi~~ ~cavo Wnus cre~
n lop
cf"n tin 4halto iV. Finally, the accuracy
of the prediction for the rise time is correlated with
empirical results.
Chapter VII introduces a speed up
capacitor and analyses its effects on the rise time.
In Part III, computer programs are written for the
static and transient methods developed in the previous
-7..
0)
\.; ,%
:lj4
N
,
)
31L Ci,
V-I CHARACTERISTICS OF THE PARALLEL SCHMITT CIRCUIT
xI.
duc
1V
0A, ie1c.)o
Ac
e-
chapters and in addition, the computer is used to optimize
useful functions of the system.
Chapter VIII contains the
organization of the static design program and describes its
three subroutines, STAND, for standardizing resistance values,
VLMIT, for calculating the limits on VF and V
and GAIN, for
calculating the collector currents at which thegain exceeds
one.
The transient design program is presented in Chapter IX,
where numerical methods are used to solve exactly the set of
non-linear differential equations derived in Chapter VI.
Using these programs, Chapter X develops an overall system for
minimizing the power or the hysteresis subject to a set of
static requirements and a minimum rise time.
Finally, the
conclusion is presented in Chapter XI.
1.3
THE PARALLEL SCHMITT CIRCUIT
The Parallel Schmitt circuit (Fig. 8) is represen-
tative of the multivibrators of Class B.
Since its in-
vention by O.H. Schmitt in 1938,2 it has gained widespread
use in many pulse circuit design applications.
its V-I characteristics of Fig. 7,3
As shown in
the Parallel Schmitt
circuit has four clearly defined regions.
There are three
positive resistance regions where Q1 or-Q 2 * is either active
2.
See Reference (2)
3.
See Reference (3)
-9-
Vs
SOutf't
66
1E
'F %
C Q V- c.
THE PARALLEL SCHMITT CIRCUIT
-10-
or saturated and an active negative resistance region where
are in the active state.
and Q
both Q
1
The usual opera-
2
tion of the circuit is confined to regions I, II, and III.
An alternative mode of operation with V-I characteristics
shown in Fig. 9,
contains a region in which the second
transistor is s&turated.
It is rarely used and so only
the first mode of operation shown in Fig. 7 is considered
in this paper.
It may be appropriate to note here that whenever
experimental verification is done in the paper, the
transistors used are Fairchild 2N70P npn silicon transistors. Their complete characteristics are shown in
Appendix I.
-11-
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u ~o.i)
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LL0 )S
IF
9
re
AN ALTERNATIVE MODE OF OPERATION
o V\Q, I
G(% --
-I
11 1
CQgto
C~v~
Qz
6kc
~C~Xve..
-12-
CHAPTER II
STATIC ANALYSIS
2.1
BREAKPOINT ANALYSIS OF THE PARALLEL SCHMITT CIRCUIT
Based on a plot of the input V-I characteristics of
the Parallel Schmitt circuit (see Fig. 7), breakpoint
analyses can be done at the holding and firing voltages,
A simple transistor model,
VH and VF.
(see Fig. 10)
which includes only the current gain characteristic
(1 c is used.
IB
) and a base-emitter junction voltage drop,
The junction voltage is assumed to be that of a
typical diode, varying exponentially with collector current
as shown in Fig. 11.
VG denotes the base-emitter junction
voltage drop at Cutin, where the transistor is on the
denotes the junction voltage
BE
well into the active region. In the examples chosen in this
threshold of conduction and V
paper, the Cutin current (IG) is approximately 0.125 ma.
and the active region current (IA) is 10 ma. with a deviation of not more t~hn .02 volts along the whole range of
current as shown in Graph I.
Because of the steepness of
the slopes of these curves, these two values are used for
VG and VBE throughoutregardless of the collector current
level.
The variation of D.C. current gain, A, with collector
current for 2N708's is shown in Graph II. (Compare
Fairchild 2N708 Specifications, Appendix 1).
with
-13-
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10
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BASE-EMITTER JUNCTION CHARATERISTICS
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2111 EXPRESSIONS FOR VF
.I
At the firing point, F , Q
is on the threshold of
conduction with a junction voltage of VG and negligible
collector current flow, IG; Q2 is active with VBE and IEF
(See Fig. 12). Using the equivalent circuit of Fig. 13
the following expressions are derived.
VF'- VF -VG -+VBEzZ)
=VS +VJ E 2 (
VF
+.x)
Rc
Ae
(g)
C-Yg
1E
R8~
Where VBE2 and
(I?
+/
are the values of these variables at the
operating colleqtor current level, IEF.
The analysis is
done in terms of VF the voltage at the base of Q2, after it
has been transformed from the input firing voltage, VFV
because of its convenience.
2.11
ANALYTIC EXPRESSION FOR VH
Similartly, at the holding point, H, by assuming Q
is active and Q2 is at cutin, the following expressions are
found (See Fig. 14 and 15).
terms of VH
Again the analysis is done in
the voltage at the base of Q2 at holding.
VH' ZVH - VBI +VGZ
'=V
z4
+ ( c/E )
Rec+ r'x+Re + RC(4
Rs
R
~
3
-17-
a
1
7.
*1~
V&l
VfI
a
PARALLEL SCHMITT CIRCUIT AT FIRING
1131
-f
VFVsr1
go VF
V k 0 a v, e.
EQUIVALENT CIRCUIT AT FIRING
I
+
44
VGa
VBE,
Ro
iz E
I.
PARALLEL SCHMITT CICUIT AT HOLDING
ai cu~
z
zc_
1441
xI4
VBE,
I
Ft c Q r e 1137
EQUIVALENT CIRCUIT AT HOLDING
VHA
-19-
The Input terminal current at holding,IH, is given by
(4,+)4)
.1
THE ALLOWABLE ERROR IN FIRING VOLTAGE FOR MAXIMUM
2.2
VARIATIONS IN TRANSISTOR CURRENT GAINS
Detailed examination of the Schmitt circuit (Fig. 8)
shows that. R 0 is completely decoupled (except that Q2 cannot
be saturated)from the rest of the network and is simply
determined by the desired output voltage swing.
expression for RO is given in Section 2.4
The exact
Hence there are
only four unknowns RE, RC, RX and RB involved in the circuit.
By specifying the nominal firing and holding voltages and
through the use of Equations (2) and (4), two constraints are
specified.
The two additional constraints required to solve
for the four unknowns are given by
, the error in VF for
maximum variations in the transistor current'gain of Q2 and
IEF
,
the emitter current at the firing point.
It should be made clear at this point that the choice of
constraints is completely arbitrary.
The above constraints
were selected because they were felt to be the ones most
useful to the designer and because thoy ;crz folt te bo the
91qcs mest k~ef-lto
easily specified.
7h
to e s ' gg r ant b c Ethey can be
As it turns out,
this choice proves to
-20-
be very suitable for the optimization in Part III.
variation in
is defined as the allowable percentage
VF as the D.C. current gain of Q2 varies from 6"/1Y7Ito
/My.
It is obtained by taking the partial derivative of V
with respect toPin Equation (2) and setting VBE to zero.
-
Re-R
In principle a method of partial derivatives is not
valid for finding I because there are as much as 400%
changes in
.
1
should really be found by considering
the differences between VF at,/nAxand at/>"v.
However,
in practize, the difference between the two methods is so
small as* to make the simplicity of taking partial derivatives
desirable.-' A comparison of the two methods and the errors
involved in choosing the derivative is shown in Appendix 2.
* This method yields an n'
_E__.U_=
as follows
/)'eex
-21-
Furthermore, the1 in Equation (5) is defined in terms of
a typical Ot which is
-fl7na and
the geometric mean of
'1flAx.
Graph II shows that for any reasonable value of collector
current (:
than 25%.
to
Ze7//'n4) #zL-E
vO-
t' with a variation of no more
Henceforth, for simplicity, all
Se
will be equal
- regardless of collector current level.
The two limits onq are also derived by imposing the
and RC be non-negative.
condition that R
VIC-
I-Viv~
2.3
THE FOURTH CONSTRAINT:
(7)
THE EMITTER CURRENT AT FIRING
The set of necessary constraints is completed by assuming
a certain value of IEF' the current in the emitter branch
(RE branch) at the firing point.
7yc
_
_-_V
___V'
__..
( 9)
e
The selection of IEF is governed by four conditions.
First,
the transistors must be operating in a region of appreciable
current gain (
=40 or more), which means thd, typically,IEF
has to be greater than a milliamp.
Second, the size of IEF
-22-
determines the current available at the collector of Q2 and
hence the load that can be connected to that point.
Third,
the power consummed in the circuit is inversely proportional
to IF
EF
This property is treated in greater detail in Part III.
a.VL S.3)
in which IEF is adjusted for a minimum power optimization.
Finally, as will be apparent in the transient analysis of
Part II, the cutoff frequency, fT, decreases with collector
current. (See Graph V)
Thus a low current level, IEF, will
slow the response of the circuit.
2.4
OUTPUT REQUIREMENTS
The Parallel Schmitt circuit is commonly used to drive
a device e.g. a diode gate, which draws current only when the
ciruit is in one state.
The two possible situations are
illustrated in Fig. 16 and 17.
They show in Case 1, a load
which draws a current, IL, when the output is high (circuit
in state (10) and in Case 2 one which delivers a current, IL'
when the output is low (circuit in state (01) ).
Thus the
output voltage at the collector of Q2 varies from VS to
V0 for holding and firing respectively where V0 is the
minimum output voltage.
In the following discussion, Case 2
is chosen for the output load condition.
The output resistance is given by
2:,CF -g
in order not to saturate
Q2,
Z.<
-
v
-23-
tL
u tomae4
-&
'*Fl uve. t C
C 0, sr I ) 0 Q A-V \Jt
L 0 Ck C
'4-
P\O
-
OF
kjvej(2 11
vooaeck
-24-
The minimum value for IEF
2.5
is given by
SOLUTION FOR UNKNOWNS
With the four Equations (2),
(4), (5), and (8), a unique
set of values for the unknowns RE , RC
found.
,
RX
and RB
can be
To facilitate calculations a set of normalized
parameters is introduced:
eE(qf
No physical significance can be attached to
S
but c,. is
the inverse of the value of the resistive divider ratio on the
is the unloaded voltage gain of Q2
'
base of Q2 and
The static design procedure is as follows:
Pick the desired values of VF' VH and V
ii)
Find the value of the circuit constants
.
i)
44/A
VG and VBE from data sheets (See Appendix 1)
or by actual measurement.
Pick the value of IEH governed by the considerations in Section 2.3
iv)
Find the limits on '
,
iii)
by Equations (6), and (7).
Et.
-25-
v)
vi)
Pick the desired value ofaIbetween these limits.
Determine the value of VO and IL as dictated by
the output requirements.
vii)
Calculate the required output resistance by:
.74F - IL.
checking to see that Q2 is not saturated
(Equation 11).
Solve for the normalized parameters,
V4's - V91 ZI
4
-'.-..
VA'f-
(
viii)
e
-26-
Solve for unknowns.
x)
V
tee
4
-- VSE,
= te
/9
(782
(z.,')
The above is an outline of a procedure for the sequential solution of the resistance unknowns, .At no point is a
simultaneous solution necessary if the unknowns are calculated in this order.
An approximate set of equations
which neglects the effects of base emitter junction voltage
drops are given in Appendix 3.
While they are quite in-
accurate, their great simplicity makes them useful in
applications where only rough solutions are required.
-27-
CHAPTER III
THE TERMINAL V-I CHARACTERISTICS
3.1
THE DIFFERENT MODES OF OPERATION
The Schmitt circuit can be considered simply as a
device with the V-I characteristics shown in Fig. 18.
Boundary conditions,
imposed in the form of a source voltage
and a source resistance connected at the input terminals,
appear as a load line on the V-I characteristics curve
(Fig. 18, 19). The most important factor which affects the
operation of the circuit is whether the magnitude of the
source resistance is greater or smaller than the magnitude
of the negative resistance of the device., From expressions
for VF, VH and IH the absolute value of the negative resistance is found
feN
to be,
(-f
&e
(%
The three possible modes.-of operation are considered below.
The first is the astable mode with the value of the
RS greater than the value of the negative resistance (RS >RNI)
the load line intersecting the V-I characteristic at only
one point in the (11) region. With purely resistive elements
connected across its terminals, the circuit is stable
in this condition. However,any energy storage elements,
whether they are introduced purposely or as a result of
-28-
rt
)I
)I
604)
k1l Astable operation
(2) Bistable Operation
(3) Monostable Operation
L-
I
-29-
strays, appearing in the form of
parallel capacitance
across the terminalsAwill cause the circuit to oscillate.
It is the potential for this behavior which allows this
mode of operation to be called astable.
The circuit 'free
runs' with its own characteristic frequency through the limit
cycle F-F 1 -H-H1
(shown in Fig. 18) Generating what is known
as relaxation oscillations at it terminals.
The second is the bistable mode with Rs less than the
absolute value of the negative resistance (Rs <IRD. 'The load
line intersects the V-I characteris ic at three points, two of
which are unstable with a stable point in the middle.
This
mode is characterized by a switching behaviour between the two
stable states even in the absence of any energy storage.
The
Circuit changes state- whenever the input voltage increases
to the firing or decreases to the holding voltages regardless of the input wave shape.
The third way ;is the monostable mode which is equivalent to the bistable mode ( Rs.<N
except that the load
line intersects the V-I characteristics at only one stable
point.
With a R-C timing circuit at its input terminals, the
circuit can be made to traverse a full limit cycle and return
to its single point of equilibrium.
Every input pulse regard-
less of shape produces an output pulse of constant shape and
duration
3.2
as preset by the circuit and the R-C time constant.
WAVEFORMS OF NON-ZERO RISE TIME
For any given device, with V-I char,3cteristics as
-30-
shown in Fig. 18, biased in ;the bistable mode, the circuit
switches instantaneously between the two stable states.
In an ideal circuit where no reactive elements are present,
the terminal variables can change instantaneously.
However,
in reality, each transition from F to F1 and from H to H1
has associated with it a finite rise time, which is accounted
for by postulating some energy storage.
This can be done in
two ways.
3.21
ANALYSIS WITH A LUMPED REACTANCE OUTSIDE THE DEVICE
In a device such as the Parallel Schmitt circuit, this
"inertia" can be introduced in the form of a series inductance at the input terminals
4
(Note: in a device with a
voltage controlled V-I characteristic, it can be done by
introducing a parallel capacitance).
The method assumes
that during transistions, the circuit actually follows the
V-I characteristic in the negative resistance region.
The
discrepancy between the voltage on the load line and the
device terminal voltage, is taken up by the energy storage
element.
Based on this assumption, one can arrive at a
prediction for the rise time.5
4.
See Refernce (4)
5.
See Reference (5)
However, the main disadvantage
-31-
of this approach is that the value of this lumped series inductance reflects the inertia of the device as well as the
stray reactances in the contacts and the leads.
In the
absence of any theoretical basis for picking the value of
this energy storage, an appropriate value is usually chosen
from experience or by trial and error.
3.22
ANALYSIS OF THE DEVICE AS A REGERNERATIVE FEEDBACK
AMPLIFIER
This second method treats the device as a regernative
feedback network containing.,two blements, the transistors.
The "inertia" of the device is manifested in the diffusion
and recombination time consants in the base of these
transistors.
Hence, by assuming a 'Charge Control model'
for the transistors, the rise time is found in terms of
physically measurable parameters of the circuit.
While the first method is by far the/simpler, its
difficulty lies in the fact that it trIds to pick a
reactance which will give the correct rise time without
first knowing that rise time.
The accuracy of the solntion
is entirely dependent on the value of this energy storage
element.
The second method has the advantage of being
based on physically measurabIe quantities.
However, the
analysis, even in its simplest form is formidable and at
points relies heavily on a numerical solution on the
-32-
computer.
The latter method is chosen for Part II of this
project.
3.3
THE HYSTERESIS
Assuming again that the circuit is biased in the
bistable mode, a phenomenon is observed, as
the
circuit
is switched from one state to the other by changing
Vg.
(Fig. 19)
UsingEFigi 18, consider a case in which the
circuit starts off in (01), it switches to (10) as V
reaches VF and continues along the load line in the (10)
state for increasing V-.
However, as Vi is decreased,
it is found that the circuit no longer triggers, i.e.
changes state, at VF, but is returned to the (01) state
only when VH is reached.
If the output waveform at the
collector of Q2 ( See Fig. 7) is plotted for a sine wave
input, the above phenomenon is immediately apparent, (see
Fig. 20).
This difference between the trigger voltages
for the positive and negative going transitions is known
as the hysteresis, H , of the circuit.
From the V-I
characteristic curve it is equal to VF - VH.
It should be made clear that a hysteresis is inherent
in any device with a negative resistance region.
In fact,
the value of the negative resistance is directly proportional to the hysteresis as. shown in Equation (22).
In
some applications in which a distinct trigger level is
-33-
-
VF
-
N
a'
I
I'
I
I
I
I
I
I
Il
-'_
__
i/f
1-
I vlll, j
I
I
I
of.
01
I.
61I
Z7A'PcT
4ki4'
6C77/cJ1-rf1
.s 24r4 6~ee
V.H
-34-
required for both the upward and downward transitions, it
may be desirable to minimize the hysteresis.
However, as
will be seen in the following chapters, the switching
speed is faster for a larger value of hysteresis and so,
a choice must be made to decide between a fast transient
response or a smaIl hysteresis.
In any case the hysteresis
is both an important static characteristic and a measure of
the dynamic behaviour of the circuit.
-35-
CHAPTER IV
LOOP GAIN :ANALYSIS
4.1
DERIVATION OF THE LOOP GAIN
The transistor model used to derive the incremental
D.C. loop gain is shown in Fig. 21. The effects of the
which is inversely proportional to
base resistanceW
the collector current, is included because it can vary
from 0.1 to 10
-ohms over a range of IC from 10 to 0.1
ma. The frequency dependence of
p
is not accounted for
and so the expressions derived are only valid for D.C.
conditions. Substituting the model into the circuit of
Fig. 7 (see also Fig. 22), and conveniently opening the
loop at the collector of Q, (no equivalent loading is
necessary as the resistance of the collector current
source of Q, appears to be infinite) the equivalent
circuit shown in Fig. 23 results.
into the node where the
Introducing the current I
loop is opened4i the gain is given by,
e9-
_
Assuming that /7f/
_
_
_
_
_
and that /'6
_
_
77
_
_
_
_
_
_
_
_
-36-
f~B
p
tAA*
r
go
C.
I'
0
E
TRANSISTOR MODEL USED IN LOOP GAIN ANALYSIS
(fl*~
~ ~ow% 'zC-
silo
Y.~
16
t~
a
P.
j
THE EQUIVALENT CIRCUIT FOR LOOP GIAN ANALYSIS
( LOOP OPENED AT COLLECTOR OF QZ
)
Li.
L
-37-
L
mxtl-Isr
1.
~J'c.
p
I
I
liz
~~2;i e3
I
*
kE
EQUIVALENT CIRCUIT FOR CALCULATING THE GAIN
-38-
R~X
where the
and
4c 7P ,
r4lf
I)e
are dependent on the total collector
current levels IC, and IC2 of the circuit.
4.2
PROPERTIES OF THE LOOP GAIN
The D.C. loop gain of the circuit is intimately
related to the transient performance. Although the
exact relation can be found by putting the frequency
dependence of
into the model for the transistors, it
is not done because a more direct approach can be used
(see Part III). The exact relationship can be determined
by empirical methods, if desired, but, in any case, one
can be certain that a circuit with a higher loop gain
provides a faster rise time. In fact, the circuit is not
regenerative and will not show switching behaviour if
the gain is at no point greater than one. Hence the
loop gain provides a figure of merit, for transient
performance, from purely static considerations. Also, the
gain expression is important in calculating the range
of collector current over which the gain exceeds one.
The collector current I,, at which the gain just exceeds
one indicates the point where the circuit is going into
the adtive region (11). It corresponds to the current,
IG at cutin, where the transistor is on the threshold of
conduction in the D.C. sense or just beginning to
switch regeneratively in the transient sense.
By assuming the following relationships, the gain
as a function of IC2, the collector current of Q2 is
II
-C.=
F
le.-+
The exact dependence of
but for most purposes
et
(
obtained.
(--7,)
on IC is given in Graph II,
can be assumed to be equal to
a constant. Relation (27) implies that RE is large enough
so that the emitter branch is assumed to be a current
source. Setting R
= 0 and substituting in Equation (24),
which is the maximum gain at each collector current level.
It can be seen from Equation (24) that any positive value
of Rs will tend to decrease the gain.
-40-
A plot of loop gain versus IC2 is shown in Graph
III for some typical examples. It is observed that increasing hysteresis implies higher gain and larger
ranges of collector current for which the circuit is
in the active state.
___
-
~
-
___
-
___-----------
-
--
124
r
0
S
7
T
+r
CeA\ec* 4 !~,-
a~e?~
-42-
4.3.
RELATIONSHIP OF LOOP GAIN TO OTHER CIRCUIT FUNCTIONS
To show that the loop gain is consistent with the
other static circuit functions, conditions for a regenerative circuit are rederived using that expression.
The
upper limit on RS for the circuit to be regenerative from
the"V-I characteristic Approach" in Chapter III, is given
by Equation (22).
Setting the loop gain greater than one in Equatidnh (24)
results in the same expression.
(The slight discrepancy between Equations (22) and (29)
is because some terms were neglected in the gain expressA
ionbut since
can be disregarded.)
in typical circuits the difference
Applying this result to the discussion
in Chapter III, the gain is found to be greater than one
for circuits biased in the bistabl6 or monostable mode
and less than one for those in the astable mode.
Furthermore, for the circuitto be regenerative the
hysteresis must be greater than zero.
Setting the junction voltages to zero in Equations (2)
and (4) and using the above condition,
Z> ex
(p1)3
Again an identical constraint is obtained by setting all
base resistance to zero and the gain equal to br greater
than one in Equation (23).
(3z)
Hence it can be seen that conditions for a regenerative
circuit derived from the expression for the loop gain is
completely consistent with those derived from the "V-I
Characteristics Approach" and the hysteresis.
Further-
more, the above shows that when the circuit is regenerative
in the bistable and monostable modes, it's loop gain is
greater than one and when it is non-regeneratile-lin,
astable mode, it's loop gain is less than one.
the
-44-
CHAPTER V
POWER CONSUMPTION
5.1
ANALYTIC EXPRESSIONS FOR THE POWER AT THE BREAKPOINTS
From a consideration of the equivalent circuits at
the break points F and G of fitgures 12 and 14 and neglecting all voltages, the following analytic expressions
for the power consumption at firing, PF
,
at holding PH
PCe
-
+
are obtained.
2(x'*'
)~
(3)
Using the equivalent circuit as shown in Fig. 25 at
saturation, S
,
can be derived.
(defined in Fig. 7) the power at saturation,
-45-
EQUIVALENT CIRCUIT AT SATURATION
-46-
5.2
POWER DISSIPATION IN THE CIRCUIT
For a typical case in the bistable mode of operation
the load line sweeps out a limit cycle as marked in Fig. 25.
The power dissipated in the (01) region is
given by PF
However, PH provides only the minimum and PS the maximum
power consumped in the (10) state.
The power distipated in
the active region (11), is negligible because of the
comparatively short times spent in that region.
circuit is given by a linear combination PF
,
PH
and P
,
Hence, the total power consumed in the
order of 50 ns.)
the values of al
(of the
a 2 and a3 being determined by the driving
function (e.g. duty cycle of a pulsed input.)
5.3
MINIMUM POWER CONDITIONS
Careful observation of Equations (33) and (34) shows
that the PF and PH can each be separated into two components.
Considering Fig. 26, the power at firing can be
rewritten:
_
'
'8&
(( :?7
)
46
-47-
p
LooAd Vt~e
--. ow1.
A
a
Li
'4.a
I
Limit cycle
H
: 0
-
F - F
S - F1 -H -H1 - 0
I
I
+
LIMIT CYCLE FOR BISTABLE MODE OF OPERATION
DEVICE
Vs
p()
PC,6)
tE
THE TWO COMPONENTS OF POWER FLOW IN THE PARALLEL SCHMITT
CIRCUIT
-48-
Therefore, to minimize each component of PF
the values
,
of the resistances RE and RB must be at a maximum.
From
Equation (18),
Picking a maximum value of RE corresponds to a minimum value
Alsofrom Equation (5), a partial derivative of/It
of IEF.
with respect to RB is taken,
+
d ie (c
(A'c,'L'x)
The fact that it is always positive implies that a maximum
RB corresponds to a maximum q
.
The arguments are entirely
Hence, a minimum power consumption at.
analagous for P
holding and at firing results for a minimum IEF and maximum
.
Finally, considering PS as a function of RB
and
and R
is also minimized for maximum R
E2
B
S
_
'
show that P
_
_
_
[
~
Ae
_
_
_
_
X~6
?'~J
~
VL (
[~~74 Aup
-
.
RE in Equation (35), partial derivatives are obtained which
7
-49-
Thus, to minimized each component PF f H and P
and hence
the total power consumption, IEF must be a minimim and 4 a
maximum.
The implications of making IEF small, but within the
limits set by Equations (Ii) and (10), is that the current
gain
small.
of Q, and Q2 drop off as the currents become too
It will be seen in Part 3 that this lowers the
value of the cutoff frequency, fT and hence slows the rise
time. The effect of increasing t
in VF caused by variations in
is to increase the error
of
and so, in this case
there is a tradeoff between the accuracy of VF and the power
consumption.
-50-
PART II
CHAPTER VI
TRANSIENT ANALYSIS
6.1
THE CHARGE CONTROL THEORY
Observing the one-to-one correspondence- between the
dperating state, as given by the terminal currents, and
the interqal charge distributions in a transistor, Beaufoy
and Sparks proposed, in 1957, 6,7
as a charge-control device.
to study the transistor
The dynamic behaviour of a
transistor can be conveniently explained in terms of the
transient charges in the minority carrier distributions
in the base.
Based on the following assumptions:
I)
uniform base region-disregarding the
properties of the space chwt e layer,
ii)
iii)
iv)
v)
Low-level injection in the base
a one dimensional model
lifetimes in the emitter and collector regions
negligible as compared to those in the base
because of high impurity concentrations,
recombination takes place in the base only,
6.
See Reference (6)
7.
See Reference
(7)
-
-51
and considering only forward injection, the following charge
relations are derived:
Tg
where
dt
1B = Base current
I
C
= Collector current
Q, = stored base charge
= Recombination time constant in the base
= Diffusion time constant in the base
The first term in Equation (42) models the component
of base current necessary to replenish minority carriers
lost by recombination in the base.
The second reflects
any transient changes in the current levels.
In Equation
t43), the collector current is assummed to be proportional
to the stored base charge.
These two equations form the
basis for the simple charge control model used in the
transient analysis.
6A'11
Relationships with other transistor parameters
Ze~
___(~
-52-
The current gain-bandwidth product 6.;r is given by:
Changes in Time Constants with Collector Currents
6.12
The diffusion and recombination time constants are
directly related to the D.C. current gain
band-width product f
.
From Equation (45).
I
fT and
and the gain
(467
as a function of Collector current is readily
available in most transistor specification sheets (See
Appendix 1) or can easily be measured.
An experimental
can be used
setup for measuring high frequency current gains and
8
The results of both methods
hence fT ( fT = f
of deriving
Z
and Tg
are also included.
Graphs V i
through VII show curves derived from Fairchild 2N708
8.
See Reference (8)
7
gOT
'u-
9.--
7-
6-
4-
3 -
98.
76
4-
3-
7-fi
:44!~f
-
4
----------
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1111
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ti
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tf
i~I]
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rr,~~~L~
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A~'IFF
~~
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ow
4
_oo~
i
TL1
-r
__
_
rf~-
40
-- 444
H~f~j+
ni-tv '-r-rrrr-rrtw
ti-i-Tm- 'ri--rrrrr-'i-rr-ttrnrt
-ii-tt
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r
ri-i-i
ii I'
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t
i--ii-i--tiui-r1--ti-ri- 1
2Ld2iEddThdR2tZ21L2>~
. ..j . . .
,
; .I
-
- - f - I I. f -
T
~44 frjt
4
77
t-t-~a
~~II
If
-- 't-
U
I
I~iI -VI
I
~':
J>:
1- 444-
YTiJ
U -V
!I~
iju7i1t-
I
I
I
J
I h~1,I
;ili
4-~-~
hi
T
f
I
-Ll-
-A
Olt
--
4
t T
nil
+4-
II
+
LI
i
i
i
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--
''~ij~
t'd
4
g'~j
{2;
LAIR
L.Z
~1u
[V L11
~Th
---- J--VL
TI
7
frLJ
IT
cs-%v la
-60-
Specification sheets (Appendix I).
Graphs VIII through XI
are derived by actual measurement with the above method.
Alternatively r
andN
can be measured directly
9
by methods well covered in the literature.
6.2
DERIVATION OF A SET OF SIMULTANEOUS DIFFERENTIAL
EQUAT IONS
Substituting the above model into the Parallel
Schmitt Circuit, the following equivalent circuit results.
(See Fig. 27).
Below is a set of simultaneous differ-
ential equations derived by using Equations (42) and (43)
for both Q
and Q2
29
d
9.
See Reference (9)
W
e4
-
FIGURE 27
EQUIVALENT CIRCUIT FOR TRANSIENT ANALYSIS
c-
-62-
Where:
(4?)
*___R
(') )(53
-r7
The two equations (48) and (49 ) model the tran-
sition process through the active region (11). (See
Fig. 8).
They correspond physically to a case in which
the input voltage is taken up to either VF or VH and
then the regenerative action of the circuit is allowed
to take over to switch the circuit into the other state.
It will be seen that a very small incrementadrive, .s
e-cr noe 4oth auren
cxcodecr~~
ih ,ecry to
a is
~-~tnn i. ),is necessary to accomplish
-63-
this transition.
The difficulty of solution of Equation (48) and (49)
lies in the fact that
conditions.
2.=fk),
77
and
T8
change with operating
yhese functions of the
life times can be derived from plots of fT and
versus IC or can be measured directly.
6.3
THE TWO METHODS OF TRANSIENT ANALYSIS
Most analyses of time varying linear or piecewise
linear systems can be perfoemed in terms of total quantities or incremental quantities which are perturbations
from some fixed operating level. The Parallel Schmitt
circuit is no exception and is amenable to both these
types of analyses if we are to assume that the diffusion
and recombination time constants do not depend on collector current levels. If the non-linear system is
analysed, with these depedences included, then the
total variables approach is found to be more convenient.
6.31
Analysis involving total variables
The transient behaviour can best be described in
terms of total collector current levels ICl and IC2
-64-
of Q, and Q2 . Turning back to Equations (48) and (49),
it is observed that these equations are derived from
Fig. 27 (which has source and input voltages) and hence
involve the total quantities IC1 and IC 2 . These equations,
are characterized by a driving function on the right
hand side, to account for the fact that switching always
occurs at some finite operating level i.e. at VH or VF,
and non-linear coefficients 2a
and 7B which are func-
tions of IC1 and IC2* However, for a linear approximation
7"
and ? 8
are assumed to be constant with current.
A solution of Equations (48) and (49) will yield Icit)
and IC 2 (t), which contain a homogeneous and a particular
solution.
This method, when the full non-linearity of the
and ?-
are accounted for, is particularly adaptable
to numerical integration on the computer, because
2'
and ?'S are given in terms of changes in total currents.
6.32
Analysis involving incremental quantities
The transient solution can also be obtained by
considering the incremental changes in collector current
levels iC 1 and iC2. Again, for a linear solution the
and ?'g
can be assumed to be constant with small
perturbations in total ICIs. If the equations below
-65-
are substituted into Equations (48) and (49),
Ze:
=
a
C(
where Io and I' are E.C. current levels when the circuit is excited by VH and VS, )thefollowing equations
are obtained to describe the transient behaviour, in
terms of incremental quantities,
1
.
Z 7/
It is seen that in the quiescent state the incremental
currents are zero as expected.
linear as it implies that a linearization (of
2
,f
)
The "incremental method" of analysis is inherently
has been performed around the operating points (I0 and
I.').
When the non-linearities are introduced, the
functional dependence of 21 and 2B
on the incremental
-66-
currents iC1 and iC2 can be obtained by transforming the
origin of the coordinates to the operating points. These
methods are at best troublesome and are not preferred to
the "total variables approach" in non-linear analysis.
6.4
BOUNDARY CONDITIONS
The boundary condition in the transient analysis
is 3provided by the constraint that the collector currents
-e.~
wme, ontq6,
have to be continuous across t=O.
For the analysis involving total variables, the
exbitation needed for switching is provided by a change
in VH, defined as A
.
However, notice that the excitation
is applied in the form of a negative change in VHrA.,
rather than an"intuitively obvious" positive excitation.
This is immediately obvious if one considers a case in
)
which the load line sweeps down towards VH (See Fig. 25
At holding, any positive change in VH will drive the
circuit rapidly back into the (10)
state while only
a decrease in VH can accomplish the transition.
Using the consttaint of continuous collector current
at t=O, the currents at t=0- are obtained by solving,
c 1
k
CS I
LeiAK
2.,
k~k
-67LJ-1
and using the continuity condition,
Resubstituting into Equation (48) and (49) with the
excitation -A,
Hence the boundary conditions, the slopes of the collector
current at t=0, are obtained.
In a linear approximation method, which will be
developed fully in Section 6.5, there are well defined
complex frequencies and the currents as functions of time
are in the form of growing and decaying exponentials.
The tetminating condition, for switching from (10)
to the (01) state at VH, is reached when either IC,
or IC 2 becomes i&e-t zero or equal to IEF respectively.
(See Fig. 28). The rise time is given by the time th6A10%
to the time it takes t6 reach the 90% of the final value.
The boundary conditions for the incremental analyses
-68C
II
C
0I
~'o4
I
"F%
\4ckm e\Jrkov
11
A
I.- v eo,
ATV
c62..R
s)
to 4.1 ,,
I
r
kz
NUk
\Q
AppOXA.cC~t
I%~* %~k~L Vh~
e~~A ~
-69-
are exactly the same as those derived for the total quantities, except that the total quantities are replaced
by incremental ones. Using the fact that before and just
after the excitation,-A, is applied at t=0, the
currents iC1 and iC2 are zero, the equivalents of
Equations (58) and (59)
are rederived.
It may be well to point out that the magnitude of
A
in this and the "total variables analysis", is immaterial
as long as it is finite. Although the rise time on the
absolute time scale depends critically on A
of the rise time is independent of A
, the value
if it is taken as
the time difference between the "90% and 10% points".
(See Fig. 30).
Unlike the total variable analysis, a plot of the
incremental currents versus time starts off at the
origin as shown in Fig. 29. One exponential growing in
the positive direction and one going in the negative
direction. The tetminating condition is reached when the
-70-
total incremental change i.e. the sum of iC1
and i C2'
has reached IEF*
The method involving'total quantities are used
throughathe rest of the paper because, in the opinion
of the author, it is conceptually easier and has more
relationship with the J.C. conditions.
6.5
TRANSIENT SOLUTION BY LINEAR APPROXIMATION
The fact that the diffusion and recombination time
constants, 27
and
Z8
, vary with collector current,
introduces non-linearities int Equations (48) and (49).
Their exact solution, which will be completed in Part III,
is only possible by humerical techniques on the digital
computer. When completed, the solution to the output
waveform at the collector of Q2, will show an "S"
shaped curve, in which the rise time is given by the 10%
and 90% points (Fig. 30).
However, for the average
designer who desires only a rough prediction of the
rise time, a linear approximation can be readily performed
by hand.
current and for convenience
For this linear,
to be constant with
and
'b
:
.
The method assums 27 and
time-invariant system, a unique complex
-71-
go
10 I0
IWIJJ
/,-,/~et
;.7~ma-
)~6/2/F1/-6/f
AR
-4
4/Q/ a
6/7?2A/MA.
-72-
frequency, S, can be defined. The associated homogeneous
equations of Equations (48) and (49) are:
A, $1f 4 6.s .,
-L)
C
?061
,A----
[ .5 1
===0
0-46.)
c16[6s?/
-
~7#k
.'iel. ez-fz -; -,L-2
Zez
4
.I
(T3)
The characteristic equation is given by:
-tl -)
[(s
$81
+ -'I
.+-L~
F'65
_.
4 -_1_
.0
..---02
(4)
i
Setting
/- z:5'>
-
S2--.5
-:-
..
ee2-t
-
"7
-0.'
Z-z
J
and letting
(a6)
74
a"7)
/--
24z
-73-
the result is
-.4A*#
~Zo
6.6
Zti-
STABILITY OF THE TRANSIENT SYSTEN
The homogeneous solution to the transient system
assuies the form,
z
<f I 0(
where S+ and S
X= C:f Ie
0
> It
,L&z
are given by the solution to Equation (68)
The transient behaviour of the system is entirely
dependent on the values of S+ and S_. An imaginary part
of S+ andthus S_ also (complex conjugates),will result
in an oscillat6ry type of behaviour, while the sign
of the real part will determine whether the solution is
a decaying or a growing exponential.
6.61
Conditions for imaginary roots
Writing equation (65) in a simpler form:
07
5 24(=h
_
/
where
)
(75
Assuming that there are imaginary roots the following
inequality must be true,
This results in the condition
(737)
,42<"Xq
and by substitution for A and B,
The normalized parameters
c4 ,
,
,and (T~--
(7a)
e,
-75-
all positive numbers, as given in Equations (12),(13),
(14) and (50). Hence the above equation
shows a contra-
diction and Equation (68) can only contain real roots.
6.62
Condition,
for two positive roots
The condition for both roots to be real and positive
is given by
(77)
(70)
By substitution and extensive manipulation, condition (77)
yields,
(17,q)
)
4s
_r
and condition (78) yields
(69)
(c>< *')
It is obvious that Equation (79) and (80) cannot
be satisfied simultaneously and so the case of two real
positive roots is also impossible.
-76-
6.63
Condition for one positive and one negative root
The condition for one positive root is supplied by,
S-< 0
(78)
This condition implies the opposite of Equation(80),
2s
<
f
&
(C-')
(0 /)
which can physically be imposed on the circuit.
6,64
Condition for two negative roots
Two negative roots require that
I :, 0
a >--(z)
(78)
which results in the conditions , respectively,
( g /.,)
e~
-_______
It may be noticed that Equation (83)
is automatically
-77-
satisfied if EQuation (81) is satisfied because the right
hand side of the latter dominates the right hand side
of the former.
The above analysis >shows that there are only two
possible cases for the solution to Equation (68).
The first is shown in Fig. 30%)in which one root is
positive (S+) and one root is negative (S-). The condition
for this mode of operation is given by Equation (81).
Considering ag&in Section 4.3 it is observed that the
bistable mode of operation, with loop gain greater than
one and source resistance smaller than the magnitude
of the negative resistance, corresponds exactly to the
case of one positive and one negative pole in the transient analysis. The condition for this mode of operation,
Equation (22) is rederived in Equation (81),
The second case of two poles in the left half plane
(See Fig. 30 )is given by Equation (79). Also, from
Section 4.3 it can be seen that this describes the
astble mode of operation with loop gain less than one and
non-regenerative behaviour.
-78-
L)to
I-
I'
X1(5:-
: ;ao)
A POLE ZERO PLOT OF A
REGENERATIVE CIRCUIT WITH ONE POLE
IN THE RIGHT HALF PLANE
4~
)
F7145; qo cj
A POLE ZERO PLOT OF9A
NON-REGENERATIVE CIRCUIT WITH BOTH POLES
IN THE LEFT HALF PLANE
-79-
6.7
CALCULATION OF RISE TIMES AND EXPERIMENTAL VERIFICATION
Using the method developed in the previous section
the following procedure can be used to find ]he rise time
of a given circuit:
and then
,
,and ,
L
,
,
,
1) Find the &ormalized parameters
S
2) Calculate the roots S+ and S_ by solving Equation (68)
3) Find the particular solutions IC1(0) and
1
C2(O)
by equation (54) and (55).
4) Find the boudary conditions( and
using
Equation (58) and (59).
5) The solution is of the form
Resubstitute IC1(t) and IC2(t) into Equations (48)
and (49) to find C3 and C4
6) Use the bourdary
conditions of step (4) to solve for
.
the unknowns C1 and
C2
In Equations (69) 4nd (70) there is, in each of them,
a term with a positive exponent and one with a negative
-80-
and C are of the same order of
1
C2
.L
S
magnitude, the ratio of these two terms is equal to
exponent.Assuming that C
For practical examples (e.g. S +=0.1,
S =2,
t=50), the
terms with the positve exponent is found to be very much
greater than the other (e.g.
k0::"\'
00")
and hence the
negative exponential term is neglected. The collector
current is then given by,
QrI 0 0')
- - I t (_0
)
Tc t ct) = C-\ el
Considering Fig. 20, which illustrates how the rise
time is measured, the time for the waveform to reach the
90% point is given by (noVe C
is always negative)
-1
tCo
(3
~
2-- 6
)
and the time to reach the 10% point is given by,
hence,
-t (-Ci
Q~c))
Thus, if the rise time is taken to be the time between the
90% and the 10% points, then.
it is completely independent
-81-
of the
constants of the circuit and is given by Equation
(93c).
The rise times for the numerical examples shown
in Table I were actually measured in the Laboratory.
g%= 4ri '1nt
TI;:
p to 4 -G;5:r in 16 rph-4-4 XII E. Using
Example #1 as a point of comparison,
the following ob-
servations are made:
1) A larger hysteresis results in a faster rise time
(#2 and #3)
2) A smaller current IEF resulats in
slower rise time
(#4)
3) A larger#\ also results in a slower rise time (/5).
4) A coupling resistance
results in a slower rise time
(/6)
It is clear that the above observations bear
out all that is mentioned in the previous chapters.
A fast switching speed corresponds to a high hysteresis
and a high current. Increasing R
and
/
will reduce
the transient responde. The experimental results show
that the rise time can be predicted to within 100% of
the true value quite comfortably. The times are consistently
low because much of the capacitance in the transistor
(e.g. collector base capacitance) has been neglected in
the simple charge control model used.
-82TABLE I
RE
Rx
RS
3
4
5
0.91
0.91
1.8
0.91
0.91
0.51
0.3
2.7
1.0
0.68
0.51
5.1
o 3
3.0
10.0
15
15.0
15.0
30.0
82.0
15.0
0.22
0.22
0.22
0.22
0.22
0.22
0
0
0
0
0
5.0
1
2
0.91
5.1
10
10
10
10
10
10
8
9
4
8
8
8
0.1
0,1
0.1
0.1
0.3
0.1
10
5
10
10
)
18
t'(C4ll):
16.0
6
12.2
10
13
KSL
\j G M
10
60
100
40
42
V\S.
-83-
CHAPTER 7
THE SPEED UP CAPACITOR
In practical application of the Parallel Schmitt
circuit use is always made of a speed up capacitor
Cy
across RX
.
(See fig. 31)
provides extra base
t off'
The added capacitance
drive for Q 2 during the 'on' and
transitions and so improves both the rise and fall
times of the circuit.
Alternatively, CX
can be regarded
as a short circuit for RX for high frequencies and so
helps to increase the loop gain during transitions.
In
short, faster rise and fall times can be had for almost
nothing.
The two minor drawbacks of the speed up
capacitor are:
7.1
i)
it puts a heavier A.C. load on the collector
of Q.
ii)
inoz the highest repetition rate VMA
it :zr'
which the circuitcan be driven as time
must be allowed for CX to discharge over
each cycle.
NEW EQUATIONS INCLUDING CX
Another analysis is performed with the speed up
capacitor CX
,
added in parallel across RX in the
equivalent circuit shown in Fig. 32.
With the assump-
-84-
vs
+R
E
El-
1.
1.
-F%
( Q r -e
PARALLEL SCHMITT CIRCUIT WITH SPEED UP CAPACITOR CX
-85I
X1
Y.
%
Lc
RE
4-
Figure 32
EQUIVALENT CIRCUIT WITH SPEED-UP CAPACITOR CX
*1
-86-
tion that
<:/=
a new third order characteristic equat-
ion is obtained.
+~
~
--t.
z
Zs2
7.2
EFFECTS OF THE SPEED UP CAPACITOR
Numerical solution of the third order polynomial
show that
i)
A pole is introduced at the origin (S
ii)
The pole in the left half plane (S_)
remains unchanged
iii)
The pole in the right half p3anme(S+)
is moved further out to the right.
)
of Equation (69)
( as compared with S+ and S_ before CX is added)
The results prove that the rise time is increased
as was expected but in addition an extra pole S is
0
introduced near the origin. In the limit as C becomes
X
infinitely large, S0 moves into the origin. No special
significance is attached to S
as it is a constant term
in an expression involving positive exponentials.
In
actual practice, C X is often determined empirically by
selecting a value which makes the output at the collector
of Q
a square wave for a step input.
2
Figure 32A
POLE ZERO PLOT BEFORE ADDING CX
jet)
.5+
Figure 32B
POLE ZERO PLOT AFTER ADDING CX
-88-
CHAPTER VIII
STATIC PROGRAM
8.1
THE STATIC SYSTEM
A program is written in FORTRAN to solve for the
four unknowns RE , RC , RX , and RB by the method
While the computer is used
illustrated in Chapter II.
here simply as a computational aid, valuable subroutines
are added for convenience and to provide more information.
A brief description of the Subroutines:
ardize resistance values.
STAND, to stand-
VLIMIT, to calculate the
maximum and minimum VF and V
and GAIN, to calculate the
range of collector current over which the gain exceeds
one, are given in the next section.
the system is illustrated in Fig
8.2
A block diagram of
33.
THE SUBROUTINES
Subroutine STAND is used to convert the resistance
values calculated in the program into standard resistances (either the 10%,
the user.)
5%
or 1% set to be determined by
The first step in the prodedure is testing
to see if the unknown resistance is within the range from
one to ten.
If it is larger than ten, it is divided down,
-R9PROGRAM TO DIMENSION A PARALLEL SCHMITT CIRCUIT
k/
4
,
i~P
00#"Aw$7- -1
'mto
7'M6
.5/T46
zufrriz
6'vP 4,ng
CAIICO&MAMAl
7 Ot
V~fcefndV
.Sureo7v
No
~4~6eQ~t-
Alb
44W"fAf%1
Nk.
V I
V///
007*P(17.
1
-iq\3ve
2la
-90SUBROUTINE STAND
E%/7
&L TANP
roAwP 6e r)
6
I
I
No
TEMA% .. AeC-)
I
4p
Af o7l
7eMPA
K~I
-1
TEMP,
/0
7~MP~ ~
.1
Mzbl#/
=
I
avv,
Mo
)(k
d?$Av Vt
A/0
~d43
f
-1
a6
e/) ");eM
_I
"V--k C 0111- v
7-m
I
SUBROUTINE VLIMIT
3TAeT
A4AVt
,E~4'
Aff
C4C V4 A7d MAIC
VC and tAl/
/'*I.C A/~f
AIA
I_____
A~~t'V6
k
Yt Qr e
-92-
and if it is smaller than one it is multiplied up, to
that range.
Thevalue of the resistance is then compared
with a standard array and is converted to the nearest
standard value.
The final answer is given after the unknown
is transformed back to its original decimal range.
Subroutine VLIMIT calculates the absolute minimum
and maximum values of VF and VH by assuming that the
circuit parameters are at the limits of their
tolerances.
specified
The right combination to produce a maximum
or minimum, e.g. whether Rc should be +5% or -5% for a
maximum VF, is determined by a series of partial derivatives of VH and VF with respect to the R's.
of limits are useful for
Such a set
Worst-C.ase designs in which the
designer has to know and allow for a maximum variation
in each circuit function.
Subroutine GAIN is used to findli and 12 the collector currents at which the gain is equal to one, by simply
solving a quadractic equation derived from Equation (29).
trpaiiznt;-olt cT t~~.
-93-
8.3
VERIFICATION OF *D.C. PROCRAN PREDECTIONS WITH
ACTUAL RESULTS
The Static Program was used to generate a series of
Schmitt circuit designs for the following variations in
the four input constraints VT
VH
and IEH
,
(See
Appendix III)
1.)
VF held constant at 10 volts
2.)
VH varied from I to 10 volts
3.)
Al varied from 10 to 30%
4.)
IEH varied from 1 to 10
ma
The other circuit constants were picked to be:
5.)
Vs = 15 Volts
6.)
t
7.)
VBE1
VBE2 = 0.62 Volts
8.)
VG1
G2 = 0.53 Volts
9.)
VO = 13 Volts
10.)
=
60
IL = 1 ma
The computer designs were tested at low frequency,
1 KC , on a bread board which contained decade resistance
The firing and holding
, R and R .
, B
0
B
X
E
voltages were found for each design and plotted in Graph XII.
boxes for R
The results show an amazingly accurate prediction with
mean deviations of 0.05 Volts for
for
4\;z-20% and .38 Volts for
a VF above the 5% error line.
\=10%
(=\30%.
,
0.35% Volts
Yo design gave
OlAtm-) \I.t\
01
-L
IF
0I
_q
----------
I
I
---- -I
.... ...
.
a:
q
q:
:
p 7 T
. . .........
p
.. ...... . ..... ... ..
: _ . , : ... ....
,"
.
..
.. .. ......
......... .. ... ... . .....
..... ...
=-7-7
7 7' 7
---- --........ ....il- 1 -.11 11
.........
q
77
T:
r
: : :
: :
:: ::
'' :
. .. . . . .. .
.. . ..
:
............
1:
.
-- -
... ...... .
..... . ...
--- ---
......... ...
....... . ..
fl
4
.....
.... .....
.... ...............
.
7;
. ..... ......
-.7 -:7'-
TT:7
i q
.
.........
.
.... ...
p
:s'
_77
.......
......
..............
.
..........
001
o
j,
IMP
......
....
7T.
w
: 11Ir Ir I..........
p
. ........ ........
.
----------
-
--
.. ...
!
-A
p ...
-77777777
t-
7 7 7
... ......... ....
. ........
. .... ...
4-
IF, I - - I
lwvp: I I I I
L
ly \A 0 Vl 'D
fqz li 'I n 4% *% -4A
..........
A
-95-
CHAPTER IX
THE TRANSIENT SYSTEM
9.1
GENERAL REMARKS
As was mentioned in Section 6.2 the coefficients
of the simultaneous differential equations of the
transient analysis, Equations (45) and (46), are
functions of the currents 1.1 and Ic2 .
Hence any closed
form solutions are almost impossible to attain and the
only recourse left is to adopt a numerical integration,
technique.
A program in FORTRAN is written for the num-
erical integration procedure illustrated in the next
section.
9.2
THE TRANSIENT PROGRAM
For the Transient Program one requires functions
describing the changes of the diffusion and recombination
time constants (1
i
c
.
and Te
) with collector current,
The information necessary to find these are supplied
as data p6ints from the cutoff frequency f
gain
and current
, versus collector current, curves which are
readily obtainable from specification sheets or by actual
-96-
experiment.
A least squared error polynomial is generated
- for each set of data and analytic functions of
and
in terms of Ic are then found by Equations (43) and (44).
With these expressions and assuming the boundry conditions
of Section 6.4 (p.69).
Equations (45) and (46) are inte-
grated numerically by the Runge Kutta technique (See
Appendix 6).
Three output matrices giving the values of
I., and Ic2 at the different time increments will yield
an exact plot of current versus time.
Due to a lack of time the methods preented above to
solve the full non-linear transient problem were not implemented in a computer program.
However, the block
diagram for the numerical integration is given in Fig. 36,
and the program for finding the least squared error
polynomial is presented in Appendix 5.
Successuf com*-
pletion of the transient program will give the non-linear
"1St
shaped curve of Fig. 30 for a final solution.
-97TRANSIENT PROGRAM
F
. . ---. . .
(
, . -.
6
-
e. . . .-
w,, Xg
ed ,.
AMM+M.+e
a=
e8,ee - ----. I
-
ex .4
N
A/No '4A1,'N
CA4Cc.4A4d
oed r
x(r .:Tf)
Y0 +0m*
7 c r
= TC.v.>
+
X/O 4fJ'.-=Vo f- Al-t
Te..): ro
Xi(1o).= O
slo
xC/oo>=
,f44-*z4AT $Z.WNe
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a
-98-
CHAPTER X
THE SYSTEM FOR OPTITIZATION
10.1
POWER MINIMIZATION
It was stated in Section
5.3
that the power con-
sumption in the circuit can minimized
by minizing IEH
and/'\.
The latter variable, which is a measure of how
closely output VF zorresponds to the specified VF , is
usually determined by the particular application and cannot be changed.
However, the conditions on IEH is much
less restrictive and it can be adjusted for a minimum
power design.
It was mentioned before that a small IEH
results in a lower i
and a slower rise time.
In this system a simple loop is used to find an
optimized circuit with minimum power consumption subject
tgo a given rise time.
current I
EH
Starting with a minimum possible
(from Equation (90 ) as the fourth boundary
condition, the D.C. program is used to find the unknown
resistances.
These are then supplied as input to the Tran-
sient program to calculate the rise time.
If this rise
time is greater than the one required, the loop is repeated
for a larger value of IEH, if it is smaller the computation is terminated and a minimum power circuit subject to
-99-
a set of criteria,
results,
10.2
r
input conditions, minimum rise time.
The block is illustrated in
Fig.la
I
HYSTERESIS MINIMIZATION
As was pointed out in both Part I and Part II the
hysteresis is a measure of the transient performance.of
the circuit as well as an important D.C. quantity.
A
large hysteresis design corresponds to a circuit to high
loop gain and fast switching speeds.
However in certain
D.C. applications the hysteresis may be a hindrance if,
for example, the -tserwants to trigger at one particular
voltage both for the upward and downward transitions.
The
following system minimizes the hysteresis subject to a
certain rise time.
V
It starts of by picking the smallest
possible and increases from that value in small incre-
H
ments until the rise time criterion is satisfied.
other three constraints VF
as
,
The
EH are left untouched
their values are assumed to be determined by other
criteria.
A flow chart is shown in the next page.
'v
-100POWER OPTIMIZATION SYSTEM
xN PoT PATA
c/twr~tw--low
= TE- 1
T
p. e4 ewA4
Pc. PaoeAA1
Ye uuv
37
-101-
ZoI"'.7-/,47
EffM/
/V/\
70 ZAA
[le
t.
ripr
/c
7Av
F~ , ce
CHAPTER XI
CONCLUSION
11.1
THE CONCLUSION
This thesis presents a complete method for the
static and transient design of the Parallel Schmitt circuit.
The four unknowns of the circuit are calculated subject
to four input constraints and the rise time for the
dimensioned circuit is found by a method of linear approximations. These procedures are mechanized on the digital
computer and results are obtained for experimental verification. Methods for a complete transeint analysis,
which includes all the non-linearities of the system,
and for optimization of important circuit functions were
presented byt were not implemented. A summary of each
chapter is given in Section 1.2.
The predictions of the static system proved to be
extremely accurate. The error in VF is less than 1% for
an tY\
design of 10% and less than5% when ft
is 30%.
Conditions for a regenerative circuit were obtained
separately by considering the gain, the V-I characteristics
the hysteresis and the stability of the transient system,
Thet were all found to give consistent results.
The transient analysis was based on a linear
-103-
approximation-using the charge control model for the
transistor. They power of this model is clearly demonstrated
by the simplicity of the form of the two simultaneous
differential equations and the ease with which the
non-linearities of the system are accounted for. The
rise time predicted by this linearized approach were found
to be consistently low as one would expect, because
base collector capacitance in the transistors and stray
capacitance in the circuit leads were neglected. There
were some fluctuations in the measured and calculated
rise times but for most part, the latter was within 50%
of the former.
The computer was found to be a powerful aid to
circuit design as, in addition to being a computational
tool, it allowed the numerical integration of the nonlinear differential equation for a complete transient
analysis and the implementation of a closed loop for
finding circuits of minimum power and hysteresis subject
to a minimum rise time requirement.
While the thesis was concerned only with the details
of the Parallel Schmitt circuit, the methods of analysis
that it has developed is by no means limited to that
circuit alone, Based on these methods, a general scheme
for designing multivibrator circuits can be evolved and
eventually used to build up a library of different classes
of multivibrators on the digital computer.
11.2
SUGGESTIONS FOR FURTHER STUDY
There are many problems that arose in the course
of this thesis which warrant further investigation.
Some of these are:
1)
The full non-linear transient solution should be
completed by the numerical integration technique
suggested in Chapter 9. A more realistic "S" shaped
waveform can be obtained.
2)
Using this transient program the closed loop systems
for designing circuits with minimum power and minimum
hysteresis subject to a certain rise time can be
implemented.
3)
The transient analysis can be investigated in terms
of a frequency dependent loop gain obtained by including a frequency depeddence in the transistor model
used to derive the gain expression. The results of
the an&lysis should be consistent with the one
derived in this thesis.
4)
The static and transient design procibdures can be
extended to other classes of multivibrators such as
the Eccles-Jourdan circuit and the Series Schmitt circuit.
tcr designed specifica!!y as a high-speed suturatotIcoic switch to repiace
s . In addition
\2N70" is oriented toward Satellita and Conventional smal-
ctL
uads the rang- , useful currant gain down to the microampere region. Otr
;.increased maximum ratcngs, reduced s::rage time, higher beta, and lower
'S
to
.s *:decassors.
TA and SATURATE D V0C ore includLd to completely characterize the
design over a wiuc family of operating conditions. These transistors are derements of MlL-S-19503.
s on
S.
-65
No Time Limit)
,
Ln C
.a
j
Vo
S
age
(R6 <
10 2)
.6 Wa t
.135 Wat
. Voits N
20 Volts
[Note 41
[Note 41
15 Volts
5.0 Volts
CHARAOTERIST!CS
V
irrnt
vN.
G:2i [ Note 51
LD
..t Gain [Note 51
S
VC
s
C
In Resistance [Note 61(
C f Current
.L
o1 'C -.
.40
=
6.0
50
25
15
300 mc)
if Currer
se Brea!cdown Voltage
r tr Sustaining Vcltage [Note 4 & 51
(12>0
S L-u
of tinc
Vo!ts
Volts
Volts
Volts
I
uA
40
20
Volts
Vo ts
5
Volts
nsec
40
r.sec
LSee circuit on page 4]
75
2955., 297.159, 2981877,
7
S 13
pf
0.1
10
25
fnts:
Ie
ohms
cr.Ldown
re
Voltage
uCurrant
r Cuooff Currant
'
of page 5]
nSee circuit on page 41
.c3w~nI- .
JS K
3.0
.
2
.20
.40
Voltage (-550C)
itance
s
UN!TS
15
.72
tion Voitzge (-550C to +1251C)
y Current Gain f = 100 mc
E
K:AX.
120
15
_-_'t*ion V\2tage
Satu.'rtion Voltaga
-'s
/.
ro ar tornouroture uless otherwise note>
L
za3
C to +300C
2000 0 Maximum /
300 CMaximum
[Noce 2 &'
[Note 2
[Nota 2 &3]
25'C
10c
25'C
perature
fu. -Iprature
0
&
-.
2i2tter
Sustaining
Voltage
[Note
45]&
Tme
Lonstar.u
[Note
71
-_'on
0
Volts
3
2
30
22525,
CE= 1
I,A
3034205. other pazcnts
erCding.
V
SE 14
].
,
2:
.N
A
,
0
I
LJCT0FR
CAM'PA
A PC
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INSTRUY
A"T
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TYP CAL CC LE nTr1 CME2
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6
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COLLECTOR VOLTAGE
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VCE
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VOLTS
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40
CCLLECTOR CURRENT
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30
= s
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on Trans;sor Curve Tracer.
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.~cor-
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Type
F~req Lienoyow-Sctora9e
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TO
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200'
100
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50
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5
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50
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630
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TA
I
%RN~0%. BASE 0C040KT
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4
Fairchild N
LK> A D7iCused Silicon Pra
-- ~c'
High 7requ ercy a.nd Low Storage T7
MF. P-RCPrAWT7rc": 27-1-0
-rV2.2iN
T 601.0
vV
0P-IT
p.
PULSE
T2
1
7
uI77~
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V Vp-p
V,
2l) V;-~
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/
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T7
LC-IECT0C-T VEJ 7M?; C"* TET~STICS
VS. F
E~+3 I T1
I.
o2*
271
LV
1b.
7r""'
[Meast:Ted in t~ne circuit above!
5
5K0
b,^V~
o2'-400,uA
-
200
-7
50-
18
-
1 .2
-* 1 VV,/2-07-.
20
Re-
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00
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1-0-.-,...-.-.volt
5
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9
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pf
610
h !mpcdrcE Pr-
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10 ;J
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1
+6
10141
Vdc
I
0--
- -
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-- 4 Vdc
t
11Vdc
AO.
-LD
ASSURED
CUSTOM
TEST
ER
PRO
AM
Mo
.0025 uf
V
V 2SE
Sarnpdnn
Ciioscope
Qq Ui v L1int.
rnat-on
Ml ddl
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Goneralor
12-Au
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50o,
Vcc10 Vdc
-
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t--
I
nSec.
Vc
0%
-_____
I
:-'s document is a complete procurement specification which can be referred to a, a purchase contract. It
the Jlowv-ng options for procurement purpoces.
Ali requirements of pa-es 1, 5, 6, and 7 apply except paragraph -3.3 belcw (Power burn-in).
All requirements of pages 1, 5, 6, and 7 apply.
5.0 QUALITY AND RELIABILITY ASS7UAN'
non covers detailed requirements for high
y.
transistors suitale for use in space
Vxtreme environments.
31 100% Processing Steps -P
-cssin
L-De
In
early faiiures are described
3.2 Normal Lot Acceptance -Each
iri G
sall meet the requ4:emen,
acceptcance condiions for operation lfe, stcrage
e rirunmn-ie
sts are assurcd by acuLW iet,
r
a ure rate In conserv-wily designcd
S re ar ved at by engi 1ing jul dmenn
'
.c to :vioes actually tested by Fairchild
xv an shown to have a failure rate of .002%
-.s.
The
vendor
3not
required
tooemoni
rte
devices shipped.
C PRCVI:0
steso
e
L
A
:e
I
ILL U!
0-
tion. Parts sold as 2N703-1 or 2.70L',-2 sl
a cco-
panied by variables data on the latest comid i cf
conuincous production submitted to TLble Ii - &rouo S
'.
inspection.
DEFINiTIONS
3.1 LTD (Lot Tolerance Percent D ctive)- Thi ar
of a sarmpdng pln is he rmnaimm
c!
which wil be aoccoted by tne :ornwi
7&NS
con idence.
r- - Test procedures e
o conform to
1...
osign Tests -Tosts
-D(
-.-
Q-
pc
,ng procod -es used are Der
- OS shad, be pockEd in the vondor'c;
ao
ervw'ise specifEad on the po:-
r. fT
a:d
Ere
r.u.3c
y bas by the
buy r's roEw by recuest. L u
2.2 Surn In-Do-
n
s ;o
cn
ces which
hrve br operated for
.
Yl.,iU10
7
100h
(30mW) :or to Group A 7nsp~c'iOn.
a
t
__
pon
Fairchild NPN Diffuzed Silon
--.---
X7 C2-'
Temprctures
Operation Junction Temperature
Storage Temperature
.
200*C Maximum
-651C to +3001C
[/ximum Voitages
Maximum
Cocector to Ease Voltage
Colector to Emitter Sustaining Voltage
[Note 4 (SE
20 Volts
VCEO (sutl
Collector to Emitter Sustaining Voltage
[Note 41
15 Volts
Emitter to Base Voltage
:
Tota! Dissipation at Case T7T
rC
2
at Case Tc e'a)rature
:Nte 2 & 3'
2
at Ambient emperaure 25%
L linoto
70re2.e 25"]
[
2
1
40 Volts
VCE (sust)
V1o
~Th
RATINCS 1,-te 11
Maxum
V so0
~
.
.*BSC!UTE M XI1J
F nr.
5.0 Volts
AILURE PATES
Estimated Maximum Failue Rate in Conservatively Designed Equipment 'in %/1000 hours)
= .01
:ECTRiCAL CHAfkCTE[STICS
'5*c free air temperature unless otherwise noted)
SYMBOL
TABLE I -
CIHARACTERISTIC
BVCCO
BVo
(sat)
Vn (sat)
VCE
Collector to Emitter Sustaining Voltage
[Note 4 E 5]
Collector to Base Breakdown Voltage
Emitter to Base Breakdown Volta7e
DC Fuise Current Gain fNote 51
Collector Saturation Voltage
Base Saturation Voltage
60U
Mm.LIMITSMax.
!NSP
units
15
Volts
41
5.0
SC
Volts
120
0.72
0.4
0.3
Volts
Volts
25
-1
nA
nA
25
nsco
7CT0N
Som
LT%
-o i g
TEST CONITION
1C = 30 mA
lau sed)
= -.0 /A
IE
Volts
I
c= 1
I0 = 1c
V
=
=
7A
1, =
V
10
13
7=
CU 25
nAI
7 C-
'~!
oCofector Cutoff Current
Emitter Cutoff Current
Charze '*rage Time Constant
[See circuit on page 51
IE
20
cC
!c = 0
Ic = ,
2
V =
10 mA
-
VCEO (sust
GRCUP A
EUDE~DLOP III
Cb
Vc (susL)
0
har (-55 C)
har
ICex
Coficotor Cutoff Current
Hi7h Fr-ecncy Current Gain (f = 100 mc)
C'"Put Capacitance
Co!;ctcr to Emitter Sustaining Voltage
Nte 4 & E
DC Pulse Crr-nt Gain [Note 5]
D"
(125*C)
Curren
15
=
3.0
5.0
2
pf
Volts
15
20
20
20
20
Gain
VC (sat)
Collector-Em tter Cutoff Current
Turn On Time ISee circuit on page 4]
Turn Off Tim- [See circuit on page 41
Coliector Spfuration Voltece
V' (sat)
rK
10
pA
20
20
7
nsec
nsoc
C.A
Ease ;dura-ion Votags (-55 C)
r.9
Bass
50P-ms
20 10
5AVC
(-55'C o + 125,C)
istance
'>
-f=
jc
i~ote 131
A
'=
/2
I
c
0
V
ve
A
I ursd
ic = 10
V
V
Ic = 0.5 PA ,c, = 1. V
V =
V
V, = C y
Volts
20
20
Ic= 1
.
ICZ5 1r
,
Ic = 7.0 mA
W's
20
Ic = 7.0 mA
.
Ic (HOOC)
:.-
2?
a,-
T2LE
S
yp e
-
~100%
0I
GR
Examination or Test
759
Con6itions (TA = 25"C
Hih Temperature S abilization
2
-
psi 2% detergu-t solu
(In- pressure6 k'&LC.gent test)
Conditions (TA = 25*C
unless otherwise
specified)
25
cck Test
'ibration Fatigue
200
.,73
C,C2
100-2000-100 cps, 20
Constent Acceleration
-herrnal Shock
40,000 ,, 2 orentations
-65'C to +1251C, 5 cycles
-65C to +200'C, 10 cycles,
MIL-STD-2026 Method 106A
,,oisture Resistunce
g peak acceleration, 3
END PCINTS
Emitter Cutoff Current
Jollector Saturat'on Voltage
2:: Saturation Voltae
2305A
S'J200UP Il
1
2^13
2
20'6
Shock Test
Vibretion Fatigue
Vihreion, V/ariable Frepuency
.corsant
Acceleration
Thermal Shock
:
o
.porature Cycling
-'sture Resistance
Stor-a Life 1000 hours
02
!c = 10 mA, VCE = 1.0 V
i = 0
VCS = 20 V
I
0
, s=4.0
Ic = 10 mA, L = 1.0 mA
Ic = 10 mA, 1 = 1.0 mA
orientations
hr. at each temp. extreme per cycle
Symbol
DC Pulse Current Gain [Note 51
Collector Cutoff Current
11
iW
2000 g, 0.2 ms-c, 5 blows in each of 6 orientations
20 1, 40 cps, 95 nours, 3 orientations
Pc = 30
Vibration, Variable Frequency
Temperature Cycling
1021
,n mir tes
-
SOSOROUP
Gperating Life (1000 hours)
.
E iNSPECTIoN
I1IAIL2 GR U?
Examination or Test
.pe
200^C (min), for 24 hours (min)
3 cycles -65C to +200 0 C
25,000 r (min), Pulsz Widtin 20 L c (mri
10- co/sec (max)
Temperature Cycing
riih Impact Shcck ( ax.: on>y)
..rme Li Sea' Lek' Test (Radiflo)
Gross
Hermetic, Scal LoTest
,
g
t70
-
urleso otr'erwise
.
r
.
-L.-W
Units
hFE
ICEO
iao
E=
VcE (set)
Vs (sat)
nA
rA
Vcts
Voits
LIM)TS
Min. Max.
22
150
50
200
0.44
0.65 0.83
25
300 , 0.2 m sec, 5 b!cws in each of 6 orientations
20 g, 40 cps, 3 hours, $ orientations
100-2000-.00 ops, 20 g peak acceleration, 3 orientations
, 2 o rietti ns
40,C
+12500, 5 cyc'os
-CC
-65 0 0 . +20-00, 10 cyces, hr. at each temp. axtrer- par cycle
M!L STO-2023 Method 106A
2000C
D~NTS
for Subgroup I
:- osphere
SPV
END PO
Merings or Destructive
Corrosion
10
or
,'3.-CP V
*~y
20'.
S
pp,.
plor
or
No !!M~ibe
END PC;NTS -LA!ure
!1
.ne
. Leobs
Break
SEiue
e
'-
D'o
oadout
of
End
-j
END PC0.TS-?Er .:d 20o Mi-37-202
(No ectrical Er, ?oi:ts Are ApD o-L,
Points
irnrnediotely after test
wnon y.
7
of -. ;group I and test 7 of subgroup
H.
O,.r
:ess .n
tio--
suroups
AfjVeNP1X
-
- II ,r
oP ~e2oe~
V1!; -
,
/:
-
A 41klpl -..
AO 22
. og "E,
cx.
4!Fel2 tVAT
-..
=
X-e
Te V:
Ap
"2
0,
oA 1 r,,
tAR-ZN C -Z::5
jg
i L&2!)ou)5~4l
-
6/V
(c7t.
-1.43.
/7
>LeP,
.- 077o.
,IA7XA'1 1
gl,
-6- 740
P7 P/~A~fe~/v6-g~.
70
-",L
12761
721
723
%
2
ke~(~
7'
-lWb,4~ 1P1 2/~A/p/X
IL'.
~7iWC7e2A/
/V6&z~C7A/c~
J6-&
)
I-
-lgoft
-
2c
V/I
~70L
(Or~
/
Ici -=r
~
aq
lAglmaq-
IE" TD IYxTW08/30
C
1050.3
PROGRAM TO DIMENSION A PARALLEL SCHMITT CIRCUIT (D.C)
C
PKCOMMON REtRCRXRB VSERRERVBETAXBETANBETATI
IVBE1,VBE2,VG1,VG2,TAUlTAU2,TAUB1,TAUB2,XIEFALPHA
VS=15.0
BETAX=120.0
BETAN=3.0_
VO=13.0
XIL=1.0
VF=1.0
0*._VE1O62
VBE2=0.62
VG2=0.53
TA=0.0
DO 77 K=193
1
__ETA=ETA+0.
_
XIEF=11.0
D 0884J=1_91,00
XIEF=XIEF-1.0
VH=0.0
DO 99 1=1,100
VH=VH1.0-----------C
C
NORMALIZED
PARAMETERS
C
--------------
VE1=VF+VBE2-VG1
------------------------------------
VH1=VH-VBE1+VG2
R0=(VS-VO)/(XIEF-XIL)
BETAT=SQRTF( BETAX*BETAN)
Q=(BETAX-BETAN)/BETAT
DELTA=(VS*ETA)/((VF1*Q)-(VBE2*ETA))
ALPHA= C(VS+ CDELTA *VBE2) 3VF1 )DELTA--------------GAMMA=((VS/VHI)-ALPHA)/(1.0-(VG2/VH1))
--
C
TEST TO SEE-IF
ETA IS TOO SMALL----------
101
IF(DELTA*(BETAT+1.0)-GAMMA) 101,100,100
PRINT 102
102
FORMAT (14H ETA TOO SMALL)
-
GO TO 99
C
C
TEST TO_ SEE
100
201
202
IF ETA
IS TOO LARGE
__
IF(Q*(VS-VF1)/(VS-VBE2)) 201, 200,200
PRINT 202
FORMAT (14H ETA TOO LARGE)
GO TO 98
C
C
TEST TO SEE IF CIRCUIT IS REGENERATIVE
200
301
302
IF (VF1-VH1) 301,300,300
PRINT 302
FO RMA t19H VF SMALLER THAN VH)
GO TO 88
_____
-
-
-
C
PAGE 1
-5
)
-
\
PAGE 2
)
08/30 1050.3
C
C
TEST TO SEE IF IEF IS TOO SMALL
300
IF(XIEF-XIL) 4019400t,o
401
PRINT 402
402
FORMAT (17H IEF IS TOO SMALL)
GO
C
C
TO
77
TEST TO SEE IF VH IS TOO SMALL
400
IF( VH1)
601
602
PRINT 602
FORMAT (45H VH SMALLER THAN DIFFERENCE
GO TO 98
601, 600 , 600
-
---
IN JUNCTION DROPS)
CALCULATE UNKNOWN RESISTANCE VALUES
600
RE=(VF1-VBE2)/XIEF
RC=GAMMA*RE
RX=(DELTA*RE*(BETAT+1.0))-RC
RB=CRC+RX)/(ALPHA-l.0)
C
GMAX=(BETAT*RC)/(RC+RX+U(ALPHA/40.0).(4.0/XIEFf)
CALL GAIN(XIlXI2)
C
PRINT
OUTPUT
-
C
PRINT 2 ,RERCRXRBROGMAXXII,XI2
FORMAT (F1O.5,5X-F1O.5-5XFIQ.5,5XF1O.5,5XFLO.5,5XF1O.5
1,5XFl0.5,5XF10.5)
99
CONTINUE
88
77
98
CONTINUE
CONTINUE
CALL EXIT
END (1,0,
TIME
=
0.38 MIN.
----- -
----
--
--
--
---
-
--
---
- - - - - - - -
-
JOB
0 10 r0 90 iv0 q0 90 v1 t0,000
-
2
)
08/30 1050.3
C
C
PAGE 1
SUBROUTINE TO CALCULATE ICi AND IC2 AT WHICH GAIN = 1
--SUBROUTINE
GAIN(X11,X2 12)
_
)
COMMON RERCRXRBVSERRERVBETAXBETANBETAT,
VB2VBE,VV, VGG2
,.TAU 2,TAUUB1
TAUB2,XIEFALPHA
A=-XIEF
B=(ALPHA*BETAT*XIEF)/((40.0*(BETAT-1.0)*RCLRX)___
Xll =(-A-SQRTF((A**2.0)-(4.0*8)))/2.0
(4.0*B)/2.0
X12 =(-A+SQRTF.( (A* 2.0
RETURN
END(1,0,0-,O,0,,0,0
0,0,
,-,-,
0)
__.04_MIN.____________________
-----------
-------------- --------------------------------------------------------------
)
JOBTIME__
)
,I
)
)
}7jk
NAME ORIGIN ENTRY
GAIN
00144 00152
(F2EF) 01052 01242
RSTRTN_07042 07333
JOBTM 07042 07101
EXITM
07436_07444
.READ 07555 07630
(-C-SH
) 07555_07617
(IOH)
10300 10543
DCEXIT_15172_15335
(TEF)
15345 15450
(BSR)_ 15345-15443
(EXE)
15510 15517
.PRINT_16403_16507
(STHM) 16403 16416
.SETUP
(SPHM)
(FIL)
NAME ORIGIN ENTRY
MAIN 00266 00274
FTNPM 01052 01100
TIMLFT 07042 07117
TIMER
07042 07157
EXIT 07436 07470
.TAPRD 07555 07625
IOHSIZ 10300 13642
.03311 15153 15155
DFMP
15172 15227
(RCH)
15345 15447
_(WRS)_ 15345 15442
(IOU)
16350 16355
A.TAPWR 16403_16502
(STH)
16403 16417
(SCHM)_16403_16425
.FOUT 16403 17343
ERROR 17603 17607
(WTC)
17777 20066
(RDC)
20163 20242
(RER)
20163 20176
LDUMP 20634 20637
MOVIE) 20643 20643
PROGRAM LENGTH =
21204. LOWEST COMMON = 77435
_
_
EXIT
NAME ORIGIN
(RCPM) 01052
(FPT)
06544
STOPCL 07042
ENDJOB 07436
.SCRDS 07555
(CSHM) 07555
(FIL)__ 10300
SFDP
15172
DFAD
15172
(REW)
15345
(1OS)
15345
RECOUP 16375
(SCH)_ 16403
(SPH)
16403
.COMNT 16403
(BST)
20123
SQRT
20266
NAME ORIGIN ENTR
.SETUP 01034 01041
(F2PM) 01052 01067
KILLTR_07042_07301
(TIME) 07042 07045
.LOOK 07555 07770
(TSHM) 07555 07574
CR TN) 10300 13512
.03310 15153 15155
DFSB
15172 15212
(ETT)
15345 15446
(RDS) 15345 15441
(TES)
16372 16374
.PUNCH 16403 16463
(SPHM) 16403 16415
.CLOUT 16403 17340
(WER)
17777 20013
SQR
20266 20272
.-
.-
.
ENTRY
02351
06553
07141
07522
07772
07573
13475
15255
15175
15445
15352
16400
16430
16454
16507
20134
20272
NAME ORIGIN ENTRY
FTNBP
01052 01077
(FRM7). 07042 07347
RSCLCK
CLKOUT
.READL
(TSH)
07042 07134
07436 07470
07555 07630
07555 07604
10300 10540
STQUO
DFDP
15172 15261
(TCO
15345 15451
(WEF)
15345 15444
(TRC)
15345 15452
.SPRNT 16403 16627
(STHD)
16403 16446
(PRNT)
16403 17026
.PNCHL 16403 16463
(RDPM) 20163 20257
EXP(3 20376 20402
)
LIBRARY ENTRY POINTS,
SQRT
EXP(3
-.---
.96 MINUTES ELAPSED SINCE START OF JOB
W-01
F)
4.95122
5.23806
5.45644
-- -- -----14.61962
14.61962
14.61962
14.61962
14.61962
14.61962
14.61962
5.62826
14.61962
1.54825
16.24402
3.41369
4.42734
5.06416
5.50135
5.82006
6.06271
6.25362
16.24402
16.24402
16.24402
16.24402
16.24402
16.24402
1.74178
3.84041
4.98075
5.69718
6.18902
6.54757
6.82055
18.27453
18.27453
18.27453
18.27453
18.27453
18.27453
18.27453
7.03532
18.27453
1.39343
3.07232
3.98460
16.24402
__
.22222
.22222
.22222
.22222
.22222
.22222
.22222
.22222
45.34677.00814
27.86631
18.36779
12.40032
8.30353
5.31698
3.04321
1.25426
. 30956
.25000
.25000
.25000
.25000
.25000
.25000
.25000
.25000
45.34677
.00733
.01193
.01812
.02689
.28571
.28571
.28571
.28571
.28571
.28571
.28571
.28571
45.34677
27.86631
18.36779
12.40032
8.30353
5.31698
3.04321
.00651
.01061
.01611
.02390
.03579
.05613
.09895
1.25426
.24765
27.86631
18.36779
12.40032
8.30353
5.31698
3.04321
1.25426
.01326
.02014
.02988
.04473
.07016
.12368
9.99186
9.98674
9. 97986
9.97012
9.95527
9. 92984
9.87632
9. 69044
8.99267
.04026
8.98807
8.98188
8.97311
8.95974
.06314
.11131
.27860'
8.88869
8.72140
8.93686
VJFSMALLER THAN VH
ETA TOO SMALL
ETA TOO SMALL-.-1.18375
1.18375
1.18375
1.18375
1.18375
1.18375
1.18375
1.18375
5.44412
3.34550
2.20515
1.48872_
.99688
.63833
.36535
.15058
)
ETA TOO SMALL
SETA- TOO SMALL
.94700.---4,35530
_.b .94700
2.67640
S.D
.94700
1.76412
b-*
.94700-.19098-4.55774
'V
.94700
.79751
2:D
.94700
.51067
clotD
.94700
.29228
to-lb
.94700_.12046
-IVFSMALLER THAN VH
ETA TOO SMALL
ETA TOO SMALL
1.05222
4.83922
1.05222
2.97378
1.05222
1.96013
1.05222
1.32331
1.05222
.88612
1.05222
.56741
1.05222
.32476
1.05222
.13385
7.99349
7.98939
7.98389
7.97610
7.96421
7.94387
7.90105
7.75235
)
'n- !
EXECUTION
2.
5.95490
3.98753
2.55333
1.46142
.60232.VH
22.78872
73.09811
2.00000_-,
24.75608
26.19029
27.28220
28.14129
73.09811
73.09811
73.09811
73.09811
2.00000
2.00000
2.00000
2.00000
12.40032
8.30353
5.31698
3.04321
1.25426
.00598
.00895
.01403
.02474
.06191
1.99402
1.99105
1.98597
1.97526
1.93809
- 'T-
43.55297
26.76399
17.64121
11.90979
13.93426
30.72324
39.84602
45.57743
146.19621
146.19621
146.19621
146.19621
9.47000
7.97506
49.51216 -
146.19621
9.47000
9.47000
9.47000
5.10666
2.92283
1.20464
52.38057
54.56440
56.28259
146.19621
146.19621
146.19621
0.
0.
0.
0.
0.
0.
0.
0.
45.34677
27.86631
18.36779
12.40032
8.30353
5.31698
3.04321
1.25426
44.59700
23.17546
14.42939
.00081
.00133
.00201
.00299
.99919
.99867
.99799
.99701
.00447
.99553
.00702
.01237
.03096
.99298
.98763
.96904
.00385
.00741
.01191
9.99615
9.99259
9.98809
VF SMALLER THAN VH
ETA TOOSMALL
-
--
-
- - -
-
ETA TOO SMALL
IEF IS TOO SMALL
8.59081
4.46434
2.77956
.94700
.94700
.94700
2.95412
7.08060
8.76537
38.60570
38.60570
38.60570
.22222
.22222
.22222
9.68084
38.60570
.22222
9.67696
.01779
9.98221
1.28895
.94700
.89410
.94700
.60625
.94700
.38710
.94700
.21468
.94700
VF SMALLERTHAN VH_
ETA TOO SMALL
10.25599
10.65084
10.93868
38.60570
38.60570
38.60570
.22222
.22222
.22222
6.69123
4.64147
3.14720
.02578
.03727
.05520
9.97422
9.96273
9.94480
11.15783
38.60570
.22222
2.00955
.08713
9.91287
11.33025
38.60570
.22222
1.11448
.15991
9.84009
9.54535
3.28236
42.89522
.25000
44.59700
.00346
8.99654
8.99333
9.67696
.00667
.01072
.01601
6.69123
.02320
8.97680
4.64147
3.14720
2.00955
1.11448
.03354
.04968
.07842
.14392
8.96646
8.95032
8.92158
8.85608
.4
.28571
. 59700
4.570.00
00308
48.25712
7.99692
.99
7.99407
.94700
1.05222
.1.05222
_
_-1.86409
1.05222
--
1.05222
1.05222
__
4.96038
7.86733
42.89522
.25000
23.17547
3.08840
9.73930--
4-42.89522
.25000 ---
14.42939
.25000
.25000
.25000
.25000
.25000
.25000
8.98928
8.98399
2.07121
10.75649
42.89522
1.43216
11.39554
42.89522
.99344
.67361
.43012
.23854
11.83426
12.15409
12.39759
12.58917
42.89522
42.89522
42.89522
42.89522
3.69265
8.85074
10.95671
12.10105
12.81998
13.31355
13.67335
48.25713
.28571
23.17547
48.25712
48.25712
48.25712
48.25712
48.25712
.28571
.285711
.28571
.28571
.28571
14.42939
9.67696
6.69123
4.64147
3.14720
13.94729
48.25712
.28571
2.00955
14.16281
48.25712
.28571
1.11448
.00593
.00953
.01423
.02062
.02981
.04416
.06971
.12793
4.22017
10.11514
55.15100
55.15100
.33333
.33333
44.59700
23.17547
.00269
.00519
6.99731
6.99481
1.05222
1.05222
1.05222
1.05222
VF SMALLER THAN VH
ETA TOO SMAL L
1.1 -8375
1.18375
)
4.73500
4.73500
4.73500
4.73500
4.73500
VF SMALLER THAN
ETA TOO SMALL
ETA TOO SMALL
9.47000
9.47000
9.47000
9.47000
10*73852
5.58042
3.47445
1.18375
2.33012
1.18375
1.61118
1.18375
1.11762
1.18375
.75781
1.18375
__.48388
1.18375
.26836
1.18375
VF SMALLER THAN VH
ETA TOO SMALL
12.27259
1.35286
6.37763
1.35286
--
7.99047
7.98577
7.97938
7.97019
7.95584
7.93029
7.87207
1.35286
3.97081
12.52196
55.15100
.33333
14.42939
.00834
6.99166
1.35286
1.35286
1.35286
2.66299
1.84135
1.27728
13.82977
14.65141
15.21548
55.15100
55.15100
55.15100
.33333
.33333
.33333
9.67696
6.69123
4.64147
.01245
.01804
.02609
6.98755
6.98196
6.97391
1.35286
.86607
15.62669
55.15100
.33333
3.14720
.03864
6.96136
0
)
.55301
.30669
MALLER_ THANVH_
VF__
ETA TOO SMALL
__1.57833
16.18607
-
__14.31802
.
1.57833
1.57833
1.57833
1.57833
1.57833
18.23114-- 1.57833
------64.34283 -- .40000
1.57833
1.57833
55.15100
55.15100
15.93976
64.34283
-4.92353
7.44056
4.63261
11.80099
14.60895
64.34283
64.34283
3.10682
16.13473
64.34283
2.14824
1.49016
17.09331
17.75140
64.34283
64.34283
_.33333
2.00955
.33333
1.11448
-44.59700
_
_.40000
.40000
.40000
.40000
.40000
.40000
23.17547
14.42939
9.67696
8
1.01042
.64517
.35781
18.59638
64.34283
18.88375
64.34283
.40000
.40000
6.93901
6.88806
.00231
.00445
.00715
.01067
5.99769
5.99555
5.99285
5.98933
.0-1547
5.98453
4.64147
3.14720
2.00955
1.11448
.02236
.03312
.05228
.09595
5.97764
5.96688
5.94772
5.90405
44.59700
23.17546
14.42939
9.67696
6.69123
4.64147
3.14720
2.00955
1.11448
.00192
.00370.00596
.00889
.01289
.01863
.02760
.04357
.07996
4.99808
4.99630
4.99404
4.99111
44.59700
23.17547
14.42939
9.67696
6.69123
4.64147
3.14720
2.00955
1.11448
.00154
.00296
.00476
.00712
.01031
.01491
.02208
.03485
.063971
3. 99846
3. 99704
3.99524
.00115
.00222
.00357
.00534
.00773
.01118
.01656
2.99885
2.99778
2.99643
6.69123
--
.06099
.11194
3
)
1.35286
1.35286
VF SMALLER THAN VH
_
_
_
_
_
_
_
_
_
_
_
_
_
_
_
_
_
_
_
_
77.21140
77.21140
77.21140
77.21140
77.21140
77.21140
77.21140
77.21140
96.51425
96.51425
-
_
_
_
_
.66667
.66667
.66667
.66667
.66667
.66667
.66667
.66667
96.51425
96.51425
96.51425
96.51425
96.51425
96.51425
96.51425
_
.50000
.50000
.50000
.50000
.50000
.50000
.50000
.50000
.50000
77.21140
-
_.66 667
128.68566
1.00000
128.68566
128.68566
128.68566
1.00000
1.00000
1.00000
193.02850
193.02850
2.00000
2.00000
193.02850
2.00000
193.02850
193.02850
193.02850
2.00000
2.00000
2.00000
1.00000
128.68566
1.00000
128.68567
128.68566
128.68566
1.00000
1.00000
1.00000
3.03126
54.69341
193.02850
2.00000
4.73500
1.93552
55.78914
56.65125
193.02850
193.02850
2.00000
2.00000
85.90813
29.54121
386.05700
0.
44.64338
70.80596
386.05700
0.
9.47000
9.47000
--
44.59700
23.17547
14.42939
9.67696
6.69123
4.64147
3.14720
2.00955
1.11448
128.68567
-.
4.73500
4.73500
1.07342
VF SMALLER THAN VH
-ETA TOO SMALL
__
4.98711
4.98 137
4.97240
4. 95643
4.92004
3.99288
3.98969
3.98509
3.97792
3.96515
3.93603
2.99466
2.99227
.04797
2.98882
2.98344
2.97386
2.95203
44.59700
23.17547
.00077
.00148
1.99923
1.99852
14.42939 1.00238
9.67696
.00356
_.02614
)
_
))
TOOSMALL
1.89400
17.18163
5.90824
1.89400
8.92868
14.16119
1.89400
5.55913
17.53074
1.89400-3.72819
19.36168
1.89400
2.57789
20.51197
1._89400
1.78819
21.30168
1.89400
1.21250
21.87736
- - 1.89400
.77421
22. 31566
1.89400
.42937
22.66050
-F
_SMALLER THAN VH
ETA TOO-SMALL
S2.36150
21.47703
7.38530
2.36750
11.16084
17.70149
-2.3675.0_
6.94891------- 21*91342
2.36750
4.66023
24.20210
2.36750
3.22237
25.63997
2.36750
2.23524
26.62709
2.36750
1.51563
27.34671
2.36750
.96776
27.89457
2.36750
.536711
28032562
VF SMALLER THAN VH
ETA TOO SMALL
3.15667
28.63604
9.84707
___3.15667_
14.88113
3.4199
3.15667
9.26521
29.21790
32.26947
3.15667
6.21364
3.15667
4.29649
34.18662
35.50279
3.15667
_
2.98032
3.15667
2.02084
36.46227
3.15667
1.29035
37.19276
3.15667
.71561
37.76750
yF SMALLER THAN VH
ETA TOO SMALL
4.73500
42.95406
14.77060
4.73500
22.32169
35.40298
4.73500
13.89782
43.82685
9.32047
48.40420
4.73500
4.73500
6.44473
51.27994
4.73500
4.47048
53.25419
1.99762
1.99644
1.99484
6.69123
4.64147
3.14720
2.00955
1.11448
.00516
.00745
.01104
.01743
.03198
1.98896
44.59700
23.17547-
.00038
.00074-
.99962
.99926
1.99255
1.98257
1.96802
)
SETA
9.47000
9.47000
S 9.47000
9.47000
-9.47000
9.47000
27.79564
18.64093
12.88946
8.94096
6.06251
3.87105
9.47000
2.14684
87.65370
96.80840
102.55987
106.50838
109.38682
111.57829
386.05700
386.05700
386.05700
386.05700
386.05700
386.05700
0.
0.
0.
0.
0.
0.
14 2939
9 7696
6 9123
4 4147
3 4720
2.0955
.00119
.00178
.00258
.00373
.00552
.00871
.99881
.99822
.99742
.99627
.99448
.99129
113.30249
386.05700
0.
1. 1448
.01599
.98401
VF SMALLER THAN VH
SETA _ TOO_ SMALL
IEF IS TOO SMALL
~
ETA TOO SMALL
.94700
.94700
.94700
.94700
-.94700
.94700
J.94700
.94700
--
VF _SMALLERTHAN
ETA TOO SMALL
1.05222 1.05222
1.05222
1.05222
8.71527
- 4.57428
8.67395
12.81494
2.88358
1.96489
1.38773
.99149
.70263
.48271
.30969
H
H-_
9.68363
5.08254
3.20398
2.18322
S11.05222
1.54192
1.05222
1.10165
-- 1.05222 ---------8070
1.05222
.53635
* 05222 ------34108.9726
VF SMALLER THAN VH
__
ETATOOSMALL__
_
_
.00352
.00671
9.99648
9.99329
14.50564
85.20206
15.42433
85.20205
16.00150
85.20205
85.20205
16.68659
85.20205
16.90651
.01065
.01566
02222
.03119
.04421
85.20205
9.1 267
6 i 501
4 1 491
3
867
2 4 269
1&6441
t6781
9.98935
9.98434
9.97778
16.39774
.22222
.22222
.22222
.22222
.22222
.22222
.22222
_
_
_
85.20205
_
_
_
_
_
9.63773
14.23882
16.11738
17.13814
17.77944
18.21971
18.54066-------18.78501
___
-
30.0 047
15.! 224
_
_
__
_
_
_
_
_
_
___
.06479
.10226
9.96881
9.95579
9.93521
9.89774
____
94.66895
94.66895
94.66895
94.66895
94.66895
94.66895
.25000
.25000
-. 25000
.25000
.25000
.25000
94.66895
. 25000
.42269
94.66895
.25000
.66441
94.66895
.25000
.06781
3 .05047
1 .77224
.94267
.77501
.78491
.41867
.00316
.00603
.00959
.01409
.02000
.02807
.03979
.05831
.09204
8.99684
8.99397
8.99041
8.98591
8.98000
8.97193
8.96021
8.94169
8.90796
8
_
_
_
_
_
_
_
_
_
_
_
_
_
_
__
10.84244
16.01867------18.13205
19.28041
20.00187
20.49717
20.85824
106.50257
.28571
106.50257 ----------. 28571-1
106.50257
.28571
21.13314
106.50257
21.34942
_
_
_
_
_
_
3 .05047
.77224
.94267
.00281
.00852
7.99719
7.99464
7.99148
106.50257
.28571
.77501
.01253
7.98747
106.50257
.28571
.78491
.01777
7.98223
106.50257
.28571
41867
.02495
106.50257
7.97505
.42269
.66441
1.06781
.03537
7.96463
.05183
7.94817
106.50257
.28571
.28571
.28571
.08181
7.91819
12.39136
18.30706
121.71723
.33333
30.05047
.33333
15.77224
.00246
.00469
6.99754
121.71722
121.71723
.33333
i9.94267
.00746
6.99254
-.
.00536
6.99531
1.35286
4.11941
20.72234
1.35286
1.35286
1.35286
2.80699
1.98246
1.41641
22.03475
121.71723
.33333
6.77501
.01096
6.98904
22.85928
121.71722
.33333
4.78491
.01555
6.98445
23.42534
121.71722
.33333
6.97817
1.00376
23.83799
121.71722
.33333
.03095
6.96905
1.35286
.68959
1.35286
.44241
VF SMALLER THAN VH
ETA TOO SMALL
1.57833
14.52545
1.57833
7.62381
1.57833
4.80597
1.57833
3.27482
1.57833
2.31288
24.15216
24.39934
121.71722
121.71722
*33333
.33333
3.41867
2.42269
1.66441
1.06781
.02183
1.35286
04556
.07158
6.95464
6.92842
14.45659
142.0O0343
.40
30.05047
.00211
5.99789
21.35823
142.00343
_40000
15.77224
.00402
5.99598
24.17606
25.70721
26.66916
142.00343
142.00343
142.00343
9.94267
6.77501
4.78491
.00639
.00939
.01333
5.99061
5.98667
27.32956
142.00343
.40000
.40000
.400
.40000
3.41867
.01871
5.98129
1.57833
-
I----
.22222
.22222
_
1.18375
10.89409
1835
5.71785------1.18375
3.60448
1.18375
2.45612
1.18375
1.73466
1.18375
.2936
1.18375
.87829
1.18375
.60339
1.18375
.38711
_VF_ SMALLER THAN VH
ETA TOO SMALL
___1.35286
12.45038
1.35286
6.53469
-
85.20206
85.20206
17.07954
_
~
)
.94700
----
-
1.65248
-
-
--.
1
1.17105
1.57833
.80452
1.57833
.51614
1.57833
VF SMALLER THAN VH
ETA TOO
27.81099
28.17752
28.46589
142.00343
142.00343
142.00343
.40000
.40000
.40000
17.34791
L_
2.42269
1.66441
1.06781
.02652
.03888
.06136
5.97348
5.96112
5.93864
4.99824
4.99665
SMALL
1.89400
1.89400
1.89400
1.89400
1.89400
17.43054
9.14857
25.62988
170.40411
170.40411
.50000
.50000
30.05047
15.77224
5.76717
3.92979
2.77545
29.01128
30.84866
32.00299
170.40411
170.40411
170.40411
9.94267
6.77501
4.78491
.00176
.00335
.00533
.00783
.01111
3.41867
.01560
4.98440
2.42269
.02210
4.97790
4.99467
4.99217
4.98889
1.89400
1.98297
32.79547
170.40411
1.89400
1.40526
33.37319
170.40411
.50000
.50000
.50000
.50000
.50000
.96543
33.81302
170.40411
.50000
1.66441
.03240
4.96760
.61937
34.15907
170.40411
.50000
1.06781
.05113
4.94887
21.78817
21.68489
213.00514
.66667
L_30.05047
2.36750
2.36750
2.36750
2.36750
2.36750
11.43571
7.20896
4.91224
3.46931
2.47872
.66667
15.77224
.00426
3.99574
38.56082
40.00374
40.99434
213.00514
213.00514
213.00514
213.00514
213.00514
.00141
.00268
3.99859
32.03735
2.36750
1.75657
41.71648
213.00514
1.20678
2.36750
.77422
2.36750
VF SMALLER THAN VH
42.26628
213.00514
42.69884
29.05090
3.15667
3.15667-15.24761
9.61195
3.15667
6.54965
3.15667
4.62575
3.15667
3.30496
--- 1.89400_
1.89400
VF SMALLERTHAN_
ETA TOO SMALL
____,2.36750
ETA
TOO
H
__
36.26410
.66667
_-
__-9.94267
3.99732
6.77501
4.78491
3.41867
.00626
.00889
.01248
3.99374
3.99111
3.98752
2.42269
.01768
3.98232
1.66441
1.06781
.02592
.0409O
3.97408
213.00514
.66667
.66667
.66667
.66667
.66667
.66667
28.91318
42.71647
48.35213
51.41443
53.33833
284.00686
284.00686
284.00685
284.00685
284.00686
1.00000
1.00000
1.00000
1.00000
1.00000
30.05047
15.77224
9.94267
6.77501
4.78491
.00105
.00201
.00320
.00470
.00667
54.65912
284.00685
1.00000
3.41867
.00936
55.62198
284.00685
1.00000
2.42269
.01326
2.99895
2.99799
2.99680
2.99530
2.99333
2.99064
2.98674
56.93179
284.00685
1.00000
1.06781
.03068
2.96932
43.36977
64.07470
72.52819
77.12164
426.01029
426.01028
2.00000
2.00000
2.00000
426.01028
2.00000
80.00749
426.01028
2.00000
4.78491
81.98868
426.01028
2.00000
83.43297
426.01028
2.00000
84.53255
85.39769
426.01028
426.01028
2.00000
2.00000
3.41867
2.42269
1.66441
1.06781
.0070
.00134
.00213
.00313
.00444
.00624
.00884
.01296
.02045
1.99930
1.99866
426.01028
30.05047
15.77224
9.94267
6.77501
86.73954
128.14940
145.05638
154.24328
160.01497
852.02058
852.02057
852.02057
852.02057
852.02057
0.
0.
0.
0.
0.
.00035
.00067
.00107
.00157
.00222
.00312
.00442
.99965
.99933
.99893
.99843
.99778
.00648
.01023
.99352
.98977
3.95910
SMALL
3.15667
2.34210
3.15667
2.98056
.01944
1.66441
1.00000
284.00685
56.35503
T_1.60904__
3.1566?
1.03229
3.15667
VF SMALLER THAN VH
ETA TOO SMALL
43.57634
4.73500
22.87142
4.73500
14.41792
4.73500
9.82447
4.73500
6.93863
4.73500
4.95743
4.73500
4.73500
2.41356
4.73500
1.54843
4.73500
VF SMALLER THAN VH
ETA TOO SMALL
87.15269
9.47000
45.74283
9.47000
28.83585
9.47000
19.64895
9.47000
13.87725
9.47000
-
-3.51315
__
_
30.05047
15.77224
9.94267
6.77501
4.78491
9.91487
163.97736
852.02057
0.
3.41867
7.02630
9.47000
4.82713
9.47000
3.09686
9.47000
*VF SMALLER THAN VH
ETA TOO SMALL
166.86593
852.02057
2.42269
169.06510
852.02057
170.79537
852.02057
0.
0.
0.
9.47000
IEF_
IS
TOO
SMALL ~
------------
1.66441
1.06781
7
1.99787
1.99687
1.99556
1.99376
1.99116
1.98704
1.97955
.99688
.99558
-------------------------------------------------------------------------------------------------NX
---------------------------------------------------------------------------------------------------c
G -*-PRGGRAM -TG -D I-ME4S iG(4 -A -P-ARA66E-6 -SCHM I-T-T- -Crl-R-C-U I-T- - D-o-G)_._ ----------------------------------c
------------C-GMMGN -RE TRE rf4Yv -rR& rVS!rER14 rEf4V rB&TAXr&ETAt4 r&CT-AT- r ---------------------------------1VBEltVBE2tVGltVG29TAU19TAU2tTAUB19TAUB2tDIEtALPHA
E) 1 MENSieN R( i e.
VS=15*0
------------BETAX=125OrD ---------------------------------------------------------------------------BETAN=30*0
- - - - - - -
- V07-
ja
rG
X I L = 1
- - - - - -
- - - -
- - - - - - - - - - - - - - - - - - - - -
- - - -
- - - - - - - -----
-
- - - - - - - - - - - - -
- - - - - - - -- -
- - - -
-
- - ---
0
VBE1=0*62
------------VBEa=0w&2 -----------------------------------------------------------------------------VG 1 =0 9 5 3
------------VGa=Gw5a ------------------------------------------------------- ---------------------ETA=0*1
ER7R-=-&-v-G 5
ERV=0*1
------------VH=GwG -------------------------------------------------------------------------------DO 99 I=lsl00
------------VH=VH+Iwo ---------------------------------------------------------------------------c
47
r- f'%
f-% A M
c
------------XlsF=l9wo ---------------------------------------------------------------------------VF1=VF+VBE2-VG1
------------VHlmVH-VBEl+VG2 ----------------------------------------------------------------------RO=(VS-VO)/(XIEF-XIL)
r- Ir A .r - r- e%
_r _
r.,
7-r-1-0
T. A X_* BE A N
Q=(BETAX-BETAN)/BETAT
------------DEE TA= k-VS4 ETA -Y A - -VF-I*Q - -, VBE- 2*ETA -Y - -----------------------------------------------------ALPHA=((VS+(DELTA*VBE2))/VF1)-DELTA
------------- GAMMA= (-V&AVHl)--AbFHA-Y/----------c
C T
To
T-1-
c-
GC=
T C
CT A
T r
^% fl\
cc, lk
c
------------101
PRINT 102
------- &R -- FORMAT-- f-14H-ET-A-T-E)& -,SMAELGO TO 99
C
TEST TO SEE IF ETA IS
-------------------------------------------------------------
TOO LARGE
100
IF(Q*(VS-VF1)/(VS-VBE2))
202
FORMAT
20112009200
(14H ETA TOO LARGE)
c
----------------------------------------------------c
------------------------------------------------------------301
PRINT 302
-3-0-2--re
GO TO 98
VP
sm-p tttR
7HAN
VH)
----------------------------------------------------------------------------------------------------
-
-
-
-
-
- -
-
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-
---
- - -
- -
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- - - - - - - - -
- - - - - - - - - - - - - -
- - - - - -
- - -
- -
-
-
-
-
-
-
-
c
---------------------------------------------------------C
------- a&O - - FF (-X- f-E-F-X- I-b -4& 3: v-4-&-a r4G& -------- ------ ---- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - (7
401
PRINT 402
402
FORMAT (1711 lEF 15 :FGG---c-p
GO TO 98
E ------------------------------------------------------------------------------------------C
TEST TO SEE IF VH IS TOO SMALL
--------- ----------400
IF(VH1) 60196009600
6.
'L- I'
z
602
FORMAT (45H VH SMALLER THAN DIFFERENCE IN JUACTION DROPS)
------------ 69-TG-9& -----------------------------------------------------------------------------cz
C
G--C-AL-C-L46ATE-L4NKNOW14-RE-SI-ST-AN-E-VAr6UE-S -----------------------------------------------------zz
C
I-An
m c* (-V.F 1-,Vcl c -) I I v 1 FF
lz
RC=GAMMA*RE
---------- RX = 4-D &6 T-A* R 6*4 B 9 T-A T-+ I- v Q - - -R ----------------------------------------------------------oz
RB=(RC+RX)/(ALPHA-loo)
------------:-R(-14-=Rs -----------------------------------------------------------------------------R(2)=RC
f n %_rlv
-
R(4)=RB
R(-5*n
-----------------------------------------Ll
Re ------------------------------------N=5
------------ CA 6 6 - S T AN D - 4-R-t'*P4 - - - - - - - - - -- - - - - -- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 91
RE=R(l)
RE-=R-(2)
RX=R(3)
-----------------------------------------------RO=R(5)
------------ X- PE F= i-V F I-V R Ek)- ? -RE - - - - - - - - - - - - - - - - - - - - - - - - - - - XIEH=(VH1-VG1)/RE
..- ,I.r.F XlEll
C
-----------------------------------------It
-----------CALL GAIN(XI19XI2)
------------ -466-V61-MI;4-VFMAX-rVHMAXrV-MI-F4vVHMI-P4) -------------------------------------------------ALPHA=(RC+RX+RB)/RB
6AMMA=,RE/RE
DELTA=(RC+RX)/(RE*(3ETAT+1*0))
-----------Y-Y -------------------------VHA=VBEI+(VS/ALPHA-VG2)/(GAMMA/ALPHA+loo)
------------ RN=ABSF tff
------------------------PF=((VFA/RE)*VS)+((VFA/RB)*V5)
I RE) 9 V5) + ( (VI 1A RB)
I I I v , IIIM/
' I I= 1-1
-r-"
OVS)
PS=(VS*VS)/(RC+((RE*(RX+RB))/(RE+RX+RB)))
E- - - - - - -- - - - - - 7- - - - - - - - - - - -- - - - - - - - - - - - - - - - - -- - - - - - -- - - -- - - - - - - - - - - - - - - - - - - - - - - - - - - - - -- - - C
PRINT OUTPUT
zt
-
.
r!' -VT
2
PRINT 29VFAqVHAqREtRCtRXqRBqRO9RNq
.!VFMAX V-HMAXqVFMiNq HMfN96MAXiXi!9Xi2obfE
FORMAT (FlOo595XtFlOo5i5X9FlOo5i5XtFlOo5i5XtFlOo5t5X#FlO*5
-------------------------------------------------------------------------------------------------
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-
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-
-
-
- - -- - - -- - - - - - - - - - - - - - -- - - - - - - - - - -- - - -
-
-
------------------------------
-
-----------------------------------------------------------
lt5XqFl0*5s5XqFl0*5)
99---EGNT-I-NU- --- -- ---- ------------------- --- --- -------------------- -- ------------ ------- ----6z
98
CALL EXIT
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DIMENSION R(1000)95(1000)
------------
ttt=trO
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17
S ( 2 )= 1 o 1
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-----------S 22
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51
5 2
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-- --- ---- -- -S f- 2 5
1 fy w 0 - - - - - DO 20 J=19N
5
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-- ----------S
S
C
G
TEST RESISTANCE VALUES
IF
(R(J)-10*0) 5'0921951
C
E -- NGRMA6 I-Z-E- -RES I-ST-ARC-E-VALUES -EiRE-A-E-R -T++A*-T-Et4 ----------------------------------------------c
C
TEMPI-R(d)
51
DO 52 K=1910
-----------IF
(TEMPl-1090)
53t53952
53
XM=K
O=TEMPI
GO TO 21
------------- 7---------------------------------------------------------------------------C
NORMALIZE RESISTANCE VALUES LESS THAN ONE
-----------------------------------------------------------------------------------------TEMP2=R(J)
DO 62 t lw!0
TEMP2=TEMP2*10*0
---------------------------------------------------------------------------------------------------z
60
----------------------------------------------------- I-------------------------------------------
%D
2-G
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62
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XM=-L
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Q=R (J)
1z
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E - -C-9M PLA R E -W I- TH - S TA14D ARD -AR R A Y-------------------------------------------------------------c
------------------------------------------------------------------
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11
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SAVE=(S(I)+S(I+1))/2,0
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IF(Q-SAVE) 20910910
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R(J)=S(I)*(10*0**XM)
lz
RETURN
END
cz
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C
-F I-NO -;HE -MAX I-MUM -AND -M I-N I-ML414 -VALL4SS -GF-VF--At4D -V --------------------------C
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RBT=RB*(1*0-ERR)
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VHMIN=((VST-(ALPHA*VG2))/(ALPHA+GAMMA))+VBE.1
RST-URN --------------------------------------------------------------------END
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SUBROUTINE TO CALCULATE IC1 AND IC2 AT WHICH GAIN = I'
E -----------------------------------------------------------------------------------------SUBROUTINE GAIN(XI1sXI2)
------------ eOMME)N-RErRerR-)(YR-&rV-&rERRrE-RVrBE-T-AXr&E-T-A-Nr&ET-AT r- ------------------------------------'Z
1VBEltVBE21VG19,VG2tTAUltTAU2iTAUBltTAUB2tDIEtALPHA!
RETURN
END
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1z
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51
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-------------------------------------------------------------------------------------------------
-------------------------------------------------------------------------------------------------
----------------------------------------------------------------------------------------
z
-------------------------------------------------------------------------------------------------
BIBLIOGGRAPIIY
1.
Millman and Taub, Pulse Dittal and Switching Waveforms.
McGraw-Hill, 1965.
2.
Schmitt, O.H., A Thermionic Trigger. Journal of
Scientific Instrument, v. 15, Jan':1938, p. 24.
3.
Skilling, J. K., Complementary Transistory Make
Series Schmitt Circuit Practical. Electronics,
Aug. 31, 1962,
4.
Zimmerman, H. J., and Mason, S. J., Electronic
Circuit Theory. Wiley and Sons, 1960.
5.
Skilling, J. K., Simple Method for Plotting Tunnel
Diode Switching Waveforms.
6.
Electronics, Dec. 14,1962.
Beaufoy R., and Spork J. J., The Junction Transistor
As a Charge Control Device. ATE Journal v. 13,Oct.1957,
p.p.
310-327.
7.
Gray, P. E. et. al. PEM. v.2,SEEC Wiley and Sons,1964.
8.
Faran J. J., A simple Way to Measure High Frequency
Current Gains
9.
.
Electronic Design, Oct. 12, 1964.
Searle C. et. al. ECP v. 3, SEEC
Wiley and Sons ,1964.