Donner Model 3000 Analog Computer Operating Handbook
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Operating Handbook
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Do n n e r Mo d e l 3 0 0 0
A n a lo g Co mp u t e r
A DY A ' Y C E i }
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Operating Handboqk
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Donner Model 3000
.a
Analog Computer
DONNER MODEL SOOO
ANALOG COMPUTER
TABLE
OF CONTENTS
E:!i""t
Page
Warranty
Receiving Inspection
Repairs
General Description
Specifications
Theory of Operation
Operating Instr uc t ions
Servicing
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ILLUSTRATIONS
{igure
1. Higb Gain DC Amplifier:
Schematic Diagram
2. Ampfifier Transfer Characteristic:
Typical
Operational Amplifier', Model 8000 Computer
3a. Symbolic Diagram of High Gain Amplifier Suitable
for Analog Computer Apptications
3b. Symbolic Diagram of Operational Amplifier
4. Operational Amplifier, General Case
5. Operational Amplifier Illustrating Algebraic
Summing of Arbitrary Input Voltages
6. Operational Amplifier lllustrating Sign Changing
7. Operational Amplifier Illustrating Multiplication
or Division by a Constant
8. Operational Amplifier Illustrating Simple Integration
9. operational Amplifier lllustrating the Integration of an
Algebraic Sum
10. Operational Amplifier ILlustrating a Summing
Integrator
1 1 . Computer Arrangement for Solution of General
Second Order Differential Equation
1 2 . operational Amplifier connection for Gain Adjustment
1 3 . Operational Amplifier Connection for Balance
Adjustment
t 4 . Problem Board Connections to One Integrator
rnvolving COMPUTE-RESET and HoLD-OPERATE Relays
1 5 . Amplifier Drift During the s econd FuIl Day of operation
(Co n t . )
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TABLE OF CONTENTS
(Cont. )
Photographs
3.s
Model 3000 Brochure:
Model 3000 Computer
Photographic
Views of
40
DRAWINGS
Drawing Number
E50
821
E25
E2t
Mo d e l 303 4 Problem Board - Layout
Mo d e l 300 0 P o we r S u p p ly - S c h e ma t ic , S e c t io n A
Mo d e l 3 0 0 0 P o we r S u p p ly - S c h e ma t ic , S e c t io n B
Model 300 0 Amplifiers and Switching Circuits - S c he m a t i c
ADDENDA
Indruction Sheet, Poten tiometer Strips Models 3 0 ? 1 a n d 3 0 7 3
Ihtr Sheets on Computer Accessories
Goputing
Component Assortm ent List
Sqgested Comp uting Facilitie s
Car#need Cataiog
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WARRANTY
Donner instruments are warranted during a period of one year from
date
of shipment to original purchaser to be free from defects in material
and workmanship. This warranty does not apply to vacuum tu.bes,
except as they are warranted by tube manufacturers.
The liability of
Seller under this warranty is limited to replacing or repairing any instrument or component thereof which is returned by Buyer at his
dur in g su ch p e rio d and whic h h a s n o t b e e n s u b jL c t e d t o mis u s e"*p".r""
, neglect,
im pr op e r installations, rep a ir, a lt e ra t io n , o r a c c id e n t .
S e lie r s h a l l h a v e
the right of final determination as to the existence and eause
of a defect"
In no event shall Seller be tiable for collateral or consequential
damages.
This warranty is in lieu of any other warranty, express, implied
or
statutory, and no agreement extending or modifyiagit will be
binding upon
seller unless in writing and signed bya duly authorized officer.
.RECEIVING INSPECTION
Every Donner instrument is carefully inspected and is
in perfect working
order at the time of shipment. Each instrument should be
checked as
soon as received. If the unit is damaged in any way or fails
to operate,
a claim should immediately be filed with the transportation
company.
REPAIRS
whenever a Donner instru me n t re q u ire s s e rv ic e , t h e n e a re s t
Do n n e r
representative should be contacted; all representatives
wili provide
i m m ed iate se rvice or a rra n g e f a c t o ry re t u rn s wh e n , r" " " ru rry .
Please specify both model and serial number in all correspondence
coil.cer ning Do n n e r in strume n ts. A d d re s s a ll in q u irie e
o n o p e ra t io n o r
applications of Donner instr u rn e n t s t o y o u r n e a re s t
s a le s re p re s e n t a t i v e
or sales Manager, Donner s c ie n t if ic c o mp a n y , g g g
G a lin d o s t re e t ,
Concord , Ca liforn ia.
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Operafing Handbook
A n a lo g Co mp u t e r
Model 3000
The Do n n e r M:d e l 3000 is a c o mp a c t
e le c t ro n ic a n a lo g c o mp u t e r f o r th e
p r ecise' quantita tive so lution of l in e a r (a n d
c e rt a in c la s s e J o f n o n -rin e a r) di f f e r e ntial equations a n d tra n sfe r fu n c t io n s .
T h e in s t ru me n t c o n t a in s t e n DC o pe r a . .
tional amplifiers, any one of which may
serve the functions of addition, subtractron,
multiplication or division by a constant,
sign changing, or integration. problems
e x pr essed as diffe rential equations a re
e n t J re d in le ria s o f e re c t ric a l c o mp on e n t s
o n a detachable pro b lem b o a rd. s t a b ilit y
a n d a c c u ra c y o f t h e c o mp u t e r a re
satisf actor y for pro b lem so lution time s
u p t o 1 0 0 s e c o n d s o r mo re , t o p e rmit
a
c
c
urate
recording with conventional pen recorders.
However, amplifier bandwidth and
relay oper atio n speed a re adequat e
f o r re p e t it iv e -s o lu t io n o p e ra t io n
up to 10
c ycl es per se cond with oscillo sco p e
re a d o u t .
The M cdel 3 0 0 0 is packaged in a
t wo -mo d u le c a b in e t , c o mp le t e wit h
all
n ecessar y powe r supplies. It ca n re a d ily
b e a c c o mmo d a t e d o n t h e d e s k o r
be n c h
of the user' where more than ten
op"""iio.ral amplifiers are required,
two or
m o r e M odel 3 0 0 0 co mpute rs ma y
e a s ily b e in t e rc o n n e c t e d t o s e rv e
a s a s in gl e
l a r ger com puter. The l\lb d e l g o b O
c o mp u t e r . L q u ire s o n ly o n e o r mo re
det a chabl e pr oble m b o a rds, p lus com p u t in g
c o mp o n e n t s , t o t e f u lly o p e ra t io n al .
SPECIFICATIONS
Am pl i fier s
The ten o p e rational a mplifier s e mp lo y
a s t a b le , h ig h -g a in DC c irc u it ,
with
a pentode driving a cathode-follower
output. A vR tube coupring element
allows
b o th i nput and outp u t sig n a ls to be c e n t e re d
p re c is e ly a b o u t L . ro v o lt a g e .
E ac h
a m pl i fier has the fo llo win g ch a ract e ris t ic s :
G ain: Basic g a in o f 1000,
b y p o s it iv e f e e d b a c k t o mo re t h a n
30,0 0 0 .ve r mo st o f-in
thceref a
u slle d
e u 1 o u , ra n g e . A v e ra g e g a in o v e r
full range gre a ter th a n 1 0 , 0 0 0 (o p e n
lo o p c h a ra c t e ris t ic ).
Bandwidth: When used as a negative
Jeedback amplifier with a gain
of 10,
amp lifie r p h a se sh ift rea c h e s I
degree at a signal frequeicy
of
appro ximate ly 10, 0 0 0 cp s .
Input Irp-edan-:_ Input impedance
of each amplifier is that of an
open_
gr id p e n tode,a mprifier. c o mp u t in g
r" * ilt * n c e s ma y h a v e a n y v a lue
fr orh 2 b x toS to zo x io 6 o h ms .
Gr id C urrent:
Tota l grid curren t in t h e in n rri * rrl" ra
f f i. . inuo r d e r o f 1 0 - i b ' : j 1 " ^ jll".- a*o
| eeorefa
p e^rra tio n a 1 a m p limp
s , n ayo
n d re g u la rly lie s b e lo w
I millimicroamp e re.
In normal use as a negative
feedback amplifier, the very
reduce s out p u t imp e d a n c e o f
t h e u n it to less than one ohm.
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Operating Handbook
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output iritage may have any value
between + 100 and
load currents up to 5 milliamperes
of either polarity
r"esistance 20,000 ohms).
peak power output
of any
roxirnately 0. b watt.
ggqg,$--._ -_
i0 0 0 cp s, ma x imu m in t e rc o u p lin g
t o t h e a mp lif ie r n ex t
:u 'rt'twlrl$on pro b lem b o a rd
is a p p ro x ima t e ly 4 0 d b d o wn f ro m fr . l l
o u tput, with unity g a in a mp iif ie rs a n d
imp e d a n c e re v e l a t 1 me g o h m .
\{a ximum inte rco u p ri n g t o a ir o t h e r
a mp t if ie rs is a p p ro x ima t e ly 6 0 d b
d o wn from full outp u t . c o rre s p o n d in g
in t e rc o u p rin g f ig u re s a t s i g n a l
frequency o f 60 cp s 3 re 6 0 d b
jt
.
anO SO
Hum Level: AC hum level on the output
of any operational amplifier
is
normally about 1 milli volt,
more than 90 db down from ful1
output.
D r i ft:
S h o rt-te rm random d rif t is le s s t h a n
! 2 mv u n d e r n o rma l o pe r a t i n g
co n d itions. Long_per io d d rif t is 1 e s s
than 4 mv/hr after two-hour
wa rmu p .
over l oa d : A mp -ifie rs o p e rat e wit h o u t
o v e rlo a d u p t o + 1 0 0 a n d - 1 0 0 vo l t s
ou tput at 5 millia mpere s .
A s 1 0 a d e u rre n t is re d u c e d t h e o u rp ut
voltage range is increased, but
should not be relied upon beyond
appro ximate ly t tto v o lt s . A p p ro a c h in g
o v e rlo a d o r a c t u a l o v er . l o a d
with attendant nonlinear operation
of tarrf ampli.fier is indicated by the
lighting of the co*esponoing neon
ramp"on the amprifier panel.
Adi ustments: P o tentiome ters wit h
s lo t t e d s h a f t s , p ro v id e d f o r G a in A d j u s t ment and for coarse DC Balance adjustment
of the invididuai
a mplifiers, are conve n ie n t ly ro c a t e j
o n t h e a mp rif ie r c h a s s is ju s l
inside the comp u ter cab in e t . T h e
F in e DC B a ia n c e a d ju s t me n t s a r e
controlled by knobs which are located
on the front panel.
M e ter
The amplifier chassis is equipped
with a 4L12,, zero-center meter
which
is used for coarse and fine balance
adjustment of eacn operational
amplifier.
The
meter may also be used as a visual
monitor on the outpui or any amplifier
during
computer operation, three ranges
being provided.
Five isolated power supplies are
provided to set initial-condition
voltages
or other input functions.
Each power suppry h""voltage output which may be
connected for either polarity,
?
and which'is variable
by potentiometer control
from zero to 100 volts at up io
s milliampu"""
ioaa.
output terminals of the
individual power supplies are
avail able from the_row of
iacks on the power supply
panel' just above the problem
board.
The initiai-condition
power supplies have a
long-time stability better than 0.
5To furL-scare value.
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Analog Computer
Initial -.condition Retavs
Five low-level and five high-level double-throw relay poles, with terminals
available on the problem board, are operated by the coMpuTE-RESET
switch on
ttre power supply panel. They may be connected to set in or remove initial
conditions, or to apply a system disturbance (step function) at the start of a problem
solution.
Diode Limiters
The plate and cathode connections of two thermionic diodes are available
on the Model 3034 (and Modet 3038) probtem Board. The diodes (a Type
6ALb
tube), have their plate and cathode leads brought through the connector
which
accepts the problem board
Hold Relavs
Five si'ngle-throw relay poles are actuated by the HOLD-OPERATE
.
switch
on the power supply panel to arrest problem solution for readout of parameters.
switching back to OPERATE continues the solution.
Main Power Supplies
Both positive and negative high voltage supplies are regulated
to approxim ately 0.25%. Outp u ts a re +3 ? 0 v o lt s a t 1 8 0 millia mp e re s ria x imu m
and -300
volts at 130 milliarrPeres.
Heaters of the input pentodes in the operational
amplifiers are VR-transformer
regulated for stability of DC amplifier balance.
Dimensions
com pute r cabin e t zr r1 2 w id e x rg rlz h ig h x 1 b in c h e s d e e p .
Problem board 21 wide x 2 high x 14 inches deep.
Weight
Approximately
102 pounds (net); 110 pounds (shipping).
Input Power Requiremi:nts
1 0 5 - 1 2 5vo l ts, 6 ! cps, 3b 0 watts; zL} - 250 volts, b0 cps, special or de r .
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Operating Handbook
Page
4
Model
Juuu
THEORY OF OPERATION
General
The Donner Model 3000 Analog Computer* is a DC electronic differential
analyzer which solves physical or mathematical problems by fundamental analogy
between two equations or sets of equations. One set of equations expresses the
problem which the computer is asked to solve. The second set is either
explicitly or implicitly set up by the computer operator in order to form a consistent quantitative analogy between the two sets of equations.
fn common with other modern analog computers, the Model 3000 yields
the time-dependent solution of differential equations automatically through the
use of operational amplifiers.
These versatile computing units serve any of
the fundamental functions of integration, muttiplication or division by a constant,
addition, subtraction, and sign changing, as required to reduce the differential
equations to be Eolved to a closed representation in analog form. Direct
analogies between single electrical components and components in the physical
system are not necessary. Instead, straightforward rules of procedure permit
progressive setup of the differential equations to be solved, through the steps
of repeated integration and summation of terms necessary to find the variables
of final interest.
Operational Amplifier s
The ten operational amplifiers in the Model 3000 Computer are all
identical and are described by the simple circuit of Figure l, page 2b.
Each amplifier meets the prime requirements for reliable and accurate
performance in an electronic analog computer intended for both repetitive
and extended time solutions:
1.
Z.
3.
4.
5.
I"ry high forward gain, from DC up to tens of kilocycles.
Very low phase shift, from DC to several kilocycles-.
Balanced operation, so that zero input corresponds to
zero output, and positive or negative input signals result
in proportionate output signals of opposite signs.
Excellent zero stability as a DC amplifier.
Very low grid current and very high input impedance.
*A great many design aspects of the Model 3000 computer are
directly related to characteristics of simplified analog computers originated
in the Systems Development Section, Aviation Ordnance Department, Naval
ordnance Test station, Inyokern, california,
and used extensively at
NOTS since 1949.
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6.
7.
Very low output impedance; large output voltage range, over which
tire foregoing criteria are satisfied.
Output and input of opposite algebraic signs, so that negative f eedback results when output and input are connected through a passive
imp e d a n ce.
Operation of the amplifier of Figure L, Page 25, relies upon a Tlpe 6AU6
high-gain input pentode, and a direct-coupled Type 6BQ?A dual triode operated
as a cathode-follower output stage. The composite load impedance of the output cathode follower is a series arrangement of a Type OA2 voltage regulator
tube and one triode section of a Type LZAV7. Returned to a regutateA sou""u
of - 300 volts, the second cathode follower maintains essentially constant plate
current over a wide range of plate voltage. A high-level ampliiier output
voltage, which is balanced about zera for zero input voltage, is generated with
respect to ground at the junction of the OA2 voltage regulator tube and the
single triode section of the l2AV7. The second identical section of this dual
triode serves a duplicate function for an adjacent operational amplifier.
The cathode of the input pentode is returned to a potential which can be
varied up or down over a small range within a few volts of zero or ground
potential. The COARSE DC BALANCE potentiometer establishes
a net
positive potential at the cathode, while the FINE DC BALANCE potentiometer
permits sensitive control of cathode potential over a small range.
In order to
minimize input grid current and maintain very high gain over the desired
operating range of t tOo volts, the input pentode is operated with elevated
screen potential and with plate load resistor and supply voltage of unusually
high values. with circuit parameters as shown in Figlre 1, page 2b,
basic
voltage gain of the pentode is approximately 1000.
If the control grid of the 6AU6 pentode is held at ground potential,
the
level of plate current is established by cathode potential under the control
of
the coarse and fine balance potentiometers. For any such cathode potential,
corresponding to a fixed negative grid bias, the plate potential of the pentod!
is followed within a few volts by the cathode of the parallel-connected
Type
6BQ7A dual triode. The potential of the amplifier output connection
is lower
by the nominally constant drop of 150 volts across the OA2 regulator
tube.
An increase in cathode potential of the pentode, introduced by the coarse
or fine balance potentiometers, is equivalent io greater negative grid
bias,
and increases plate potential.
The identical increase in potenfial at the grids
of the Typu 6BQ7A dual-triode cathode follower output stage produces
an almost
equal rise in potential at the parallelled cathodes and also at ihe
amptifier
output connection. Similarly, a decrease in cathode potential of
the 6AU6
results in a decrease in the potential at the amplifier output connection.
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The normal operating point of the 6AU6 cathode
is approximately + 2
volts'
with the grid at ground. po,tential, plqte cument
will be approximately
60 microamperes and plate potential about
145 volts. with this value of grid
potential on the 68 Q?A dual triode, its
cathode potential will be approximately
150 volts'
The potential at the amplifier output terminal
will therefore be near
zero' 11
output is found to be other than zero when
'nplifier
the grid of the
input pentode is grounded, a readjustment of
6Au6 cathode fotentiat with one
or both of the DC balance potentiometers
will bring amplifier output to zero.
The coARSE Dc BALANCE potentiometer
can compensate for gross
offset in amplifier output voltage at zero
input vortage. The FrNE DC
BALANCE potentiometer has a much more
limited r*rrgu at the amplifier output,
and is used for final, accurate setting of 6AU6
cathode potential in order to
make zero amplifier output voltage
with
potential on the
input grid' once this adjustmenihas"Ir"u"pond
".io
been made, amplifier
output voltage
will be proportional to input grid voltage
over an output range of ! 100 volts.
operation of the amprifier of Figure 1, page
2s, has so far been
described without reference to the po"itirr"
ieedback introduced and controlled
by resistors R10 and R11, connected between
amplifier output and the cathode
of the input pentode. suppose that a small positive
voltage is applied at the
amplifier input. The resultant increase
in plate current of the 6AU6 will
lower the potential of the 6AU6 plate and
the direct-coupled 6Be?A dual
triode grids, and will give rise to a negative
amprifier output voltage.
The effect of the conductance through tte
connection of R10 and
Rl1 is to move the cathode of the input pentode
"""iu.
in the same direction as the
output. This is equivarent to a further
irr""u*"" in the potential;;;;"Td;;
grid, and represents positive or regenerative
feedback. The result is that
less signal is necessary on the input grid
to obtain a given output vortage.
Increasing the conductance of the feedback
path by decreasing R10 can
increase positive feedback to the point
of infinite gain, so that the ratio of
output voltage to the initiating signal on
the input grid inereases without limit.
Infinite gain can be achieved under one
set oi-lp"."ting
conditions, but the
changes in tube characteristics over the
operaiing
impose a practical
linit on average gain at the extremes
of the range. ""nge
Experimental measurements of output
voltage versus input voltage for
a typical amplifier in the Model 8000
computer are shown graphically in
Figure 2' Page 26- Infinite gain over
the full operating range would be repreeented by the straight line en = 0-, extending
rrom
100 volts-output to + 100 volts
output. The curve for the ufiioaded amplifllr (R1 = or) shows that a maximum
grid signal'of 5 millivolts is required
for operation over the full + 100 volt
range,
and that average gain over most of the
r"nj" is much greater than 20,000.
Tbe lowest value of average gain under
fulf 1oad (R1 = 20, 000 ohms) is 10, 000
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A nalog Computer
at full positive range, where a grid signal of 10 millivolts is required.
Even
under full load, average gain exceeds 30,000 over most of the operating range.
The amplifier of Figure 1, page 2b, is shown in symbolic form in
Figure 3a, Page 27. As indicated in the diagram, the gain A is verJr high, and
the input and output are of opposite algebraic sign.
When a high gain amplifier such as that of Figure 1 is used in an analog
computer application, it is made an operational amplifier by the addition of
two passive external impedances, as shown in fhe diagram of Figure 3b.
One impedance,-Zi, is connected in series wit\.the input driving voltage, ei.
The other impedance, Zf , is conneeted directly between output and input of the high gain amplifi.er and therefore introduces negative feedback. In the
schematic of Figure 1, 21 would be cqnnected between the bottom of the
OA2 VR tube (upper outpul terminal) and the grid of the 6AU6.
with the addition of input impedance zi and feedback impedance Zf,
the gain of the amplifier of Figure 1 becomei virtually independent of afl circuit parameters exeept Zi and Zy
The general case is illustrated in
Figur e 4, P age 28, wh e re n se p a ra t e in p u t v o lt a g e s , e 1 , €2 , e
3 , . . . . . €n ,
are fed to the amplifier inplt through n separatelnput imp6aantes,
21,
,t,
A
single
feedback
21,
is
connected
directly
ffiedance,
-....2n.
??,'
between input and output of the high gain amplifier'.
Since input voltage,
output voltage €e, of the amplifier have opposite algebraic signs,
"g,
-".19 gain is defined by the equation
amplifier
"g
(-A ) = e o .
If the input currents contributed by the separate input voltages are i1,
iZ.
i3.-. . . iq, and if the feedback current is i1, then continuity of
requires that
"or"ent
i1 + i2 + i3 +.....
+ ir, = i1 + i,
where i* is the current into the input grid.
Ll
€- t
-t"*Z-l
al
and
;,
ef
€r
I
- €q
=
-
But
C n-€g
€ci
Lh-
Za
I s " €"
zf
The current equation therefore becomes
€z -€9
Zz
.
't'
en-
Zn
Qa
e s- SP
z+
+ 2s
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4.q1og Computer
Making use of the equation for amplifier
rewritten
h
:
e, *ef r
Z;
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:--
(_o
Z4
gain the cument equation may be
ft *#) * js
A,s phown by the characteristic curves of Figure 2, page
26, the value of amplifier gain, A, is 10,000 or more overthe full
range o-top"""iion at maximum
rated load. Terms with the coefficient tle, may thereforsbe
neglected in
comparison with unity or with normal values of ei.
In addition, the value of
grid current in the amplifier
of Figure t has reen f";";;;-i;e
consistenly under
1 millimicroampere
(.(
amp) oira"" all normal operating conditions.
Lo-9
since other currents iri ttre
equation above will nearly always lie between
one
hundred and five million times this varue, i* may
be safely neglected.
The
resulting equation
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shows that circuit parameters of the high gain amplifier
do not enter the
expression for gain of the operationar amptirier.
Instead, gain for each input voltag.e is determined by the ratio of
the feedback impeiance to its particular series input impedanee.
The various funetions which may be served by
the generalized operational amplifier of Figure 4, page 2g, are accomplished
by using appropriate
input and feedback impedances. For argebraic
summing of input vortages,
sign changing, and multiplication
or divlsion by a constant, the feedback
imPg$ance zl gndall input impedanees ziare
lesistqrs.
These operations
are illustrated in terms of specific examiles
in the diagrams of Figures s,
I
2e-31. In pnacticaloperation,-in"_-jli3d-L*
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For the important process of integration, the
feedback impedance Z1
is a capacitor and the input impedane""
resistors.*
The characteristic
operation of such an amangem'ent can be"t"seen
clearly in terms of the
simple integrator of Figure g, page 32. Since
ig = 0, the cument through
the input resistance Ri is continuous :with
the charging current on the feedback
capacitor Cg.
*For this case, using operational
ealculus nomenclature,
operational amprifier equation ee = -
*
eo= T ur(*/*,):
h
the generalized
ei(zglz1) becomes
+#_ ^F
The output voltage is therefore the summation
lt ,nu time integrals of the
input voltages.
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t
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r
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Operating Handbool
Page
I
Analog Computer
Model
3000
If the voltage across the capacitor is V and its instantaneous charge is q(t),
the chargi.ng current is
*\*
W
t/+\:
! s
'
Jt
J/^_t-) = c +*
=
dt-
But the negative feedback operation of the high gain amplifier is sueh as to
keep €o i 0, so that the input gri.d is essentialty held at ground potential for
any noFmal value of output voltage. The current equation therefore becomes
ei :
K;
t-4 jJTV
d€a
:-L+ A
dF
I
*
I
I
r
I
r
I
r
It follows that
f
€o= Fi
!.
(
C+ Jo
er Jl +eJ
The arbitrary constant of integration
across C1 when t = 0.
'J*=o
t =o
is supplied by the voltage
These principles may be readily extended to the summing integrator of
Figure 9, Page 33. Again, since ig I 0, the total input cument is continuous
with charging current on the feedbalk capacitor.
Therefore, since ug 3 0,
the current equation is
+ tr:c€#= -c+*+
Solving for: the output voltage
n
€o : - # J - * ffr* **J*__o
I
showing that the output is the sum of the time integrals of the input
voltages, with sign inverted.
The use of an operational amplifier as a
sunrming integrator is illustrated quantitatively in the diagram of Figure 10,
Page'34., Since Ri and Cg always appear as a product, megohms and microfarads may be substituted directly into the equations in lieu of ohms and farads.
Operational amplifiers may be used under restricted circumstances to
form derivatives of applied voltages. However, because special precautions
must be observed to avoid instability, their use for this function is not
recommended.
Fortunately, it is rarely necessary to employ an operational
amplifier as a differentiator in the normal course of solving differential
equations with the electronic analog computer.
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A nalog Computer
Solution of ,Differential
E quations
By means of more complicated input and feedback impedances, single
operational amplifiers may serve a large variety of other special functions,
such as the generation of the electrical analogs of Laplace transforms.
However, their basic role in the Model 3000 Analog Computer involves their use
in combination to solve differential equati.ons. A typieal simple problem which
recurs frequently in such fields as mechanieal vibrati.on, ciriuit analysis,
and control systems is the solution of a general second order differential
equation, which is often expressed as follows:
d^e"
=
jlr. + 2f*n *tr + r,.rieo
-i
gi
To solve such a problem with the Model 3000 Computer, a formal procedure*
may be adopted in which it is assumed that an input signal representing
dtgo
dt 2
, the highest derivative,
is available to a specified operational
amplifier in the computer.
If this amplifier is connected as an integrator,
then its output voltag^e will be proportional to the next lower derivative (wiitr
sign reversed), This voltage may serve as input to the next operatg
tional amplifier, again connected as an integrator.
go , the dependent variable.
rts output will represent
The highest deriiative
in the differential equation to be solved by the
computer may be expressed mathematically in terms of lower derivatives,
' the dependent variable itself, and the driving function. In the present example
deOo
dtL
I
II
t
=
+-c,rl gi
-z g d " * ?
-u rl o o
As a final step in setting up the computer to solve the problem,
the highest
derivative is so expressed in circuit form. Lower order terms
are taken
from the amplifier outputs where they are assumed to be generated
through
the integration process.
The input driving function is supptied from an
*Detailed information on theory and procedures
in the use of operational
amplifiers for the electronic analog solution of physical problems
is given
in the book, trBasic Theory of the Electronic Analog computertt
by Dr.
R. C" H. Wheeler. This book, published by Donner Scientific
Company,
is available to users of Model 3000 computer equipment.
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Analog Computer
external function generator or is synthesized by other operational amplifiers
in the computer. A11terms are combined in the proportions specifi"d Uy tt"
di.fferential equation, and are fed together into a summit g
a"y
neeessary changes of algebraic sign are introduced by additional
"*flifi"". indi.vidual
operational amplifiers, output and input of each amplifier being of opposite
sign. The output of the summing amplifier is then connecteAto the amplifier
input where the highest derivative was first agsumed to be introduced.
t
t
l
I
I
t
t
t
l
I
I
i
l
l
t
An arra"ngement of operational ampLifiers to solve the $econd order
differential equation written above is shown in Figure 11, page Bb. As
shounr
there, the highest derivative is synthesized in the proportionl speei.fied
by
the differential equation. In this way, the unique requirements of the
are imposed on the solution delivered by the computer.
"qortiol
In order to generete the correct definite integral at the output of
each
operational anplifier connected as an integrator, it is necessary to
appty
the initial conditi'on voltages which correcily define the varioue congtants
of
integration. These voltages are maintained by separate sources until
the
ttme t = 0; then the voltage sources are si.multaneousLydieconnected
and
the problem ie released to the computer for solution.
Functional Arrangem ent
The Model 3000 Computer is comprised of three basic eections:
the
Amplifier section, the power supply section, and the cabinet.
As ehown
in the front-page photograph of Donnei Model 3000 Brochure, the
Amplifier
Panel and Power supply Panel are respectively the upper
ro*ur sections
of the complete computer, and are housed in iis cabinet. "od
The completely
detachable Problem Board, a separate item, plugs into two multi-conductor
connectors near the bottom of the p_owersupply panel, and is
normally
supported by the surface on which the computer is set (desk or table-top).
Amplifier geqtion
The Amplifier Section contains the ten operati.onal amplifiers
of the
computer, arranged side-by-side on a single chassis. As
shown ln
the top view of the Amplifier Section inside the Modei gOOO
bro"trore,
the coARsE BALANCE contrors are arranged in a row along
the back.
Next in order toward the front of the chassis is the row of oeUo
input pentodes; the 6BQ7A output dual triodes; the row of GAIN settinj potentiometers;
the oA2 voltage reference tubes; and the LzAvT dual triodes,-elch
of
which is shared between two amplifiers.
The front panel of the Amplifier
Section is furnished with a variety of
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A nalog Computer
Model 3000
controls for both selection and adjustment, and a 4llz't zero-center
meter
which serves two main indicating functions. In addition, a row
of lights near
the top of the panel serve as individual indicators of actual
or impending
overload for the ten operational amplifiers.
Arranged in a row just below the overload lights are the
amplifier
FINE BALANCE controls.
To the right of the trneter, which is centered in
the lower part of the panel, is the function selector and
meter range switch.
To the left of the meter is the amplifier selector switch.
Terminals for
connecting to an oscilloscope or other high-impedance readout
device
are located berow the serector switch on ihe right.
The purpose of tie amplifier selector switch is to connect
the meter
circuit to any one of the ten operational amplifiers for
the functions of
adjustment or indication, available on the selector switch
at the right.
The
function and range selector switch has seven positions: proceeding
clockwise,
the first three concern adjustments of the selected
amplifier:, and the last
three involve range switching of the meter, which is
then connected to the
amplifier output; the center position disconnects the meter
from the selected
amplifier, but leaves the amplifier output eonnected
to the output jaeks
below the selector switch.
Gain Adjustment
Again proceeding clockwise, the first position on the
function and
range selector switch is marked GArN.
As shown on the schematic,
Drawing 823' the operational amplifier selected by
the selector switeh
on the left is automatica[y connected as shown in Figure
12, page 86.
A 60-cycle signal of 50 volts peak-to-peak is applieo
to ttr" amplifier,
connected as a sign changer with_gain of unity. The
resulting grid signal
is brought to the output jack labeled AMpLTFTER INpuT,
,rrJtL" corresponding output signal is connected to the output jack
labeled AMPLIFIER
OUTPUT. If these output jacks are connected respectively
to the vertical
and horizontal inputs of an oscilloscope with high y-axis
glin, the
resulting trace will be a straight line having an
inclination related to
amplifier gain. Infinite gain is indicated by- a hortzontal
trace, since
grid pignal is required for an output extursion
up to t zi-"ort".
1o
For less than infinite gain, a finite grid signar of p"ih"p"
2 or 3 milivolts will be required for an amprifiLr output of
2b vorts.
The GAIN adjusting potentiometers located in
the center of the
amplifier chassis have a range of adjustment
which extends beyond infinite
gain' under such circumstances, the slope
of the trace on the oscilloscope
screen is reversed, a positive-going input signal producing
a positive_
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A n a lo g Co mp u t e r
Operaiing Handbook
P a ge
IJ
Model
3000
going output signal. As the characteristic curves of Figure 2, page 26,
confirm, the desired gain setting of each operational amplifier corresponds
to "infinite'f gain of the unloaded amplifier over an output range of t zs voLts
or more. Gain setting can therefore be made by adjusti.ng for a horizontal
oscilloscope trace as descritjed above.
Balance Adjustments
I'he second and third positions of the function and range selector
switch are marked CoARSE and FINE, respectively, corresponding to
coarse and fine balance adjustments of the amplifier selected by the
amplifier selector switch on the left. Setting of the right-hand selector swirch
to coARSE connects the amplifier as shown in Figure L3, page B?. As an
operational amplifier with input voltage at IN and output voltage at OUT,
amplifier gain is set at a fixed value of 10 by the ratio of feedback to input
r esi stance . (S e e Fig u res 4 , 5 , 6 , 7 . 1 T h e in p u t t e rmin a l o f t h e a mpl i f i e r
is connected directly to ground potential, so that no external input voltage
is introduced. As shown in Figure 1, and as discussed in the earlier
section on Operational Amplifiers (see Page 4), the potential of the amplifier
output terminal may then be adjusted to zero or ground potential by properl.y
positioning the cathode potential of the 6AU6 input pentode. (Note that
the problem board must be removed during the balancing operation). This
is the function carried out on the selected amplifier by adjusting the setting
of the corresponding coARSE DC BALANCE or FINE DC BALANCE
controls, when the function selector switch at the right side of the
amplifier panel is set on COARSE or FINE.
Figure 13, Page 3?, shows that when the function selector switch is
set on COARSE, the indicating rneter on the amplifier panel is connected
to read 20 volts full-scale across the amplifier output. Since the amplifier
is connected for a gain of 10 and has no external input voltage, the t z0
volt oulput range corresponds to t 2 volts equivalent input signal due to
unbalance.
If the cathode of the 6AU6 input pentode is far from its proper potential
the COARSE DC BALANCE potentiometer at the rear of the amplifier
chassis must be adjusted, to bring amplifier balance within range of
the FINE DC BALANCE iontrol on the amplifier panel. At the same
time, the meter reading of the output voltage can be reduced within the
t4volt range of the FINE position of the function selector switch,
shown as the alternate switch position on Figure 13. At an amplifier
gain of 10, the du@ut range of t 1 volt corresponds to an equivalent input
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Page
A nalog Computer
One minor division on the meter scale is
signal range of t 100 millivolts.
then 20 millivolts, which represents 2 millivolts at the amplifier input.
Using the FINE DC BALANCE adjustment and the FINE position of the
function selector switch, amplifier unbalance may reasily be reduced below
2 millivolts for a gain-of-ten amplifier.E Drift characteristics of the ten
operational amplifiers of a typical Model 3000 Computer on the second full
day of operation are shown in Figure 14, Page 58. The drift per hour is
shown to be less than 4 millivolts in all cases.
Meter rrOFFrr and O_utputR3nge Switc\ing
The first three positions of the function and range selector switch corcern
adjustment of the selected amplifier, preliminary to normal use for computing functions. The remaining four positions relate to ampli.fier output
indication in normal use.
In the first of these four switch positions, the panel meter is entirely
disconnected from amplifier output. However, the output voltage of the
selected amplifier remains connected to the,AMPLIFIER OUTPUT and
GROUND jacks below the function selector switch, so that connection may
be made to an external high-impedance indicator or recorder.
The three other positions of the function and range sdector switch
connect the panel meter across the output of the seleeted amplifier, with
full-scale range indications of t 100 volts, t 20 volts, and t 2 volts,
respectively.
In all cases, the output terminals of the selected amplifier
remain connected to the output jacks below the right hand selector switch.
xlf the potential at the amplifier output is es above ground due to unbalance
and the input terminal is connected to ground as shown in Figure 13, a
eo
must flow between the amplifier output and ground
current
R1 + R1
(since L g = O). The voltage rise of the grid terminal with respect to ground
will then be
s5
R;
R ,' + Kf
The actual grid-terminal
balanced output is, therefore,
factor
* o ('t !\tB rlL fix€ E>
unbalance associated with a particular unIess than the output meter reading by the
In the Model 3000, this factor is approximately 11.
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Operating Handbool
Page
Analog Connputer
Model 3000
15
As an output indicator, the panel meter is of value as a monitor and
as a quantitative readout means for data, within its limited speed of response.
For rrtore rapidly varying output data, quantitative presentation may be
made visually on an oscilloscope or graphicatly on a high-impedance pen
recorder connected between the AMPLIFIER OUTPUT and GROUND
jacks, below the function and range selector switch.
-Powg,T.STppIyP,aLe1
The Power Supply Section contains the main regulated power supplies
for the operational amplifiers,
the separate regulated initial condition power
supplies with their output controls, the relays participating in computing
operations, and the connectors which carry supply voltages to the amplifiers
and conduct the computing functions to the Problem Board. Top and bottom
views of the Power Supply Section are shown in photographs inside the
Mode1 3000 Brochure. As shown in the top view, the right-hand half of
the ehassis contains the hi.gh voltage transformer and the regulating circuitry
of the negative and positive power sup