YEW Series 3300 Analog Computer
Series3300
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All Solid.State
Low-drift and stable operational amplifiers
High Speed Computation Low Speed ConversionType
While observing wayeforms on a Cathode-ray oscilloscope, you can
simultaneously record th€m rvith an X-Y Recorder (in combination
with Waveform Translator for Recorder).
ComputationImpedanceot O.L%
0.1%computation
accuracyis ensu:ed
for all linearcomputing
elements
and such nol-tinear computing elements as multipliers and variable
diode function generator.
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GENEFAL
DESCFIPTION
One of the most outstanding features of yEW
Series3300Analog Computer family is that they have
a summing integratorwith a wide range of time constants covering both low speedcomputations and high
speedrepetitivecomputations. Due to the employment
of this unique integrator,YEW Analog Computerscan
provide advantagesof both high spesd and low speed
computations. Particularly, the YEW original ,,High
SpeedRepetitive Computation Low SpeedConversion,'
method makesthe YEW analog computersdistinguished
from all other analog computers in the market.
The following two types of computing systemsare
availablefor any 3300-Series
Analos ComDuter:
High S peed R e p e ti ti v e C o mp u ta ti o n
Low Speed Gonversion Type
In this type of computingsysremthe high-speedcomputed solution waveforms are obsetved on a
cathode-rayoscilloscope
and at the sametime recorded
by an X-Y recorder after the solution is low_speedc onr er r ed by th e u n i q u e s a m p l i n g ry p e * uui for.
translator. The large waveformson the X_y recorder
facilitate highly accurate readout. The adoption of
s am pling m et h o d e n a b l e sth e re c o rd e rl o a i curarel v
record even such solutionsas conrain high frequency
components. This system consistsoi computing ele_
ments accurate to 0.1%. This js recommendedfor
high precisionanalysisin generallaboratories.
High SpeedT'Low Speed
Com put at ions S e l e c ta b l e T y p e
This system is provided with a mode selection
switch on its hont panel to switch over from the
high-speed repetitive computation to the waveform
computation so that the solution shown on the cathoderay oscilloscopemay be recorded by an X-y recorder
or a pen-writing oscillograph. This system consistsof
computing elements with 0.5"1 acatracy This is recommended for simple computation or educational
purposes.
training
To give full play to rhe functions as the analos
c om puler .v ar io u sry p e so f l i n e a r a n d n o n -l i n earcoml
puting elementsare made compatiblewith the yEW
Series3300 Analog Computers. The computing.ele_
ments are all usablecommonly for Types 3301 througb
3306Analog Computers. Therefore,rne same accuracy
is guaranreedin borh !mall-sizeand large-sizesystems.
and c ons eque n tl yb u i l d i n g u p fro m a s m a l l -si /e uni l .
to a large-sizesystem requires no extra device for
adjustment.
To sum up, the YEW Analog Computers are the
products to exactly meet the requirements of today's
scientific and industrial activities. They are epochmaking systems designed with an extremely rational
mind on the basis of a long time experienceof YEW
in analog and pulse techniques.
FIELD OF APPLICATION
The scope of application of analog computers is
limitless. The following ate some examples of phenomena or systemsthat can be simulated by analog
compute6 :
Fi el d
Phenomenaor Systems
ElectricPower........-Powersystem, characteristicsof
rotors.
Electronics ............Linearand non-linearcircuits,distributed constant system.
Automatic Control...Processanalysis,designingof control units.
Atomic Power.........Dynamicharacteristics
of atomic
pile, control system.
Mechanical
Engineering. . . . .. . . .. .Vibrations of beams, vibration
s5srem ol spri ngs.
P hysi cs....-.............Thermal
propagati on,so und system, fluid analysis.
Chemistry.......
-.......Chemicalreactions,reaction velocity.
Automobile ............Ridingcomfort, changegears.
A i rcraft................._C omputati of
ons vi brations and
stability.
S hi p .... ... . ...... .... ...y7x1g5
Architecture ..........Eadhquakeresistance
of buildings
and bridges.
Civil Engineering . . .Flood, tidal waves.
Mathematics .........Non-linear differential equation,
algebraic equation with multiple
unknowns.
B i ol ogy..................E nvi ronmental
ci rcumsta nces
and
growth of animals and plants.
Medicine and
Physiology ............Simulationof living bodies.
Economics ............Business
cycles,economicgrowth.
OUTSTANDING
FEATURES
C ompl etel y S ol i d-S tate
with increased
All circuitsare silicon-transistorized
reliability.and lesspower consumption. Reducedsize
provides more conveniencefor operation.
H i gh P reci si on
Computingelementsare accurateto 0.1%. Highly
stable metal film resistorsand polystyrolcondensers
are usedas compul i ngi mpedance:.
A ccurate R ecordi ng of S ol uti on
Accurate recording of any solution waveform is
attributed to the sampling type wavelorm translator
incorporated.
S ummi ng Integrator w i th Tw o S el ectabl e Tim e
Constants
Time constantfor integratoris changeableto I sec
and 1/l0sec fuomthe front panelfor easierobservation
and analysisof sohltion variation.
E xcel l ent S tabi l i ty
FET choppers in operational amplifrers provide
very stable operationwith minimum drift.
B ui l di ng B l ock S ystem for Increasi ng Fl exi bilit y
Series3300Analog Computers employ 'separate
power supply system", so that a larger systemcan
be made only by building up additional units
on the basisof Type 3301,each of which has an rn-asily
diviclual power sttpply. Therefore,it is very easy to
i ncrea.ethc .omtrul i ngcafabi l i ri e\.
Modul ar C onstructi on
Computing elementsfully gmploy modular construc(i on to faci l j tal e repl acementor e\pan5j o n as
required.
TYPES
AVAILAFLE
Prepatch
Board
Analog Computer
Type 3301
Type 3302
Tvpe 3303
Tvpe 3304
Tvpe 3305
Type 3306
P repatch B oards w i th Graphi c D i spl ay
Very convenientfor referenceto block diagrams
or drawingsof operatingprinciple
Max. 10
Max. 26
Max. 36
Max. 36
Max. 72
Max. 72
Provided
Provided
A ppl i ca bl e for H ybri d C omputati ons
can perform
The large-scalesystemof 3100-Series
si mpl e hybri d computati onsi f di gi tal l ogi c uni ts ar e
incorporated. In addition, complicated large-scale
hybri d compul ati ons can al so be made i f a digit al
computeri s connectedto the Y E W anal ogcompu t er .
..E}IJILDINGE}LOCK"
EXPANSION SYSTEM
The YEW Series 3300 Analog Computer family is
flexibly built up from the minimum unit of 10 operational amplifien up to the large-scalesystem of 72
opgrational amplifiers, In other words, a system of
minimum required size for a particular analysis can
easily- be composed by selecting exactly necessary
computing elementsonly. The computing elements
L ine ar C om put ing Elem ent s
t'
-Tr
g
No n - l i n e a r C o m p u t i n g E l e m e n t s
I
I
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I
I
T
ir
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:t
*t
Type 33Ol
Max. l0
Type 3302
M a x.2 6
o p e .a ti o n a l a ftplifier s
ope.r r ional am pline.s,
$
Auxiliary Devices
rrrrtrrrrrr
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can freely be changed in accordance with the size of
the problems. The varietyof computingcapabilitiesof
YEW Analog Computgrs satisfiescomputing requirements better than any other analog computer ever
produced in the world. The illustration below shows
the entire line-up of the YEW Series 3300 Analos
C omputersi ncl udi ngrari ous computi ngel ement s.
r/-
Co m puting Elehenr s ( buitr - in)
n u x ir iar r
Devic€s ( builr - in)
llI
A u xiliar y Devices ( exter nally connecr ed) Types 3303 & 3304
----f
lOOitiotat
co nputing
Type3 3305 & 3306
Max. 36 ope.al i onalampti fi ers Mar(. ?2 ope.ational amplifiers
F€arures for incre.siDs
eftciency( b!ilFin)
FUNCTIONS OF
COMPUTING ELEMENTS
LINEAF
COMPUTING
ELEMENTS
Coef f ic ient Po te n ti o m e te r
Thjs is a 1-turn variable resistorfor setting coefficients and can be set at an accuracy ol 1i1000by
making this unit balancewith the referencecoefllcient
potentiometer provided in the computation control
unit . A lo- tu rn h e l i p o t c a n b e a tta c h e dt o the uni t
upon requesl.
Dual S um m i n g Amp l i f i e r
A pair of summingamplifierelementsare contained in one unit. When a feedbackcircuit is made by
shorting its upper right and left holes with a boule
plug and multiple inputs are connectedto it, this unit
providessumming functions and producesan output
of reversedpolarity. " SJ" is a summing junction
terminal. In case there is only one input, this unit
works just as a polarity reversingunit. If the feedback circuit formed by the bottle plug is removed,
this unit becomesa high-gain operationalamplifier,
which is used for direct simulation of a control system
by connecting arbitrary input impedance and feedback
impedancethrough SJ (summing junction) terminals.
It can also be used for non-linear coemcieot generation
if free diodesare used in combinatioxwith it.
Dual Summing Integrator
A pair of summing integrators specifically designed
for high-speed computation are contained in one unit.
When a feedback circuit is made by shorting either
of its two upper capacitors with the output side by
means of a bottle plug, and then a number of inputs
are connected. this unit performs summation and integration and provides an output of reversed polarity.
"IC" is a terminal for the initial value of variables
at the output side and provides a reversed polarity.
(Dual summing integrator specifically designed for
low-speed computation to be used for applied measurement is also available upon request.)
lntegrator Summer
This unit consists
of a summingamplifierand a
summrng lntegrator for high-speed,llow-speed comp u t a t i o n . T h e s u m m i n g i n t e g r a t o r c o n t a i n s a ca p a ci to r
f o r l o w - s p e e d c o m p u t a t i o n w h i c h i s a u t o m a ti cr l l y
changed over by the computation mode selecting signal
from the computation control unit. The method of
patching in this unit is the same as in the unit for
high-speed only.
Coefficient
F€edback Circuit
(by 6horting with bottte ptug)
D ual S umml ng
A mpl i ti er
Integrator
NON-LINEAF
COMPUTING
Multiplier {Time DivisionType)
This is a high-efficiency
multiplierwhichemploys
th e t im e div is ion te c l tn i q u e o f mu l ti p l i c a ti o n. B y
ch anging t he pos i ti o n o f th e b o ttl e p l u g s , a si ngl e
u n i t c an per t br mt h e th re e fu i c ti o n s o f mu l ti p l i cati on,
d i vis ionand s quarero o t.
Free Diode Resistor
This resistorconsistsof a unit which providesreferencevoltagesof +10V and -l0V and two diodes
which ar9 incorporatedinto the unit. This resistoris
used in combinationwith computing elementsto generate various non-linear elements (saturation, dead
band simulation and hysteresis).
Va riable Diode Fu n c ti o n Ge n e ra to r
This unit approximatesan arbitrary function by
meansof l0 broken lines. The position and inclination angle of each broken line can be adjusted from
the holes on the surface of the patch board with a
screwclrrver.
Fi xed Diode F unc ti o n Ge n e ra to r
This unit generatesa fixed function which is approximated beforehand by broken lines.
Multlpli€r
(Time Dlvlsion Typs)
Free Diod€
R€slstot
Varlbble
Diod€
ELEMENTS
The following kinds of fixed function generators are
avai l abl e:
Sine Diode Function Generator
Cosine Diode Function Generator
X'? Diode Function Generator
?-Log Z Dtode Function Generator
6'Comparator
This unit containssix voltagecomparatols.In
combi nati on w i th an 8-A nal og or an 8-E l ect r onic
or used
Switch, this unit is usedfor signalchangeover
as a non-linear element such as saturation, absolute
value,etc. This unit is also used in combinationwith
x Logi c A ..embl ) l or l ogi c computrti on..
S .A nal og S w i tch
8-E l ectroni c S w i tch
The 8-Analog and 8-ElectronicSwitchesare electronic switches,the former using mechanicalrelays and
the l atterusi ngFE T' S . E l ch oftheseuni ts i s composed
of four pairs each of make-contactsand break-contacts,
which are used being connected to the SJ terminals
of Summer or Integrator.
S i ne D i od€
Xt Oiode
Gon€rator
Gsnerator
6-comParator
8'Electronlc
\NAVEFOFM
TtrANSLATOF]
solutionwaveFor analysisof low-speed-computed
forms, a pen-writing oscillographhaving a liequency
responseof about l00Hz is generallyused.
Hotyever, the recording width of a pen-writing oscillograph is 40mm or so, and it is difficult to expect a
better accuracy than 2-3% from it,
This means that the record analysisby low-speed
conversionplaces a limit on the final recording accuracy even if the accuracy of the computing element
is increased.
In high-speed computation, each single computation
is performed within a very short time and this computation is repeated. Once the coemcient is fixed, the
same solution waveforms are repetitively obtained.
Using pulse tgchniqugs, this Waveform Translator
samples these continuously repetitive waveforms point
by polnt and strings up these points, thereby converting them into waveforms which are completely analogous to thg original waveforms,changing so slowly that
the X-Y recorder can follow. Since the amplitude and
timg saaleon the recording paper accurately correspond
to those of the solution waveform and only the recording speed is converted to a lower speed,the waveform
is reproducedon the recording paper with an accuracy
of +0.5%, however complicatedit may be.
Since high-speed computation is continued even when
recording is being carried out, there is no need of
changing over the integrating time constant (capacitor
of integrator) from a high speed to a low speed by
means of a relay or the like.
FOF trECORDEF
Consequently,the translator reliability increases and
it provides a solution waveform which is very stable
and has excellent reproducibility. A solution waveform at a different parameter can also be recorded
being superposed on the same recording paper, and
this feature provides convenient comparative observation.
Waveform Tran.lator
for Recorder
-
(S horti nc rvi th bottl e P l uc )
Setti ne
of ti m e
bas e
+ (shorti nc w i th bottl e pl uc )
Setti ne
of r ec or c l i ng
sPeed
S tart and reset contro l
+ Output Y
.-- Output X (T)
Function Generation with Free Diodes
o
Absolute Value
Dsad Band Simulation
Hysteregig
9
COMPUTATION CONTFIOL
UNITS AND
AUXIUAFIY DEVICES
TYPE
A CONTtrOL
UNIT
This is a control unit to be used for Types 3301
and 3302 Analog Computers. It consists of a computation controller for sta , rest and stop, a voltmeter
to measurecomputation output voltages or set the coefficient potentiometer accumtely, and a refgrence coefficient potentiometer. The high-speed computation
time is a constant 55 ms.
TYPE
A CONTFIOL
PANEL
This is a console-typecontrol panel for Types 3303
(3304)and 3305 (3306)and consists of the following
componenls:
a Power source for refergnce voltage (provided with a
referencecoemcientpotentiometer
and a voltmeter)
a Control signal generator (high-speed)(Computation
time can be switched in four stagesof lOl2DlsOllOO
ms.)
a Control signal generator (low-speed)(This unit performs low-speedcomputation control and switching
of high-speedcomputations.)
a Signal distribution (This unit distributes control
signals and computation signals to their respective
panels,)
a Waveform Translator (A two-channel wavgform
translator is built in.)
CATHODE-FAY OSCILLOSCOPE FOFI MONITOFIING
This oscilloscope
is used lor monitoring the solution waveformson a high-speed
computer. Withthisoscilloscopeemploying the brightness modulation system,
it is possiblg to observg the waveforms and phasesof
four channels (maximum six channels) simultaneously.
The cathode-ray oscilloscopeis a 9 inch square type
ano very easy Io se9.
Sys t em :
Brightness modulation system
9-inch electromagnetic deflecCathode-ray
:
tion type
Oscilloscope
Number of Channels: 4
ll2l5 Y ; accuracy *51
Vertical Amplifier :
Time Base:
Synchronizedwith control signal generator
10
a,,h /r-"1 ty 2r z
DIGITAL VOLTMETEFI
<TYPE 2BO5>
fl
t t'
This is an extremely stable, noise-rejectedintegrating type digital voltmetercapableof lopv resolution.
It is used for calibration of computing voltages,measurement of output voltagesof computing elementsand
setting of the coefficient potentiometer.
MeasurementMethod: Feedback pulse width modulatio[ counting method
Max. Indication:
59900
Accuracy :
IO.0l% of reading +l digit
u
DELAY
o
ll
tf
DEVICE
As a dead time element, this device is used for a
procasssimulator and for forecasting business cycles.
It maintains the amplitudes of input signals as they
are and delays time only. Delay time can be changed
with the dial. Since this device adopts the delay circuit
of a newly developed / t modulation system, there
is no disturbance in waveforms at rise time as is gxperienced with the Pad6 system.
LOGIC ASSEMBLY
<TYPES 3351 S.3352>
This assembly widens the scope of application of
analog computers. lt is capable of such functions as
logic judgement, counting and storage, and makes
possible such automatic computations as A-D/D-A
conversion and sequencecontrol.
Type 3351Logic Assembly consistsof the followina
C.P. Res is t or Count er
.. .......................1
G . P . I nd i c a to r
.....................1
Cloc k a n d C .P . In d i c a ro rT e rm i n a l................1
F lip- f lo p In d i c a to r
...............1
Cloc k G e n e ra to r
..................1
T ie P oi n ts
...........................1
For details,a separatecatalog is available.
X-Y FIECOFDEFI
<TYPE 3077>
This is a single-penX-Y recorderto be usedin combination with the Waveform Translator for Recorder.
It has a recordingarea of 250X250mm and records
the solution waveform of an analog computer accurately and in a large form.
Voltage Divider:
0.1mV/cm- l0 V/cm (changedover
in l6-steps)
+0.3% of full scalespan
HO\N TO SELECT
COMPUTING ELEMENTS
1.
F ir s t det er m in e th e a p p ro x i ma te n u mb er of
unit s of ope ra ti o n a l a m p l i fi e rs a c c o rd i ng
t o t he s c ale o f y o u r c o mp u ta ti o n a n d the
pr obable f ut u re e x p a n s i o n o f y o u r a n al og
c om put er .
Select the most suitablg analog computer from the
following according to the number of units (operational
amplifiers) required (see page 5).
If you require lessthan 10 units: Type 3301
Analog Computer
'fype 3302
If you require 1l to 26 units:
Analog Computer
If you require 25 to 36 units:
Type 3303
or Type 3304
(Prepatch system)
Analog Computer
If you require 37 to 72 units:
Type 3305
or Type 3306
(Prepatch system)
Analog Computgr
Then select the ones you require out of a variety of
computing elements,while making sure that the number of computing elements,you have selectedis within
the number of units shown in the following table (Do
not include the Coefficient Potentiometer nor Dual
Free Diode Resistorin the number):
Type
Number
of Units
3301
3302
13
3303 . 3304 3305 . 3306
18
How to Select Coefficient Potentiometer
The one-turn Coeffcient Potgntiometeris suffcient
for all purposes. The ten-turn Coefficientpotentiometer
has the advantage of making the setting of coemcients
slightly smoother. The number of Coefficiehtpotentiometers that can be equipped to various analog computers is shown in the following table:
Type
3301
3302
Number
of Units
8
16
3303 . 3304 3305 . 3306
36
72
4.
How to Select Type A Gontrol Panel (For
Types 3303-3306 A nal og C omputersl
The component units of the panel vary according
to computing systems.
High-speed computation:
Control Signal Generator (low-speed) is not required.
High-speed/low-speedcomputation selectabletype :
Waveform Translator is not required.
Low-speed computation :
Neither Control Signal Genehator (high-speed)nor
Waveform Translator is required.
Three units of Signal Distributors arg required in
any case.
36
Count the Waveform Translator for Recorder as one
of the above-mentioned
computingelements.
2.
How t o S elect S u m m i n g In te g ra to r
For high-speed computation and high-accuracy
analysis,use:
Dual Summing Integrator (Code 33l7ll)
Note: When Type 3301or 3302AnalogComputeris employed for high-speedcomputationand highaccuracyanalysis,
addoneWaveformTranslator
for
Recorder,
For high-speedcomputation plus low-speed-computed
solulion waveform recording,use:
Integrator Summer (Code 331811)
For low-speedcomputation such as in applied measurement! use:
Dual Summing Integrator (Code 331751)
L2
3,
5.
Other Devices
The 36-unit Analog Computer can be provided
with the following devices: One Monitoring Oscilloscop9, or any two units out of the Digital Voltmeter,
Delay Device and Logic Assembly.
The 72-unit Analog Computpr can be equipped with
one each of all the above-mentioneddevices.
> For EducationalTraining Use {
The fol l ow i ng compuri ng el emenrshavi ng 0. 5oo
computation impedance accuracy are also available
for training students on analog computers:
Dual Summing Integrator
Code 331721
(for high-speed)
Dual Summing Integrator
C ode 331761
(for low-speed)
Integrator Summer
Code 331821
Dual Summing Amplifier
Code 331621
Coefficient Potentiometer
C ode 331531
o
tta
i
r .r r
i* !
a.Ar .t
I
I
I
t
I
t
t
l.
r illr
;
1-i;.i-f
f -' , " -:
I
l ;n,l
a
t a.-t
I tl_:N
I -,:.,^ |
t:l1i
r !-r.
'-.
'i}r
.ti
I
I
,
,I
I
I
I
,
,.
I
I
I
a
I
. tl,
I
.l
/*l
l {L'r
r *t
r'
ftl
?
?
I
l,
tI
f,
f.
I
I
t
a,
j {tr
flit
ili.r
{-:-r
?
?
I
the
a
a
a
, .i
,-.1
r;i
,
I
.ga
In a series resonancecircuit, the switch K is placed
to E side to charge the capacitor C, and next, the switch
is placed to L-R side, Then, let us observe the state
of this discharging current,
E:6.94 V, C:1,2
pF, L:5.1
mH, R:201)
(I) FROMFORMATION
TO PREPARATION
OF EQUATION
OF BLOCKDIAGRAM
(Ti me S cal i ng)
Although the equation (7) has given the yoltage
which is within the range of +10V, the solution
contains (r: /i^5-taaq
a frequency component of
L or
+ r R i- i(l.i, a t- o ....................................(r)
about 2 kHz.
Becauseof the frequency response of the computing
SinceI idt:q. we obtain
J
element and the necessity of recordi.og the solution,
A2^
A^
L:- ; - R * +1 .:o; ir r:0. q .cE ......... . . . . . . \ 2 )it is necessaryto do time scaling to reach near @:1.
dr.
dt
L
T:Ft ................
........... . . . ( 8)
1f we divide the equation (2) by L and substitutenumeriwhere T is the computer time after the time scaling
cal values, we obtain
and p is the so-called "time scale factor."
A2a
d^
To make <o:1 in this problem, it is necessaryto make
1. 92 103 = + 1 .6 3Y l 0 3 q :0 ;
(lt'
ot
x loa, but we adopt i3:10a for the
F: lt'lxrc":t.Z8
-+
convgnienceof later conversion.
Now, since T:10!t, we. obtain
dQ _ ,n,,dQ drQ _ ,.,, dQ
-' "
-' "
dt
dr'
dt,
dr
If we substitute the above into the equation (7) and
learrange it, we obtain
(Formation of Equation)
If the circuit current at the time switch K is placed
to L-R side is denoted by i, we obtain
dza'\
:--:1!
(Scaling)
In computation with an analog computer, the indspendent and dependent variables are replaced by
time and a voltage respectively. Since the range of
computation voltages of the YEW Series 3300 Analog
Computersis -10V through +10V, it is necessary
that variations in th9 voltage of dependent variables
be within this range. If we assumethat the variable
in the computer, which correspondsto the actual
variable q, is Q volts, we obtain the following conv9tslon I
. . ... . ..... . ..(4)
Q : aq . . . . . . . . .. . ..
d is called the " scale factor " and can generally be
obtained from the following equatlon:
Max. computation voltage
d<
Max. value of dependent variable
In the presentproblem, we obtain from the equation (3)
10
t.2 z 1 0 c ..................... . . ...(6)
" . T J - l0"
In consideration of convenience in later conversion,
we selecta:106.
The equation after the scaling will be
.lat
n tot-:-
a I <1a\-n.
" --- dr
i f t:0, Q:8.33
Here, the differential term of the highest degreein the
above equation is kept at the left side, while the rest
of the terms are transposedto the right side for preparation of the next step.
dT,
d2a't
*:
qr.
.ln
-0.392#ol
1.630:
(P reparati on of B l ock D i agram)
Now we will illustlate by block diagrams(Figs. 13) how to solve the equation (9) by the combination
of computing elements.
Set up a seriesconnection of two Summi:rg Integrators
and assumethat the input terminal a is drQ/dTr.
Eyely time the input signal passesthrough one com.12rl
drl
puting clement, the sigq is invelted, and the yoltages
F1.92. r03F+ 1,63/l03Q 0r
ii
at points b and c bring about the relation illustrated
if t-0, Q-8.33...................
...................(7) in Fig. 1.
74
a
-
(rrlPATGHING
Patch cords are used in connecting computing
elements according to the Block Diagram. The time
constant of the Summing Integrator is ordinarily set
at 15. A bottle plug can be conveniently used for
connecting two adjoining units,
Take out these signals of -dQ/dT and Q and form the
terms on the right side of the equation (9). Now, a
value above I aannot be set.by the Coefficient Potentio- d!
meter. Therefore, in order to set the value of 1,63,set or
0.163 on the Coemcient Potentiometer and multiDly
the gain of the computing elementten times.
ff
F
"o.o.
",.,"
(III)SETTINGOF COEFFICIENT
POTENTIOMETER
( 0 .3 e 2 :;+r .n a )
(".*,j$_r.o:o)
The equation (9) means that the voltages at points a
and d in the diagram (Fig. 2), which was formed in
the way explained aboye, are equal. Therefore, the
Block Diagram can be completed for the time being
by connectingthese two points by a dotted line. The
initial yalue of Q is given to the IC terminal of INT,
by inverting its sign at the output side.
On looking gloser at the dia$am in Fig. 2, it is found
that INTI, a Summing Integrator, can add aqd integrate
a multiple number of inputs. Thus SM2 and SMg
become unn€cessary;an{ finally, the Block Diagram
shown in Fig.3 is completed.
INT
'
-
Set the computationmode swilch to RS and rhe
voltmeter function switch to PS, For setting the value
of, say, 0.29, first set the REF POT of the Computation Control Unit to 0,29, Then while depressingthe
setting push-button of the Coemcient potentiometer
to be set, using the index finger of the right hand,
turn the kDob with the thumb and middle finger, so
that the pointer deflection of the voltmeter comes to
zero (center).
5'
LNT.
F la . 3
15
coiii'!' "r' 1T:'1i'
{lv) }'llc$l"SPEED
rjil ,i{, .F,1,,.. .i,: -i tria..lill..r,_,i.,,i
iltii
Airer ' r he s et t ing of t he pot ent iom c t c i i s c o m p l c t e d ,
turn thc c om put lt ion m ode s \ r it c h i o R O , a n d t h c
l n t r o d u c c t h e s o l u {i o n \ o l t a g e i n t o th e j n p u t tcr hjg h-spe ed c onr p! r t at ion s t at e is as s u m e d . l n t r o d u c e
n t i n r l o i t h e Wa \ c l o r n l T r a n s l a t o r a n d co n n e ct i ts
thc soL ut ion \ olt ages int o t he os r llln s t o p e . a n d t h e
o r . r r n u r t e r m i n a l w i t h t h e X - y R e c o rd e r . Se t TIM E
so lutio n wav ef or n' r sc an be obs c r v c d. If l h e o u t p u t o f
B A S E o r d i n a r i i y t o 5 0 m s , a n d s e t pEN Sp EED to
the TRIG terminal of the Computation Control Urlit
FAST il the wavcforms are simple ones, to SLOW if
is used as thc horizont:rl synchronizing signal of the
lhe
waveforms are complicated oncs, and to MEDIUM
-;."
Oscilloscopc, stationary waveforms ccn bc obtnin,;d.,
cases. Short the holes of SHORT RESET
. in ordi1,]nr,v
Tf the ti nr e c ons t ant of t he Sum m ing I n t e g r o t o r i s s e t
b e l o r e h a n d w i t h a b o t t l e p 1 u g . Wh i l e m a j n ta i n i n g
' the state of high,speed computation, lower the pen of
at 0.1S, *aveforms, u,hich are made slower, as if the
computation tinc {ere elongated ten times, can be
ihe X-y Recorcler, remove the bottle plug, and the
obtaioed, Therefore, you can analyze the initial statc
wavelorm will be recorded from left to rjsht. Lift
in detail at the setting of 1S and find the general trend
the pen and jnsert the bottle p1ug, and the pen will
at the setting of 0.1S.
return to its original position.
Futing
I llme
il t 's e t
rd for
S OLU TION WA V E FOR M
ar o.ls
nd the
! \'aluo
mputarng the
ometer
hand,
ger, so
mes to
RECORDING
N) SOLUT]ON
BY
LOW-SPEED
COMPUTATION
lntroduce the solution voltage into the input terminal of the pen recorder. Set the computation mode
switch first to RS. Select the proper sensitivity of the
pen-recorder and start feeding the recording paper.
Then cha.ge over the computation mode switch to
OP, and the low-speed computation will start and the
solution waveform will be obtained on the recording
paper. The waveforms on the cathode-ray oscilloscope
n atu rall y dis appear dur ing low- s peed c o m p u t a t i o n .
15
L€t us analyzethe followingMathieu's
equationx:
i*+
ot"
12(1+ €coszt)v:0 ;
if t:0,
y:2
*Mathieu's equation is used when Laplace'$ equation i$
analyzed by m€ans of cylindrical coordinates and when
vortex movement in an elliptical cylinder or attenuation
of magnetic force in a metallic cyli[der is analyzed. It
is orle of the most important equations in eleatrical and
mechanical engineering.
If we assume that coemcients I and 6 haye th€
following values, we can procefd \trith programming
immediately without scaling :
10Z t ) 0, 12e) 0
(Programming)
I-et us proc€cd with programming by modifying
the given equation,
:-L: - )z {y +€ cos2t.y}; if t=O, y:2
dt.
(Generatlon of cos 2t)
The generalized cos (1rt can be obtained as the
solution of the following €4uation :
A2!
E + ar 2x = 0:
dtz
if t= 0 - x = 1
The above equation can b€ made into the following
Block Diagram :
Olle Coefficient Potentiometer could set the value of
d but the method shown in the above Diagram has
been adopted, because a, can be directly read out and
the unbalance among the computation voltageo of the
respectivecomputing elements can be diminishe.d.
(Ghcle T€rt)
A tri&snometrical function is generated by setting
th€ above-mentioned 4, to 1, and ths quantity of attenuation of its amplitude is us€d as a guide in judgement of the characteristics of the analo! computing
clement (sce the specifications on p. 20).
Clrclo To3t I
4 9 - xtn %
I
L7
EXAMPLE OF SOLUTION WAVEFORIiI U=rO, t=1.O1
F
I
2
L€t us analyze the following simultaneous difrerential equations with two
unknowns :
2i+ l+ 3Y+ 66x
8y : 0
4y + i+ 8i+ 16y - 1' 15x : 0
I f t : 0, x : 3, y :
5, i: i: 0
First we divide the above equationsrespectively
with the coemcientsof i and y,and obtain
i + 0. 5i + l. 5i + 3 3 x 4 y :0
y + 0.25Y+ 2i + 4y + 3.75x:0
Then we assumethat T:2t and perform the time
scaling of the above equationsto obtain
X - - 0. 25X - 0. 7 5 Y - 8 .2 5 X+ Y
Y:
0. 125Y x Y 0 .9 3 7 5 x
I f T : 0, X : 3 , Y:
5 , * :V:0
n. ti
I or5
Let us solve the following
equation :
xri 2x- 5x + 6:0
algebraic
The analysisof differentialequationsis the specialty of an analog computer,but variousstudieshave
been carried on to solve algebraicequationsalso with
an analog computer. The following is one of the
examplesof this type application:
We divide the above-mentionedequation by 5 to
facilitate setting th9 coemcient.and obtain
0.2x3 0.4x'?-x + 1.2:0
W e usex= t and consi der(t):0.2tr 0.4t' : t+ 1. 2.
By programming this equation,we obtain lhe Block
Diagram as shown below. We are going to obtain
the value of t just when the output (t) has passed
through 0 in its downward curve. In caseof x<0,
(becauset cannot bg a negative value)
we use -x-t
and repeat th9 same procedure after re-writing the
equation accordingly.
o
0 .6 f +0 . 8 r + I
rrl
\r
rl \r
+l 0 V
( - lOV)
18
10V
1 0 V X >0
( +1 0 V )- 1 X <0 )
!
controller
Suppose there is an automatic control system that maintains
a constant level of water in a tank. Let us analyze the level
variations that may occur when the piping undergoes pressure
changes (external disturbances).
The transfer function of the water level svstem can be exDressedby the following equation:
-nR: Tl S +r m
w her e
i-
T S +r P
b: Lev el c hans e c odponent of l be r ank
R : Pi pi ns .es i s l anc e
/.: C hange c om ponent of pr es s ur e head of pi pi ng
m : C hans € c om ponent of fl ow r ar e
T : T i m € c ons tant of the tank
Ifwe assumgthat the controller performs Pl (proportional+integral)control,this systemcan be expressed
by the following Block Diagram:
SOLUTION WAVEFORM
Desired value
Kcn+;t )
Now we will find the variation of h when we assume
T:12 sec
R:6.8 m3/sec
p- l m ( : + l 0 V)
and causg the constants Kc and Ti to change.
Since we are dealing with analysis of the changecompodent, the desired value *ill be 0.
SPECIFICATIONS
1. GENERALSPECIFICATIONS
R efe ren ceVo ltag e: +10V, l0v wit h ac c ur ac y+ 0. 1 %
circle Test : High PrecisionHigh Speedtype ; +0.05%lcycle
(r-1 0 J, coe lllcre nt= l) . High- SpeedLow- Speed( om p u '
c y c lel- - l. c oem c r enl - 1 ,
ratio ns Se leclab lellpe; ' ip%
Normal Operating Condition: Temperature;5-35"C (41'
95'F) Hu midity; 80% M ax .
Power Supply: AC 220V +10%,50-60 Hz. OtherVoltages
are also availableupon tequest.
Dimensions:
166x 497x 400m m ( 6% x l9% x 15 %" )
T yp e 3 30 1........-... . . . .
316x 497x 400m m ( 12% x r g% x 15 %" )
T yp e 33 02 ........... . . . .
Types 3303& 3304......992x570x550mm(39x22)ix20%")
1100x 550mm (39x 43% x 20%'/)
Types 3305& 3306......992x
2. COMPUTATION
CONTROLUNITS
T Y P E A CONTROL UNI T
for Types 3301 & 3302 Analog Computers
ReferenceVoltage : + 10V, - 10V with accuracy*0.1 %.
O utp ut Cu rren t: 5 0m A M ax .
Mode Control: OFF; power olT. RS; reset,
OP; o pe rate . HD; hold.
RO; repetitiveoperation.ComputationTime; 55ms+3ms.
Re stTime ;5ms + 3 m s at 50H2, 12m s * 3 m s at 6 0 H z EXT; Computation control from external signal
CoefficientSetting Potentiometer: 5 k!). Linearity , +0.1%
DC Voltmeter; Measuringrange; 0.1/0.3/l/3/10/10
V
(center-zeroscale)
TYPE A CONTROL PANEL
for Types 33O3-3306 Analog Computers
ReferenceVoltage: +10V, 10V with accuracy+0.05%
Output Current: 200mA Max.
Mode Co ntro l: RS; r es et . CO M ; oper at e. HLD; h o t d .
REP COM ; repelitive operation.
Computation Time ; 10/20/50rrl00
nsec
CoefrcientSetting Potentiometer: 5k O. Li neariry; + 0.05%
DC Yoltmeter : Measuringrange; 0.1/0.3ril
V
//3/l0,/30
Mode Control Signal Distribution:
Cr : COMPUTE/RESET signal
Cr; ./100 sisnal
C a; HOLD sign al
Sampling Type Waveform Translator :
Number of Channels; 2
Input; + l/2,/5/10
v
Time Base; 5/10,120i
50/100
m sec
Outp ut Yolta ge ; + lV
Recording Speed; 30-120sec/trace
Accl.Iracy| +0.5%
3. LINEARCOMPUTINGELEMENTS
D UAL SUMMING AM PLI FI ER C o d e3 3 1 6 1 1
Input and FeedbackResistors:
100kO X5, 10k0 X 2, accuracy+ 0 .1 %
Inpu t Termin al: 1, 1 , 1, 1, 1, 10, 10,SJ
C oeficie nt: 0.1 ,I,1 0
DUAL SUMMING INTEGRATOR Code 331711
(Repetitive Mode only)
Integrating Capacitors: 0.| 7rF. 0.01,,rF.accuracy+0.1%
Input Resistors: 100k O X 3, l0 k O X 2, accuracy+0.1%
Dielectric : Pol)styrene
I n p u t T e r m i n a l : I , l . l . I 0 . 1 0 ,S J , l C
DUAL SUMM ING INTEGRATOR Code 331751
(Operate Mode only)
I n t e s r a t o r C a p a c i t o r s : I / ! F ( +0 . 1 %) , 0 . 1t F ( +0 . 1 %)
Input Resistors: I MO Xl, 100kO X2, acc\r^cy +0.\%
Dielectric: Polystyrene
l n p u t T e r m i n a l : l , I , l , 1 0 .1 0 ,S J ,I C
INTEGRATOR SUMMER Code 331811
(Operate and Repetitive Mode)
INTEGRATOR
Integrating Capacitors: 0.1tF, 0.01/rF, accl]ja.y +0.1% ;
l 0 r F , l , , r F ,a c c u r a c y+0 . 5 %
Input Resistors: 100kO x I, l0 kO x 2, accuracy+0.1%
Dielectric: Polystyrene
(0.1,/r
F,0.01fF) polycarbonare( 10,,/F,
I /,F)
l n p u t T e r m i n a l : l , l , l , 1 0 ,1 0 ,S J ,I C
SUMMING AMPLIFIER
Iftput and FeedbackResistors:
1 0 0k O x 5 , l 0 k O x 2 , a c c u r a c y +0 . 1 %
Input Terminal: l. l. l. t. t, t0, t0,S.
COEFFICIENTPOTENTIOMETER Code 331511
Type : Wire-wound resistor
R o t a t i o n : 1 0t u r n s
Resistance: 50000,acclrracy+5%
Linearity | *0.25%
COEFFICIENTPOTENTIOMETER Cod€ 331521
Type: Metal film resistor
Rotation: I turn
Resistance: 50000,accuncy + l0%
4. NON-LINEAR
COMPUTINGELEMENTS
MULTIPLIER (Time division type) Code 331911
O p e r a t i o n s: M u l t i p l i c a t i o n ,d i v i s i o n ,s q u a r er o o t
Multiplication
Functi on:
F!,F.
E at t:
D C A ccuracy:
Frequency
#
IU
+ 0.1%( * l 0mV ) at 20"C -10'C (68-86'F)
C haracteri sti c