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Патент USA US3025010

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March 13, 1962
l.. TABAcK
3,025,000
FUNCTION GENERATOR FOR GENERATTNO A FUNCTION
OF Two INDEPENDENT VARIABLES
Filed oct. 4, 1957
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ATTORNEY:
March 13, 1962
|_. TABACK
3,025,000
FUNCTION GENERATOR FOR GENERATING A FUNCTION
OE TWO INDEPENDENT VARIABLES
Filed Oct. 4, 1957
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March 13, 1962
|_. TABACK
3,025,000
FUNCTION GENERATOR FOR GENERATING A FUNCTION
OF Two INDEPENDENT VARIABLES
Filed Oct. 4, 1957
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BY
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nite States Patent il* tiìce
1
FUNCTKON SENER-1191i FÜR GENEäATltNG A
FUNCTÍÜN @if TWO HNDEPENDENT VARIABLES
Leonard Tabacir, Mount Rainier, Md., assignor to the
United States of America as represented by the Secre
tary of Commerce
Filed Get. 4, 1957, Ser. No. dtiäßäli
6 ‘Ciaima (Ci. 23S-197)
3,025,000
Patented Mar. 13, 1962
2
FIG. 2B is a schematic diagram detailing the circuit
construction of the voltage-controlled pulsed attenuator of
FIG. 2A;
`
FfGS. 2C, 2D, and 2E are waveforms showing the
operation of the voltage-controlled attenuator for various
input settings;
FlGS. 2F, 2G are diagrams showing the principle of
operation of the vonage-controlled attenuator;
FiG, 2H is an explanatory diagram;
The present invention reiates to the generation of func 10
FIG. 3 is a circuit diagram showing lthe construction of
tion representing signals for use in connection with elec
a triangular wave generator employed with the present
trical analogue computers. Specifically, the invention con
invention; and
templates an improved device for generating an arbitrary
FiG. 4 isa diagram of the output system employed.
function of, for example, two independent variables.
The present invention contemplates a device comprising
The need of a function generating means in order to 15 a number of individual mechanisms for generating func
represent nonlinear phenomena for the simulation of phys
tions of a first variable at successive fixed values of a
ical problems in analogue computers is app arent. In gen
second variable in combination with means for inter
eral, function generators provide an output manifestation
polating linearly among the function generators under
which varies in some arbitrary but controllable way in re
control of one of said variables. An over-all block dia
gram of a preferred embodiment of the function generator
in accordance with this invention is illustrated in FIG. 1.
The apparatus comprises a plurality of individual function
For example, in copending application, Serial No.
generators indicated as 1000, 1001, 1002, etc. each of which
651,121, now Patent No. 2,998,193, for an Electronic
will produce or generate a different discrete function of
Analogue Computer for Radioactive Fallout Prediction, 25 an applied input variable x. The x variable is in the form
tiled on April 15, 1957, by H. K. Skramstad et al., which
of a signal applied in parallel to the function generators'
is assigned to the assignee of the present case, it is neces
1000 through 1002 etc. While an embodiment employ
sary to generate a particle radioactivity factor which is ex
ing three function generators is illustrated, as indicated in
pressed as a function of two independent variables, height
the broken `line representation in FIG. 1, as many function
and time of particle fall. No familiarity with the mathe 30 generators as is desired can be incorporated in the appara
matical functions underlying the radioactivity factor is
tus of the present invention.
necessary in accordance with the instrument of the present
Each of the function generators 1000 etc. shown in
invention, since the function is incorporated in the instru
FIG. 1 are of conventional type and are therefore only
sponse to an 4applied input manifestation. In many in
stances the function generator must provide an output
which is a function of two independent input variables.
ment as a family of curves and it is necessary only to
symbolically shown. A typically commercially available
manipulate the controls in order to obtain any desired 35 unit satisfactory for such purpose is the Goodyear Aircraft
function within «the range defined by the curves.
Company GN-215-N3 function generator. The output
The usefulness of a function generator is measured by
of each function generator 1000 through 10402 corresponds
such characteristics as flexibility, that is, the diiiiculty of
to an arbitrary function of x such as f0(x), f1(x), f2(x)_,
setting up the function generator «and the ease with which
etc. The output of each function generator, except the
it can be changed from one setup to provide different 40 first one, 1000, is applied to a respective voltage-controlled
types of functions; frequency response, for example, the
pulsed attenuator 1011, 1012, as indicated in FIG. 1.
range of input and output frequencies which can be
Each function generator 1000 etc. will accordingly pro
handled without introducing intolerable errors in either
vide an output signal representing a different discrete func
phase or magnitude; and finally, accuracy; or specifically,
tion of the input signal representing the variable x.
the manner in which the output conforms to the desired 45
Each of the voltage-controlled attenuators 1011, 1012 is
function. The present invention is intended to improve
a form of time division multiplier, the general principles
upon the deficiencies of prior art devices in connection
of which are described on pages 223-226 of Electronic
with the above-enumerated criteria.
Analog Computers, by Korn and Korn. Each attenuiator
It is accordingly an immediate object of the present in->
functions to combine the particular f(x) signal generated
vention to provide a function generator for generating an 50 `by the function generators 1001, 1002 with a signal rep
arbitrary function of two independent variables which will
resenting the second independent variable y to provide an
work at electronic speeds and which is sufficiently iiexible
output which is a function of both x and y.
to be adaptable for the generation of a wide variety of
The specific construction and mode of operation of
optional functions.
such pulsed attenuators is fully discussed in connection
it is a further object of this invention to provide a func
with the description of FIG. 2. At this point in the de~
tion generator which will accurately provide an output
scription, however, it can be stated that each attenuator
signal that conforms to any desired arbitrary function of
provides an output signal pulse having a duration propor
two independent variables.
tional to the applied input variable (y), and an amplitude
Another object of this invention is to provide a function
corresponding to f(x), already referred to.
`
generator which is completely electronic in operation.
60
The outputs of the attenuators `1011, y1012, together with .
Still another object of this invention is to provide a
the output from the »first function generator 1000, are
function generator which is adjustable in accordance with
applied to a filter circuit `102 which filters out any carrier»
any desired function of two variables.
signal introduced by the triangular' wave employed in the
Other uses and advantages of the invention will become
operation of each of the attenuators as will be described.
apparent upon reference to the specification and drawings 65 In this manner, a signal which represents a function of
in which:
two independent variables f(x,y) is obtained for applica
FIG. 1 is a block diagram illustrating the functional
tion to a summer 103.
arrangement among the elements comprising the present
The signals representing function f1(x) and f2(x)
.
generated by the function generators 1001 and 1002 are
FIG. 2A is a functional block diagram illustrating the 70 also applied to an inverter 104 and through a second filter
invention;
construction of a voltage-controlled pulsed attenuator em
ployed in the present invention;
105 to the summer 103. The gain of the inverter ampli
tier 10d is less than one-half and provides anoutput which i
3,025,000
3
is, subtracted from the signal applied to summer 103.
The purpose of such subtractive effect is to compensate
for residual signals which inherently arise from the func
tion generators‘even when the outputs derived should'be
zero.
4
The Equations Sa-Sc are general, permitting the ad
justment for a function f(x, y) using any desired y in
crement. However, it is simpler to set the function gen
erators for equal increments k. Combining the above
Ul Equations 5a-5c and making theA increments equal to k:
Each of the attenuators `1011, 1012 are energized se
quentially as> will be described in connection with the de
tailed description of FIGS; 2A and 2B.
afgifte@ #framprîïpmkj _111,111
Before considering the specific construction of the
various elements of the invention, the principles under 10
(5a)
which may be expressed in terms of the outputs of the
lying the apparatus diagrammatically shown in FIG. 1
will ñrst be discussed.
A representative plot of a function of two independent
variables, x and y, is indicated in FIG. 2H, That is, each
function generators thus
(5b)
curve 20, Z1, and Z2 shows an arbitrary relation between 15
For any selected value of x indicated by the broken line
variables x and y for different assumed values of y. The
in FIG. 2H, the value of f(x, y) represented on each of
assumed value of y in connection with curve 20 is 0 and
the curves 20, 21, and 22 is f0(x), f1(x) and f2(:c), re~
spectively. It will be obvious that if the function gener
the curve- is accordingly designated f(x, 0). Similarly,
curves 21 and 22 are labeled f(x,a) and Hach), respec
tively, since they indicate the arbitrary relationship be 20 ators 1000, 1001, and 1002 shown in FIG. 1 were set to
obtain such values respectively, in accordance with Equa
tions 5tz-5c the apparatus would be able to provide a
f(x, y) for three different ñxed values of y. It will also
be obvious that by the addition of sufficient function
ship between x and y can be plotted in this manner.
Considering for the moment the block diagram of FlG. 25 generators as symbolized in broken lines in FIG. 1 to
represent additional curves (FIG. 2H), the apparatus can
1'J it will be apparent that the output signal derived from
lbe employed to implement almost any arbitrary function
the apparatus of this invention is composed of the sum
of two independent variables such as Í3(x), fn(x), etc.
mation of the outputs of the various voltage-controlled
The usev of function generators alone is, however,
attenuators 1011, 1012 etc. and the output from inverter
amplifier 104 together with its associated filter 105. The 30 neither sufficient nor economical in the attainment of al
high degree of selectivity of a desired function. rl`he ap
output, f(x, y) can be expressed as
tween x and y for assumed values in which y equals a and
b, respectively. It will be understood that any desired
number ofy curves showing Various degrees of relation
paratus of the present invention therefore also provides
means for interpolating for Vvalues lying between those
represented by'the'curves in FIG. 2H.
The feature for accomplishing interpolation in accord»
ance with the present invention is based on the follow
ing considerations. As is well known, interpolation for
a point y, the value of which is f(y), between two values
where A is the gain of the inverting amplifier and filter
f(a) and f(b) for values of the variable equal to a and b
combination 104, `105 and has an approximate value of .2. 40 respectively is obtained as follows:
The values of G1, G2, etc.7 the respective gains of the
voltage-controlled attenuators 1011, 1012, lie between .2
b-a
for fixed increments k and a=0
and> .8, the gains being controlled by the independent in
put variable y in the following manner.
The values of the gain G1 are
(7a)
G1=.2 for y<0
G1=.8 for y>0
For a given value of X Equation 6a reduces to Equa
tion 7a thereby showing that the device linearly inter
polates along the y axis.
(3a)
The various functions of x for example, f0(x), f1(x),
f2(x), designatedv in FIG. 2H may readily be generated
by the respective function generator 11000, 1001, 1002, etc.
The values of the gain G2 are
GET-@+2 for a<y<(a-i-b)
Ö2=~2 for y<a
shown in FIG. 1. The respective functions are indicated
in FIG. 1 -a‘s output signals from each function generaÍ
tor. The respective attenuators 101, 1012 connected to
(3b)
02:.8 -for y> (a -Jf-b)
the outputs of the f1(x) function generator «.1001 and
Substituting the values of G1, G2, etc'. from Equations
3a, 3b in Equation 2:
f2(x)‘ function generator 1002, provide respectively, inter
polation by modifying such input signals in accordance
60
Returning to a consideration of FIG. 2H in which each
of the' curves represents a particular value of y held at
an arbitrary constant ‘0, a, b, etc., in order to obtain a
with the
a m
la’
k
factors Adefined in Equation 6.
As will be described in
value corresponding to f(x, y) the following equations 65 detail, each such attenuator receives signals correspond
ing to f1(x), f2(x) and modifies such signal with a second
must be satisfied
applied signalcorresponding to
a, .v_-ZC.
k
Íc
70 etc., to provide an output corresponding to
-k
It will be apparent that Equations 5a-5c specify the
settings of the corresponding function generators 1000,
1001, 'a?'d 110011.
ä, fle) and yk fax)
respectively. The unmodified foQc) signal from Afunction-
75 generator 1000 together with the respective outputs from
spettano
E'
¿à
to?
attenuators Zitti and M12 are then accumulated in sum
gate circuit 205 symbolically indicated in FIG. 2A is
representative in FIG. 2B by the series gate tube V205A
and parallel gate tube VZtiSB. The “y” input variable is
mer 103 to provide an output signal corresponding to
Equation 6b; namely,
applied at input terminal Ztltib shown at the left-hand por~
tion of tFIG. 2B, while the triangular carrier signal ob
tained from the mechanism of FIG. 3 to be described is
Voltage-Controlled Pulsed Attenuazors
The construction and operation of the voltage-con
trolled pulled attenuators will, M312 designated in FIG.
l is detailed in connection with the block diagram of
FIG. 2A, the detailed circuit diagram of FIG. 2B, and
the waveforms illustrated in FIGS. ZC-ZF. Referring to
FiG. 2A each attenuator comprises a comparator 200 to
which there is applied both a repetitions triangular input
signal to input terminal 2Min and another input signal to
terminal êtitib representing the y variable which is also
applied at terminal Z'ätia. The voltage corresponding to
the input variable "y” applied at terminal 26% is limited
to a potential between 0 and ‘+10 volts above ground by
the lO-volt bias on the cathode of the diode of VZtiflb
and the inversely connected diode Vâtttia. The diode
V2M prevents the grid of the left~hand section of the
D.C. amplifier V262 from going negative.
A poten
tiometer RZtit? is connected to a -SOO-volt source as in
dicated and therefore provides an adjustable means for
determining the point at which the anode terminal of
diode VZtiftb will be positive. In this manner adjustment
shown in FIG. l. The output of the comparator is ap
of the corresponding potentiometer R290 in each at
plied to a gate circuit 205 coincidentally with the Kx)
tenuator determines the amplitude value of the applied
signal obtained from an appropriate one of the function 20 “y” signal that will result in energization of the attenua
generators 1661, dtìíig. The output of the gate circuit 2%
tor. The attenuator Mill, MM2 may thereby be energized
is applied to the -íilter MBZ shown in FIG. l. The wave
in sequence depending on the amplitude of the respective
form of the signals are indicated in FIG. 2A adjacent
y, y-Jc, etc. signals applied. The resistors RZdtiA and
each of the circuit components.
Rìtiûlì comprise summing resistors.
The construction and operation of the voltage-con~
When the y input variable voltage applied to terminal
trolled attenuator can be explained by considering the
2691; reaches a value large enough to malte the left~hand
waveform shown in tFlG. 2F of the drawings. The tri~
grid of D.-C. amplifier V 2%2 positive, the resulting signal
angular shaped wave shown in FIG. 2F corresponds to
is amplified and applied to a gate driver tube V263. The
the triangular input carrier signal indicated in the block
gate driver tube Vïtiâ comprises a bistable circuit which
diagram of FIG. 2A. The triangular wave illustrated in FIG. 2F is shown relative to a zero voltage reference
level indicated by the broken line in FIG. 2F. As will be`
described, the comparator in each voltage-controlled at
tenuator is a device which is controlled by the triangular
wave so that it will conduct at voltage conditions defined
by the portions of the triangular wave which are above
the zero reference level indicated in FIG. 2F.
Speciñcally, conduction will be obtained in the regions
defined by the rising and falling portions of the triangular
is adapted to be driven to either of two states of con
ductivity by the signal applied to the left-hand grid of
the amplifier VZiiZ. That is, when a positive signal is
applied to the left-hand grid of VZGZ, a positive signal
will also be applied to the left-hand grid of the gate
driver V263. Accordingly, the plate of the right~hand
section of gate driver V263 will be positive and such
positive signal will be transmitted through the upper
chain of neon tubes VZddA to `the series gate tube
VZÜSA. The (x) input signal applied to terminal ZtlSa
Wave included between points a and b and between points 40 of the gate will therefore be transmitted through the
c and d, respectively. It will therefore be obvious that
series gate tube VZÈBSA to the filter 162- shown in the
the resulting output signal will have a duration or pulse
block diagram of FIG. l. In other words, under the
width corresponding to the distances a-b, and c-d indi
above-described conditions, the f1(x) output of the par
cated in lFIG. 2F. It will also be apparent that each such
ticular function generator ltitil applied to terminal 265e:
pulse will necessarily occur at a frequency deñned by 45 of the voltage-controlled attenuator appears at the output
the frequency of the triangular wave. The comparator
of the gate.
therefore functions as an on-off device which generates
Similarly, if the resulting signal applied to the left-hand
a pulse having a width or duration corresponding to the
grid of the D.-C. amplifier V202 is negative then the
distances a-b, c-d, etc.
plate of the right-hand section of the D.-C. amplifier
By shifting the triangular wave relative to the reference 50 will be negative and the resulting negative signal applied
level, it will be apparent that the duration or width of
the output pulse can be selectively varied. Such action
is illustrated in FIG. 2G. The upper reference level line
corresponds to the 0-voltage reference level line indicated
in FIG. 2F, while the lower reference level line indicates
the result obtained when the level of the triangular wave
is increased relative to the reference level. It will be
obvious from FIG. 2G that the desired pulse width will
obtained at the plate of the right-hand section of the
V2ti3 and applied through the chain of neon tubes
VZtMA to the grid of the VZÜSA gate will cut that tube
off. As a consequence the positive signal derived at the
increase from an amount corresponding to r11-b1 to an
gize the shunt gate VZtlSB.
to the left-hand section of the gate driver V2M will cause
the bistable V293 to flip. The resulting negative signal
left-hand plate of the gate driver V203 `«vill be applied
through the lower chain of neon tubes VîtìétB to ener
The applied itx) signal
amount corresponding to :z2-b2 consequent to a shift in 60 from the function generator will now be cut off by the
the reference level. The “y” input signal designated in
series gate and the shunt gate will maintain a low imped
FIG. 2A provides the described effect of shifting the
ance at the input of the filter.
amplitude `of the triangular wave in the manner indicated
From the above description, it will be clear that the
in FIGS. 2F and 2G. The variable "y” will therefore
determine the duration of the derived pulse signal. Stated 65 polarity of the y input variable signal determines both
the duration of conduction of the series gate VZtiSA and
in another way, the pulse width will correspond to the
energization of the shunt or cutoff gate VìdSB. The
factor "y.”
output pulse obtained from the voltage-controlled atten
FIG. 2B shows a circuit diagram implementing the
uator therefore will have a duration determined by the
mechanism diagrammaticaliy shown in FIG. 2A. The
portions of the circuitry shown in FdG. 2B corresponding 70 y input variable. Since the f(x) signal from the func
tion generator is conducted through the series gate
to the blocks indicated in :FIG 2A are labeled with cor
VZdSA, the amplitude of such output pulse signal will
responding reference numerals. The comparator 26d
be determined by the x variable. Figs. 2C, 2D, and 2E.
comprises an attenuator circuit including diodes VZt'iGb,
are typical oscilloscope traces showing the output ob
V2M, a D_C. amplifier comprising the twin triode V2tl2,
V293 and banks of neon tubes VZMA, VZMB. The 75 tained from each voltage-controlled attenuator. Since
8,025,000
7
It will be clear from the above description that theI
function generator of the present invention is completelyl
electronic in operation. It operates satisfactorily at sig
nal frequencies up to 100 c.p.s. and a high degree of
function selectivity is obtainable because of the flexibility
the output signal is modulated by the triangular wave-in
put as described, the output produced comprises a series»
of pulses' having an envelope corresponding to the out
put of the function generator. The width of each pulse
comprising the envelope as shown in FÍGS. 2C, 2D, and
2E corresponds to the y input variable. FIGS. 2C, 2D,
and 2E also'illustrate the eñect of adjusting the attenu
ator from a full-on condition to a full-off condition.
Triangular Wave Generator
The triangular wave generator employed for generat
in the number of individual function generators that can
be used. While linear interpolation is employed it will
be apparent from the description that nonlinear inter
polation is obtainable by suitable shaping of the sav/tooth,
signal. The device operates at electronic speeds, limited
only by the sawtooth frequency as this frequency deter
mines the design of the filters.
10
ing the referred-to triangular wave input signal applied
to the voltage-controlled attenuator of FlG. 2B is illus
t'ratedy in FIG. 3.
yIt will be apparent that the embodiments shown are
only exemplary and that various modifications can be
made in construction and arrangement within the scope
of invention as defined in the appended claims.
What is claimed is:
l. A device for generating an output signal represent
The triangular wave generator com
prises a conventional operational amplifier 400 connected
as an integrator by means of the capacitor C-itifì. A bi
stable» device comprising the» twin triode Vdt'ifi controls
the input signal ofthe operational amplifier. Assuming
that the left-hand section of the tube V400 is conducting,
ing a function of two independent variables comprising:
then the plate signal output of the left-hand section will 20 first means responsive to a first input signal representing
be negative and the output of the integrator circuit com
a first> of said variables for generating a signal which is>
prising the operational ampliñer 400 will increase linearly
an arbitrary function of said first variable for a fixed
at a rate determined by a summing resistor R460 and
value of said second variable, second means_responsive to
said first input signal for generating signals representing
the capacitor C400. The output of the operational am
plifier is connected to the grid of the right-hand section
additional functions of said first variable for correspond
of the twin triode V400 and therefore as the output of
ing fixed values of said second variable, third means re
sponsive to said additional function generating means
the integrator increases positively, the right-hand sec
and to second input signals representing discrete values
tion of the tube V400 will consequently be turned on
of said second variable for providing output signals pro
thereby extinguishing the left-hand section in a conven
portional to a function of said signals generatedvby saidv
tional manner. The resulting positive signal output ob
second means and said second variableA signals and meansv
for cumulatively'combining the outputs of said ñrst and“
third means to provide an output signal which is a func
tained from the left-hand section of the two triode ap
plied to the integrator comprising operational ampliñer
400 will therefore result in a linearly decreasing signal.
tion of said two variables.
The resulting output of the generator circuit shown in
FIG. 3 is therefore a triangular wave as indicated adja
35
2. The invention of claim 1 in which said third means
cent the output terminal. Such output signal comprises
comprises a pulse generator for providing an output pulse
the triangular wave input appiied at terminal Moa in
FIG. 2B.
having a duration corresponding to said second Variable
and an amplitude corresponding to said first variable.
3. The invention of claim 2 including a triangular
Wave generator and comparator means in said pulse gen
erator responsive to said triangular wave generator and
Output System
The portion of the block diagram included in the
broken line outline in FiG. 1 comprising the output sys
tem. and. is further detailed in FIG. 4 of the drawings.
The outputs from `the function generators 1061' 1002 etc.
are applied through appropriate summing resistors R600
said second variable signal for determining the duration
and frequency of said output pulse.
4. The invention of claim 3 including a plurality of’
said pulse generators each connected to a respective one»
of said additional function generating means, and ampli
tude sensitive means in each of said pulse generators re
to amplifier 401 which together with resistor R401 com
prises inverter 104 designated in FIG. l. As indicated
in FIG. l the output of the first function generator
sponsive to said second variable signal for energizing
1000 as well as the outputs from each of the voltage
each of said pulse generators in sequence.
controlled attenuators 1011, 1012 are applied to the filter
5. The invention of claim 4 including a filter for said
102. Such construction is detailed in FIG. 4 in which
triangular wave signal connecting said pulse generators
the. ñlter 102 is represented by the RC combinations
to said combining means.
RC402, RC403, and RC404 to which the outputs of func
6. The invention of claim 5 including means for in
tion generator 1000 and attenuators 1011, 1012, respec
verting the outputs of said second means and a second
tively, are applied. The filter 105 designated in FIG. 1 55 trlangular wave signal filter connecting said inverting
is indicated', by an RC network RC405 in FIG. 4to which
means to said combining means.
the output of the inverter is applied. The resulting out
puts from all the referred-to i’ilters are applied through`
References Cited in the file of this patent
appropriate summing resistors R406, R407, and R408 to
UNETED STATES PATENTS
the summer 103 which comprises an operational ampli
fierv 403.
The output accordingly comprises a signal
representing an arbitrary function of the variables x and
y, as derived in accordance with the above-detailed de
scription.
2,773,641
2,794,965
Baum ______________ __ Dec. ll, 1956'
Yost ________________ __ June 4, 1957
2,801,351
2,878,999
Calvert et al __________ __ July 30, 1957
Lindsey et al. ________ __ Mar. 24, 1959
It will be recalled from the description of FIG. 2,v (i54
that the output waveform of the voltage-controlled pulsed
attenuators 1001, 1002, etc., includes the triangular Wave
carrier signal generated by the triangular wave generator.
The filter 102 shown in FIGS. l and 4 functions to par
t-ially filter out such carrier signal so that the signal ap
plied to the. summer 103 is essentially similar to the out
puts of the function generator.
OTHER REFERENCES
Amemiya: A New Diode Function Generator, I.R.E.
Trans. on Electronic Computers, fune 1957, pages 95-97.
Model F2V Function of Two Variables (Philbríck),
‘ received in Div. 23, December l1, 1957, pages l-15.
A Palimpsest on the Electronic Analog Art (Paynter),
1955;` pages 266-270.
. .n
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