Two Variable Function Generator Program for HYDAC
TWO VARIABLE FUNCTION GENERATOR PROGRAM FOR HYDACX
INTRODUCTION
GENERAL DESCRIPTION
These notes describe the capabilities of a HYDAC
program for the generation of arbitrary functions
of one or two variables. The realistic simulation
of most physical devices and systems requires such
physical
capability to describe mathematically,
phenomena involving the variation of quantities as
functions of other quantities.
In the diagram of Figure 1, the characteristics of
the Function Generator Program -- referred to as
F(x,y) -- are defined uniquely by the input - output
relationships shown. Figure 2 is a block diagram
of the basic F(x,y) program, showing the major
operations.
toR2
Functions of a single variable are satisfactorily
represented in analog simulations by the Diode
Function Generator or the Pot Pa.dder. Functions
of more than one variablearenothandledso easily,
however, and their representation is made usually
by approximation even after considerable experimentation.
The HYDAC program used in the study described
is an effective and economical means for representing functions of one or more variables with
convenient, rapid setup from punched paper tape.
It is designed to expand the problem solving capthrough
ability of the analog computerbyproviding,
the general pu4)ose components of the EAI Digital
Operations Systems (DOS), flexible, accurate, and
rapidly set function generators for the simulation
of arbitrary functions of analog voltages.
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FuilCt|otl VALUES
Ar a"EAKPotxts
f2 ( Xq r X5 )
IIULTIPLEXEO
ANALO6
I NPUTS
I ono.ou
> VOLIAGE
ourPurs
J
o-0,1,2,...,15
b0,tr2,...,t5
n-O1,2,,..,15
FIGUREl. GenerolChorocteristics
of F(xy) Progromlor HYDAC
L---
BENEFITS
Several benefits are provided through this simulation technique. The DOS Function Generatorprogram is a general purpose HYDACprogramimplemented by the interconnection of a portion of the
complement of components in the DOS. It is possible, then, to use those DOS components not used
in the Function Generator program for additional
logic control and computing ftrnctions.
Added to this flexibility
are the economics of
time
sharing
the program
which.make
component
to
the
analog
or hybrid
doubly
attractive
addition
a
simulation laboratory.
*T ro d e Mo rk
P ri n te d i n U .S .A . 464
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FIGURE2. Block Diogromof F(xy) Progrom
@ El ec tr oni c As s oc i o l e s , I n c . ,
Al l R i ghts R es er v ed
Bul l ei i n N o. ALH C 6 4 0 2 0
PROGRAM OERATION
In the F(x,y) program, a curve is considered to be
described by 15 straight line segments (Figure 3)
that connect values of a function, f(x), defined at
16 evenly spaced values (breakpoints) of the variable, x. A function of two variables is defined by
several curves, one for each breakpoint of the
second variable, y (Figure 4).
With suitable interpolation betlveen t'alues of the
function at breakpoints, a funetion oftwovariables,
f(x,y), defined by Y curves, can be represented by
16 Y data points, each of which defines the value
of functions at breakpoints in X and Y.
Figure 5 is a diagram illustrating the interpolation
scheme used in the F(x,y) program. Linear interpolation is used for both one and two variable
generation.
FIGURg 3. F unc t ionof o SingleVor ioble
FIGU R E 5. D i ogrom l l l ustroti ng
F(xy) Interpol ol i on S c heme
With additional buJfering and control circuitry,
the F(x,y) program can be expanded to include the
generation of Variable Break Points and Functions of Three Variables.
FIGURE4 . Func iionof Two Vor iobles
EAI'
ELECTRONIC
For complete details on the basic F(x,y) program,
please write for Application Study 1.3.6h, Bulletin No. ALHC 6384-lab.
ASSOCIATES, INC. tong Branch,New Jersel
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