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APPENDIX 2
UNIT SCALING
The process of scaling an analog computer circuit is simplified if the reference voltage of the
computer is used as a unit for measuring amplifier outputs. On a ten-volt computer, such as
the 580,
this means that one unit is defined to be equal to ten volts; all signals, when mea-
sured in units, will be:s. 1. 0000 in magnitude.
There are a number of advantages to such an approach. One of the most obvious (but not the
most important) is the fact that the DVM reads in units (when reference voltage is measured
on the DVM, the result is +1.0000). This location of the decimal point is determined by the
fact that the DVM is used for pot-setting as well as amplifier readout, and pot-setting must
be :s. 1.0000 in magnitude.
If
reference voltage is used as the unit of measurement, then
amplifier outputs are also :s. 1. 0000 in magnitude. Hence the decimal point is correctly lo-
cated in all cases.
The relation between a problem variable and the corresponding computer variable becomes
somewhat simpler in terms of unit scaling. For example, if a problem variable P has a
maximum value of 50 Ibs, then the corresponding computer variable is simply [P/50], which
has a maximum value of one. In unit scaling, every computer variable is Simply the ratio of
the corresponding problem variable to its maximum value.
If
the scaling is done in volts, then the computer variable is ten times the ratio of the problem
variable to its maximum value. Thus, if P :s. 50 Ibs, then the computer variable would be
[P/5].
On a hundred-volt computer, the computer variable would be [2P].
This pOints out
another advantage of the "unit scaling" technique -
it
is machine-independent: the scaled
variable would be [P/50] on either machine.
Probably the greatest advantage of unit scaling is the way it Simplifies the scaling of non-linear
circuits. For example, the product of two variables that are :s. 1 in magnitude will also be :s. 1
in magnitude.
If
a multiplier has scale inputs X and Y (-l..:s.X:s. 1, "-1:s. Y
.:s
1) then the output
will simply be the product XY (-1 :s. XY
.:s
1).
If
scaled in volts, the output would be XYI10 or
XY /100, depending on the reference voltage of the machine. Similarly, expressions for square,
square root, log exponential, and trigonometric functions are generally simpler when expressed
in terms of units.
A2-1
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