Other examples of the application of com plex operation to the solution of problem s are given in
the section on OPERATION.
SCALE FACTORS
In the operation of the analog computer two factors must be considered. The first of these is
the amplitude factor. In general, the output of each am plifier must be kept within the range
±100 volts, the actual value depending on the am plifier used in the computer. In order to keep
the output within the specified lim its, it is generally necessary to scale down the input voltages.
It is not always possible to determine before hand the range of the voltages, in which case a
trial run can be made and after the voltages are observed, the proper amplitude scale factors
can be chosen. Sometimes it is possible to estimate the range of voltages from the physics of
the problem .
The other factor is time. If the product R iC f = 1 when Rf is m easured in ohms and Cf is m eas
ured in farads, the computation is said to be in real time. This is so, for example, when Rf =
1 megohm and Cf = 1 jufd. (RiCf = 10® ohms x 10_® farad = 1) If the computer is operated such
that the solution is obtained in le s s time than is required for the physical solution to o ccu r, the
operation is said to be faster than real time. This is very useful if the physical occu rren ce which
is being simulated requires considerable time. Tim e is also saved, permitting the solution of
m ore problem s in the same length of machine time.
Another advantage is that machine e r r o r is decreased, especially the e r r o r due to the leakage
resistance of the feedback capacitors. In general, the solution of a problem on the computer
should not require m ore than l t o 5 minutes. Longer solution tim es require special precautions.*
REPETITIVE OPERATION
It is desirable, for many problem s, to repeat the solution and observe the effect on the solution
of changing the various param eters of the problem . This is made possible by repetitive o p e r
ation. Some means is provided for automatically resetting the computer and re-running the
problem . A cathode ray oscillo sco p e is convenient for observing the solution in this case.
Generally, one of the computer am plifiers is used to provide the sweep for the oscilloscop e .
Details of operation w ill be discussed in the section on OPERATION.
ACCURACY
A s was shown previously, the higher the am plifier gain the le ss will be the e r r o r in each com
puting operation. Thus the accuracy depends in part on the gain of the operational am plifier.
A ccu ra cy also depends on the precision of the computing components, such as r e sis to rs and
capacitors. Tim e is also a factor in accuracy. In general, long runs introduce e r r o r s due to
am plifier drift and capacitor leakage.
* Goode and M achol, SYSTEM ENGINEERING (M cGraw-Hill Book Company, In c ., New York,
1957), Pages 278-283.
Clarence L. Johnson, ANALOG COMPUTER TECHNIQUES (M cGraw-Hill Book Company, In c .,
New York, 1956), Chapter 3, Pages 20-44.
Korn and Korn, ELECTRONIC ANALOG COMPUTERS (McGraw-Hill Book Company, Inc. ,
New York, 1956), Pages 30-35.
Jam es B. Resnick, "Scale Factors for Analog Com puters", Product Engineering, M arch, 1954.
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