An Arbitrary-Function Generator and its Application to the Study of Some Non-Linear Systems on the Electric Analog Computer

Citation

Buchholz, Werner (1950) An Arbitrary-Function Generator and its Application to the Study of Some Non-Linear Systems on the Electric Analog Computer. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/qafc-cv17. https://resolver.caltech.edu/CaltechTHESIS:02202024-220557703

Abstract

An arbitrary-function generator, capable of furnishing an output voltage which may be any given single-valued function of the input voltage, is described. It was constructed for use with the Electric Analog Computer at the California Institute of Technology. In principle it is an optical follower system containing a cathode-ray tube and a phototube with an opaque mask representing the desired arbitrary function.

The working model constructed is accurate to about one or two percent, has a phase shift of 3½ degrees at 2 kc and a limiting time delay of about 50 microseconds with the beam traversing a step equal to the maximum height of the function pattern employed.

Sources of error are analyzed and suggestions are made for possible improvements. A major problem which has not been solved yet satisfactorily is the local deterioration of the cathode-ray tube screen due to fatigue.

A number of non-linear problems are solved with the aid of this device, all of them dealing with second-order systems having a single degree of freedom and only one non-linear term in the equation. Among the systems discussed are series circuits with a non-linear capacitance, or mechanical systems with a non-linear spring; non-linear damping; oscillating systems, including systems behaving according to Van der Pol's equation; and mechanical systems made unstable by the presence of static (dry) friction greater than the dynamic (Coulomb) friction.

The results obtained appear to support the conclusion that the generator introduces only one or two percent of distortion, plus a small phase shift at the higher frequencies. The device makes possible the solution of many non-linear problems, hitherto inaccessible, at relatively high natural frequencies and repetition rates.

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