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


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.


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.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:(Electrical Engineering and Physics)
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Electrical Engineering
Minor Option:Physics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • McCann, Gilbert Donald
Thesis Committee:
  • Unknown, Unknown
Defense Date:1 January 1950
Record Number:CaltechTHESIS:02202024-220557703
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:16298
Deposited By: Benjamin Perez
Deposited On:22 Feb 2024 20:17
Last Modified:22 Feb 2024 20:18

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