Contains reports on two research projects

Fine, S.

Razi, S.

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X. ANALOG COMPUTER RESEARCHProf. E. A. Guillemin S. Fine S. RaziProf. R. E. Scott N. DeClarisA. THE DESIGN OF COMPUTING ELEMENTSA regulated power supply can be viewed as a computer problem in which informationis fed in from the supply and the load. To test these ideas, a power supply was con-structed with cascade-connected series tubes. This has been shown to alter the regu-lation range of the supply.Controlled triode rectifiers, rather than diode units at the input to the supply, havebeen shown to increase the regulation of the supply, particularly with respect to inputvariations.The effect of transients on power supply regulation has been considered, and aconstant-current, regulated-output, voltage supply constructed.An attempt was made to evaluate the importance of nonlinear elements in regulatedpower supplies. Although considerable emphasis was placed on elements which possesslow incremental resistance (such as voltage regulator tubes), it is possible to use ele-ments which possess a higher incremental resistance and obtain good regulation. Apower supply using two thyrite resistors was constructed and tested.S. FineB. NETWORK THEORY1. Network Synthesis for Prescribed Transient Response(The following is an abstract of a thesis submitted to the Department of ElectricalEngineering, August 1953, in partial fulfillment of the requirements for the degree ofMaster of Science. )The past few years have seen a great shift of interest from synthesis for steady-state response to synthesis for transient response. The problems of synthesis facedduring World War II further emphasized the need for analysis of transient behavior ofelectrical networks. Various methods of synthesis for transient response have beeninvented. The method considered in this thesis is the one devised by Professor E. A.Guillemin of the Department of Electrical Engineering and published in the QuarterlyProgress Report of January 15, 1952. The method considers periodic repetitions ofthe transient function f(t) in several ways, such that an appropriate combination of theseperiodic functions cancels out everywhere except over the period of the duration of thetransient. The relevant periodic functions are expanded into Fourier series and theirLaplace transforms are taken. The system function for the network is obtained as aratio of polynomials which are the numerator polynomials of the Laplace transforms of-53-(X. ANALOG COMPUTER RESEARCH)the periodic functions under consideration.For the purpose of synthesis it is necessary to make some approximation to theinfinite sum of terms in the Fourier series expansions. The main advantage of thismethod is that it allows approximations to be made in the time domain rather than inthe frequency domain, and a more definite knowledge of the error between the true func-tion and the approximated function is obtained. Approximations can be made either infrequency domain or time domain. In fact, the common practice in the past has been tomake approximations in the frequency domain, but research in recent years has provedthat neither the degree nor the validity of the approximation is necessarily preservedwhen translations are made from time domain to frequency domain or vice versa. Havingapproximated the appropriate periodic functions by finite sums of Fourier components,the Laplace transforms are taken and the expression for the system function is obtained.It turns out, however, that the approximated polynomial in the denominator of thesystem function is not always Hurwitz and, therefore, the system function is not alwaysrealizable. Depending upon the number of terms taken to approximate the infinite sum,the polynomial P(s) may or may not be Hurwitz. A transient considered first was tri-angular in shape. The work carried out showed that the Hurwitz character of the poly-nomial P(s) has an "oscillatory nature" that depends upon the number of terms takento approximate the infinite sums. A half-sinusoidal pulse and a rectangular pulse werenext considered. An interesting fact was observed: if the zeros of both the odd and theeven parts of the polynomial P(s) vary their position in the s-plane with the approxima-tion made, the polynomial may not always be Hurwitz. If, however, the zeros of eitherthe odd or the even part are fixed or are controlled in some way and the zeros of theother part vary with the approximation, the polynomial P(s) is Hurwitz regardless of theapproximation.The next step in this research was to decide on a convenient method of synthesis,construct the network, and observe the experimental results. The experimentalresults agreed fairly well with the theory.S. Razi-54-

Analog Computer Research

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Analog Computer Research

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