A polynomial computer

A computer for solving polynomial equations, performing Fourier synthesis, and displaying system functions is a valuable asset to an electrical laboratory. A number of successful computers have been built for such purposes but each has its limitations. The design of a versatile and precise instrument superior to existing computers is the purpose of this study. Using a voltage analogue of the function, this computer is designed for the solution of 20th - degree polynomials with real coefficients, 10th - degree polynomials with complex coefficients, and Fourier synthesis of either even or odd functions to the 20th harmonic or mixed functions to the 10th harmonic. Provision is made for the addition of circuits which will plot the magnitudes and angles of the polynomial or will form combinations of two 10th-degree polynomials. The computer, using servo phase-shifters harmonically geared in pairs and excited with a two-phase, 400-cps carrier, generates a polynomial term by term in exponential form. The coefficients and radial components of the terms are obtained by the use of precision potentiometers. The terms are summed by operational amplifiers which, mounted as a separate unit, can be removed from the computer for other analogue computations. The radial and angular components of the independent variable, p, of the polynomial may be constant or linear functions of time. The display consists of a long-persistence cathode-ray-tube on which the zeros of a polynomial are automatically plotted. For greater accuracy, zero positions may be determined manually by using a null indicator. Fourier synthesis can be performed with minor changes in the output circuit. The periodic function may be displayed continuously or point by point. The major part of the computer, the phase-shifter unit, has been built and most of the other components partially assembled. Completion and testing of the computer will be part of a further project.Applied Science, Faculty ofElectrical and Computer Engineering, Department ofGraduat

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