Since the inception of the electronic analog computer as a useful engineering tool, the need for practical methods of solving nonlinear problems has steadily increased. This paper describes a passive, nonlinear device which, when used with operational amplifiers, provides the means for obtaining a large class of functions. These are obtained to a degree of accuracy and reliability not previously possible with a simple, economical device. A basic varistor squaring unit is described. The unit has been compensated for the various types of error inherent in the varistor itself, and is capable of providing approximately fifteen of the most basic and commonly used nonlinear functions.

Since the publication of a previous paper1 the uses of Thyrite2 in the synthesis of nonlinear transfer functions in analog computing have been greatly expanded. Moreover, new and considerably improved methods of Thyrite selection and matching have been developed. The present paper shows how rational exponents can be represented. Functions of the form y = kxn, with 1/δ ≤ n ≥ 6 are readily obtained. Circuit configurations generating the functions 1 - (2x/π)1.74and 1 - [2/π(x-π/2)]1.74which provide excellent approximations to the cosine and sine functions, respectively, are given and an improved quarter-square multiplier using Thyrite squaring is discussed. A study was also made of the physical factors influencing the performance and accuracy of Thyrite and quantitative experimental data regarding these factors are presented.

An investigation into the use of thyrite as an inexpensive nonlinear element in the electronic analog computer indicates that this material has great value as a device capable of delivering an output voltage proportional to the square of the input voltage. The factors discussed are the characteristics of the material and the means by which these may be modified to produce a device capable of squaring with an accuracy of 1.25% from dc to frequencies in excess of 1000 cps. This ability to square makes possible the more important operation of the multiplication of two variable voltages.