Rational approximations to the complex current gain of transistors†

Abstract

ABSTRACT The necessity for using rational approximations to the theoretical expressions for transistor parameters, in particular the current gain, is discussed. Equations based on a minimum-mean-square-error criterion in the frequency domain between the theoretical expression for current gain and a general nth order rational approximation are derived. The equations are linear and simultaneous, and can be solved for any order and range of approximation. The solutions are the optimum coefficients of the approximating transfer function. The Taylor approximation is shown to be a special case of the least-squares approximation where the range of frequencies is reduced to zero. The equations are solved to give second-order approximations for transistors of both the diffusion and the drift types. Various values of range are taken, including the case where the range tends to zero, i.e. Taylor approximation. The numerical values of the optimum coefficients are tabulated and the characteristics of the approximating...