A large signal frequency domain analysis of circuits containing junction diodes and bipolar transistors

Abstract

The analysis of ac circuits has been limited to either a linear approximation or slightly nonlinear distortion analysis in either of which the fundamental component of the signal can be treated as a single sinusoidal wave. If the nonlinearity is great, or in other words, if the signal is so large that it should be expressed as a Fourier series, it is necessary to consider the generation of harmonics in each term of the series, as well as all possible intermodulation products. In this paper, the analysis of a circuit containing junction diodes and bipolar transistors is shown to be possible by using a Newton algorithm to solve the equations expressing the complicated interrelation of dc, ac, and finite numbers of harmonic components. The nonlinearities of a transistor are expressed in terms of an exponential function of a diode and a diffusion capacitance, and the modified Bessel generating function is applied to express the harmonics and the intermodulation products. A transistor model in the frequency domain, expressed by these generating functions, is capable of describing the fluctuation of the dc bias point and diffusion capacitances due to ac or harmonic components, which are considered to be constant in the ordinary analysis for small signals. Branin's method [8] of dc analysis is extended to analyze circuits containing dc, ac, and harmonic components, and a further method of analysis which reduces the size of the Jacobian matrix, is also suggested.