Approximate Large-Signal Analysis of IMPATT Oscillators

Considerable insight into the large-signal operating characteristics of IMPATT oscillators has recently been obtained by D. L. Scharfetter and H. Iv. Gummel through numerical calculations involving a complete modeling of the physical processes taking place in the diode.1 They solve the one-dimensional partial differential equations for the generation, diffusion, and drift of holes and electrons, as well as Poisson's equation and the differential equations for the circuit in which the diode is embedded. Their analysis, which has led to improved understanding of IMPATT diodes and insight into new modes of oscillation, includes most of the important physical effects. Since their model is so detailed and accurate, their analysis is a large-scale computer project. Even after the computer programs are debugged, analysis of IMPATT diodes is relatively expensive. 3S3 384 TI-IE BELL SYSTEM TECHNICAL JOURNAL, FEBRUARY 1969 Another possible method is small-signal analysis, which is tractable numerically and more economical.2-4 However, small-signal analysis gives only a limited amount of information about large-signal oscillation. An intermediate model has been presented by W. J. Evans. 5 However, his simplified large-signal model requires short transit-time in the drift region. He obtained a single first-order differential equation for the diode current, and was able to solve analytically for the (large-signal) diode current and voltage as a function of time. Unfortunately, the restriction to short transit time and his use of other approximations severely limit the applicability of his results.