A Nonlinear Order-Reducing Behavioral Modeling Approach for Microwave Oscillators

This paper describes a novel technique to model the transient, steady state, and phase-noise behavior of microwave oscillators in the hardware description language VHDL-AMS. It can be applied to a large variety of both single-ended and differential voltage-controlled oscillators independently of their architecture. The model is derived from data obtained by a more complex circuit-level model. As opposed to input-output models of a microwave two-port, where the output follows more or less the applied input signal, the output of an oscillator depends mainly on its former state. Thus, approaches developed for input-output modeling cannot be applied. The technique proposed in this paper approximates the dynamics of the oscillator by a system of two first-order ordinary differential equations. The oscillator´s nonlinear characteristics are reproduced by a multilayer perceptron neural network. In addition to reproducing the oscillator´s large-signal waveform, its phase- noise characteristic in the l/f² and flat region is emulated. Finally, a VHDL-AMS implementation of the model is proposed and associated issues are addressed. The suitability of the model for oscillators at millimeter waves is demonstrated by examples working at 60 GHz.