Nonlinear System and Modeling in Time Domain Subsystem

Nonlinear models of microwave subsystems are iden- tified from time domain measurements. Scattering functions in the form of nonlinear time domain functions are used to derive a system identification model instead of an equivalent circuit. The advantage being the simplicity of the measurement and the developed models and the speed and accuracy of the simulation of the entire system. I. INTRODUCTION ONLINEAR circuits and subsystems are usually modeled N using equivalent circuits. Parameter extraction of the equivalent circuit is achieved by optimizing the network to match a large number of measured data points. The four scattering parameters (5'11 ,912, ,921 and ,922) are measured over the frequency range of interest and for different bias conditions and/or different power levels. It is obvious that a large number of measurements have to be performed and the optimization process is subsequently lengthy as all the data points have to be matched. Until now time domain measurements have not been con- sidered because there is no previously existing method of modeling the nonlinear network from the results of the time- domain measurements. It is worth pointing out that the Fourier and Laplace transforms do not apply to nonlinear networks and thus there is no obvious duality between frequency and time domain measurements. For nonlinear networks, the shape and amplitude of the input time domain functions used is important and depends on the type of network or system to be charac- terized. A blanket use of impulse functions is not suitable as in the case of linear networks. Another problem facing the nonlinear systems designer is that working with equivalent circuits is unnecessarily complex and is not required. The systems designer works with individual subsystem blocks and requires the modeling to be at the subsystem level of hierarchy rather than at the level of equivalent circuits represented by basic circuit elements. Given the above problems facing the systems designer, we ask the following questions: Is there an alternative to make a large number of mea- surements in the frequency domain and at several bias conditions?