Time-domain analysis of nonlinear transducer networks

Abstract

The existence of computer methods for the construction of network system equations from a netlist description and numerical methods for the solution of initial-value problems in mixed differential-algebraic equations (DAE’s) allow the time-domain analysis of networks containing nonlinear elements. This paper will demonstrate these techniques in application to electromechanical transduction systems exhibiting small- and large-signal nonlinear behavior. Nonlinear constitutive equations defining electromechanical elements in transducer networks will be developed in the proper form for inclusion in a modified nodal formulation. It will be shown that consistent sets of initial conditions can be determined from a modified netlist under limited circumstances, but these limitations do not significantly constrain the utility of method in this application. In fact, this approach opens the method up to elements with static behavior, such as permanent magnets or electrets. Time-domain behavior of the system is numerically derived from the descriptor equations by a backward difference formula (BDF) DAE integrator appropriate for stiff systems.