Lumped equivalent model synthesis for a passive element with frequency-dependent and/or temperature-dependent characteristics for EMC simulation

This paper proposes a black box approach which synthesizes lumped circuit model of the Foster type for a frequency-dependent characteristic element by the least squares method systematically. However there are two numerical difficulties to model them. One is the numerical stability problem which comes from limitation of effective numerical digits of data especially for wide frequency band ranges. The other is the passivity problem of extracted lumped parameter models which often have negative element values. This paper proposes a new method which eliminates the problems. Furthermore a passive element usually has not only a frequency-dependent but also a temperature-dependent characteristics. This paper extends the above basic model to a modified one which can include both characteristics. The extended nonlinear model is based on a set of the basic models at sampled temperatures and is derived as interpolation of the basic models. The extended model is described in VHDL-AMS and is flexibly utilized as one of libraries. Finally synthesized model examples, for example, inductors, capacitors, an induction motor, and temperature-dependent elements, are demonstrated.