Electrothermal CAD of power devices and circuits with fully physical time-dependent compact thermal modeling of complex nonlinear 3-d systems

An original, fully analytical, spectral domain decomposition approach is presented for the time-dependent thermal modeling of complex nonlinear (3-D) electronic systems, from metallized power FETs and MMICs, through MCMs, up to circuit board level. This solution method offers a powerful alternative to conventional numerical thermal simulation techniques, and is constructed to be compatible with explicitly coupled electrothermal device and circuit simulation on CAD timescales. In contrast to semianalytical, frequency space, Fourier solutions involving DFT-FFT, the method presented here is based on explicit, fully analytical, double Fourier series expressions for thermal subsystem solutions in Laplace transform s-space (complex frequency space). It is presented in the form of analytically exact thermal impedance matrix expressions for thermal subsystems. These include double Fourier series solutions for rectangular multilayers, which are an order of magnitude faster to evaluate than existing semi-analytical Fourier solutions based on DFT-FFT. They also include double Fourier series solutions for the case of arbitrarily distributed volume heat sources and sinks, constructed without the use of Green's function techniques, and for rectangular volumes with prescribed fluxes on all faces, removing the adiabatic sidewall boundary condition. This combination allows treatment of arbitrarily inhomogeneous complex geometries, and provides a description of thermal material nonlinearities as well as inclusion of position varying and non linear surface fluxes. It provides a fully physical, and near exact, generalized multiport network parameter description of nonlinear, distributed thermal subsystems, in both the time and frequency domains. In contrast to existing circuit level approaches, it requires no explicit lumped element, RC-network approximation or nodal reduction, for fully coupled, electrothermal CAD. This thermal impedance matrix approach immediately gives rise to minimal boundary condition independent compact models for thermal systems. Implementation of the time-dependent thermal model as N-port netlist elements within a microwave circuit simulation engine, Transim (NCSU), is described. Electrothermal transient, single-tone, two-tone, and multitone harmonic balance simulations are presented for a MESFET amplifier. This thermal model is validated experimentally by thermal imaging of a passive grid array representative of one form of spatial power combining architecture.