An original, fully analytical, spectral domain decomposition approach is presented for the time-dependent thermal modeling of complex non linear three-dimensional (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-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 non linearities 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 non linear, 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

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The first completely physical electro-thermal model is presented that is capable of describing the large signal performance of MESFET- and HEMT-based, high power microwave and millimeter wave monolithic and hybrid ICs, on timescales suitable for CAD. The model includes the effects of self-heating and mutual thermal interaction on active device performance with full treatment of all thermal non linearities. The electrical description is provided by the rapid quasi-2D Leeds Physical Model and the steady-state global thermal description is provided by a highly accurate and computationally inexpensive analytical thermal resistance matrix approach. The order of the global thermal resistance matrix describing 3-dimensional heat flow in complex systems, is shown to be determined purely by the number of active device elements, not the level of internal device structure. Thermal updates in the necessarily iterative, fully coupled electro-thermal solution, therefore reduce to small matrix multiplications implying orders of magnitude speed-up compared to the use of full numerical thermal solutions capable of comparable levels of detail and accuracy.

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