Derivation of Multi-Grid Discrete and Analytic Green´s Functions Free of Poles in Terms of Transverse Waves

A derivation, in the spatial domain, of discrete and analytic Green´s functions, free of poles, in terms of waves is presented in the context of the TWF-method. The proposed derivation results from physical considerations based on the separation between higher order and lower order modes contributions. The discrete Green´s functions render possible multi-grid analysis of complex circuits by partitioning them into sub-blocks of different scales. The use of analytic Green´s functions leads to important computation time reduction. The validation of the derived discrete and analytic Green´s functions is demonstrated through a realistic RFIC example including the effects on substrate coupling of floating/grounded seal ground rings. Comparison of the obtained simulation results with measurement data and with results obtained using other relevant methods shows satisfactory agreement