S-Parameter Macromodels Incorporated into FDTD Simulation of Transmission Line Networks

The Finite Difference Time Domain (FDTD) method for the numerical solution of Maxwell’s equations is widely used for simulation of microwave and high speed digital circuits. Frequently, large scale circuit simulations include features whose electromagnetic behavior is desired to be found, interconnected by networks whose behavior is known a priori, either through measurement, simulation, or analytical models. If the known, “circuit-like” parts of the problem can be separated from the pertinent electromagnetic features and replaced by behavioral macromodels, computational savings a can be realized. The technique presented allows for these “circuit-like” components to be described by macromodels based on the S-parameters at their connection points and integrated into an FDTD simulation. This technique is applicable to a class of problems composed of a mixture of circuit and electromagnetic features, where the known behavior of the circuit features can be separated from the other electromagnetic interests. 1 Macromodeling Macromodeling is a common practice in circuit simulation, where a complex system is represented by a simplified model at its connection points. Logic circuits or operational amplifiers are frequently encountered examples of macromodels. Methods for extracting low-order models of complex systems is an active area of research which is being investigated by a number of researchers [1]. The method presented here uses established extraction techniques to derive transfer functions, and then seeks to plug those derived macromodels back into the FDTD method to enable system level simulation of large circuits.