Discrete-Time Network and State Equation Methods Applied to Computational Electromagnetics

The representation of electromagnetic structures by lumped element circuits is revisited. Net- work models can be established by a subsequent ap- plication of system identification and circuit synthesis methods to data obtained by numerical simulation or from measurement. Network models provide a com- pact description of electromagnetic structures and can contribute significantly to the formulation of electro- magnetic field problems and their efficient solution. On the field level network methods are introduced by seg- mentation of the electromagnetic structures and appli- cation of the field form of Tellegen's theorem. Methods for synthesis of lumped element models for lossless as well as lossy linear reciprocal multiports and for ra- diating structures are discussed. The state equation method as a general framework for lumped element network description is presented. Discrete time repre- sentations on the basis of Richards transformation and wave digital filter formulation are introduced. I. Introduction The design of modern high-speed analog and digital elec- tronics makes use of distributed passive circuit struc- tures. The modeling of distributed circuits requires full- wave electromagnetic analysis. Usually the whole circuitry contains lumped as well as distributed subcircuits con- nected via interconnects or transmission lines such that each interconnect or connecting transmission line carries a single transverse mode only. This allows the segmen- tation of the circuits by cutting through the connecting transmission lines. The circuit segments obtained in this way, exhibiting a number of n open transmission lines each of them carrying a single transverse mode only in the considered frequency band, is called a multiport or n-port, respectively (1). Whereas lumped element multi- ports can be treated by methods of network theory (2) distributed circuits require electromagnetic full-wave mod-