Advancements of the partial element equivalent circuit formulation

The Partial Element Equivalent Circuit (PEEC) formulation is derived from an electric field integral equation. The PEEC formulation provides a full wave solution to Maxwell's equations while transforming the problem into the circuit domain where circuit analysis techniques can be used. The focus of this work is to extend the PEEC formulation through basic understanding and unique contributions.; The basic understanding of the PEEC formulation has been advanced through this work by providing detailed derivations of each equivalent element from the electric field integral equation. A specific example is used to provide additional understanding into the PEEC formulation. Derivations for conductors and dielectrics, both perfect and lossy are also included. In addition, the PEEC formulation is extended to include scattering and lossy inhomogeneous dielectrics.; A traditional MOM formulation is derived and compared with the PEEC formulation. Both the differences and similarities are discussed. PEEC results are compared with a transmission line method for a 2 conductor transmission line structure. PEEC results are also compared with a MOM formulation for both input impedance and radiation for an antenna structure.; Since the PEEC formulation transforms the problem into the circuit domain, partial elements are intermediate observables. The system of linear equations is formed though using a systematic method for writing circuit equations which enforce the continuity equation. Two efficient approaches to matrix fill are presented here, along with the corresponding generalized stamps. In addition, a new coefficient of potential model is introduced which leads to a more efficient matrix fill.; In addition, input impedance for 2 antenna structures is monitored for a large range of frequencies. It is shown that the instability due to the finite discretization of the problem in the time domain corresponds to a negative real input impedance in the frequency domain. By using circuit analysis techniques, the cause of this instability is identified, and a stabilization scheme is introduced. This stabilization scheme is presented in a general form suitable for applications to other integral equation formulations.