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The Partial Element Equivalent Circuit (PEEC) method provides an electric equivalent circuit for a physical geometry. This circuit can be combined with external passive/active lumped elements, enabling the simulation and co-design of combined circuit and electromagnetic (EM) structures. The resulted circuit can be solved in a dedicated solver, or equivalently can be exported to a SPICElike solver. In this paper, the inclusion of passive and active lumped circuit elements in PEEC method has been studied and a combined solver has been developed. To demonstrate the capability of the solver, three structures are examined. All examples include a transmission line-PEEC model and active components. Results are compared with those from OrCAD, where an analytical model for the transmission line is used. Good agreement between the results shows the feasibility of using PEEC to solve this type of mixed problems. Also, comparison has been made in terms of implementation and feasibility for the aim of developing the optimal EM solver with active elements support. It is shown that SPICE is not a suitable choice to solve the PEEC models and, a specialized solver can solve the system in a much faster way. On the other hand, all the definitions and models of circuit devices e.g. transistors, MOSFETs, etc. should be implemented in the specialized solver, which raises a tradeoff between the solution time and the implementation time.

Photonic crystal (PhC) lenses with negative refractive index have attracted intense interest because of their application in optical frequencies. In this paper, two-dimensional PhC lenses with a triangular lattice of cylindrical holes in dielectric material are investigated. Various physical parameters of the lens are introduced, and their effects on the lens response are studied in detail. The effect of the surface termination is investigated by analyzing the power flux within the PhC structure. A new lens formula has been obtained that shows a linear relation between the source distance (distance between the source and the lens) and the image distance (distance between the image and the lens) for any surface termination of the PhC lens. It is observed that the excitation of surface waves does not necessarily pull the image closer to the lens. The effects of the thickness and the lateral width of the lens are also analyzed.