Mixed electromagnetic and circuit simulations using a higher-order hybrid formulation

Standard surface impedance approximations are invalid at frequencies approaching DC, since the cross sections of conductors are smaller than the skin depth. Hence, a volumetric formulation is typically used at these low frequencies for broadband simulation as necessitated in digital or ultra-wideband systems, since the skin effect can be modeled explicitly. This modeling requires fine and frequency dependent volume meshing. However, an approach using higher-order elements and/or bases may alleviate these requirements. The paper presents a tightly coupled circuit and hybrid boundary element (or integral equation)/finite element based electromagnetic simulation. The hybrid boundary element/finite element formulation is coupled with a technique for representing circuit-to-EM connections. Results are presented to validate the hybrid formulation compared to the boundary element formulation.