Circuit Oriented Electromagnetic Modeling Using the PEEC Techniques

Chapter 9Skin Effect Modeling

The skin effect results in nonuniform current flow in conductors for higher frequencies or fast transients in the time domain. Essentially, the current density is reduced in the inner parts of conductors. In fact, the modeling of skin-effect has a long history, for example, [1]. Skin-effect is an important area of early research for large transmission lines (TLs), transformers, and power stations. Today, power engineering applications are even more important.

The solution of most electromagnetic (EM) problems include the modeling of the broadband skin-effect loss for the conducting planes and 3D conductors, for example, Refs [2, 3], or [4]. Three-dimensional problems are present in connectors, on printed circuit boards (PCBs) and other common geometries. Frequency domain applications include radio frequency (RF)/microwave on-chip circuit issues such as the modeling of coils with the correct Q-factor, which is sensitive to losses. Skin-effect losses are also important for modeling of the antenna efficiency and gains in an integrated circuit (IC) environment. Clearly, the inclusion of the skin effect in solving large problems is important. The assumed current flow in a model can be in one direction (1D), two directions (2D), or all three directions (3D).

Reliable solutions exist today for the one direction (1D) current flow in TLs [5]. However, the 2D or 3D current flow as is the case of many partial element equivalent circuit (PEEC) models are much ...