Circuit Oriented Electromagnetic Modeling Using the PEEC Techniques

Appendix C

Computation of Partial Inductances

The computation of partial inductances represents a key component for almost all partial element equivalent circuit (PEEC) models, perhaps even more than the partial coefficients of potential in the following section. Many lower-frequency high-current problems can be solved with inductance-only models. Some references on this subject are [1–3] and also [4–7].

The evaluation of partial inductances Lp for the most general case involves the evaluation of a sixfold integral of the form (C.1) which is (5.15), or

C.1

where the details are given in Chapter 5.

The example formula (C.1) applies to the case where conductors 1 and 2 are bars or cells that are not necessarily parallel to each other. Obviously, for the partial self-inductances , the conductors 1 and 2 are the same. This case leads to a singularity if the points coincide such that . An advantage of an analytical solution for is that the singularity can be eliminated if two of the integrals for the same surface can be analytically evaluated.

In general, we need to consider a larger ...