Partial element equivalent circuit

The transition from a design tool to the full-wave method involves the capacitance representation, the inclusion of time retardation and the dielectric formulation.

The PEEC method was extended to more generalized problems, including dielectric material and retardation effect.

Starting year 2006, several research projects have been initiated by the faculty of Computer Science and Electrical Engineering of Luleå University of Technology in Sweden in the focus area of PEEC with the emphasis on computer-based solvers for PEEC.

PEEC is widely used for combined electromagnetic and circuit problems in various areas such as power electronics, antenna design, signal integrity analysis, etc.

The classical PEEC method is derived from the equation for the total electric field at a point[2] written as where

In the figures on the right, an orthogonal metal strip with 3 nodes and 2 cells, and the corresponding PEEC circuit are shown.

By using the definitions of the scalar and vector potentials, the current- and charge-densities are discretized by defining pulse basis functions for the conductors and dielectric materials.

By defining a suitable inner product, a weighted volume integral over the cells, the field equation can be interpreted as Kirchhoff's voltage law over a PEEC cell consisting of partial self inductances between the nodes and partial mutual inductances representing the magnetic field coupling in the equivalent circuit.

Then, the coefficients of potentials are computed as and a resistive term between the nodes, defined as The rigorous full-wave version of the PEEC method is called (Lp,P,R,t) PEEC, where Lp is partial inductance, P is the Maxwell potential coefficient (inverse of capacitance), R is resistance, and t is the time-delay.

Integration of a PEEC model directly into a circuit simulator is computationally expensive for two main facts.

One is that a large number of circuit elements are generated for complex structures at high frequencies, and the other is that the circuit matrices based on modified nodal analysis (MNA) are usually dense due to full inductive and capacitive coupling.