Partial element equivalent circuit

A 10x10x10 cm cube is modelled in the frequency domain. The cube is excited with a unitary current pulse in one corner.

A 19x43x38 cm (LxWxT) case with one opening (19x10) in the front is modeled in the time domain.

Partial element equivalent circuit method (PEEC) is partial inductance calculation used for interconnect problems from early 1970s which is used for numerical modeling of electromagnetic (EM) properties. The transition from a design tool to the full wave method involves the capacitance representation, the inclusion of time retardation and the dielectric formulation. Using the PEEC method, the problem will be transferred from the electromagnetic domain to the circuit domain where conventional SPICE-like circuit solvers can be employed to analyze the equivalent circuit. By having the PEEC model one can easily include any electrical component e.g. passive components, sources, non-linear elements, ground, etc. to the model.

Numerical modeling of electromagnetic properties are used by, for example, the electronics industry to:

• Ensure functionality of electric systems
• Ensure compliance with electromagnetic compatibility (EMC)

History

The main research activity in this area has been and are performed, by Albert Ruehli at IBM Thomas J. Watson Research Center, starting with a publication in 1972. At that time the foundation of the PEEC method was presented, i.e. the calculation of the partial inductances. The PEEC method was extended to more generalized problems, including dielectric material and retardation effect.

The PEEC method is not one of the most common techniques used in EM simulation software or as a research area but it has just been starting to gain recognition and for the first time there is a session at the 2001 IEEE EMC Symposium named after the technique. In the mid 90's, two researchers from the University of L'Aquila in Italy, Professor Antonio Orlandi and Professor Giulio Antonini, published their first PEEC paper and are now together with Dr. Ruehli considered the top researchers in the area. 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 under the name MultiPEEC.

Theory

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

${\vec {E}}^{i}({\vec {r}},t)={\frac {{\vec {J}}({\vec {r}},t)}{\sigma }}+{\frac {\partial {\vec {A}}({\vec {r}},t)}{\partial t}}+\nabla \phi ({\vec {r}},t)$

where ${\vec {E}}^{i}$ is an incident electric field, ${\vec {J}}$ is a current density, ${\vec {A}}$ is the magnetic vector potential, $\phi$ is the scalar electric potential, and $\sigma$ the electrical conductivity all at observation point ${\vec {r}}$.

PEEC model reduction

The rigorous full-wave version of the PEEC method is called (Lp,P,R,t) PEEC, where Lp is partial inductance, P is potential coefficient (inverse of capacitance), R is resistance, and t is delay. If available, reduced model of the full-wave version can be used. For example, if the EIP structure is electrically small, the delay term t can be omitted and the model can be reduced to (Lp,P,R) PEEC model. In addition, if frequency is sufficiently high so that w*Lp >> R, we can omit R term and use approximate (Lp,P) PEEC model. According to various modeling situations, (Lp) and (Lp,R) models are also useful.

Frequency domain analysis

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External links

• Partial Element Equivalent Circuit (PEEC) homepage
• Electromagnetic Modelling Process to Improve Cabling of Power Electronic Structures