Partial element equivalent circuit: Difference between revisions

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conductivity all at observation point <math>\vec{r}</math>.
 
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. Pulse functions are
also used for the weighting functions resulting in a Galerkin type
solution. 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. The partial inductances are defined as
 
<math>
\vec L_{p_{\alpha \beta}} = \frac {\mu}{4 \pi}\frac{1}{a_{\alpha}
a_{\beta}} \int_{v_{\alpha}} \int_{v_{\beta}} \frac {1} {|
\vec{r}_{\alpha} - \vec{r}_{\beta}|} d v_{\alpha} dv_{\beta}
</math>
 
===PEEC model reduction===