| Coupling Electromagnetic Devices to Electric
Circuits using Parameter Extraction
One of the most efficient techniques
for analyzing electromagnetic devices coupled to electric circuits is to
determine a reduced, circuit
model for the device and to use this model -characterized
by Kirchhoff's rather than by Maxwell's equations- to solve the coupled
problem.
Usually, the order of the
system extracted by discretization of Maxwell's equations is O(n), where
n is the number of cells in the discretization mesh. This number can become
excessively large, especially if the device's geometry is complicated.
Consequently, an order reduction is necessary. This is done by determining
a system with a much lower order of complexity, but with approximately
the same input-output behaviour as the initial device.
The paper presents a survey
and attempts a classification of the most popular and efficient methods
for determining reduced models for
electromagnetic devices:
-
Methods based on knowledge of the equations characterizing
the device (e.g. the electromagnetic applications of PVL, or techniques
to reduce the dimension of the system of equations itself);
-
Methods based on knowledge of input/output behaviour
of the device (among them, the 4SID method).
A special section of the paper is dedicated to the
correct formulation of the coupled problem, and presents a set of boundary
conditions which ensure the uniqueness of
the solution.
The presented numerical results
focus on electromagnetic devices in quasi-static
and time-varying state, and are the result of the cooperation with
Fachgebiet Theorie Elektromagnetischer Felder from Technische Universitaet
Darmstadt, Germany. |
