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HFSS and Planar EM Simulators >
Planar EM Technical Notes >
The MPIE Method

The MPIE Method

To generate a solution from which S-parameters can be computed, Designer employs the mixed-potential integral equation (MPIE) method. The method of moments (MoM) is applied to the MPIE to solve for J, the current distribution on the 3D surface mesh. Then the S-parameters and the radiated fields are calculated from J.

In Designer, the surface of the geometric model is automatically divided into triangles and rectangles. This collection of triangles and rectangles is referred to as the mesh. A volume mesh is not generated inside the model because at high frequencies the skin depth is so small that a surface mesh is sufficient.

Once the 3D surface mesh has been generated, the following MPIE is applied to it:

where

• is a unit vector perpendicular to the face of the triangles.

• j is the imaginary unit, .

• w is the angular frequency, 2pf.

• A is the magnetic vector potential.

• f is the electric potential.

• Z_s is the surface impedance.

• J is the current density.

The current normal to the edges of the triangles is calculated.

Note

The MPIE method is unstable at low frequencies. The Designer loop tree discretization is a re-ordering of the MoM matrix that provides a highly stable solution at very low frequencies.

The topics for this section include:

Representation of the Current

Method of Moments

Size of Mesh Versus Accuracy

Loop Tree Discretization

MPIE Method Implementation

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