The MPIE Method (Planar EM Only)
To generate a solution from which S-parameters can be computed, the Ansys Electronics Desktop (AEDT)TM electronics systems design platform 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. The S-parameters and the radiated fields are calculated from J.
In the Ansys Electronics Desktop (AEDT)TM electronics systems design platform, 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.
- Zs is the surface impedance.
- J is the current density.
The current normal to the edges of the triangles is calculated.
The MPIE method is unstable at low frequencies. The Desktop loop tree discretization is a re-ordering of the MoM matrix that provides a highly stable solution at very low frequencies.