Calculating the PI Impedance

The Zpi impedance is the impedance calculated from values of power (P) and current (I):

 

(1)

The power and current are computed directly from the simulated fields. The power passing through a port is equal to the following:

 

(2)

where the surface integral is over the surface of the port.

The current is computed by applying Ampere's law to a path around the port:

 

(3)

While the net current computed in this way will be near zero, the current of interest is that flowing into the structure, I-, or that flowing out of the structure, I+. In integrating around the port, HFSS keeps a running total of the contributions to each and uses the average of the two in the computation of impedances.

Note:

Zpi calculation is modified when a symmetry E plane touches a port. The current on the symmetry E plane is included in the Zpi calculation for a port with more than one conductor, where as for a single conductor port, such as a waveguide, the current on the symmetry E plane is not included in the Zpi calculation.