S-Parameters

One of the most important features of HFSS is the capability to categorize an electromagnetic structure in a compact manner using the concept of S-parameters. S-parameters are available for projects that contain ports and this document focuses on the case when the S-parameters are related to the eigen modes of the ports. The use of S-parameters for terminals are described in Modes to Terminals Conversion.

At each port, the modal representations of the electric and magnetic fields assuming K modes are:

		(1)
		(2)

where a_m and b_m are unitless complex amplitudes of the incident and reflected modal fields, respectively. Given a particular electromagnetic structure, it can be categorized in terms of the incident and reflected/transmitted modal amplitudes using the NxN generalized S-matrix, S:

(3)

where a and b are unitless complex modal coefficient vectors. The size of these vectors, N, is the total number of modes obtained by adding up the number of the modes on all ports.

An entry of the S-matrix, S_ij, specifies the multiplication factor to be applied to the incident modal amplitude a_j to get the reflected/transmitted modal amplitude b_i given that all the other incident modes are turned off. This can be described mathematically as:

(4)

HFSS automatically provides an S-matrix when a project contains ports. The following links contain information on various topics related to S-matrices.

• Post Processed S-Matrices
• Passivity
• Alternative Matrix Characterizations