HFSS15: Terminal-Based Models for Circuit Analysis

It is possible to use the transformations developed above to compute terminal-based admittance (Y), impedance (Z) and pseudo-S-matrices (S_p). First consider the admittance case. A relationship of the form i =Yv is needed that gives the vector of terminal currents i = [i_k] as a function of the vector of terminal voltages v = [v_k]. It is known that

(1)

and

(2)

It is also known that the incident and scattered modal amplitudes are related by b = Sa, where S is the modal S-matrix computed by HFSS. Therefore:

(3)

(4)

Here I denotes an identity matrix of the same size as S. i can then be solved for in terms of v by eliminating the incident wave variable a.

(5)

(6)

The terminal-based admittance matrix Y is identified from the above expression as:

(7)

A similar relationship can be developed for the terminal-based impedance matrix:

(8)

It is also possible to convert the terminal-based admittance and impedance matrices into a terminal-based “pseudo-S-matrix” S_p. To do this, a reference impedance matrix must be specified. Then standard formulas are used to convert the terminal impedance matrix Z into the terminal S-matrix

(9)

Z_ref can be either a user defined diagonal reference impedance matrix or the terminal characteristic impedance matrix, Zo, which is the matched case for terminal-based models.

The terminal S-matrix S_p relates the intensities of the incident and reflected pseudo-waves at the terminals.

(10)

These pseudo-waves are defined by:

(11)

(12)

Note that the units of a and b are watts^1/2. The terminal voltages and currents can also be written in terms of the pseudo-waves.

(13)

(14)

Unlike true waveguide modes, the pseudo-waves a and b have no associated propagation constant. The pseudo-waves represent linear combinations of several modes, which may all have differing propagation constants. HFSS is still capable of performing de-embedding on the terminal-based S-matrix, but this is accomplished by first de-embedding the modal S-matrix and then performing the transformation back to a terminal-based S-matrix.

For the normalization of terminal voltages in the Fields Post Processor, see Scaling a Source’s Magnitude and Phase.