#### 5.2.8.4. Scattering Coefficients (S), Impedance (Z), Admittance (Y), Voltage Standing Wave Ratio, Stored Energy, Power Loss by Impedance Boundary

• The scattering coefficients (S) are available to view in either generalized (raw) format or renormalized format. An entry in the generalized scattering coefficient matrix relates the "amplitude" of a mode entering one port to that of a resulting mode exiting the same, or different port. The "amplitude" in this case is defined to be the ratio of the actual mode electric or magnetic field amplitude (of the inward or outward traveling wave) scaled by the amplitude when the mode is carrying unit power into/out of the port. By virtue of this definition, the square of the S-matrix entry is related to the power in the corresponding mode, and the sum of the squares of entries along any column or row of the generalized S-matrix must be equal to unity in the case of a lossless reciprocal network.

The renormalized S-matrix is computed using

where Zref is the diagonal matrix of port/mode impedances you defined, Z is the port impedance matrix (described as follows) and Y is the port admittance matrix.

There are two ways to arrange the S-matrix. On the Data Source tab, change Frequency (GHz) to All. For a 2-port problem, the resulting scatting coefficient table looks like this:

Each row of the scattering coefficient table contains data for a given frequency, and each column contains data for a given port combination. From the column labels, you can tell that this table shows the complex magnitude of the scattering coefficients. If you set Frequency (GHz) to a particular frequency, the scattering coefficient table displays as:

Here, Frequency (GHz) is set to 1, so that this table shows the same data as shown in the first row of the previous table. Now, however, the data is arranged in the format of the original scattering-coefficient matrix.

• In the Analyst simulation, the current density and voltage are calculated for each port. At the end of each AMR step, these quantities are used to calculate the impedance parameters, Z, according to

Here, S is the generalized S-matrix, VA and IA are the forward reference plane-shifted voltage and current, and VB and IB are the backward reference plane-shifted voltage and current. The admittance, Y, is given by Z-1.

• The Voltage Standing Wave Ratio (VSWR) at each port can be displayed, with all other ports terminated in with the specified port terminations.

• Stored electric and magnetic energy fields can be displayed by material, for both volumetric and port fields.

• The Stored Energy By Material table displays stored electric and magnetic energy, by material versus frequency. This table will only include frequencies that field output as been requested at.

• The Power Loss by Impedance Boundary table displays power loss on impedance boundaries (by name) versus frequency. This table will only include frequencies that field output as been requested at and only if wall loss field output is enabled.

• The impedance matrix, the admittance matrix, and the renormalized S matrix represent the reference plane shifted system. In the generalized S matrix, reference plane shifts are only applied on entries showing interactions between wave guide ports.

All of the above results can be viewed by changing the Primary/Qualifier 3 parameter.