S-Parameter Definitions

Scattering parameters describe a microwave network by relating incident and reflected waves at each port. In Flex RF, those wave amplitudes are computed from the port voltage V, port current I, and reference impedance Z_ref.

When Z_ref is real, such as a standard 50 ohm reference, the supported definitions produce the same S-matrix. They differ when Z_ref is complex, which is common for lossy transmission lines when the line characteristic impedance is used as the reference.

Wave Amplitudes

The incident and reflected wave amplitudes can be written as:

a = F * (V + Z_ref * I)
b = F * (V - Z_ref_prime * I)

F is a scaling factor. Z_ref_prime is either Z_ref or its complex conjugate, depending on the selected definition. The S-matrix relates these quantities as b = S * a.

Supported Definitions

Definition	s_param_def	Reflected-wave impedance	Main behavior
Pseudo-wave	"pseudo"	Z_ref	Default definition. For complex Z_ref, reciprocal devices are not guaranteed to have S12 = S21.
Power-wave	"power"	conjugate(Z_ref)	Relates wave amplitudes directly to delivered power and keeps passive reflection coefficients bounded.
Symmetric pseudo-wave	"symmetric_pseudo"	Z_ref	Keeps reciprocal S-matrices symmetric while using a complex scaling factor.

Set the definition on TerminalComponentModeler with the s_param_def field. The resulting MicrowaveSMatrixData records which definition was used.

Power Relationship

For power waves, the net power delivered by a port is:

P = 0.5 * (abs(a)^2 - abs(b)^2)

For pseudo-waves and symmetric pseudo-waves, an additional cross term appears when Z_ref is complex. This means the net power is not simply the difference between incident and reflected power. The cross term disappears when Z_ref is real, so all definitions reduce to the familiar power relationship.

Comparison

Definition	Reciprocal S12 = S21	Condition for S11 = 0	Passive abs(S11) <= 1
Pseudo-wave	No	Z_in = Z_ref	No
Power-wave	Yes	Z_in = conjugate(Z_ref)	Yes
Symmetric pseudo-wave	Yes	Z_in = Z_ref	No

For pseudo-waves and symmetric pseudo-waves, S11 follows the familiar impedance-match form and vanishes when the input impedance equals the reference impedance. For power waves, the conjugate in the reflected-wave definition means S11 = 0 requires a conjugate match when Z_ref is complex.

Related Pages

Page	Why open it
Terminal Component Modeler	Configure the component modeler that extracts the S-matrix.
RF Mode Analysis	Compute characteristic impedance for transmission-line modes.
Impedance Calculator	Calculate impedance from field data and path integrals.