Definition of S-parameters

S-parameters describe the response of an N-port network to voltage signals at each port. The first number in the subscript refers to the responding port, while the second number refers to the incident port. Thus S21 means the response at port 2 due to a signal at port 1.

In case of two-port network:

where:

a_i = transmited signal parameter

b_i = reflected signal parameter

S_ij is a complexe number: S_ij = R_Sij + jX_Sij

S11: input reflection coefficients or input return loss

(refers to the ratio of signal that reflects from input port (b₁) for a signal incident on input port (a₁) ).

Remark:

- If we want to measure S11, we inject a signal at port 1 and measure its reflected signal (no signal must be injected into port 2)

- a₂=0 if Z_L=Z_c (There are not output reflection. Output line is adapted)

S22: output reflection coefficients or output return loss

(refers to the ratio of signal that reflects from output port (b₂) for a signal incident on output port (a₂) ).

Remark:

- If we want to measure S22, we inject a signal at port 2 and measure its reflected signal (no signal is injected into port 1)

- a₁=0 if Z_S=Z_c (There are not input reflection. Input line is adapted)

S12: reverse transmission coefficients (output to input)

Remark:

- a₁=0 if Z_S=Z_c (There are not input reflection. Input line is adapted)

S21: forward transmission coefficients (input to output)

Remark:

- a₂=0 if Z_L=Z_c (There are not output reflection. Output line is adapted)

Unity

S-parameters have no unity. it is a voltage ratio.

S-parameter magnitudes are presented in one of two ways, linear magnitude or decibels (dB).

The angle of a vector S-parameter is almost always presented in degrees (but of course, radians are possible).

Impedance relations

Input impedance may be obtained from the S11 by means of the following expressions:

(z_ref is usual selected at 50Ω)

Input reflection coefficient:

Voltage and Current relations

Voltage Gain

Converting Two-Port S-Parameters to Z-Parameters

The two-port Z-parameters may be obtained from the equivalent two-port S-parameters by means of the following expressions.