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Scattering Parameters

## S-Parameters

S-Parameters are the measurement values derived from a Vector Network Analyzer (VNA). The S-Parameters describe how signals are going through a device. S-Parameters describe the relationship between different ports of the device in terms of amplitude and phase for a defined frequency bandwidth.

The S-parameters can be saved e.g. as  S1P-, S2P– or S4P-file that contains all the combinations of the reflection and transmissions. S4P shows how the DUT behaves with a signal in both forward and reverse directions. For a two port network, SParameters are defined as: S11 is the input port voltage reflection coefficient
S12 is the reverse voltage gain
S21 is the forward voltage gain
S22 is the output port voltage reflection coefficient

The S-parameter matrix is used to determine the reflection coefficients and transmission gains from both sides of a twoport or analog multi-port network.

S-Parameters allow to determine Gain, Return Loss, VSWR and Insertion Loss values.

Details and formulas can be found on Wikipedia.

Return Loss, Insertion Loss, S-Parameters

Return loss, also known as reflection loss, is a measure of the fraction of power that is not delivered by a source to a load. If the power incident on a load is Pi and the power reflected by the load is Pr, then the return loss in decibels is

RLdB=10logPiPr

The better the load is matched to the source, the lower the reflected power and hence the higher the return loss. RL is a positive quantity if the reflected power is less than the incident power. If the load has a complex reflection coefficient ρ, then

RLdB=10log∣∣∣1ρ2∣∣∣=20log|ρ|

That is, the return loss is the negative of the input reflection coefficient expressed in decibels.

When generalized to a terminated two ports, the return loss is defined with respect to the input reflection coefficient of
the terminated two port. The two port has the input reflection coefficient

Γin=S11LS12S21(1−ΓLS22)

where ΓL is the reflection coefficient of the load. Thus the return loss of a terminated two-port is

RLdB=−20log|Γin|=−20log∣∣∣S11LS12S21(1−ΓLS22)∣∣

If the load is matched, i.e. ZL=Z0 (the system reference impedance), then

RLdB=−20log|S11|

This return loss is also called the input return loss since the reflection coefficient is calculated at Port 1. The output return loss is calculated looking into Port 2 of the two-port, where now the termination at Port 1 is just the source impedance.