## Measured Quantities

This section gives an overview of the measurement results of the network analyzer and the meaning of the different measured quantities. All quantities can be selected in the Trace submenu.

The definitions in this and the following sections apply to general n-port DUTs. An analyzer with a smaller number of test ports provides a subset of the n-port quantities.

### S-Parameters

S-parameters are the basic measured quantities of a network analyzer. They describe how the DUT modifies a signal that is transmitted or reflected in forward or reverse direction. For a 2-port measurement the signal flow is as follows.

Extensions to the signal flow

The figure above is sufficient for the definition of S-parameters but does not necessarily show the complete signal flow. In fact, if the source and load ports are not ideally matched, part of the transmitted waves are reflected off the receiver ports so that an additional a2 contribution occurs in forward measurements, an a1 contribution occurs in reverse measurements.

The 7-term calibration types Txx take these additional contributions into account.

The scattering matrix links the incident waves a1, a2 to the outgoing waves b1, b2 according to the following linear equation:

The equation shows that the S-parameters are expressed as S<out>< in>, where <out> and <in> denote the output and input port numbers of the DUT.

Meaning of 2-port S-parameters

The four 2-port S-parameters can be interpreted as follows:

- S11 isthe input reflection coefficient, defined as the ratio of the wave quantities b1/a1, measured at PORT 1 (forward measurement with matched output and a2 = 0).

- S21 is the forward transmission coefficient, defined as the ratio of the wave quantities b2/a1 (forward measurement with matched output and a2 = 0).

- S12 is the reverse transmission coefficient, defined as the ratio of the wave quantities b1 (reverse measurement with matched input, b1,rev in the figure above and a1 = 0) to a2.

- S22 is the output reflection coefficient, defined as the ratio of the wave quantities b2 (reverse measurement with matched input, b2,rev in the figure above and a1 = 0) to a2, measured at PORT 2.

Meaning of squared amplitudes

The squared amplitudes of the incident and outgoing waves and of the matrix elements have a simple meaning:

|a1|2 | Available incident power at the input of a two-port (= the power provided by a generator with a source impedance equal to the reference impedance Z0)
|a2|2 | Available incident power at the output
|b1|2 | Reflected power at the input of a two-port
|b2|2 | Reflected power at the output
10*log|S11|2 (= 20*log|S11|) | Reflection loss at the input
10*log|S22|2 | Reflection loss at the output
10*log|S2 1|2 | Insertion loss at the input
10*log|S12|2 | Insertion loss at the output

#### Multiport Parameters

The multiport S-parameters
extend the standard 2-port S-parameters
to a larger number of incoming and outgoing waves. For a 4-port DUT,

,

where again ai (i = 1 to 4) denote the incident, bi (i = 1 to 4) denote the outgoing waves, and the S-parameters are expressed as S<out>< in>.

The indices of the S-parameters described so far number the output and input ports of a DUT; the parameters are referred to as single-ended S-parameters. The S-parameter description can also be used to differentiate between different propagation modes of the waves at the output and input ports. This results in the so-called mixed mode S-parameters
. The analyzer measures either single-ended or mixed mode S-parameters.