A measurement result in a four-port system is affected by forty eight systematic error terms. The signal flow graph of error effects in the four-port system is represented in the figure below. The graph describes the case where Port 1 is the stimulus source.
S11a, S12a, S13a, S14a, S21a, S22a, S23a, S24a, S31a, S32a, S33a, S34a, S41a, S42a, S43a, S44a — actual value of DUT parameters
S11m, S12m, S13m, S14m, S21m, S22m, S23m, S24m, S31m, S32m, S33m, S34m, S41m, S42m, S43m, S44m — measured DUT parameters values
Four-port error model
Systematic error terms in a four-port system are represented in the table below.
Description |
Stimulus Source |
|||
|---|---|---|---|---|
Port 1 |
Port 2 |
Port 3 |
Port 4 |
|
Directivity |
Ed1 |
Ed2 |
Ed3 |
Ed4 |
Source match |
Es1 |
Es2 |
Es3 |
Es4 |
Reflection tracking |
Er1 |
Er2 |
Er3 |
Er4 |
Transmission tracking |
Et21, Et31, Et41 |
Et12, Et32, Et42 |
Et13, Et23, Et43 |
Et14, Et24, Et34 |
Load match |
El21, El31, El41 |
El12, El32, El42 |
El13, El23, El43 |
El14, El24, El34 |
Isolation |
Ex21, Ex31, Ex41 |
Ex12, Ex32, Ex42 |
Ex13, Ex23, Ex43 |
Ex14, Ex24, Ex34 |
After determination of all the forty eight error terms for each measurement frequency by means of a four-port SOLT or TRL calibration, it is possible to calculate the true value of the S-parameters: S11a, S21a, … S44a.
note |
When using a four-port calibration, all sixteen measurements S11m, S21m, … S44m need to be known to determine any S-parameters. That is why updating one or all of the S-parameters necessitates four sweeps: with each port as a signal source. |
For a detailed description of calibration methods, see Calibration Methods and Procedures.
