There are two signal flow graphs considered for two-port measurements. One of the graphs describes the case where Port 1 is the stimulus source, the other graph describes the case where Port 2 is the stimulus source.
The signal flow graphs of error effects in a two-port system are represented in the figure below.
For normalization the stimulus value is taken equal to 1. All the values used in the model are complex. The measurement result in a two-port system is affected by twelve systematic error terms.
These terms are also described in the table below.
Description |
Stimulus Source |
|
---|---|---|
Port 1 |
Port 2 |
|
Directivity |
Ed1 |
Ed2 |
Source match |
Es1 |
Es2 |
Reflection tracking |
Er1 |
Er2 |
Transmission tracking |
Et1 |
Et2 |
Load match |
El1 |
El2 |
Isolation |
Ex1 |
Ex2 |
After determining all twelve error terms for each measurement frequency by means of a two-port calibration, it is possible to calculate the actual value of the S-parameters: S11a, S21a, S12a, S22a.
There are simplified methods, which eliminate the effect of only one or several of the twelve systematic error terms.
note |
When using a two-port calibration, all four measurements S11m, S21m, S12m, S22m need to be known to determine any S-parameters. That is why updating one or all S-parameters necessitates two sweeps: first with Port 1 as a signal source, and then with Port 2 as a signal source. |
For a detailed description of calibration methods, see Calibration Methods and Procedures.