The two-port VNA typically uses one of the following error models.

12 Term Error Model

For a two-port VNA in the forward state, the 12-term error model represents systematic errors in the measurements as shown in the figure below.

In the context of a two-port VNA, the forward and reverse states are defined as follows:

  • The forward state is where the VNA source generates a stimulus signal on port 1 while port 2 is terminated.
  • The reverse state is where the VNA source generates a stimulus signal on port 2 while port 1 is terminated.

The error terms depicted in the forward state are as follows.

Error Description
ED(1,1)
 Forward directivity; an ideal directional coupler produces an output signal in the coupled arm that is proportional to the measured signal traveling in one direction of the main arm, while producing no output for a signal traveling in the opposite direction.
ES(1,1)
 Forward source match; the mismatch between the DUT input and the network analyzer port 1.
ERT(1,1)
 Forward reflection tracking; reflected signal loss across frequency.
EL(2,1)
 Forward load match; the mismatch between the DUT output and the network analyzer port 2.
ETT(2,1)
 Forward transmission tracking; the transmitted signal loss across frequency.
EX(2,1)
 Forward isolation; a fraction of incident signal may be radiated or conducted from port one and detected at the port two receiver. This causes isolation error or crosstalk.
Note The difference between the coupler output (coupled arm) and the measured input signal (through arm) is the coupling factor. Values of 10 dB to 30 dB are common, which means that the coupler output RF power is 10 dB to 30 dB less than the input signal passing in the through arm in the proper direction. In theory, a directional coupler should produce no output for a signal traveling in the opposite direction; however, in reality, a signal traveling in the opposite direction through the coupler produces an unwanted response at the coupler's output, which is known as coupler leakage. The difference between the coupling factor and the coupler leakage is known as coupler directivity.

The reverse state error model is shown below.

The forward and reverse error terms sum-up to a total of 12 errors. User calibration needs to adequately account for these 12 error terms so that the VNA can apply the proper correction factors to the measured data.

10 Term Error Model

Many applications do not require additional isolation calibration as the VNA isolation is sufficient. The 10-term error model is same as 12 term error model with the isolation error terms E_X (2,1) and E_X (1,2) set to 0. Forward and reverse state 10 term error model is shown in the following figures.

8 Term Error Model

The 8-term error model differs from the 10-term model in requiring measurements at all four test receivers when performing error correction for a two-port VNA: the two incident waves r_1 and r_2 and the two scattered waves s_1 and s_2, as shown in the following figure.

In practice, the load match at each port changes depending upon whether the port is a source or a load. Therefore, 10-term and 12-term error models have different error terms depending upon forward or reverse source direction. However, the 8-term model does not change with source direction, because the change in load impedance is captured in changes in the incident waves at each port.

Wave Formalism Error Model

You can also model error correction with T-parameters. The table below shows an example of the transformation of the wave-formalism error model.

Uncorrected waves Corrected waves
Incident wave r Incident wave
a
Scattered wave s Scattered wave b

For a two-port VNA, the wave-formalism model is shown in the following equation.

In general, for each port i in any N-port VNA, the wave-formalism error model simplifies to

Here, error correction transforms the measured waves r_i,s_i (uncorrected) to the corrected waves a_i,b_i at VNA port i. By convention, the error model is normalized such that α_i=1 for all ports i. For measurements expressed in ratios, the correction model is overdetermined and you can set one carriable independently.

Note Typically, K_1 is set to 1.