# Dynamic Correction of the Influence of Long Measuring Path Irregularity in Antenna Tests
## 5 Measurement Results
### 2P Calibration  
The two-port VNA model contains 12 error terms. In addition to the mentioned 1P VNA terms, the following errors are included in the model: load match \(\dot{E}_{L}\), transmission tracking \(\dot{E}_{T}\) and isolation \(\dot{E}_{X}\). Due to the VNA model symmetry, the obtained six error terms describe it in one of the probing directions, e.g., forward. Similar six parameters describe the error model in the other--reverse--probing direction. Conventional 2P error correction is carried out in three stages: (a) 1P calibration of ports; (b) response measurement of two ports through the adapter; (c) optional measurement of error terms \(\dot{E}_{X}\) with two MLs, otherwise considered \(\dot{E}_{X}=0\). Proposed dynamic 2P error correction assumes the use of a phase-stable test cable as a thru adapter. During the measurement, the test cable is subjected to mechanical impact, thus the thru adapter will also be affected in the same way. It is allowed to use an assembly of measuring cables, provided that the phase-stable unit is subjected to mechanical impact as shown in Figure 7a. The proposed extension adapter consists of one or two phase-stable cables at the ends and a conventional measuring cable to ensure the required length between ports. The scattering parameters of such an adapter must be known, i.e., measured separately. The described approach is similar to calibration with a known adapter (<Defined Thru>) (AN 1287-11 <Specifying Calibration Standards and Kits for Agilent vector Network Analyzers>>, Agilent Tech., USA, 2009), but differs in that the calibrated cables are not static during the measurement. A generalized scheme of the measuring setup is shown in Figure 7b, where the dotted line at the antennas indicates possible changes in spatial coordinates during measurement and the dashed one indicates the calibration plane. Similar to the conventional 2P calibration, the first step is to consistently measure the reflection of standards in calibration plane, where the measuring antenna and the AUT are connected, respectively. The second step is to measure response between ports through the adapter. Further, the isolation between ports is optionally measured to determine the \(\dot{E}_{X}\) parameter. The technique was tested at the far-field test setup. The scheme of the measuring stand is shown in Figure 8. The horn antenna of the measuring complex was taken as AUT. Measurements were carried out in the frequency range of (0.8-6) GHz. Figure 9 shows the corrected magnitude \(\Gamma_{in}\) and phase \(\varphi_{in}\) components of the AUT reflection coefficient for azimuth positions of the turntable. The gray solid line depicts direct measurement and the red one after the data correction has been applied. The stability of the corrected parameter along the azimuth coordinate indicates the measurements repeatability. The obtained reflection coefficient coincides with the measurements corrected via built-in VNA calibration process and is in good agreement with the antenna manufacturer's specifications. Figure 7: Dynamic calibration: (**a**) full two-port SOLT calibration standards with defined thru; (**b**) generalized antenna measurement diagram with 2P VNA. Figure 10 shows an example of the experimental evaluation of the measuring cable contribution depending on the angle of the AUT rotation at given frequency. The purple and blue lines correspond to the co-polarized and cx-polarized radiation patterns of the AUT. The red line corresponds to the total radiation pattern. Black lines correspond to radiation patterns after dynamic calibration is applied. And the teal line corresponds to the difference in the total characteristics obtained. Figure 11 shows a comparison of the traditional 2P VNA calibration and the presented dynamic by difference in the AUT radiation patterns obtained. The first curve (purple line) corresponds to the use of error correction during traditional full two-port SOLT VNA calibration in the specified position of the measuring stand.