## E.2 Mismatch uncertainty between measurement receiver and the probe antenna

37.5443GPPConformance testingRelease 16TSUniversal Terrestrial Radio Access (UTRA) and Evolved UTRA (E-UTRA)User Equipment (UE) Over The Air (OTA) performance

If the same chain configuration (including the measurement receiver; the probe antenna and other elements) is used in both stages, the uncertainty is considered systematic and constant 0.00dB value.

If it is not the case, this uncertainty contribution has to be taken into account and determined by the following method.

In a measurement configuration, when two elements (devices, networks…) are connected, if the matching is not ideal, there is an uncertainty in the RF level signal passing through the connection. The magnitude of the uncertainty depends on the VSWR at the junction of the two connectors. In practical measurement system there are probably several connections in a test set-up, they will all interact and contribute to the combined mismatch uncertainty.

The total combined mismatch uncertainty is composed of 2 parts:

1) The mismatch through the connector between two elements

2) The mismatch due to the interaction between two elements

## E.2.1 Total combined mismatch uncertainty calculations

### E.2.1.1 Mismatch uncertainty through the connector between two elements

Hereunder, a measurement configuration:

Figure E.2.1.1-1: Mismatch uncertainty through the connector

Г _{MR} is the complex reflection coefficient of the Measurement Receiver

Г _{cable4} is the complex reflection coefficient of the cable4

S_{21} is the forward gain in the network between the two reflection coefficients of interest

S_{12} is the backward gain in the network between the two reflection coefficients of interest

Note that S_{21} and S_{12} are set to1 if the two parts are directly connected.

The uncertainty limits of the mismatch are calculated by means of the following formula table 1 of [26]:

Mismatch limits(% voltage) =

These mismatch limits are divided by because of the U-shaped (table 1 of) [26] distribution of the mismatch uncertainty and give the following standard uncertainty:

U_{mismatch} (% voltage) =

To convert this standard uncertainty in dB, we divide it by the standard uncertainty conversion factor (table 1 of) [26]:

U_{mismatch}(dB) =

### E.2.1.2 Mismatch uncertainty due to the interaction of several elements

Previously, we presented how to determine the mismatch uncertainty between two elements through the junction (connector). Now, we introduce the other type of mismatch uncertainty, which is a result of the interaction between several elements.

Hereunder, a measurement configuration:

Figure E.2.1.2-1: Mismatch uncertainty due to the interaction of several elements

Firstly, we determine the mismatch uncertainty between junctions of the elements:

Between the MR and the cable3:

U_{mismatch1}(dB) =

Between the cable3 and the cable4:

U_{mismatch2}(dB) =

|S_{21}| and |S_{12}| are set to 1 because there is no element between cable3 and cable 4.

U_{mismatch1}(dB) =

U_{mismatch2}(dB) =

Each mismatch uncertainty due to the interaction between the measurement receiver and the cable4 is determined by means of the following formula (table 1 of) [26]:

* U _{mismatch_interaction1}*(dB) =

|S_{21}| and |S_{12}| are equal and correspond to the cable3 attenuation.

U_{mismatch_interaction1}(dB) =

We consider in the general case, the following measurement configuration:

Figure E.2.1.2-2: Mismatch uncertainty measurement configuration

In the general case, this uncertainty contribution can be calculated by:

U_{mismatch_interaction_N}(dB)=

|S_{21}|=|S_{12}| for passive elements (cables…)

U_{mismatch_interaction_N}(dB)=

## E.2.2 Total combined mismatch uncertainty

The two kinds of mismatch uncertainty contributions are combined by the root-sum-squares (RSS) method to derive the total combined mismatch uncertainty.

The total combined mismatch uncertainty is equal to:

This formula shows that the uncertainty is frequency dependent by the way of the forward and the backward gains in the network between the two components. The uncertainty upon |S_{21}| and |S_{12}| increases with frequency. One can therefore expect for the UMTS band a higher mismatch uncertainty value than in the GSM and DCS bands.

Note that for an anechoic chamber, horn antennas are usually used as probe antennas. There are two kinds of horn antennas: single-polarized and dual-polarized. With the second one, it is possible to measure the co-polarized and cross-polarized signals without any movement of the probe, which reduces the cable antenna uncertainty contribution and improves the measurement stability.

To conduct the signals to the measurement receiver, the measurement system configuration using a dual-polarized horn antenna has to be completed with an RF Relay. This device will include new mismatch uncertainty contributions, which have to be determined with the previously presented calculation methods, completed by the RF relay parameters contributions, and described in the following.