## Introduction

This article describes how to measure reflection and transmission coefficients using a Zurich Instruments UHFLI Lock-in Amplifier and a directional coupler.

Network analysis is a commonly performed in RF measurement. A network analyzer is an instrument that measures the network parameters of electrical circuits. Circuits that can be analyzed using network analyzers range from simple two-port networks such as amplifiers and filters to complex networks with an arbitrary number of ports.

Figure 1 illustrates one of the most fundamental concepts of high-frequency network analysis which involves incident, reflected and transmitted waves traveling along a transmission line. Figure 1 Incident, reflected and transmitted waves.

A vector network analyzer (VNA) measures the amplitude and phase of the wave quantities and uses these values to describe the high-frequency characteristics, such as reflection and transmission, of the device under test (DUT). Often, the term S-parameters (scattering parameters) is used to describe reflection and transmission coefficients.

### Reflection coefficient

Reflection coefficient (Γ), or S-parameter S11, is the ratio of the reflected signal voltage to the incident signal voltage: $\Gamma = \frac{V_\text{Reflected} }{V_\text{Incident}}$

### Transmission coefficient

Transmission coefficient (T), or S-parameter S21, is defined as the transmitted voltage divided by the incident voltage: $\Gamma = \frac{V_\text{Transmitted} }{V_\text{Incident}}$

Combined with a directional coupler the UHFLI can be used to measure transmission and reflection coefficients and perform a simple 1-point calibration through the LabOne User Interface.

## Transmission coefficient measurement

To calculate the transmission coefficient, the transmission and incident waves need to be measured.

The incident wave can be measured as following:

• Connect Signal Output 1 and Signal Input 1 with a short BNC cable as shown in Figure 2.
• Sweep the Input Signal 1 using the Sweeper Tab in the LabOne User Interface over the frequency range of interest. Figure 2 Setup to measure the incident wave with UHFLI instrument.

The transmitted wave can be measured by performing the following steps:

• Connect the device under test (DUT) between Signal Output 1 and Signal Input 1 as shown in Figure 3
• Sweep Input Signal 1 using the Sweeper Tab in the LabOne User Interface over the frequency range of interest. Figure 3 Transmission measurement and calibration setup.

To obtain the transmission coefficient, select the Incident wave in the History sub-tab and set it as the reference. The plot now displays the ratio between the two signals, i.e. the transmission coefficient.

## Reflection coefficient measurement

A reflection coefficient measurement can be performed using a third-party directional coupler, e.g. ZFDC-10-5+ from Mini-Circuits. The purpose of the directional coupler is to capture reflected signal coming from the DUT.

In order to calculate the reflection coefficient, incident and reflected waves need to be measured.

The incident wave is measured as following:

• Connect the directional coupler, the open calibration standard and the UHFLI device as shown in Figure 5
• Sweep Input Signal 1 using the Sweeper tab in LabOne User Interface over the frequency range of interest Figure 5 Incident wave measurement setup

In case the user doesn’t have an open calibration standard, the same can be replaced with an open directional coupler port. The incident wave measurement is based on an assumption that the wave coming from the Signal Output 1 is fully reflected at the open port.

The reflected wave can be measured as follows:

• Connect the directional coupler, DUT, the load calibration standard and the UHFLI device as shown in Figure 6.
• Sweep Input Signal 1 using the Sweeper tab in LabOne User Interface over the frequency range of interest. Figure 6 Reflection measurement setup.

After performing previously described steps, the History sub-tab of the Sweeper tab should contain the two measured wave traces. Select the incident wave and set it as a reference. Now the sweeper plot displays reflection coefficient trace as it can be seen in Figure 7.

## Conclusion

The Zurich Instruments UHFLI Lock-in Amplifier is capable of performing simple reflection and transmission coefficients measurements using a 1-point calibration. The measurements give good qualitative results. However, the following limitations should be taken into account:

• the measurement precision is limited by the 1-point calibration. VNAs usually employ a 4-point SOLT calibration (short, open, load, through) for each port.
• the precision depends on the quality of the used coupler.