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# Network Analyzer Principles

2023-09-26

When all port terminals of an arbitrary multi-port network are matched, the incident traveling wave an input by the nth port will be scattered to all other ports and emitted. If the outgoing traveling wave of the m-th port is bm, then the scattering parameter between port n and port m is Smn=bm/an. A dual-port network has four scattering parameters S11, S21, S12 and S22. When both terminals match, S11 and S22 are the reflection coefficients of ports 1 and 2 respectively, S21 is the transmission coefficient from port 1 to port 2, and S12 is the transmission coefficient in the opposite direction. When the terminal m of a certain port is mismatched, the traveling wave reflected by the terminal re-enters port m. This can be equivalently seen as port m is still matched, but there is a traveling wave am incident on port m. In this way, in any case, a system of simultaneous equations of the relationship between equivalent incident and exit traveling waves and scattering parameters at each port can be listed. Based on this, all characteristic parameters of the network can be solved, such as the input end reflection coefficient, voltage standing wave ratio, input impedance and various forward and reverse transmission coefficients when the terminals are mismatched. This is the most basic working principle of a network analyzer. The single-port network can be regarded as a special case of the dual-port network. In addition to S11, there is always S21=S12=S22. For a multi-port network, in addition to one input and one output port, matching loads can be connected to all other ports, which is equivalent to a two-port network. By selecting each pair of ports in turn as the input and output of the equivalent dual-port network, conducting a series of measurements and listing the corresponding equations, all n2 scattering parameters of the n-port network can be solved, and everything about the n-port network can be obtained. Characteristic parameters. The left side of Figure 3 shows the principle of the test unit when measuring S11 with a four-port network analyzer. The arrows indicate the paths of each traveling wave. The output signal of signal source u is input to port 1 of the network under test through switch S1 and directional coupler D2, which is the incident wave a1. The reflected wave of port 1 (that is, the outgoing wave b1 of port 1) is transmitted to the measurement channel of the receiver through the directional coupler D2 and the switch. The output of signal source u is simultaneously transmitted to the reference channel of the receiver through directional coupler D1. This signal is proportional to a1. So the dual-channel amplitude-phase receiver measures b1/a1, that is, S11 is measured, including its amplitude and phase (or real part and imaginary part). During measurement, port 2 of the network is connected to the matching load R1 to meet the conditions specified by the scattering parameters. Another directional coupler D3 in the system is also terminated with the matching load R2 to avoid adverse effects. The measurement principles of the remaining three S parameters are similar to this. The right side of Figure 3 shows the positions where each switch should be placed when measuring different Smn parameters.

Before the actual measurement, three standards with known impedances (such as a short circuit, an open circuit and a matched load) are used for the instrument to perform a series of measurements, which are called calibration measurements. By comparing the actual measurement results with the ideal (without instrument error) results, each error factor in the error model can be calculated and stored in the computer, so that the measurement results of the device under test can be error corrected. Calibrate and correct accordingly at each frequency point. The measurement steps and calculations are very complex and beyond the capabilities of humans.

The above network analyzer is called a four-port network analyzer because the instrument has four ports, which are respectively connected to the signal source, the device under test, the measurement channel and the measurement reference channel. Its disadvantage is that the structure of the receiver is complex, and the error generated by the receiver is not included in the error model.

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