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## Error model and calibration of vector network analyzer

Release date：2021-12-28Author source：KinghelmViews：204

Recently, I discussed the error model and calibration process of vector network analyzer with a colleague in the industry. I briefly sorted it out and shared it with you. Welcome to discuss it together.

The error model of vector network is really not easy to understand. Generally, only those who develop vector network or specialize in testing technology will explore it in depth. Before using vector network test, system error calibration is required. The purpose is to correct the error term introduced by the test device itself and obtain the real s parameters of DUT.

System error calibration can be divided into single port and dual port system error calibration. The former is mainly used to test the reflection coefficient and derived parameters of single port devices, and the latter is mainly used to test the full s parameters and derived parameters of dual port devices.

Single port system error calibration includes OSM (open / short / match, sometimes called OSL -- open / short / load) and normalized calibration. OSM calibration belongs to full single port calibration, which can correct the error items involved in comprehensive single port test, so the accuracy is the highest when testing single port devices! The speed of reflection normalization calibration is very fast, but only a single calibration piece of open or short can solve only one error term of reflection tracking, so the accuracy is limited.

Figure 1 is the equivalent schematic diagram of a reflectometer. The reason why the reflection coefficient can be tested is that it includes a directional element directional coupler (VSWR bridge is mostly used in low-frequency vector network), which realizes the separation of incident wave and reflected wave. Figure 1 Brief schematic diagram of reflectometer

Basic process of reflection test: the excitation source provides signal A1, which is output to the DUT through the vector network port after passing through the coupler; The signal reflected by the DUT reaches the measurement receiver meas through the coupling path of the coupler Receiver. Since the vector network port also has reflection, assuming that the reflection coefficient is s, there will be multiple reflections between the vector network port and the DUT port, and the amount of multiple reflections will also enter meas through the coupling path Receiver. In addition, since the coupler is not ideal, its isolation is also limited, which leads to a part of the excitation signal A1 being directly fed into meas through the isolation channel of the coupler Receiver。

That is, meas The signal B3 received by the receiver actually includes three parts: the signal directly reflected by the DUT, the multiple reflection signal at the test reference plane, and the signal directly leaked through the coupler isolation channel.

Before enumerating the formula, briefly introduce the identification parameters in the figure below: the coupler itself has four ports, but considering that only some parameters of the coupler are involved in the model, it is equivalent to a 3-port device here, and the ports are port1, port2 and port3 respectively Stwenty-oneIs the straight through transmission coefficient of the coupler, Sthirty-oneIs the transmission coefficient of the leakage channel, Sthirty-twoRefers to the transmission coefficient of the coupling channel.

For simplicity, the signal flow diagram in the above figure can be drawn first, as shown in the following figure:（ ΓDUTIs the true reflection coefficient of the DUT). Figure 2 Signal flow diagram during single port test

B can be obtained directly from the signal flow diagramthreeExpression for: The measured values of the simplified reflection coefficient are as follows: According to the above formula, the reflection coefficient measurement includes four error terms: stwenty-one，Sthirty-two，Sthirty-one，S。 General name (s)twenty-one&middot; Sthirty-two）It is called reflective tracking R (reflective tracking), which is called sthirty-one/(Stwenty-one&middot; Sthirty-two）It is directivity, abbreviated as D (directivity), and S is called the reflection coefficient of the source port. After simplification, there are three error terms R, D and s in single port test. During calibration, open, short and match standard parts are used respectively. Each standard part obtains an equation, which can uniquely solve the three error terms, and then correct the measurement results.

In order to expand to the case of two port test, the error two port network is introduced, which is an equivalent two port network, including four s parameters Ei,j, corresponding to R, D and s: r = e01&middot; eten，D= e00/R，S= eeleven.

Each port of vector network can obtain such an equivalent error two port network. The errors involved in dual port test are much more than those in single port test, so more complex calibration methods are needed to complete the correction of test results. Figure 3 Equivalent error two port network

The most classic dual port system error calibration is tosm (through, open, short, match), sometimes also known as sort (L, load). Tosm calibration is applicable to the 12 item error model. Finally, 10 errors are obtained through simplification, and tosm calibration can provide just 10 equations, so the solution of the error term can be uniquely determined.

Next, take the forward test of dual port network as an example to observe the possible signal paths: a total of 1 ~ 5 possible signal paths. The signal path 5 is the crosstalk of the port or the test fixture. For simplicity, this item is not included in the following formula, that is, it is considered that the ports are ideally isolated.

According to the signal flow diagram, the forward transmission coefficient s is testedtwenty-oneWhen, the error mainly comes from the transmission frequency response of the test device itself, multiple reflections of the test reference surface, etc. when mapped to the error two port network, as shown in Fig. 5, combined with the signal flow diagram corresponding to Fig. 4, s can be derivedtwenty-oneThe expression between the measured value and the error term. Figure 4 Dual port network: signal path during forward test Figure 5 Signal path and corresponding error term during forward and reverse test

The forward test will involve five errors of R, D, s, t (transmission tracking) and l (load match), SelevenAnd Stwenty-oneThe measured value of is expressed as follows: The reverse test will involve R、D、S、T、L(load match) five term error, stwelveAnd Stwenty-twoThe measured value of is expressed as follows: After tosm calibration, these 10 errors can be obtained, and then the real four s parameters can be calculated by substituting them into the above formula.

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