Research on the UOSM four-port Calibration algorithm and determination method of the Transmission error term

As one of the key techniques for vector network analyzers to achieve high precision measurement, calibration, and error correction technology has always been the focus of continuous exploration and innovation. UOSM calibration algorithm uses unknown straight-through transmission standards that do not need to be defined and known open-circuit standards, short-circuit standards, and matching standards to calibrate microwave and millimeter wave bands. Based on the study of the mature UOSM calibration algorithm, this paper proposes a method of self-calibration and comparison of the measurement data based on the unknown cut-through standard, which no longer needs the group delay parameters of the unknown straight-through standard and reduces the dependence on the calibrator. The accuracy of the algorithm and error item determination method is verified by ADS simulation and instrument actual test, and a good calibration effect is achieved. It is proved that the algorithm has the ability of accurate calibration. Due to the reduction of parameters, the stability and applicability of the algorithm are improved.


Introduction
Vector network analyzer is a kind of precision instrument based on frequency sweep measurement.In recent years, because of its wide frequency measurement range and high testing accuracy, it has been widely used in various fields of microwave engineering [1].Due to the emergence of multi-port and multi-function components and modules and the rapid growth of demand, the scattering parameters of multi-port network analyzers are required to test and analyze these devices accurately and rapidly.Therefore, the four-port vector network analyzer plays a more and more important role in modern microwave measurement technology.However, any instrument will have errors in measurement.
At this time, the use of a reasonable calibration algorithm can effectively improve the measurement accuracy and obtain reliable results.The calibration algorithm establishes the error model and signal flow diagram according to the hardware structure of the instrument and the connection relationship of the devices in the measurement process and uses the generalized node method or Mason formula to obtain the relationship between the measured data, the error term and the true value. in practice, the instrument is used to measure the relevant calibration parts, and the system error term is obtained according to the measurement results.Then these error terms are used to process the measurement results of the target device to complete data calibration, in which the system error terms have many types, such as directivity error (Ed), crosstalk error (Er), source matching error (Es) and transmission error (Et), which are caused by the non-ideality of the internal hardware of the instrument.
At present, among the existing calibration algorithms, the two-port vector network analyzer is the most abundant and mature, such as SOLT with 12 error models and UOSM and TRL with 8 error models.When the instrument is expanded to four ports, all kinds of error terms increase with the increase in the number of ports.According to certain methods, the two-port calibration algorithm can be extended to the four-port calibration algorithm.Currently, there are GSOLT [2] and Non-Ideal TRM [3] about 48 error models.In order to reduce the complexity of the calibration process and the dependence on the calibration parts, the algorithm is constantly updated.Some scholars have proposed the four-port optimization calibration technology, downgraded the calibration step, and do not need to measure the reflectometer at each test port.A multi-port RF microwave calibration method based on a selfcalibration algorithm is proposed in this paper [4].The calibration of multi-port RF microwave devices is completed based on an error correction matrix and vector network analyzer.The multi-port RF microwave calibration method effectively solves the problem of insufficient accuracy of multi-port RF microwave calibration and has the advantages of convenient operation and strong applicability.In this paper [5], a hybrid calibration method for a multi-port vector network analyzer is proposed.firstly, the calibration parts used by the port are set up, and then the straight-through method and calibration method are extracted automatically for different calibration parts.and create the connection, measure the message, and then through the measurement standard, calculate the system error, finally measure the target device and correct the measured value, and complete the hybrid calibration.The complex connection and measurement in the process of four-port calibration seriously affect the calibration speed.In order to understand the speed problem of multi-port calibration, under the premise of four-port calibration, two efficient and fast new calibration methods are introduced in this paper [6], namely, the fast calibration method and redundant S-parameter algorithm.These two new techniques simplify the calibration process and the measurement of S-parameters to the maximum extent and improve the calibration speed.However, there is an essential difference between the two.The former only simplifies the reflection measurement, but not the transmission measurement, while the latter simplifies the transmission measurement rather than the reflection measurement.
This paper first introduces the calibration principle of a vector network analyzer, the types of error terms, and the research status of the four-port calibration algorithm.Then it analyzes the error model of the two-port UOSM algorithm and the characteristics of calibration parts used, introduces in detail the error term calculation and data processing process of the algorithm in the four-port application, in which the symbol of the error term needs to be judged in the calculation of transmission error term.If the inaccurate judgment of symbols will lead to the phase oscillation of the transmission parameters of the parts to be tested, the simplest known method still requires the group delay of unknown straight-through calibrators as a known condition.Due to the non-ideality of the actual calibrator and the loss caused by the use of the device, the group delay data will deviate, which will affect the calibration results to a certain extent.In this paper, a new method to judge the phase of the transmission error term is proposed, which does not need additional data and improves the accuracy of the algorithm.Finally, the feasibility and reliability of the method are verified by experiments.

Formatting research and improvement of UOSM calibration technology
UOSM algorithm plays a very good role in calibrating the measurement of non-pluggable devices.It was first applied to the two-port vector network analyzer and then extended to the four-port vector network analyzer.For error calibration, firstly, the signal flow diagram of the system error term is established according to the internal hardware structure of the vector network analyzer or at the measurement port containing the measurement transfer device, and then based on the signal flow diagram, the corresponding formula is deduced by using Mason formula or generalized node method, and the relationship between the system error term and input and output signal is simplified.Finally, these error terms are brought into the error correction formula to modify the result data [7], and the actual value of the tested part is obtained.

Error model
The error model of the two-port vector network analyzer when measuring the device is shown in Figure 1.There are three groups of error networks between the two ports.e 00 , e 01 , e 10 , and e 11 constitute a oneport error term network, S11, S21, S12, and S22 constitute the scattering parameter network of the devices to be tested, and e 22 , e 23 , e 32 , and e 33 constitute a two-port error term network.The directional error, source matching error, and reflection tracking error of the two ports can be known through the single-port OSM calibration algorithm, and then the transmission error term is calculated by the cascade of the transmission network.The two-port UOSM calibration algorithm involves a total of 8 error items, also known as 8 error models.The error model of the four-port vector network analyzer in measuring the device is shown in Figure 2, in which 1, 2, 3, and 4 are the measuring ports, aim and bim are the parameters measured by the instrument port, the actual scattering parameters of ai and bi are the actual scattering parameters of the device to be tested, ei 00 , ei 01 , ei 01 , and ei 11 are the systematic errors between the original parameters and the actual parameters, where ei 00 is the directional error and ei 11 is the source matching error.ei 01 ei 01 is a crosstalk error, and ei 01 ej 10 is the transmission error between two ports.There are 16 errors for the four-port vector network analyzer, so it is also called the 4N error model.

Calibration standard
Calibration standards, also known as calibration parts, mainly include mechanical calibration, electronic calibration, and on-wafer calibration.In cases where on-wafer calibration is mainly used for wafer measurement [8], mechanical calibration is a single-port or two-port device with known characteristics.
For each calibrator, it is not necessary to have an accurate and known definition to satisfy some characteristic relations.The calibration standard used by the UOSM calibration algorithm is to define known circuit breakers (Short), circuit breakers (Open), matchers (Match), and unknown straightthrough connectors (Unknown thru) that are unknown but need to meet the S21=S12 condition.

Error term calculation
The parameter signal flow diagram established according to the error model is shown in Figure 3.The relationship between each error term and the measured scattering parameters and actual scattering parameters of the calibration part is deduced by using the Mason formula.By connecting the calibration part between a single port and two ports, the value of each error term is calculated, and the connection calibration part and the calculation process are described in detail as follows.

Calculation of single port error term.
Using OSM [9] single port calibration method one by one, O, S, and M calibrators are connected at each port respectively.Four groups of error terms ei 00 , ei 01 , ei 01 , and ei 11 are obtained by calibration algorithm, of which 12 error terms are known at this time, and the calculation formula of error term for each port is as follows.Smo, Sms, and Smm are the measured values of the instrument connecting O, S, and M calibration parts respectively, and So, Ss, and Sm are the nominal values of the three calibration parts.(3)

Calculation of transmission error term.
U calibrator is connected between any two ports.The relationship between the error term matrix of the two ports and the measurement data matrix of the calibrator can be obtained by cascading the transmission matrix between the ports.Under the condition that S21=S12 is known, the transmission error term ei01 ej 10 between ports can be calculated, where i j, the calculation methods of the error network matrix and transmission error term are as follows.

The determination of the symbol bit of the transmission error term.
Open root sign processing is needed in the calculation of the transmission error term, which involves the judgment of the positive and negative signs of the transmission error term.If the judgment is wrong, it will cause the oscillation of the phase result [10], of course, if the phase situation is not considered, if only the amplitude of the scattering parameter is considered, there is no need to deal with it.The new judgment method proposed in this paper is based on the principle of phase continuity change of unknown straight-through calibration parts, and the phase of the transmission error term is judged by calibrating and comparing the measurement data of unknown straight-through calibration parts.firstly, it is assumed that the symbol of the transmission error term of the frequency point is positive or negative, and the calibration data of this frequency point is compared with the data results of the previous frequency point.When the change of phase continuity is satisfied, it is the correct error term symbol.

Calibration processing
Similar to the two-port measurement, there are four error term matrices between the four-port vector network analyzer and the equipment being tested.according to the signal flow diagram, the relationship between the measured values and the real values of the scattering parameters of the four-port devices is.
The e parameter matrix is the value of the error term of each port, an and b are the real data matrix of each port of the part to be tested and am and bm are the measured values of each port of the instrument.after proper matrix operation, the scattering parameters of the four-port device are as follows.

= ( + ) S A I ED
The real parameter values of the device are known through the operation, and the focus of the calibration algorithm lies in the calculation of the error term, especially the determination of the symbol of the transmission error term.At the same time, the non-ideality of the calibration part will also bring some errors in the calibration results.

Experimental analysis and verification
In order to verify the accuracy of the UOSM four-port calibration algorithm and the effectiveness of the transmission error term determination method, two test schemes are designed.In the experiment, the MATLAB software editing algorithm is used to import all kinds of measurement data into the algorithm to calculate and calibrate the error term.

Simulation S-parameter experiment with ADS
In experiment 1, the accuracy of the UOSM four-port calibration algorithm is verified by ADS2020 software simulation.The scattering parameters of the calibrator and the device to be tested are obtained by software simulation, and then the measurement data are processed by the algorithm proposed in this paper and the existing TOSM four-port calibration algorithm.Finally, the calibration results of the algorithm proposed in this paper are compared with the real values of the devices to be tested and the results of the TOSM four-port algorithm to verify the accuracy of the algorithm.The experimental flow is shown in Figure 4.The simulated scattering parameters are compared with the other two kinds of data, as shown in Figures 6 and 7, which are the amplitude and phase of the scattering parameters, respectively.From the result diagram, we can see that the new method of judging the transmission error term sets up the error network circuit in the ADS software, replaces the calibration part, obtains the simulated data, designs the test piece, and obtains the original measurement data.In the ADS software, the error-free network circuit is built, the parameters of the calibration part and the part to be tested are used for calibration and comparison, and all the data are imported into matlab.Compared with the UOSM calibration algorithm applied to the four-port vector network analyzer, good calibration results can be achieved.

Measured S-parameter experiment
In experiment 2, the validity of the square method for determining the symbol of the transmission error term is verified by the actual measurement of the vector network analyzer.The scattering parameters of the calibrator and the device to be tested are measured by the instrument, and then the measured data are calibrated.The method proposed in this paper is used to determine the transmission error term.Finally, the calibration results are compared with the actual measurement of the instrument.In particular, the phase of the transmission parameters is compared to verify the effectiveness of the determination method.The experimental flow is shown in Figure 8 below.The S parameters are obtained by testing the 3dB attenuator with the vector network analyzer RS ZNB 20 of Roeder and Schwartz.The code is edited according to the existing algorithm, and the new method proposed in this paper is selected to determine the transmission error term.The algorithm calibration results are compared with the instrument measurement results as shown in Figure 9 below.From the result diagram, it can be seen that the symbol bit of the transmission error term is still accurate when the algorithm is calibrated by the measured S parameters, which proves that the method has the ability to accurately judge the symbol bit of the transmission error term, and verifies the stability and feasibility of the new method for judging the transmission error term from the side.

Conclusion
The calibration algorithm, as one of the core technologies of a vector network analyzer, has been constantly studied by scholars, from the initial single-port calibration to the current multi-port calibration.How to achieve a convenient and accurate calibration algorithm is the purpose of the research.In order to solve this problem, based on the study of the UOSM calibration algorithm, this paper focuses on the calculation process of the four-port UOSM calibration algorithm and puts forward a new method to judge the symbol of the error term, which reduces the dependence on calibration parts and improves the stability and applicability of the algorithm.In the experiment, simulation and actual testing verify the accuracy of the UOSM four-port algorithm and the effectiveness of the transmission error determination method.Because the method in this paper has some requirements for OSM calibration parts, and the real parameters of the three devices need to be known on time, the calibration accuracy will be affected by the inaccurate real parameters of calibration parts..

Figure 1 .
Figure 1.Error model of two-port vector network analyzer.

4 Figure 2 .
Figure 2. Error model of four-port vector network analyzer.

Figure 5
Figure 5 below is a simulation schematic diagram built in ADS2020.Each port is connected to a RLC circuit to build an error network.The device to be tested is a four-port lange directional coupler.The unknown straight-through calibration part adopts a transmission line with a certain delay, the open circuit calibration part is in the form of disconnection, the short circuit adopts the calibration part grounding, and the matching calibration part adopts 50 ȍ load impedance.The actual test situation is simulated by connecting each calibrator and the tested part between different ports.The measuring frequency band is 20 GHz to 50 GHz, the frequency step is 55.2 MHz, and the number of measuring frequency points is 544.

Figure 5 .
Figure 5. Simulation schematic diagram of S parameters of the attenuator.

Figure 6 .
Figure 6.Comparison between the calibration result and the real value of DUT.

Figure 7 .
Figure 7.Comparison of calibration results with TOSM algorithm.
The second flow chart of the experiment.