CN103983931A - Method for determining uncertainty of S parameter measurement conducted through vector network analyzer - Google Patents

Abstract

The invention discloses a method for determining the uncertainty of the S parameter measurement conducted through a vector network analyzer, and relates to the technical field of calibration methods for the vector network analyzer. The method is achieved through MCM simulation, and therefore the problem that the relevance between S parameters needs to be considered when the uncertainty is evaluated through a GUM method and the problem that the uncertainty obtained through an experience algorithm is incomplete are solved. The method starts from the definition of a calibration piece, self-calibration is conducted on the vector network analyzer based on an SOLT calibration method, the uncertainty introduced through the calibration piece is transmitted to a measured piece through the vector network analyzer, and finally the measurement uncertainty of the S parameters of the measured piece measured by the vector network analyzer and the relevance between the S parameters are obtained through the MCM simulation method so that it can be ensured that performance of obtaining the accurate S parameters of the measured piece can be achieved for the vector network analyzer and measurement accuracy can be improved.

Description

Definite method of vector network analyzer S parameter measurement uncertainty

Technical field

The present invention relates to the calibration steps technical field of vector network analyzer.

Background technology

Vector network analyzer (Vector Network Analyzer, VNA) is the most popular surveying instrument in microwave measurement field.For the S parameter measurement value that ensures vector network analyzer accurately and reliably, people have developed the self calibration of high-precision calibrating device for vector network analyzer, two port vector network analyzer collimation techniques are widely used among commercial instrument, wherein the most important thing is the SOLT collimation technique based on 12 error models.

Collimation technique generally comprises three piths: error model (Error Model), calibration process (Calibration Procedure) and error correction (Error Correction).First, determine the source of systematic error according to the hardware configuration of vector network analyzer, and then utilize error model by the relation of measured piece scattering parameter and systematic error with the formal intuition of signal flow diagram show, then calculate the size of each systematic error and preserve by Measurement and calibration part, finally, by error correction algorithms, the impact of systematic error in measurement result is removed, obtain the actual value of measured piece scattering parameter.

It has been generally acknowledged that calibrating device is completely desirable, i.e. short circuit calibrating device reflection coefficient Γ _s=-1, open circuit calibrating device reflection coefficient Γ _o=1, coupling calibrating device reflection coefficient Γ _l=0 and straight-through calibrating device S _t11=S _t22=0, S _t12=S _t21=1.But due to the imperfection of actual alignment part, cause the uncertainty of calibrating device scattering parameter (S parameter), therefore the calibration result of vector network analyzer has been introduced to uncertainty, final, vector network analyzer by uncertainty transmission to measured piece.At present, the computing method of two port vector network analyzer uncertainties of measurement mainly contain:

1) the vector network analyzer uncertainty calculation method that the vector network analyzer instructions of Agilent company provides;

2) the uncertainty calculation method that EURAMET cg-12 " Guidelines on the Evaluation of Vector Network Analysers (VNA) " provides;

3) the uncertainty calculation method that the SJ/T11433-2012 " vector network analyzer general specification " that the Ministry of Industry and Information Technology of the People's Republic of China (PRC) issues provides.

But above method has just provided the empirical algorithms of S parameter measurement uncertainty, wherein all do not consider the relativity problem of S parameter, above-mentioned several method is incomplete.Therefore, be necessary to provide a kind of more perfect S parameter uncertainty calculation method, to ensure that vector network analyzer can obtain measured piece S parameter accurately.

Summary of the invention

Technical matters to be solved by this invention is to provide a kind of definite method of vector network analyzer S parameter measurement uncertainty, described method provides a kind of definite method of more perfect S parameter uncertainty, to ensure that vector network analyzer can obtain measured piece S parameter accurately, improve the accuracy of test.

For solving the problems of the technologies described above, the technical solution used in the present invention is: a kind of definite method of vector network analyzer S parameter uncertainty, and its feature comprises the following steps:

The first step, selects the self calibration model of ten binomial error models as vector network analyzer;

Second step, selects suitable calibrating device, and the S parameter of definite calibrating device;

The 3rd step, use calibrating device to carry out SOLT self calibration to vector network analyzer, according to vector network analyzer measuring-signal flow graph, obtain the ten binomial errors based on SOLT calibration steps, and use the method for MCM Monte Carlo device simulation to obtain the probability density distribution of ten binomial errors;

The 4th step, use vector network analyzer to measure measured piece, the probability density distribution data of the ten binomial errors that the 3rd step is obtained are brought complete two port error model formula into, use MCM Monte Carlo device simulation method of testing, obtain uncertainty and the correlativity thereof of the S parameter of vector network analyzer measured piece.

Further, in the first step, vector network analyzer is by measuring the calibrating device of one group of known parameters, and the normal data of the calibrating device of compare test data and known parameters, calculates the systematic error of vector network analyzer, i.e. system self-calibration model.

Further, the S parameter determination method of second step alignment part is: the expectation value using the ideal value of calibrating device S parameter as this parameter, set the uncertainty of measurement of a discrete value as this parameter, this discrete value is by consulting pertinent literature and rule of thumb setting.

Further, described ten binomial errors are, E _dF: direction error; E _dR: inverse direction error; E _sF: forward source matching error; E _sR: oppositely source matching error; E _rF: righting reflex tracking error; E _rR: back reflection tracking error; E _xF: forward isolation error; E _xR: reverse isolation degree error; E _lF: forward load matched error; E _lR: reverse load matching error; E _tF: forward transmission tracking error; E _tR: reverse transfer tracking error.

Further, the 3rd step SOLT self-calibration process is as follows:

1) single port standard component SOL measuring process

In the time of i (i=1or2) port order port calibrating device, 12 error models are reduced to single port error model, and the reflection coefficient of single port calibrating device X is Γ _xtime, its measured value is S _mii(X), calculate measurement of reflection-factor value by signal flow diagram and can obtain following expression:

$S_{\mathrm{mii}}\left(X\right)=E_{\mathrm{Di}}+\frac{E_{\mathrm{Ri}}{\mathrm{\Γ}}_X}{1-E_{\mathrm{Si}}{\mathrm{\Γ}}_X}---\left(1\right)$

I port meets short circuit calibrating device S (Γ=Γ successively _s), open circuit calibrating device O (Γ=Γ _o) and coupling calibrating device L (Γ=Γ _l), convolution (1), can obtain

$\left\{\begin{array}{c}{S}_{\mathrm{mii}}\left(S\right)=E_{\mathrm{Di}}+E_{\mathrm{Ri}}{\mathrm{\Γ}}_S/(1-E_{\mathrm{Si}}{\mathrm{\Γ}}_S)\\ S_{\mathrm{mii}}\left(O\right)=E_{\mathrm{Di}}+E_{\mathrm{Ri}}{\mathrm{\Γ}}_O/(1-E_{\mathrm{Si}}{\mathrm{\Γ}}_O)\\ S_{\mathrm{mii}}\left(L\right)=E_{\mathrm{Di}}+E_{\mathrm{Ri}}{\mathrm{\Γ}}_L/(1-E_{\mathrm{Si}}{\mathrm{\Γ}}_L)\end{array}\right.---\left(2\right)$

While connecing matched load, can directly record isolation error E _xi=S _mji(L) (i ≠ j, j=1or2), wherein, E _difor directional error, E _rifor skin tracking error, E _sifor source matching error;

2) straight-through T measuring process

Measure while leading directly to, the expression formula that can be obtained scattering parameter measured value by signal flow diagram is as follows:

$\left\{\begin{array}{c}{S}_{\mathrm{mii}}\left(T\right)=E_{\mathrm{Di}}+E_{\mathrm{Li}}{E}_{\mathrm{Ri}}/(1-E_{\mathrm{Si}}{E}_{\mathrm{Li}})\\ S_{\mathrm{mji}}\left(T\right)=E_{\mathrm{Xi}}+E_{\mathrm{Ti}}/(1-E_{\mathrm{Si}}{E}_{\mathrm{Li}})\end{array}\right.---\left(3\right)$

E _lifor load matched error, E _xifor isolation error, E _tifor transmission tracking error;

Further, the 4th step complete two port error model formula of deriving, derivation is as follows:

1) 1 port excitation, is obtained by forward model

$\left(\begin{array}{c}{S}_{m11}\\ a_1\end{array}\right)=\left(\begin{array}{cc}{E}_{\mathrm{DF}}& E_{\mathrm{RF}}\\ 1& E_{\mathrm{SF}}\end{array}\right)\left(\begin{array}{c}1\\ b_1\end{array}\right)---\left(4\right)$

Therefore incident wave a on measured piece 1 port ₁with reflection wave b ₁expression formula as follows:

$a_1=1+\frac{E_{\mathrm{SF}}}{E_{\mathrm{RF}}}(S_{m11}-E_{\mathrm{DF}})---\left(5\right)$

$b_1=\frac{1}{E_{\mathrm{RF}}}(S_{m11}-E_{\mathrm{DF}})---\left(6\right)$

According to forward error model, incident wave a on measured piece 2 ports ₂with reflection wave b ₂be expressed as:

$a_2=\frac{E_{\mathrm{LF}}}{E_{\mathrm{TF}}}(S_{m21}-E_{\mathrm{XF}})---\left(7\right)$

$b_2=\frac{1}{E_{\mathrm{TF}}}(S_{m21}-E_{\mathrm{XF}})---\left(8\right)$

2) 2 port excitations, are obtained by backward model

${a_2}^{\′}=1+\frac{E_{\mathrm{SR}}}{E_{\mathrm{RR}}}(S_{m22}-E_{\mathrm{DR}})---\left(9\right)$

${b_2}^{\′}=\frac{1}{E_{\mathrm{RR}}}(S_{m22}-E_{\mathrm{DR}})---\left(10\right)$

${a_1}^{\′}=\frac{E_{\mathrm{LR}}}{E_{\mathrm{TR}}}(S_{m12}-E_{\mathrm{XR}})---\left(11\right)$

${b_1}^{\′}=\frac{1}{E_{\mathrm{TR}}}(S_{m12}-E_{\mathrm{XR}})---\left(12\right)$

Wherein: a ₁' be incident wave on 2 ports when excitation measured piece 1 ports, b ₁' be reflection wave on 2 ports when excitation measured piece 1 ports, a ₂' be incident wave on 2 ports when excitation measured piece 2 ports, b ₂' be reflection wave on 2 ports when excitation measured piece 2 ports.

3) incident wave on known measured piece port and reflection wave meet

$\left(\begin{array}{cc}{b}_1& b_1^{\′}\\ b_2& b_2^{\′}\end{array}\right)=\left(\begin{array}{cc}{S}_{11}& S_{12}\\ S_{21}& S_{22}\end{array}\right)\left(\begin{array}{cc}{a}_1& a_1^{\′}\\ a_2& a_2^{\′}\end{array}\right)---\left(13\right)$

By (5) formula-(12) formula substitution (13) formula, the analytical expression that can summarize complete two port measured piece scattering parameter actual values is as follows:

$S_{11A}=\frac{S_{11N}(1+S_{22N}\·E_{\mathrm{SR}})-E_{\mathrm{LF}}\·S_{21N}\·S_{12N}}{(1+S_{11N}\·E_{\mathrm{SF}})(1+S_{22N}\·E_{\mathrm{SR}})-E_{\mathrm{LF}}\·E_{\mathrm{LR}}\·S_{21N}\·S_{12N}}---\left(14\right)$

$S_{21A}=\frac{[1+S_{22N}(E_{\mathrm{SR}}-E_{\mathrm{LF}})]\·S_{21N}}{(1+S_{11N}\·E_{\mathrm{SF}})(1+S_{22N}\·E_{\mathrm{SR}})-E_{\mathrm{LF}}\·E_{\mathrm{LR}}\·S_{21N}\·S_{12N}}---\left(15\right)$

$S_{12A}=\frac{[1+S_{11N}(E_{\mathrm{SF}}-E_{\mathrm{LR}})]\·S_{12N}}{(1+S_{11N}\·E_{\mathrm{SF}})(1+S_{22N}\·E_{\mathrm{SR}})-E_{\mathrm{LF}}\·E_{\mathrm{LR}}\·S_{21N}\·S_{12N}}---\left(16\right)$

$S_{22A}=\frac{S_{22N}(1+S_{11N}\·E_{\mathrm{SF}})-E_{\mathrm{LR}}\·S_{21N}\·S_{12N}}{(1+S_{11N}\·E_{\mathrm{SF}})(1+S_{22N}\·E_{\mathrm{SR}})-E_{\mathrm{LF}}\·E_{\mathrm{LR}}\·S_{21N}\·S_{12N}}---\left(17\right)$

Wherein, S _11N=(S _11M-E _dF)/E _rF, S _21N=(S _21M-E _xF)/E _tF,

S _12N＝(S _12M-E _XR)/E _TR，S _22N＝(S _22M-E _DR)/E _RR；

S _11A, S _21A, S _12Aand S _22Afor measured piece scattering parameter actual value;

S _11M, S _21M, S _12Mand S _22Mfor scattering parameter measured value.

Next, bring the probability density distribution data of the ten binomial errors that obtain in the 3rd step into complete two port error model formula, obtain the probability density distribution of measured piece S parameter by emulation, by analyzing the correlativity between uncertainty of measurement and the S parameter that can obtain vector network analyzer measurement measured piece S parameter.

Adopt the beneficial effect that produces of technique scheme to be: the present invention is by MCM the Realization of Simulation, avoided need to considering while using GUM method evaluation uncertainty S the incomplete problem of uncertainty that between S parameter, correlativity and use experience algorithm obtain; The method is from the definition of calibrating device, based on SOLT calibration steps, vector network analyzer is carried out to self calibration, the uncertainty that calibrating device is introduced passes to measured piece by vector network analyzer, finally, measure uncertainty of measurement and the correlativity thereof of measured piece S parameter by using the method for MCM emulation to obtain vector network analyzer, to ensure that vector network analyzer can obtain measured piece S parameter accurately, improve the accuracy of test.

Brief description of the drawings

Below in conjunction with the drawings and specific embodiments, the present invention is further detailed explanation.

Fig. 1 is complete two port error models;

Fig. 2 is uncertainty of measurement transferring structure schematic diagram;

Fig. 3 is single port calibrating device measuring process schematic diagram;

Fig. 4 is the forward model in straight-through calibration;

Fig. 5 is the error term probability density distribution schematic diagram that emulation obtains;

Fig. 6 is the probability density distribution schematic diagram of the S parameter real part that obtains of emulation;

Fig. 7 is the probability density distribution schematic diagram of the S parameter imaginary part that obtains of emulation.

Embodiment

As shown in Figure 1, be complete two port error model, wherein S _11A, S _21A, S _12Aand S _22Afor the actual value of measured piece S parameter; S _11M, S _21M, S _12Mand S _22Mthe measured value of measured piece S parameter while having error to exist; E _dF: direction error; E _dR: inverse direction error; E _sF: forward source matching error; E _sR: oppositely source matching error; E _rF: righting reflex tracking error; E _rR: back reflection tracking error; E _xF: forward isolation error; E _xR: reverse isolation degree error; E _lF: forward load matched error; E _lR: reverse load matching error; E _tF: forward transmission tracking error; E _tR: reverse transfer tracking error.

As shown in Figure 2, be uncertainty of measurement transferring structure figure, namely general thought of the present invention.Wherein [S _x] be the scattering parameter of calibrating device, it comprises two parts: [S _{expectation value}] and [U (S)], the definition value that Part I is calibrating device, Part II is the dispersed numerical value of the definition value brought due to definition imperfection; [S _m(X) while] being vector network analyzer self calibration, the measured value that Measurement and calibration part obtains; [E] 12 error terms for obtaining based on SOLT error model; [S _m] measure measured value when measured piece for vector network analyzer; [S _a] be to [S _m] carry out the actual value of the measured piece obtaining after error correction.

In the uncertainty transmission structural drawing shown in Fig. 2, use the method for MCM (Monte carlo algorithm) emulation: from causing root (the calibrating device definition imperfection) of vector network analyzer uncertainty of measurement, S parameter to calibrating device is sampled in a large number according to normal distribution, sampled data is delivered to the actual value of measured piece S parameter according to the data conveying flow shown in Fig. 2, finally, probability density distribution by the measured piece S parameter actual value to obtaining is analyzed, can obtain the correlativity between uncertainty of measurement and the S parameter of measured piece S parameter.

The present invention utilize MCM emulation can by the analysis of the probability density distribution to measured piece S parameter obtain vector network analyzer measure S parameter between correlativity, concrete steps are as follows:

The first step, the self calibration model of selection vector network analyzer.Vector network analyzer is by measuring one group of known parameters calibrating device, and compare test data and known normal data, calculate systematic error, i.e. system self-calibration.The calibration accuracy of vector network analyzer depends on the error correcting technology of use, the integrality of error model, the accuracy of calibration criterion definition and the repeatability of test macro.

Two port vector network analyzer collimation techniques are widely used among commercial instrument, these methods comprise: the collimation techniques such as SOLT, TRL, LRM, LRRM, SOLR, QSOLT, choice for use of the present invention the most widely the SOLT collimation technique based on ten binomial error models as the calibrating patterns of vector network analyzer.

Second step, selects suitable calibrating device, and the S parameter of definite calibrating device.Calibrating device is generally special single port and two port devices, the calibrating device that need to use based on SOLT collimation technique is respectively short circuit calibrating device (Short, S), open circuit calibrating device (Open, O), matched load calibrating device (Load, and straight-through calibrating device (Thru, T) L).The two kinds of methods of general employing of determining of calibrating device parameter: use ideal value and determine by sizecalculation.Although these two kinds of methods can be determined the S parameter value of calibrating device, all do not provide the uncertainty of measurement of relevant parameter, this makes troubles in the time of subsequent calculations vector network analyzer uncertainty of measurement.The method that the present invention provides is: the expectation value using the ideal value of calibrating device parameter as this parameter, set the uncertainty of measurement of a discrete value as this parameter, and this discrete value is by consulting pertinent literature and rule of thumb setting, and concrete numerical value is in table 1.

The reflection coefficient of table 1 calibrating device and transmission coefficient

In table 1, only provided the numerical value under 2GHz and 18GHz frequency, other frequency numerical value can obtain by the method for linear interpolation.

The 3rd step, is used calibrating device to carry out SOLT self calibration to vector network analyzer.Concrete SOLT calibration process is as follows:

1) single port calibrating device SOL measuring process

In the time of i (i=1or2) port order port calibrating device, 12 error models are reduced to single port error model.As shown in Figure 3, the reflection coefficient of single port calibrating device X is Γ _xtime, its measured value is S _mii(X), calculate measurement of reflection-factor value by signal flow diagram and can obtain following expression:

$S_{\mathrm{mii}}\left(X\right)=E_{\mathrm{Di}}+\frac{E_{\mathrm{Ri}}{\mathrm{\Γ}}_X}{1-E_{\mathrm{Si}}{\mathrm{\Γ}}_X}---\left(1\right)$

I port meets short circuit calibrating device S (Γ=Γ successively _s), open circuit calibrating device O (Γ=Γ _o) and coupling calibrating device L (Γ=Γ _l), in conjunction with (1) formula, can obtain

$\left\{\begin{array}{c}{S}_{\mathrm{mii}}\left(S\right)=E_{\mathrm{Di}}+E_{\mathrm{Ri}}{\mathrm{\Γ}}_S/(1-E_{\mathrm{Si}}{\mathrm{\Γ}}_S)\\ S_{\mathrm{mii}}\left(O\right)=E_{\mathrm{Di}}+E_{\mathrm{Ri}}{\mathrm{\Γ}}_O/(1-E_{\mathrm{Si}}{\mathrm{\Γ}}_O)\\ S_{\mathrm{mii}}\left(L\right)=E_{\mathrm{Di}}+E_{\mathrm{Ri}}{\mathrm{\Γ}}_L/(1-E_{\mathrm{Si}}{\mathrm{\Γ}}_L)\end{array}\right.---\left(2\right)$

While connecing matched load, can directly record isolation error E _xi=S _mji(L) (i ≠ j).

2) straight-through measuring process

In the time that i port encourages, as shown in Figure 4, on i port, three error terms are by the 1st for the error model in the straight-through measurement situation of 1,2 ports) step calculates.Measure while leading directly to, the expression formula that can be obtained scattering parameter measured value by signal flow diagram is as follows:

$\left\{\begin{array}{c}{S}_{\mathrm{mii}}\left(T\right)=E_{\mathrm{Di}}+E_{\mathrm{Li}}{E}_{\mathrm{Ri}}/(1-E_{\mathrm{Si}}{E}_{\mathrm{Li}})\\ S_{\mathrm{mji}}\left(T\right)=E_{\mathrm{Xi}}+E_{\mathrm{Ti}}/(1-E_{\mathrm{Si}}{E}_{\mathrm{Li}})\end{array}\right.---\left(3\right)$

The 4th step, according to vector network analyzer measuring-signal flow graph, obtains the ten binomial errors based on SOLT calibration steps.Complete SOLT calibration process and calculate 12 systematic errors according to formula (2) and formula (3) by the 3rd step.In solution procedure, use the method for MCM emulation to carry out 1,000,000 samplings to calibrating device according to the parameter value in table 1, the result that therefore emulation obtains is the probability density distribution of ten binomial errors.Fig. 5 has provided E _dFthe schematic diagram of probability density distribution.

The 5th step, while using vector network analyzer to measure measured piece, bring the probability density distribution data of 12 error terms that obtain into complete two port error model formula, obtain uncertainty of measurement and the correlativity thereof of vector network analyzer measurement measured piece S parameter by analysis.

First, the complete two port error model formula of deriving.Derivation is as follows:

1) 1 port excitation, is obtained by forward model

$\left(\begin{array}{c}{S}_{m11}\\ a_1\end{array}\right)=\left(\begin{array}{cc}{E}_{\mathrm{DF}}& E_{\mathrm{RF}}\\ 1& E_{\mathrm{SF}}\end{array}\right)\left(\begin{array}{c}1\\ b_1\end{array}\right)---\left(4\right)$

Therefore on measured piece 1 port, the expression formula of incident wave and reflection wave is as follows:

$a_1=1+\frac{E_{\mathrm{SF}}}{E_{\mathrm{RF}}}(S_{m11}-E_{\mathrm{DF}})---\left(5\right)$

$b_1=\frac{1}{E_{\mathrm{RF}}}(S_{m11}-E_{\mathrm{DF}})---\left(6\right)$

According to forward error model, on measured piece 2 ports, incident wave and reflection wave are expressed as:

$a_2=\frac{E_{\mathrm{LF}}}{E_{\mathrm{TF}}}(S_{m21}-E_{\mathrm{XF}})---\left(7\right)$

$b_2=\frac{1}{E_{\mathrm{TF}}}(S_{m21}-E_{\mathrm{XF}})---\left(8\right)$

2) 2 port excitations, are obtained by backward model

${a_2}^{\′}=1+\frac{E_{\mathrm{SR}}}{E_{\mathrm{RR}}}(S_{m22}-E_{\mathrm{DR}})---\left(9\right)$

${b_2}^{\′}=\frac{1}{E_{\mathrm{RR}}}(S_{m22}-E_{\mathrm{DR}})---\left(10\right)$

${a_1}^{\′}=\frac{E_{\mathrm{LR}}}{E_{\mathrm{TR}}}(S_{m12}-E_{\mathrm{XR}})---\left(11\right)$

${b_1}^{\′}=\frac{1}{E_{\mathrm{TR}}}(S_{m12}-E_{\mathrm{XR}})---\left(12\right)$

Wherein: a ₁' be incident wave on 2 ports when excitation measured piece 1 ports, b ₁' be reflection wave on 2 ports when excitation measured piece 1 ports, a ₂' be incident wave on 2 ports when excitation measured piece 2 ports, b ₂' be reflection wave on 2 ports when excitation measured piece 2 ports.

3) incident wave on known measured piece port and reflection wave meet

$\left(\begin{array}{cc}{b}_1& b_1^{\′}\\ b_2& b_2^{\′}\end{array}\right)=\left(\begin{array}{cc}{S}_{11}& S_{12}\\ S_{21}& S_{22}\end{array}\right)\left(\begin{array}{cc}{a}_1& a_1^{\′}\\ a_2& a_2^{\′}\end{array}\right)---\left(13\right)$

By (5) formula～(12) formula substitution (13) formula, the analytical expression that can summarize complete two port measured piece scattering parameter actual values is as follows:

$S_{11A}=\frac{S_{11N}(1+S_{22N}\·E_{\mathrm{SR}})-E_{\mathrm{LF}}\·S_{21N}\·S_{12N}}{(1+S_{11N}\·E_{\mathrm{SF}})(1+S_{22N}\·E_{\mathrm{SR}})-E_{\mathrm{LF}}\·E_{\mathrm{LR}}\·S_{21N}\·S_{12N}}---\left(14\right)$

$S_{21A}=\frac{[1+S_{22N}(E_{\mathrm{SR}}-E_{\mathrm{LF}})]\·S_{21N}}{(1+S_{11N}\·E_{\mathrm{SF}})(1+S_{22N}\·E_{\mathrm{SR}})-E_{\mathrm{LF}}\·E_{\mathrm{LR}}\·S_{21N}\·S_{12N}}---\left(15\right)$

$S_{12A}=\frac{[1+S_{11N}(E_{\mathrm{SF}}-E_{\mathrm{LR}})]\·S_{12N}}{(1+S_{11N}\·E_{\mathrm{SF}})(1+S_{22N}\·E_{\mathrm{SR}})-E_{\mathrm{LF}}\·E_{\mathrm{LR}}\·S_{21N}\·S_{12N}}---\left(16\right)$

$S_{22A}=\frac{S_{22N}(1+S_{11N}\·E_{\mathrm{SF}})-E_{\mathrm{LR}}\·S_{21N}\·S_{12N}}{(1+S_{11N}\·E_{\mathrm{SF}})(1+S_{22N}\·E_{\mathrm{SR}})-E_{\mathrm{LF}}\·E_{\mathrm{LR}}\·S_{21N}\·S_{12N}}---\left(17\right)$

Wherein, S _11N=(S _11M-E _dF)/E _rF, S _21N=(S _21M-E _xF)/E _tF,

S _12N＝(S _12M-E _XR)/E _TR，S _22N＝(S _22M-E _DR)/E _RR；

S _11A, S _21A, S _12Aand S _22Afor measured piece scattering parameter actual value;

S _11M, S _21M, S _12Mand S _22Mfor scattering parameter measured value.

Next, bring the probability density distribution data of 12 error terms that obtain in the 4th step into complete two port error model formula, obtain the probability density distribution of measured piece S parameter by emulation, the probability density of real part as shown in Figure 6, the probability density of imaginary part as shown in Figure 7, can obtain vector network analyzer by analysis and measure the correlativity between uncertainty of measurement and the S parameter of measured piece S parameter.

How to illustrate based on SOLT calibration steps below by example, use MCM to obtain the uncertainty of measurement of vector network analyzer S parameter.

Use MATLAB7.0 to work out corresponding uncertainty calculation program (subprogram) below as follows:

M＝1000000；sE＝0.01；

% calibrating device parameter sampling

RO＝complex(normrnd(1，sE，1，M)，normrnd(0，sE，1，M))；

RS＝complex(normrnd(-1，sE，1，M)，normrnd(0，sE，1，M))；

RL＝complex(normrnd(0，sE，1，M)，normrnd(0，sE，1，M))；

S11T＝normrnd(0，sE，1，M)；S21T＝normrnd(1，sE，1，M)；

S12T＝normrnd(1，sE，1，M)；S22T＝normrnd(0，sE，1，M)；

% vector network analyzer self calibration data

SO11＝0.99；SS11＝-0.99+0.08i；SL11＝0.01i；SL21＝0.004i；

ST11＝0.001+0.002i；

ST21＝0.992-0.117i；SO22＝0.987；SS22＝-0.99+0.07i；

SL22＝-0.002+0.01i；

SL12＝0.004i；ST22＝0.003i；ST12＝0.99-0.12i；

The S parameter of %DUT

s11＝0.739-0.269i；s21＝0.158-0.081i；s22＝0.755-0.246i；

s12＝0.158-0.081i；

% positive error

ESF＝-(-SO11.*RS+…+SL11.*RL.*RO)；

EDF＝(-RL.*RO.*SS11.*SO11+…+SL11.*RL.*RO)；

ERF＝(RL.^2.*RO…*RL.*RO).^2；

EXF＝SL21；

ELF＝(-EDF-S11T.*ERF+…+ST11.*S21T.*S12T.*ESF)；

ETF

＝-ERF.*S12T.*(-ST21+EXF)./(-EDF.*S22T+…+ST11.*S21T.*S12T.*ESF)；

The reverse error of %

ESR＝-(-SO22.*RS+…+SL22.*RL.*RO)；

EDR＝(-RL.*RO.*SS22.*SO22+…+SL22.*RL.*RO)；

ERR＝(RL.^2.*RO.*SS22.*SO22^2-…+SL22.*RL.*RO).^2；

EXR＝SL12；

ELR＝(-EDR-S22T.*ERR+…+ST22.*S12T.*S21T.*ESR)；

ETR

＝-ERR.*S21T.*(-ST12+EXR)./(-EDR.*S11T+…+ST22.*S12T.*S21T.*ESR)；

% vector network analyzer measured value (M)

E＝1-ESF.*s11-ELF.*s22+ESF.*ELF.*s11.*s22-ESF.*ELF.*s21.*s12；

F＝1-ESR.*s11-ELR.*s22+ESR.*ELR.*s11.*s22-ESR.*ELR.*s21.*s12；

sm11＝EDF+((ERF.*s11.*(1-ELF.*s22)+ELF.*ERF.*s21.*s12))./E；

sm21＝EXF+ETF.*s21./E；

sm22＝EDR+((ERR.*s22.*(1-ELR.*s11)+ELR.*ERR.*s21.*s12))./F；

sm12＝EXR+ETR.*s12./F；

%S parameter uncertainty

s11n＝(mean(sm11)-EDF)./ERF；s21n＝(mean(sm21)-EXF)./ETF；

s22n＝(mean(sm22)-EDR)./ERR；s12n＝(mean(sm12)-EXR)./ETR；

D＝(1+s11n.*ESF).*(1+s22n.*ESR)-s21n.*s12n.*ELF.*ELR；

S11＝(s11n.*(1+s22n.*ESR)-s21n.*s12n.*ELF)./D；

S22＝(s22n.*(1+s11n.*ESF)-s21n.*s12n.*ELR)./D；

S21＝s21n.*(1+s22n.*(ESR-ELF))./D；

S12＝s12n.*(1+s11n.*(ESF-ELR))./D；

ux11＝std(abs(S11))；uy11＝std(angle(S11))*180/pi

ux21＝std(abs(S21))；uy21＝std(angle(S21))*180/pi

ux12＝std(abs(S12))；uy12＝std(angle(S12))*180/pi

ux22＝std(abs(S22))；uy22＝std(angle(S22))*180/pi

h1＝corrcoef(real(S11)，imag(S11))

h2＝corrcoef(real(S11)，real(S21))

h3＝corrcoef(real(S11)，imag(S21))

h4＝corrcoef(real(S11)，real(S12))

h5＝corrcoef(real(S11)，imag(S12))

h6＝corrcoef(real(S11)，real(S22))

h7＝corrcoef(real(S11)，imag(S22))

h8＝corrcoef(imag(S11)，real(S21))

h9＝corrcoef(imag(S11)，imag(S21))

h10＝corrcoef(imag(S11)，real(S12))

h11＝corrcoef(imag(S11)，imag(S12))

h12＝corrcoef(imag(S11)，real(S22))

h13＝corrcoef(imag(S11)，imag(S22))

h14＝corrcoef(real(S21)，imag(S21))

h15＝corrcoef(real(S21)，real(S12))

h16＝corrcoef(real(S21)，imag(S12))

h17＝corrcoef(real(S21)，real(S22))

h18＝corrcoef(real(S21)，imag(S22))

h19＝corrcoef(imag(S21)，real(S12))

h2＝corrcoef(imag(S21)，imag(S12))

h21＝corrcoef(imag(S21)，real(S22))

h22＝corrcoef(imag(S21)，imag(S22))

h23＝corrcoef(real(S12)，imag(S12))

h24＝corrcoef(real(S12)，real(S22))

h25＝corrcoef(real(S12)，imag(S22))

h26＝corrcoef(imag(S12)，real(S22))

h27＝corrcoef(imag(S12)，imag(S22))

h28＝corrcoef(real(S22)，imag(S22))

The uncertainty of measurement of the S parameter of the transmission calibrating device that table 2 has provided 15dB (reflection coefficient 0.8) in the time of 2GHz, 10GHz, 18GHz.

The uncertainty that table 2 this method obtains

The uncertainty of the respective point that the S parameter uncertainty calculation formula that uses Agilent to provide obtains is as shown in table 3.

The uncertainty that table 3 uses Agilent formula to calculate

Data by comparison sheet 2 and table 3 can be found, the result trend suitable, that calculate with Agilent experimental formula in the variation tendency with frequency that the uncertainty that this method provides is numerically calculated with Agilent experimental formula is consistent, and this method is verified; In addition, this method has been used the method for MCM emulation, in the time of evaluation S parameter uncertainty, the impact of the correlativity between S parameter is considered in uncertainty fully, and can be obtained the correlativity between S parameter.Therefore, the uncertainty of this method evaluation is more rationally with accurate.

Claims (6)

1. a definite method for vector network analyzer S parameter measurement uncertainty, its feature comprises the following steps:

The first step, selects the self calibration model of ten binomial error models as vector network analyzer;

Second step, selects suitable calibrating device, and the S parameter of definite calibrating device;

The 3rd step, use calibrating device to carry out SOLT self calibration to vector network analyzer, according to vector network analyzer measuring-signal flow graph, obtain the ten binomial errors based on SOLT calibration steps, and use the method for MCM Monte Carlo device simulation to obtain the probability density distribution of ten binomial errors;

The 4th step, use vector network analyzer to measure measured piece, the probability density distribution data of the ten binomial errors that the 3rd step is obtained are brought complete two port error model formula into, use MCM Monte Carlo device simulation method of testing, obtain uncertainty and the correlativity thereof of the S parameter of vector network analyzer measured piece.

2. definite method of vector network analyzer S parameter measurement uncertainty according to claim 1, it is characterized in that: in the first step, vector network analyzer is by measuring the calibrating device of one group of known parameters, the normal data of the calibrating device of compare test data and known parameters, calculate the systematic error of vector network analyzer, i.e. system self-calibration model.

3. definite method of vector network analyzer S parameter measurement uncertainty according to claim 1, it is characterized in that, the S parameter determination method of second step alignment part is: the expectation value using the ideal value of calibrating device S parameter as this parameter, set the uncertainty of measurement of a discrete value as this parameter, this discrete value is by consulting pertinent literature and rule of thumb setting.

4. definite method of vector network analyzer S parameter measurement uncertainty according to claim 1, is characterized in that, described ten binomial errors are, E _dF: direction error; E _dR: inverse direction error; E _sF: forward source matching error; E _sR: oppositely source matching error; E _rF: righting reflex tracking error; E _rR: back reflection tracking error; E _xF: forward isolation error; E _xR: reverse isolation degree error; E _lF: forward load matched error; E _lR: reverse load matching error; E _tF: forward transmission tracking error; E _tR: reverse transfer tracking error.

5. definite method of vector network analyzer S parameter measurement uncertainty according to claim 4, is characterized in that, the 3rd step SOLT self-calibration process is as follows:

1) single port standard component SOL measuring process

In the time of i (i=1or2) port order port calibrating device, 12 error models are reduced to single port error model, and the reflection coefficient of single port calibrating device X is Γ _xtime, its measured value is S _mii(X), calculate measurement of reflection-factor value by signal flow diagram and can obtain following expression:

I port meets short circuit calibrating device S (Γ=Γ successively _s), open circuit calibrating device O (Γ=Γ _o) and coupling calibrating device L (Γ=Γ _l), convolution (1), can obtain

While connecing matched load, can directly record isolation error E _xi=S _mji(L) (i ≠ j, j=1or2), wherein, E _difor directional error, E _rifor skin tracking error, E _sifor source matching error;

2) straight-through T measuring process

Measure while leading directly to, the expression formula that can be obtained scattering parameter measured value by signal flow diagram is as follows:

E _lifor load matched error, E _xifor isolation error, E _tifor transmission tracking error.

6. definite method of vector network analyzer S parameter measurement uncertainty according to claim 5, is characterized in that, the 4th step complete two port error model formula of deriving, and derivation is as follows:

1) 1 port excitation, is obtained by forward model

Therefore incident wave a on measured piece 1 port ₁with reflection wave b ₁expression formula as follows:

According to forward error model, incident wave a on measured piece 2 ports ₂with reflection wave b ₂be expressed as:

2) 2 port excitations, are obtained by backward model

Wherein: a ₁' be incident wave on 2 ports when excitation measured piece 1 ports, b ₁' be reflection wave on 2 ports when excitation measured piece 1 ports, a ₂' be incident wave on 2 ports when excitation measured piece 2 ports, b ₂' be reflection wave on 2 ports when excitation measured piece 2 ports.

3) incident wave on known measured piece port and reflection wave meet

By (5) formula-(12) formula substitution (13) formula, the analytical expression that can summarize complete two port measured piece scattering parameter actual values is as follows:

Wherein, S _11N=(S _11M-E _dF)/E _rF, S _21N=(S _21M-E _xF)/E _tF,

S _12N＝(S _12M-E _XR)/E _TR，S _22N＝(S _22M-E _DR)/E _RR；

S _11A, S _21A, S _12Aand S _22Afor measured piece scattering parameter actual value;

S _11M, S _21M, S _12Mand S _22Mfor scattering parameter measured value.

Next, bring the probability density distribution data of the ten binomial errors that obtain in the 3rd step into complete two port error model formula, obtain the probability density distribution of measured piece S parameter by emulation, by analyzing the correlativity between uncertainty of measurement and the S parameter that can obtain vector network analyzer measurement measured piece S parameter.