TWI407115B - A method and apparatus for measuring s parameter of passive circuit - Google Patents

Abstract

A method is used to measure S parameter of a passive circuit. A S parameter measuring apparatus is used in the method, which includes a measuring portion and a correcting portion. The method includes the following steps: the measuring portion measuring S parameter of the passive circuit at a required measured frequency, and judging if the S parameter accords with a demand of passivity; if not, the correcting portion correcting the S parameter to accords with the demand of passivity; at last, the S parameter measuring apparatus outputting the S parameter. The present invention also includes the S parameter measuring apparatus.

Description

Method for measuring parameter of passive circuit S and measuring device for implementing same

The present invention relates to a method of measuring S parameters and an apparatus for carrying out the method, and more particularly to a method and apparatus for measuring parameters of a passive circuit S.

The S parameter is a parameter indicating the relationship between the input and output of the circuit, thereby reflecting the electrical characteristics of the circuit, and when the frequency of the circuit is different, the relationship between the input and the output is also different, as shown in FIG. There are two passive circuits 10, which are provided with 埠1 and 埠2, for example, at a certain frequency, when input is made from 埠1 of the passive circuit 10, the 无源 of the passive circuit 10 Outputs corresponding to particular features will appear at the reflections for 埠1 and for 埠2; likewise, when input is made from 埠2 of passive circuit 10, the turns of passive circuit 10 are also Outputs corresponding to particular features appear, which are reflections for 埠2 and transmission for 埠1.

At this frequency, the relationship between the input of the passive circuit 10 and the output of the reflection and transmission can be expressed as the matrix calculation form shown in Fig. 2. The matrix in Fig. 2 is a complex matrix in which the matrix elements ( The complex numbers S ₁₁ , S ₁₂ and S ₂₁ are S parameters which represent the relationship between the input and output of the passive circuit 10 at this frequency.

Since the circuit 10 in FIG. 1 is a passive circuit, its S-parameter at this frequency must satisfy the passive condition, that is, it must satisfy real(eigenvalue[E-S×S']) ≧0, that is, [E -S×S'] The real part of the eigenvalue of this matrix is greater than or equal to 0, where S' is the conjugate transposed matrix of S and E is the identity matrix. However, when measuring the S-parameters of passive circuits at different frequencies, sometimes the S-parameters at a certain frequency cannot satisfy the above calculation formula because of the measurement instrument, that is, the passivity cannot be satisfied. condition.

In view of the above, it is necessary to provide a method and apparatus for accurately measuring the S parameters of a passive circuit.

A method for measuring a S-parameter of a passive circuit, wherein an S-parameter measuring device measures an S-parameter of a passive circuit at different frequencies, the S-parameter measuring device comprising a measuring portion and a correcting portion, the S-parameter correcting portion comprising a a matrix calculation module, a matrix eigenvalue calculation module, a correction value calculation module and a correction module, the method for measuring a passive circuit S parameter comprises the following steps: the measurement part measures the passive circuit at a certain requirement The S parameter of the measured frequency; determining whether the S parameter corresponding to the frequency satisfies the passive condition, and if the passive condition is satisfied, the S parameter corresponding to the frequency satisfies the passiveness; if the passive condition is not met, the The correction part corrects the S parameter that does not meet the passability, and the correction step is as follows: the correction part extracts the S parameter that does not satisfy the passivity, and forms an S parameter matrix S from the S parameter; the matrix calculation module Obtain the product S×S′ of the matrix S and its conjugate transposed matrix S′; the matrix eigenvalue calculation module calculates the characteristic value of S×S′, and takes out the real part real of the largest eigenvalue 实 of the real part. ); The positive value calculation module obtains a correction value ξ=real(Ψ) ^1/2 ×(1+ε) according to the largest real part real(Ψ), where ε is a very small positive number; the correction module is obtained according to the correction value ξ The corrected S parameter S ^* = S / ξ; finally, the S parameter measuring device outputs the S parameter.

The present invention also includes an apparatus for accurately measuring a parameter of a passive circuit S, the apparatus comprising a measuring portion for measuring an S parameter of the passive circuit and a correction portion for correcting an S parameter that does not satisfy the passive condition, the correction portion including a matrix calculation module for obtaining the product S×S′ between the S-parameter matrix S and the conjugate transposed matrix S′ of the matrix S, and a matrix eigenvalue calculation module for obtaining the eigenvalues of the matrix S×S′, A correction value calculation module for obtaining a correction value 根据 according to the largest eigenvalue 实 of the real part of the matrix S×S′, and a correction module for correcting the S parameter matrix S according to the correction value 。.

Compared with the prior art, the method and device for measuring the parameters of the passive circuit S of the present invention can accurately obtain the S parameter of the passive circuit.

Please refer to FIG. 1 and FIG. 3, which are a flowchart of a method for measuring parameters of a passive circuit S and an S-parameter measuring device 20 for implementing the method. The S-parameter measuring device 20 includes a measuring portion 22 and a correcting portion 23 First, the measuring portion 22 measures the S parameter of the passive circuit at a certain required measurement frequency (step 201), and calculates whether the S parameter corresponding to the frequency satisfies the passive condition (step 202), that is, calculates real (eigenvalue[ E-S × S']) ≧0 is established, if it is established, the passive condition is satisfied (step 203), the S-parameter measuring device 20 outputs the S-parameter (step 205); if not, the correcting portion 23 The S parameter is corrected (step 204), and the specific correction steps are as follows.

4 and FIG. 5, which are a flowchart of the S parameter modification step and a schematic diagram of the modification portion 23, the correction portion 23 includes a matrix calculation module 31 and a matrix feature connected to the matrix calculation module 31. The value calculation module 32, a correction value calculation module 33 connected to the matrix eigenvalue calculation module 32, and a correction module 34 connected to the correction value calculation module 33.

The steps of modifying the S parameter are: Step 301: Extracting the S parameter to be corrected; Step 302: Calculating the matrix [S×S'] by the matrix calculation module 31, and calculating the matrix by the matrix eigenvalue calculation module 32 [ The characteristic value of S×S′], since the S parameter does not satisfy the passive condition, the real part of the eigenvalue λ _min of the smallest real part of the eigenvalue of the matrix [E-S×S′] must be less than 0. That is, real(λ _min )<0, and according to the formula eigenvalue[E-S×S']=1-eigenvalue[S×S′], the largest feature of the real part of the matrix [S×S′] The real part of the value Ψ _max must be greater than 1, ie real(Ψ _max )=1-real(λ _min )>1; Step 303: The correction value calculation module 33 follows the correction formula ξ=real(Ψ _max ) ^1/2 × (1 + ε) calculated by the correction value ξ, the above formula of [epsilon] is a positive number a pinpoint; step 304: a correction module 34 correction formula S according to S-parameter ^{* =} S / ξ after calculating the corrected S-parameter S ^*, The passibility judgment for the corrected S parameter S ^* is: real(eigenvalue[E-S ^* ×S ^* '])=1-real(eigenvalue[S ^* ×S ^* '])=1-real( Eigenvalue[S/ξ×S'/ξ])=1-real(ei Genvalue[S×S'])/[real(Ψ _max )×(1+ε) ² ]; since real(Ψ _max ) is greater than 1, ε is a very small positive number, so real(Ψ _max )×(1+ε) ^{2 is} greater than Real(Ψ _max ), since the largest eigenvalue of the real part of the matrix [S×S'] is Ψ _max , real(eigenvalue[S×S'])/[real(Ψ _max )×(1+ε ² ]<1, so real(eigenvalue[E-S ^* ×S ^* '])>0 causes the corrected S parameter to satisfy the passive condition.

Then, in step 205, the corrected S parameter is output by the S parameter measuring device 20.

Referring to FIG. 1 to FIG. 5, the S parameter measurement method of the passive circuit 10 having two turns is taken as an example to describe the S parameter measurement method of the present invention. First, the measurement portion 22 measures the passive circuit 10 to measure at a certain requirement. The S parameter of the frequency (step 201), and calculating whether the S parameter corresponding to the frequency satisfies the passive condition (step 202), that is, whether real(eigenvalue[E-S×S']) ≧0 is established, and if so, Then, the passability condition is satisfied (step 203), and the S parameter measuring device 20 outputs the S parameter (step 205); if not, the correcting portion 23 corrects the S parameter (step 204), and the specific correcting step is as follows. .

Since the passive circuit 10 is a passive circuit with two 埠 symmetry, S ₁₁ = S ₂₂ and S ₁₂ = S ₂₁ in the S-parameter matrix in Fig. 2, so that the S-parameter matrix in Fig. 2 can be simplified to S = [(S ₁₁ , S ₁₂ ), (S ₁₂ , S ₁₁ )], and then the S parameters are corrected in accordance with the steps in Fig. 5. Step 301: Extract the S parameters to be corrected, and form an S parameter matrix S=[(S ₁₁ , S ₁₂ ), (S ₁₂ , S ₁₁ )], and set S ₁₁ = R ₁₁ + I ₁₁ i, S ₁₂ = R ₁₂ +I ₁₂ i; Step 302: The matrix calculation module 31 calculates the matrix [S × S'] = [(R ₁₁ ² + R ₁₂ ² + I ₁₁ ² + I ₁₂ ² , 2 × R ₁₁ × R ₁₂ + 2 × I ₁₁ × I ₁₂ ), (2 × R ₁₁ × R ₁₂ + 2 × I ₁₁ × I ₁₂ , R ₁₁ ² + R ₁₂ ² + I ₁₁ ² + I ₁₂ ² )], and then the matrix eigenvalue calculation module 32 calculates the matrix [S × Characteristic value of S']: Ψ ₁ = (I ₁₁ + I ₁₂ ) ² + (R ₁₁ + R ₁₂ ) ² , Ψ ₂ = (I _{11 -} I ₁₂ ) ² + (R _{11 -} R ₁₂ ) ² ; The values are all real numbers, so the actual part is the eigenvalue itself; comparing the magnitudes of the two eigenvalues, the larger eigenvalue Ψ _{max is obtained} ; step 303: the correction value calculation module 33 follows the correction formula ξ=real (Ψ _Max ) ^1/2 × (1 + ε) calculates the correction value ξ, ε in the above formula is a very small positive number; step 304: the correction module 34 calculates the corrected value according to the S parameter correction formula S ^* = S / ξ The S parameter S ^{* is} obtained.

Then, in step 205, the corrected S parameter S ^{* is} outputted by the S parameter measuring device 20.

An example is given to illustrate the effectiveness of the measurement method, such as measuring the S parameter of a segment of a signal line at a different frequency on a circuit board. When the frequency is 4.6372 GHz, the S parameter matrix measured by the measuring portion 22 is S= [(-0.2608352337196621+0.3476273125912422i, 0.7203853298827190+0.5405228611018837i), (0.7203853298827190+0.5405228611018837i, -0.2608352337196621+0.3476273125912422i)]; (Step 201)

The passability judgment formula of the above S parameter is eigenvalue[E-S ^* S']=[2.978085395288764×10-6,-2.487071395607110×10-6], wherein the real part of one eigenvalue is less than 0, so the S parameter is not The passability condition is satisfied (step 202), and the S parameter is corrected (step 204).

Step 301: Extract the S parameter to be corrected, and form an S parameter matrix S=[(-0.2608352337196621+0.3476273125912422i, 0.7203853298827190+0.5405228611018837i), (0.7203853298827190+0.5405228611018837i, -0.2608352337196621+0.3476273125912422i)]; Step 302: by matrix The calculation module 31 calculates the matrix [S×S′], and the matrix eigenvalue calculation module 32 calculates the two eigenvalues of the matrix [S×S′]. Since both eigenvalues are real numbers, the actual part is The feature value itself; comparing the magnitudes of the two feature values, and obtaining a larger feature value Ψ _max = 1.000002487071396; Step 303: calculating the correction value 修正=real(Ψ _max ) ^1/ by the correction value calculation module 33 according to the correction formula ² × (1 + ε) = = 1.000001243535925, ε = 1 × 10 ^{-12 is taken here} ; Step 304: The modified S-parameter matrix S ^* = S / ξ = [ calculated by the correction module 34 according to the S-parameter correction formula (-0.2608349093620819+0.3476268803047282, 0.7203844340587956+0.5405221889431238i), (0.7203844340587956+0.5405221889431238I,-0.2608349093620819+0.3476268803047282)]; The passability judgment formula of the S parameter S ^* is eigenvalue(E-S ^* ×S ^* ')=(5.465145198668697×10 ^-6 , 2.000122290161193×10 ^-12 ), and both of the eigenvalues are greater than 0, so the corrected The S parameter S ^* satisfies the passive condition.

Then, in step 205, the corrected S parameter S ^{* is} outputted by the S parameter measuring device 20.

The method for measuring the S-parameters of the passive circuit of the present invention can be applied to circuits having different numbers of turns, and can accurately measure the S-parameters of the circuit.

In summary, the present invention is in accordance with the conditions of the invention patent application, and the patent application is filed according to law. The above description is only the preferred embodiment of the present invention, and equivalent modifications or variations made by those skilled in the art to the spirit of the present invention should be included in the following claims.

Passive circuit. . . 10

S parameter measuring device. . . 20

Measuring part. . . twenty two

Correction section. . . twenty three

Matrix computing module. . . 31

Matrix eigenvalue calculation module. . . 32

Correction value calculation module. . . 33

Correction module. . . 34

Figure 1 is a schematic diagram of a passive circuit having two turns connected to an S-parameter measuring device.

Figure 2 is a diagram showing the relationship between the input and output of the passive circuit of Figure 1.

3 is a flow chart of a method of measuring passive circuit S parameters of the present invention.

Figure 4 is a flow chart of the S parameter modification method.

Figure 5 is a schematic illustration of a modified portion of the S-parameter measuring device of Figure 1.

Claims (5)

A method for measuring a S-parameter of a passive circuit, wherein an S-parameter measuring device measures an S-parameter of a passive circuit at different frequencies, the S-parameter measuring device comprising a measuring portion and a correcting portion, the S-parameter correcting portion comprising a a matrix calculation module, a matrix eigenvalue calculation module, a correction value calculation module and a correction module, the method for measuring a passive circuit S parameter comprises the following steps: the measurement part measures the passive circuit at a certain requirement The S parameter of the measured frequency; determining whether the S parameter corresponding to the frequency satisfies the passive condition, and if the passive condition is satisfied, the S parameter corresponding to the frequency satisfies the passiveness; if the passive condition is not met, the The correction part corrects the S parameter that does not meet the passability, and the correction step is as follows: the correction part extracts the S parameter that does not satisfy the passivity, and forms an S parameter matrix S from the S parameter; the matrix calculation module Obtain the product S×S′ of the matrix S and its conjugate transposed matrix S′; the matrix eigenvalue calculation module calculates the characteristic value of S×S′, and takes out the real part real of the largest eigenvalue 实 of the real part. ); The positive value calculation module obtains a correction value ξ=real(Ψ) ^1/2 ×(1+ε) according to the largest real part real(Ψ), where ε is a very small positive number; the correction module is obtained according to the correction value ξ The corrected S parameter S ^* = S / ξ; finally, the S parameter measuring device outputs the S parameter. A method for measuring a S-parameter of a passive circuit as described in claim 1, wherein the pass-through judgment real (eigenvalue[E-S×S']) ≧0 determines whether the S-parameter satisfies the passivity. Where S' is the conjugate transposed matrix of S, and E is the identity matrix. If the real part of the eigenvalue of the matrix [E-S×S'] is greater than or equal to 0, the passivity is satisfied, otherwise it is not satisfied. . A device for measuring a parameter of a passive circuit S, the device comprising: a measuring portion for measuring an S parameter of the passive circuit and a modified portion for correcting an S parameter that does not satisfy a passive condition, the correcting portion including obtaining an S parameter matrix S a matrix calculation module of the product S×S′ between the conjugate transposed matrix S′ of the matrix S, a matrix eigenvalue calculation module for obtaining the eigenvalues of the matrix S×S′, and a matrix S×S′ The correction value calculation module of the correction value 得到 is obtained by the maximum eigenvalue of the real part, and a correction module for correcting the S parameter matrix S according to the correction value 。. The apparatus for measuring a parameter of a passive circuit as described in claim 3, wherein the correction value calculation module obtains a correction value 根据 according to a formula ξ=real(Ψ) ^1/2 ×(1+ε), where real( Ψ) indicates the real part of the largest eigenvalue 实, ε is a very small positive number. The apparatus for measuring a parameter of a passive circuit as described in claim 3, wherein the correction module obtains the corrected S parameter according to the equation S ^* =S/ξ.