CN106771709A - A kind of S parameter De- embedding method of multiport network - Google Patents

Abstract

The present invention proposes a method for de-embedding S parameters of a multi-port network. First, the S parameters of the multi-port fixture are obtained, and after obtaining the S parameters of the overall fixture, matrix operations are used to remove the S parameters of the fixture. When performing de-embedding processing, use The method of incident wave/reflected wave is used for public derivation. Compared with the existing de-embedding method using electromagnetic simulation to calculate the fixture parameters, the accuracy of the present invention is higher; compared with TRL calibration, the calibration of the present invention is simple, and the calibration parts are easy to manufacture.

Description

A S-parameter de-embedding method for multi-port network

technical field

The invention relates to the technical field of testing, in particular to an S-parameter de-embedding method of a multi-port network.

Background technique

Nowadays, there are more and more multi-port devices and connectors, and the demand for testing is also increasing. In the face of various devices and connectors, special fixtures need to be made to connect to the ports of the vector network instrument. To remove the influence of the fixture in the test, two solutions are needed, the first is de-embedding, and the second is calibration.

The first method of de-embedding: use electromagnetic simulation to calculate the fixture parameters, but due to the actual processing and manufacturing of the fixture, there is a big difference from the simulation parameters, resulting in a big difference in the final test results.

The second calibration method: make special calibration parts, but because of the difficulty of making customized calibration parts and the complicated calibration process, it makes the test difficult.

Contents of the invention

In order to solve the above-mentioned deficiencies in the prior art, the present invention proposes an S-parameter de-embedding method for a multi-port network.

Technical scheme of the present invention is realized like this:

A de-embedding method for S-parameters of a multi-port network. First, the S-parameters of the multi-port fixture are obtained. After obtaining the S-parameters of the overall fixture, matrix operations are used to remove the S-parameters of the fixture. During the de-embedding process, the incident wave/reflection The public derivation is carried out in the form of waves.

Optionally, the step of obtaining the S parameters of the multi-port fixture specifically includes:

For multi-port fixtures, each port of the fixture is symmetrically spliced to form a symmetrical double-port fixture structure, and then the fixture parameters are calculated, and then the S parameters of each port of the fixture are spliced to obtain the S parameters of the overall fixture. The specific calculation process is as follows:

Step (a), after calibration, directly measure the S parameters of the overall fixture: S11, S21, S12, S22;

Step (b), S11 time-domain transformation is obtained T11, and the time at its maximum peak is recorded as _t1 ;

Step (c), S21 time-domain transformation is obtained T21, and the time at its maximum peak is recorded as t ₂ ;

Step (d), with t ₁ as the center and 2(t ₂ -t ₁ ) as the width to set the gate, intercepting S11 to obtain S11 _A ;

Step (e), similarly, can obtain S11 _B ;

It is obtained from the S-parameter relation

Among them, S11, S21, S12, and S22 are the S parameters of the overall fixture measured by the network instrument; S11 _A , S21 _A , S12 _A , and S22 _A are the S parameters of fixture A; S11 _B , S21 _B , S12 _B , and S22 _B are S parameter of fixture B;

And then get:

Since it is a symmetrical fixture, S21 _A ＝S12 _A ＝S21 _B ＝S12 _B , S21＝S12, so:

The S parameters of each port of the fixture are spliced to obtain the S parameters of the overall fixture.

Optionally, the step of removing the S-parameters of the fixture by matrix operation specifically includes:

For N-port DUT network:

For the X-port network, its S-parameters are as follows:

For the Y port network, its S parameters are as follows:

For the overall network tested by the network instrument, its S parameters are as follows:

According to the relationship between the incident wave and the reflected wave, the following matrix is established:

Among them, a _i is the incident wave of each network, and b _i is the reflected wave of each network;

And for the incident wave and reflected wave on both sides of the DUT, the relationship is as follows:

in:

Simultaneously the above equations, eliminate

get:

[S]=[C(TS-A) ^-q B+D] ^-1 (13)

So far, the S-parameter de-embedding operation of the N-port network is completed.

The beneficial effects of the present invention are:

(1) Compared with the existing de-embedding method using electromagnetic simulation to calculate fixture parameters, the accuracy of the present invention is higher;

(2) Compared with TRL calibration, the calibration of the present invention is simple and convenient, and the calibration parts are easy to manufacture.

Description of drawings

In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings that need to be used in the description of the embodiments or the prior art. Obviously, the accompanying drawings in the following description are only These are some embodiments of the present invention. Those skilled in the art can also obtain other drawings based on these drawings without creative work.

Fig. 1 is a schematic diagram of a signal model of a symmetrical two-port fixture of the present invention;

Fig. 2 is the schematic diagram of the principle of the multi-port network S parameter de-embedding method of the present invention;

Fig. 3 is a principle schematic diagram of a specific embodiment of the multi-port network S-parameter de-embedding method of the present invention.

detailed description

The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only some, not all, embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by persons of ordinary skill in the art without making creative efforts belong to the protection scope of the present invention.

With the development of electronic information technology, there are more and more multi-port devices, and the packaging forms and interface types of devices are also increasing. Using a network analyzer to test such devices needs to face the problem of multi-port fixture de-embedding.

The present invention proposes a method for de-embedding S parameters of a multi-port network. Firstly, the multi-port fixture parameters are acquired in a time domain manner, and then the S parameters of the fixture are removed by matrix operation.

In the step of obtaining the parameters of the multi-port fixture, for the multi-port fixture, each port of the fixture is symmetrically spliced to form a symmetrical double-port fixture structure as shown in Figure 1, and then the fixture parameters are calculated, and then the S parameters of each port of the fixture are Splicing is carried out to obtain the S parameters of the overall fixture. The specific calculation process is as follows:

Step (a), after calibration, directly measure the overall S parameters of the fixture: S11, S21, S12, S22;

Step (b), S11 time-domain transformation is obtained T11, and the time at its maximum peak is recorded as _t1 ;

Step (c), S21 time-domain transformation is obtained T21, and the time at its maximum peak is recorded as t ₂ ;

Step (d), with t ₁ as the center and 2(t ₂ -t ₁ ) as the width to set the gate, intercepting S11 to obtain S11 _A ;

Step (e), similarly, can obtain S11 _B .

It is obtained from the relationship of S parameters in the signal flow diagram in Figure 1

Among them, S11, S21, S12, and S22 are the overall S parameters measured by the network instrument; S11 _A , S21 _A , S12 _A , and S22 _A are the S parameters of fixture A; S11 _B , S21 _B , S12 _B , and S22 _B are fixtures S-parameters of B.

And then get:

Since it is a symmetrical fixture, S21 _A ＝S12 _A ＝S21 _B ＝S12 _B , S21＝S12, so:

The S parameters of each port of the fixture are spliced to obtain the S parameters of the overall fixture.

After obtaining the S-parameters of the overall fixture, the next step is to use matrix operations to remove the S-parameters of the fixture. When performing de-embedding processing, the incident wave/reflected wave method is used for public derivation.

As shown in Figure 2, for the N-port DUT network:

For the X-port network, its S-parameters are as follows:

For the Y port network, its S parameters are as follows:

For the overall network tested by the network instrument, its S parameters are as follows:

According to the relationship between the incident wave and the reflected wave, the following matrix is established:

Among them, a _i is the incident wave of each network, and b _i is the reflected wave of each network;

And for the incident wave and reflected wave on both sides of the DUT, the relationship is as follows:

in:

Simultaneously the above equations, eliminate

get:

[S]=[C(TS-A) ^-1 B+D] ^-1 (13)

So far, the S-parameter de-embedding operation of the N-port network is completed, the influence of the multi-port fixture is removed, and the real parameters of the DUT are obtained.

A specific embodiment is given below to illustrate the multi-port S-parameter de-embedding steps of the present invention. As shown in FIG. 3 , this embodiment uses a three-port DUT to de-embed a four-port and two-port network as an example for formula derivation.

The S-parameters of four-port network, two-port network and overall network are as follows:

Among them, S1S is the S parameter of the four-port network, S2S is the S parameter of the two-port network, TS is the S parameter of the four-port network, the DUT, and the dual-port network cascade, S is the network parameter of the DUT, S11, S21, S12, and S22 are the overall S parameters measured by the network instrument.

Using the relationship between the reflected wave and the incident wave, construct the overall relationship matrix:

Among them, b ₁ , ..., b ₉ are the reflected waves of each network, a ₁ , ..., a ₉ are the incident waves of each network, other parameters are the S parameters of the network, A, B, C, D are The split matrix, S is the S-parameter matrix of the DUT.

In addition, from the incident wave and reflected wave in Figure 3, the following relationship can also be constructed:

Simultaneous equations (16), (17), (18), eliminate get

[S]=[C(TS-A) ^-1 B+D] ^-1 (19)

So far, the influence of the multi-port fixture can be removed from the above formula, and the real parameters of the DUT can be obtained.

Compared with the existing de-embedding method using electromagnetic simulation to calculate the fixture parameters, the accuracy of the present invention is higher; compared with TRL calibration, the calibration of the present invention is simple and the calibration parts are easy to manufacture.

The above descriptions are only preferred embodiments of the present invention, and are not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention shall be included in the scope of the present invention. within the scope of protection.

Claims (3)

1. A kind of S parameter de-embedding method of multi-port network, it is characterized in that, at first obtain multi-port fixture S parameter, after obtaining the S parameter of integral fixture, adopt matrix operation then fixture S parameter is removed, when carrying out de-embedding process , using the incident wave/reflected wave method for public derivation. 2. the S parameter de-embedding method of a kind of multi-port network as claimed in claim 1, is characterized in that, the step of obtaining multi-port fixture S parameter specifically comprises: For multi-port fixtures, each port of the fixture is symmetrically spliced to form a symmetrical double-port fixture structure, and then the fixture parameters are calculated, and then the S parameters of each port of the fixture are spliced to obtain the S parameters of the overall fixture. The specific calculation process is as follows: Step (a), after calibration, directly measure the S parameters of the overall fixture: S11, S21, S12, S22; Step (b), S11 time-domain transformation is obtained T11, and the time at its maximum peak is recorded as _t1 ; Step (c), S21 time-domain transformation is obtained T21, and the time at its maximum peak is recorded as t ₂ ; Step (d), with t ₁ as the center and 2(t ₂ -t ₁ ) as the width to set the gate, intercepting S11 to obtain S11 _A ; Step (e), similarly, can obtain S11 _B ; It is obtained from the S-parameter relation $\mathrm{<span\; class="notranslate">\; S</span>}\mathrm{<span\; class="notranslate">\; 11</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; S</span>}{\mathrm{<span\; class="notranslate">\; 11</span>}}_{\mathrm{<span\; class="notranslate">\; A</span>}}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; S</span>}{\mathrm{<span\; class="notranslate">\; twenty\; one</span>}}_{\mathrm{<span\; class="notranslate">\; A</span>}}\mathrm{<span\; class="notranslate">\; S</span>}{\mathrm{<span\; class="notranslate">\; 12</span>}}_{\mathrm{<span\; class="notranslate">\; A</span>}}\mathrm{<span\; class="notranslate">\; S</span>}{\mathrm{<span\; class="notranslate">\; twenty\; two</span>}}_{\mathrm{<span\; class="notranslate">\; B</span>}}}{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; S</span>}{\mathrm{<span\; class="notranslate">\; twenty\; two</span>}}_{\mathrm{<span\; class="notranslate">\; A</span>}}\mathrm{<span\; class="notranslate">\; S</span>}{\mathrm{<span\; class="notranslate">\; twenty\; two</span>}}_{\mathrm{<span\; class="notranslate">\; B</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$ $\mathrm{<span\; class="notranslate">\; S</span>}\mathrm{<span\; class="notranslate">\; twenty\; one</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; S</span>}{\mathrm{<span\; class="notranslate">\; twenty\; one</span>}}_{\mathrm{<span\; class="notranslate">\; A</span>}}\mathrm{<span\; class="notranslate">\; S</span>}{\mathrm{<span\; class="notranslate">\; 12</span>}}_{\mathrm{<span\; class="notranslate">\; B</span>}}}{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; S</span>}{\mathrm{<span\; class="notranslate">\; twenty\; two</span>}}_{\mathrm{<span\; class="notranslate">\; A</span>}}\mathrm{<span\; class="notranslate">\; S</span>}{\mathrm{<span\; class="notranslate">\; twenty\; two</span>}}_{\mathrm{<span\; class="notranslate">\; B</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$ $\mathrm{<span\; class="notranslate">\; S</span>}\mathrm{<span\; class="notranslate">\; 12</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; S</span>}{\mathrm{<span\; class="notranslate">\; 12</span>}}_{\mathrm{<span\; class="notranslate">\; A</span>}}\mathrm{<span\; class="notranslate">\; S</span>}{\mathrm{<span\; class="notranslate">\; twenty\; one</span>}}_{\mathrm{<span\; class="notranslate">\; B</span>}}}{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; S</span>}{\mathrm{<span\; class="notranslate">\; twenty\; two</span>}}_{\mathrm{<span\; class="notranslate">\; A</span>}}\mathrm{<span\; class="notranslate">\; S</span>}{\mathrm{<span\; class="notranslate">\; twenty\; two</span>}}_{\mathrm{<span\; class="notranslate">\; B</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$ $\mathrm{<span\; class="notranslate">\; S</span>}\mathrm{<span\; class="notranslate">\; twenty\; two</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; S</span>}{\mathrm{<span\; class="notranslate">\; 11</span>}}_{\mathrm{<span\; class="notranslate">\; B</span>}}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; S</span>}{\mathrm{<span\; class="notranslate">\; twenty\; one</span>}}_{\mathrm{<span\; class="notranslate">\; B</span>}}\mathrm{<span\; class="notranslate">\; S</span>}{\mathrm{<span\; class="notranslate">\; 12</span>}}_{\mathrm{<span\; class="notranslate">\; B</span>}}\mathrm{<span\; class="notranslate">\; S</span>}{\mathrm{<span\; class="notranslate">\; twenty\; two</span>}}_{\mathrm{<span\; class="notranslate">\; A</span>}}}{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; S</span>}{\mathrm{<span\; class="notranslate">\; twenty\; two</span>}}_{\mathrm{<span\; class="notranslate">\; A</span>}}\mathrm{<span\; class="notranslate">\; S</span>}{\mathrm{<span\; class="notranslate">\; twenty\; two</span>}}_{\mathrm{<span\; class="notranslate">\; B</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$ Among them, S11, S21, S12, and S22 are the S parameters of the overall fixture measured by the network instrument; S11 _A , S21 _A , S12 _A , and S22 _A are the S parameters of fixture A; S11 _B , S21 _B , S12 _B , and S22 _B are S parameter of fixture B; And then get: $\mathrm{<span\; class="notranslate">\; S</span>}{\mathrm{<span\; class="notranslate">\; twenty\; two</span>}}_{\mathrm{<span\; class="notranslate">\; A</span>}}\mathrm{<span\; class="notranslate">\; S</span>}{\mathrm{<span\; class="notranslate">\; twenty\; two</span>}}_{\mathrm{<span\; class="notranslate">\; B</span>}}<span\; class="notranslate">\; =</span>\frac{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; S</span>}\mathrm{<span\; class="notranslate">\; 11</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; S</span>}{\mathrm{<span\; class="notranslate">\; 11</span>}}_{\mathrm{<span\; class="notranslate">\; A</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; S</span>}\mathrm{<span\; class="notranslate">\; twenty\; two</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; S</span>}{\mathrm{<span\; class="notranslate">\; twenty\; two</span>}}_{\mathrm{<span\; class="notranslate">\; B</span>}}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; S</span>}\mathrm{<span\; class="notranslate">\; twenty\; one</span>}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; S</span>}\mathrm{<span\; class="notranslate">\; 12</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$ Since it is a symmetrical fixture, S21 _A ＝S12 _A ＝S21 _B ＝S12 _B , S21＝S12, so: $\mathrm{<span\; class="notranslate">\; S</span>}{\mathrm{<span\; class="notranslate">\; twenty\; two</span>}}_{\mathrm{<span\; class="notranslate">\; B</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; S</span>}\mathrm{<span\; class="notranslate">\; 11</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; S</span>}{\mathrm{<span\; class="notranslate">\; 11</span>}}_{\mathrm{<span\; class="notranslate">\; A</span>}}}{\mathrm{<span\; class="notranslate">\; S</span>}\mathrm{<span\; class="notranslate">\; twenty\; one</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; S</span>}{\mathrm{<span\; class="notranslate">\; twenty\; two</span>}}_{\mathrm{<span\; class="notranslate">\; A</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; S</span>}\mathrm{<span\; class="notranslate">\; twenty\; two</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; S</span>}{\mathrm{<span\; class="notranslate">\; 11</span>}}_{\mathrm{<span\; class="notranslate">\; B</span>}}}{\mathrm{<span\; class="notranslate">\; S</span>}\mathrm{<span\; class="notranslate">\; twenty\; one</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 6</span>}<span\; class="notranslate">\; )</span>$ $\mathrm{<span\; class="notranslate">\; S</span>}{\mathrm{<span\; class="notranslate">\; twenty\; one</span>}}_{\mathrm{<span\; class="notranslate">\; A</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; S</span>}{\mathrm{<span\; class="notranslate">\; 12</span>}}_{\mathrm{<span\; class="notranslate">\; A</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; S</span>}{\mathrm{<span\; class="notranslate">\; twenty\; one</span>}}_{\mathrm{<span\; class="notranslate">\; B</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; S</span>}{\mathrm{<span\; class="notranslate">\; 12</span>}}_{\mathrm{<span\; class="notranslate">\; B</span>}}<span\; class="notranslate">\; =</span>\sqrt{\frac{\mathrm{<span\; class="notranslate">\; S</span>}{\mathrm{<span\; class="notranslate">\; twenty\; one</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; S</span>}\mathrm{<span\; class="notranslate">\; 11</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; S</span>}{\mathrm{<span\; class="notranslate">\; 11</span>}}_{\mathrm{<span\; class="notranslate">\; A</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; S</span>}\mathrm{<span\; class="notranslate">\; twenty\; two</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; S</span>}{\mathrm{<span\; class="notranslate">\; 11</span>}}_{\mathrm{<span\; class="notranslate">\; B</span>}}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; S</span>}\mathrm{<span\; class="notranslate">\; twenty\; one</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 7</span>}<span\; class="notranslate">\; )</span>$ The S parameters of each port of the fixture are spliced to obtain the S parameters of the overall fixture. 3. the S parameter de-embedding method of a kind of multi-port network as claimed in claim 1, is characterized in that, described employing matrix operation the step that fixture S parameter is removed, specifically comprises: For N-port DUT network: For the X-port network, its S-parameters are as follows: For the Y port network, its S parameters are as follows: For the overall network tested by the network instrument, its S parameters are as follows: According to the relationship between the incident wave and the reflected wave, the following matrix is established: Among them, a _i is the incident wave of each network, and b _i is the reflected wave of each network; And for the incident wave and reflected wave on both sides of the DUT, the relationship is as follows: ${\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; Y</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}}$ ${\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; Y</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 12</span>}<span\; class="notranslate">\; )</span>$ in: Simultaneously the above equations, eliminate get: [S]=[C(TS-A) ^-1 B+D] ^-1 (13) So far, the S-parameter de-embedding operation of the N-port network is completed.