CN110470966B - Scattering parameter measuring method and device calibration method - Google Patents

Scattering parameter measuring method and device calibration method Download PDF

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CN110470966B
CN110470966B CN201910762741.6A CN201910762741A CN110470966B CN 110470966 B CN110470966 B CN 110470966B CN 201910762741 A CN201910762741 A CN 201910762741A CN 110470966 B CN110470966 B CN 110470966B
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CN110470966A (en
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黄安东
顾滕锋
侯富诚
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Suzhou Huatai Electronics Co Ltd
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    • G—PHYSICS
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    • G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
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Abstract

The invention discloses a scattering parameter measuring method and a device calibration method, wherein the measuring method comprises the following steps: preparing N standard structural members including GSG PAD and L lengthNAnd mutually unequal transmission lines; measuring scattering parameters S of N standard structural membersN(ii) a Scattering parameter SNConverting into ABCD parameters; according to the variable Z1And Y2Constructing an ABCD matrix of GSG PAD in a standard structural part; according to the variables gamma and Z0Length L in the construction of standard structural membersNThe ABCD matrix of transmission lines of (a); constructing an ABCD matrix of a standard structural part; solving for variable Z1、Y2And/or the variables gamma, Z0(ii) a Acquiring ABCD parameter and/or arbitrary length L of GSG PADXABCD parameters of the transmission line; the ABCD parameter is converted to a scattering parameter S. The invention can realize the measurement of the scattering parameters of the transmission line with any length and the GSG PAD through the scattering parameters of at least two transmission lines with different lengths, has higher measurement precision, greatly improves the flexibility of the measurement of the scattering parameters, and can be widely applied to the calibration of devices.

Description

Scattering parameter measuring method and device calibration method
Technical Field
The invention belongs to the technical field of radio frequency and microwave, and particularly relates to a scattering parameter measuring method and a device calibration method.
Background
Radio frequency chips are widely used in modern communication systems, for example, a base station uses an LDMOS (laterally diffused metal oxide semiconductor) or GaN (gallium nitride) chip to amplify communication signals, and a mobile phone terminal uses a GaAs (gallium arsenide) chip to transmit and receive wireless signals. Each new generation of communication technology has a greatly increased communication capacity compared to the previous generation, and in order to carry such fast data transmission, the operating frequency of the rf chip needs to be continuously increased, which brings challenges to chip design and packaging. Radio frequency and millimeter wave chip design is not independent of EDA (electronic design automation) software, and active and passive device models are the key to realizing EDA-aided design. The essence of semiconductor device modeling is that a physical or mathematical algorithm is constructed to simulate the behavior of the devices in the physical world, and the model needs to continuously correct the parameters until the computer simulation result of the model is consistent with the device test data, so that accurate and reliable test data is the first step of successful modeling.
In the prior art, Through-Line-reflection (TRL) is a common calibration algorithm in the microwave and radio frequency fields, and has the advantages that any connecting head and connecting Line can be calibrated, but the TRL algorithm has a limitation on the frequency range and cannot cover full-band calibration, and for low-frequency application, the Line (Line) of the TRL structural member is very long, and if on-chip calibration is performed, a large amount of wafer area is occupied, so that the cost is increased; OPEN-SHORT method (OS method for SHORT) is a lumped parameter calibration algorithm, and the principle is that OPEN-circuit and SHORT-circuit structures are represented as lumped parameter equivalent models, the representation method is only established when the frequency is low, and when the frequency is high or the contact line of a chip is long, the calibration accuracy of the method is not ideal; L-2L (transmission line L and 2L method, L-2L for short) is a calibration algorithm commonly used in the field of microwave radio frequency, and L-2L has the disadvantage of requiring the provision of transmission lines of lengths L and 2L, respectively, which is not applicable to other lengths of transmission lines.
Therefore, in order to solve the above technical problems, it is necessary to provide a scattering parameter measurement method and a device calibration method.
Disclosure of Invention
In view of the above, the present invention provides a scattering parameter measuring method and a device calibration method, so as to realize the measurement of scattering parameters and the device calibration.
In order to achieve the above object, an embodiment of the present invention provides the following technical solutions:
a scattering parameter measurement method, the measurement method comprising:
preparing N standard structural members including GSG PAD and L lengthNAnd transmission lines which are not equal to each other, wherein N is more than or equal to 2;
measuring scattering parameters S of N standard structural membersN；
Scattering parameter SNConversion to ABCD parameters
Figure BDA0002170897340000021
According to the variable Z1And Y2ABCD matrix for constructing GSG PAD in standard structural component
Figure BDA0002170897340000022
Wherein Z is1＝1/Y1，Y1And Y2Is admittance in an equivalent model of a standard structural member;
according to the variables gamma and Z0Length L in the construction of standard structural membersNABCD matrix of transmission lines
Figure BDA0002170897340000023
Wherein γ is a propagation constant of electromagnetic wave, Z0Is the characteristic impedance of the transmission line;
according to
Figure BDA0002170897340000024
And
Figure BDA0002170897340000025
ABCD matrix for constructing standard structural parts
Figure BDA0002170897340000026
According to
Figure BDA0002170897340000027
Solving for variable Z1、Y2And/or the variables gamma, Z0；
According to the variable Z1、Y2Acquiring ABCD parameters of GSG PAD and/or according to variables gamma and Z0Obtaining an arbitrary length LXABCD parameters of the transmission line;
ABCD parameter and/or arbitrary length L of GSG PADXThe ABCD parameter of the transmission line is converted into a scattering parameter S.
In one embodiment, the ABCD matrix analytic expression of the GSG PAD in the standard structural component is:
Figure BDA0002170897340000031
the length of the standard structural member is LNThe ABCD matrix analytic expression of the transmission line of (a) is:
Figure BDA0002170897340000032
in one embodiment, the ABCD matrix analytic expression of the standard structural component is:
Figure BDA0002170897340000033
in one embodiment, the method of measurement is "according to
Figure BDA0002170897340000034
Solving for variable Z1、Y2And/or the variables gamma, Z0The method specifically comprises the following steps:
is unfolded
Figure BDA0002170897340000035
Constructing a nonlinear equation system:
Figure BDA0002170897340000036
wherein Q is A, B, C, D, and M is 1-N;
solving a nonlinear equation system at each frequency point to obtain a variable Z at each frequency point1、Y2And/or the variables gamma, Z0The value of (c).
In one embodiment, the solution of the nonlinear system of equations is performed by a fsolve function in Matlab software.
In one embodiment, the measurement method is performed "according to the variable Z1、Y2Obtaining ABCD parameter of GSG PADThe method specifically comprises the following steps:
a variable Z1、Y2Substitution of value of (1)
Figure BDA0002170897340000037
The ABCD parameter of GSG PAD is obtained.
In one embodiment, the measurement method is based on the variables γ and Z0Obtaining an arbitrary length LXABCD parameters of transmission lines ":
the variables gamma and Z0Substitution of value of (1)
Figure BDA0002170897340000038
To obtain any length LXABCD parameters of transmission lines.
In one embodiment, the standard structure is fabricated on a wafer.
In one embodiment, the wafer comprises a radio frequency silicon-based substrate.
In one embodiment, the scattering parameter S of the standard structureNMeasured by a vector network analyzer.
In one embodiment, the standard structural component comprises a transmission line with a length of L1The first standard structural member and the transmission line have a length L2The second standard structural member of (1) satisfies L1≠L2。
The technical scheme provided by another embodiment of the invention is as follows:
a device calibration method, the calibration method comprising:
GSG PAD and any length L are obtained by adopting the scattering parameter measuring methodXA scattering parameter S of the transmission line;
the device of the GSG-transmission line structure is calibrated by the above parameters.
In one embodiment, the device is a device on a PCB or a device on a wafer.
Compared with the prior art, the invention can realize the measurement of the scattering parameters of the transmission line with any length and the GSG PAD through the scattering parameters of at least two transmission lines with different lengths, has higher measurement precision, greatly improves the flexibility of the measurement of the scattering parameters, and can widely apply the measured scattering parameters to the calibration of devices.
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In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings needed to be used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments described in the present application, and other drawings can be obtained by those skilled in the art without creative efforts.
FIG. 1 is a schematic diagram of the on-chip test DUT of the present invention;
FIG. 2 shows a transmission line length L in the present invention1Structural schematic diagram of the standard structural member of (1);
FIG. 3 shows a transmission line length L in the present invention2Structural schematic diagram of the standard structural member of (1);
FIG. 4 shows a transmission line length L in the present inventionNStructural schematic diagram of the standard structural member of (1);
FIG. 5 shows a transmission line length L in the present invention1The structural division schematic diagram of the standard structural member of (1);
FIG. 6 is a schematic diagram of the structure of the GSG PAD moiety of the present invention;
FIG. 7 shows a length L of the present invention1The structure of the transmission line part of (1);
FIG. 8 is an equivalent model diagram of a standard structural member according to the present invention;
FIG. 9 is a schematic flow chart of a scattering parameter measurement method according to the present invention;
FIG. 10 is a graph of the amplitude of the input reflection coefficient S11 in the scattering parameter S of a pure transmission line with a length of 100 μm after GSG PAD de-embedding and a simulated pure transmission line in accordance with an embodiment of the present invention;
FIG. 11 is a phase diagram of the input reflection coefficient S11 in the scattering parameter S of a pure transmission line with a length of 100 μm after GSG PAD de-embedding and a simulated pure transmission line in accordance with an embodiment of the present invention;
FIG. 12 is a graph of amplitude contrast of the backward transmission coefficient S12 in the scattering parameter S of a pure transmission line with a length of 100 μm after GSG PAD de-embedding and a simulated pure transmission line in accordance with an embodiment of the present invention;
FIG. 13 is a phase diagram of backward transmission coefficients S12 in scattering parameters S of a pure transmission line with a length of 100 μm after GSG PAD de-embedding and a simulated pure transmission line in accordance with an embodiment of the present invention;
FIG. 14 is a graph of the magnitude of the forward transmission coefficient S21 in the scattering parameter S of a pure transmission line 100 μm in length after GSG PAD de-embedding and a simulated pure transmission line in accordance with an embodiment of the present invention;
FIG. 15 is a phase diagram of forward transmission coefficient S21 in scattering parameter S of a pure transmission line with a length of 100 μm after GSG PAD de-embedding and a simulated pure transmission line in accordance with an embodiment of the present invention;
FIG. 16 is a graph comparing the magnitude of the output reflection coefficient S22 in the scattering parameter S of a pure transmission line with a length of 100 μm after GSG PAD de-embedding and a simulated pure transmission line in accordance with an embodiment of the present invention;
FIG. 17 is a phase diagram of the output reflection coefficient S22 in the scattering parameter S of the pure transmission line with a length of 100 μm after GSG PAD de-embedding and the simulated pure transmission line in accordance with one embodiment of the present invention;
FIG. 18 is a graph of the magnitude of the input reflection coefficient S11 in the scattering parameter S of a pure transmission line 300 μm in length after GSG PAD de-embedding and a simulated pure transmission line in accordance with an embodiment of the present invention;
FIG. 19 is a phase diagram of the input reflection coefficient S11 in the scattering parameter S of a pure transmission line with a length of 300 μm after GSG PAD de-embedding and a simulated pure transmission line in accordance with an embodiment of the present invention;
FIG. 20 is a graph of amplitude contrast of the backward transmission coefficient S12 in the scattering parameter S of a pure transmission line 300 μm in length after GSG PAD de-embedding and a simulated pure transmission line in accordance with an embodiment of the present invention;
FIG. 21 is a phase diagram of the backward transmission coefficient S12 in the scattering parameter S of a pure transmission line with a length of 300 μm after GSG PAD de-embedding and a simulated pure transmission line in accordance with an embodiment of the present invention;
FIG. 22 is a graph of the magnitude of the forward transmission coefficient S21 in the scattering parameter S of a 300 μm pure transmission line and a simulated pure transmission line after GSG PAD de-embedding in one embodiment of the present invention;
FIG. 23 is a phase diagram of forward transmission coefficient S21 in scattering parameter S of a 300 μm pure transmission line and a simulated pure transmission line after GSG PAD de-embedding in accordance with an embodiment of the present invention;
FIG. 24 is a graph comparing the magnitude of the output reflection coefficient S22 in the scattering parameter S of a pure transmission line with a length of 300 μm after GSG PAD de-embedding and a simulated pure transmission line in accordance with an embodiment of the present invention;
FIG. 25 is a phase diagram of the output reflection coefficient S22 in the scattering parameter S of a pure transmission line with a length of 300 μm after GSG PAD de-embedding and a simulated pure transmission line in accordance with an embodiment of the present invention;
FIG. 26 shows the characteristic impedance Z measured in accordance with an embodiment of the present invention0And simulated characteristic impedance Z0A real part comparison graph;
FIG. 27 shows the characteristic impedance Z measured in accordance with one embodiment of the present invention0And simulated characteristic impedance Z0An imaginary part comparison graph;
FIG. 28 is a graph comparing the measured propagation constant γ and the real part of the simulated propagation constant γ in an embodiment of the present invention;
FIG. 29 is a comparison of the imaginary part of the measured propagation constant γ and the simulated propagation constant γ in an embodiment of the present invention.
Detailed Description
The present invention will be described in detail below with reference to embodiments shown in the drawings. The embodiments are not intended to limit the present invention, and structural, methodological, or functional changes made by those skilled in the art according to the embodiments are included in the scope of the present invention.
Also, it should be understood that, although the terms first, second, etc. may be used herein to describe various elements or structures, these described elements should not be limited by these terms. These terms are only used to distinguish these descriptive objects from one another. For example, a first standard structural member may be referred to as a second standard structural member, and similarly, a second standard structural member may also be referred to as a first standard structural member, without departing from the scope of the present application.
Referring to fig. 1, a schematic diagram of the structure of the DUT for on-chip testing according to the present invention is shown, the GSG structure is for compatibility with the on-chip probe testing system, G represents Ground, and S represents Signal. DUT (device under test) is the structure under test, and the purpose of test calibration is to remove the GSG and a section of the transmission line (i.e., contact line) in front of the DUT for contact.
Referring to fig. 2 to 4, the standard structure required for the test calibration in the present invention is shown, wherein the standard structure in fig. 2 includes a GSG PAD and a length L1The standard structure of FIG. 3 includes GSG PAD and length L2The standard structure of FIG. 4 includes GSG PAD and length LNOf transmission line L1、L2…LNAre different from each other, wherein N is more than or equal to 2.
The invention can realize the measurement of the scattering parameters of the transmission lines with any length and the calibration of the device only by the S (scattering) parameters of the test of at least two transmission lines with different lengths, and the principle of the invention is explained in detail below.
The standard structural member shown in fig. 5 comprises two parts: GSG PAD shown in FIG. 6 and length L shown in FIG. 71The transmission line of (1). Since the GSG PAD structure has symmetry, the GSG PAD structure can be characterized by pi-type structure topology, and the ABCD parameters of the equivalent model of the standard structural member are shown in FIG. 8 as follows:
Figure BDA0002170897340000071
wherein, Y1And Y2For admittance, are all plural, wherein Z1＝1/Y1Definition of Z1The purpose of (1) is to reduce the matrix.
Length of L1The ABCD parameter of the pure transmission line of (a) can be characterized as:
Figure BDA0002170897340000072
for the same reason, the length is L2The ABCD parameter of the pure transmission line of (a) can be characterized as:
Figure BDA0002170897340000073
length of LNThe ABCD parameter of the pure transmission line of (a) can be characterized as:
Figure BDA0002170897340000081
where gamma is the propagation constant of the electromagnetic wave, L1、L2、LNIs the length of the transmission line, Z0Is the characteristic impedance of the transmission line. Gamma and Z0Are all complex numbers.
According to the cascade characteristic of the ABCD parameters, the ABCD parameters of the standard structural member in fig. 2 can be characterized as:
Figure BDA0002170897340000082
the matrix expansion can be written as:
Figure BDA0002170897340000083
Figure BDA0002170897340000084
Figure BDA0002170897340000085
Figure BDA0002170897340000086
similarly, the ABCD parameters for the standard structure in fig. 3 may be characterized as:
Figure BDA0002170897340000087
wherein the content of the first and second substances,
Figure BDA0002170897340000088
Figure BDA0002170897340000089
Figure BDA00021708973400000810
Figure BDA00021708973400000811
similarly, the ABCD parameters for the standard structure in fig. 4 may be characterized as:
Figure BDA00021708973400000812
wherein the content of the first and second substances,
Figure BDA00021708973400000813
Figure BDA00021708973400000814
Figure BDA0002170897340000091
Figure BDA0002170897340000092
it can be seen that the ABCD matrix parameters of the N (1, 2, …, N) transmission line standard structural members are determined by a total of 4 variables, which are Z1,Y2,Z0And γ, and each variable is a complex number. Suppose the ABCD parameters of the standard structural component test shown in FIGS. 2-4
Figure BDA0002170897340000093
Respectively as follows:
Figure BDA0002170897340000094
Figure BDA0002170897340000095
Figure BDA0002170897340000096
for the a term in the ABCD matrix, the error equation set is:
Figure BDA0002170897340000097
Figure BDA00021708973400000918
Figure BDA0002170897340000098
Figure BDA0002170897340000099
for the B term in the ABCD matrix, the error equation set is:
Figure BDA00021708973400000910
Figure BDA00021708973400000911
Figure BDA00021708973400000912
Figure BDA00021708973400000913
for the C term in the ABCD matrix, the error equation set is:
Figure BDA00021708973400000914
Figure BDA00021708973400000915
Figure BDA00021708973400000916
Figure BDA00021708973400000917
for the D term in the ABCD matrix, the error equation set is:
Figure BDA0002170897340000101
Figure BDA0002170897340000102
Figure BDA0002170897340000103
Figure BDA0002170897340000104
the above system of nonlinear equations can be generally expressed as:
Figure BDA0002170897340000105
wherein Q represents A, B, C, D, and m is 1 … N. The purpose of the above-mentioned system of non-linear equations is to solve for Z1,Y2,Z0And γ. While the solution of the system of nonlinear equations has beenThere are more mature solutions, such as the fsolve function in Matlab software, and the detailed solution method is not described here.
Once Z is Z1,Y2,Z0And gamma are solved, the ABCD parameters of GSG PAD and pure transmission line are obtained, and the information can be used for subsequent chip calibration of GSG structure.
Referring to fig. 9, the method for measuring scattering parameters in the present invention includes the following steps:
1. preparing N standard structural members including GSG PAD and L lengthNAnd transmission lines which are not equal to each other, wherein N is more than or equal to 2.
Specifically, the standard structural member is prepared on a wafer, wherein the wafer comprises a radio frequency silicon-based substrate and the like.
2. Measuring scattering parameters S of N standard structural membersN。
Scattering parameter SNMay be measured 2 using a test device such as a Vector Network Analyzer (VNA).
3. Scattering parameter SNConversion to ABCD parameters
Figure BDA0002170897340000106
ABCD parameters are defined as:
Figure BDA0002170897340000107
4. defining an optimization variable Z1And Y2According to the variable Z1And Y2ABCD matrix for constructing GSG PAD in standard structural component
Figure BDA0002170897340000108
Wherein Z is1＝1/Y1，Y1And Y2Is the admittance of the equivalent model of the standard structural member.
The ABCD matrix analytic expression of the GSG PAD is as follows:
Figure BDA0002170897340000109
5. defining optimization variables γ and Z0According to the variables γ and Z0Length L in the construction of standard structural membersNABCD matrix of transmission lines
Figure BDA0002170897340000111
Wherein γ is a propagation constant of electromagnetic wave, Z0Is the characteristic impedance of the transmission line.
Length LNThe ABCD matrix analytic expression of the transmission line of (a) is:
Figure BDA0002170897340000112
6. according toAnd
Figure BDA0002170897340000114
ABCD matrix for constructing standard structural parts
Figure BDA0002170897340000115
The ABCD matrix analytic expression of the standard structural part is as follows:
Figure BDA0002170897340000116
7. according to
Figure BDA0002170897340000117
Solving for variable Z1、Y2And variables γ, Z0。
Is unfolded
Figure BDA0002170897340000118
Constructing a nonlinear equation system:
Figure BDA0002170897340000119
wherein Q is A, B, C, D, and M is 1-N;
solving a nonlinear equation system at each frequency point to obtain a variable Z at each frequency point1、Y2And/or the variables gamma, Z0The value of (c).
The above system of nonlinear equations is developed as:
Figure BDA00021708973400001110
Figure BDA00021708973400001111
Figure BDA00021708973400001112
Figure BDA00021708973400001113
Figure BDA00021708973400001114
Figure BDA00021708973400001115
Figure BDA0002170897340000121
Figure BDA0002170897340000122
Figure BDA0002170897340000123
Figure BDA0002170897340000124
Figure BDA0002170897340000125
Figure BDA0002170897340000126
Figure BDA0002170897340000127
Figure BDA0002170897340000128
Figure BDA0002170897340000129
Figure BDA00021708973400001210
preferably, the solving of the system of nonlinear equations is done by a fsolve function in Matlab software.
8. According to the variable Z1、Y2Acquiring ABCD parameters of GSG PAD and/or according to variables gamma and Z0Obtaining an arbitrary length LXABCD parameters of transmission lines.
A variable Z1、Y2Substitution of value of (1)
Figure BDA00021708973400001211
Obtaining ABCD parameters of GSGPAD;
the variables gamma and Z0Substitution of value of (1)
Figure BDA00021708973400001212
Can obtain any length LXABCD parameters of transmission lines.
9. The ABCD parameter of the GSG PAD is converted into the scattering parameter S, so that the error parameter S of the PAD can be obtained, and the parameter can be used for subsequent de-embedding of any GSG PAD.
Will be of any length LXThe ABCD parameter of the transmission line is converted into a scattering parameter S, and then the arbitrary length L can be obtainedXThe ABCD parameter of the transmission line is converted into the S parameter.
The device for measuring and calibrating aims at the GSG PAD structure, and the test structure of the device consists of a GSGPAD and a section of transmission line with variable length, so that S parameters of the two structures respectively obtained by the method can be used for subsequent de-embedding of other structural parts (such as passive on-chip inductors, transistors and the like) with the GSG PAD and the transmission line.
In a specific embodiment of the present invention, two standard structural members are taken as an example for explanation, and the scattering parameter measurement method includes the following steps:
1. preparing a first standard structure shown in FIG. 2 and a second standard structure shown in FIG. 3 on a wafer, wherein the first standard structure comprises GSG PAD and has a length L1The second standard structure comprises GSG PAD and length L2Satisfies L1≠L2. As in this example L1Is 100 μm, L 2300 μm, the wafer is a radio frequency silicon-based substrate.
2. Measuring scattering parameters S of a first standard structure and a second standard structure using a test device such as a Vector Network Analyzer (VNA)1And S2。
3. Scattering parameter S1And S2Conversion to ABCD parameters
Figure BDA0002170897340000131
And
Figure BDA0002170897340000132
ABCD parameters are defined as:
Figure BDA0002170897340000133
Figure BDA0002170897340000134
4. defining an optimization variable Z1And Y2According to the variable Z1And Y2ABCD matrix for constructing GSG PAD in standard structural component
Figure BDA0002170897340000135
Wherein Z is1＝1/Y1，Y1And Y2Is the admittance of the equivalent model of the standard structural member.
The ABCD matrix analytic expression of the GSG PAD is as follows:
Figure BDA0002170897340000136
5. defining optimization variables γ and Z0According to the variables γ and Z0Length L in the construction of standard structural members1And L2ABCD matrix of transmission lines
Figure BDA0002170897340000137
And
Figure BDA0002170897340000138
wherein γ is a propagation constant of electromagnetic wave, Z0Is the characteristic impedance of the transmission line.
Length L1The ABCD matrix analytic expression of the transmission line of (a) is:
Figure BDA0002170897340000139
length L2The ABCD matrix analytic expression of the transmission line of (a) is:
Figure BDA0002170897340000141
6. according to
Figure BDA0002170897340000142
And
Figure BDA0002170897340000143
ABCD matrix for constructing first standard structural component
Figure BDA0002170897340000144
Figure BDA0002170897340000145
According to
Figure BDA0002170897340000146
And
Figure BDA0002170897340000147
ABCD matrix for constructing second standard structural component
Figure BDA0002170897340000148
Figure BDA0002170897340000149
7. According to
Figure BDA00021708973400001410
And
Figure BDA00021708973400001411
solving for variable Z1、Y2And variables γ, Z0。
Is unfolded
Figure BDA00021708973400001412
The following can be obtained:
Figure BDA00021708973400001413
Figure BDA00021708973400001414
Figure BDA00021708973400001415
Figure BDA00021708973400001416
is unfolded
Figure BDA00021708973400001417
The following can be obtained:
Figure BDA00021708973400001418
Figure BDA00021708973400001419
Figure BDA00021708973400001420
Figure BDA00021708973400001421
constructing a nonlinear equation system:
Figure BDA00021708973400001422
wherein Q is A, B, C, D, and M is 1-N.
Namely:
Figure BDA0002170897340000151
Figure BDA0002170897340000152
Figure BDA0002170897340000153
Figure BDA0002170897340000154
Figure BDA0002170897340000155
Figure BDA0002170897340000156
Figure BDA0002170897340000157
Figure BDA0002170897340000158
solving a nonlinear equation system through a fsolve function in Matlab software at each frequency point to obtain a variable Z at each frequency point1、Y2And variables γ, Z0The value of (c).
8. According to the variable Z1、Y2The ABCD parameter of the GSG PAD can be obtained:
Figure BDA0002170897340000159
according to the variables gamma, Z0Can obtain any length LXABCD parameters of transmission lines:
Figure BDA00021708973400001510
9. the ABCD parameter of the GSG PAD is converted into the scattering parameter S, so that the error parameter S of the PAD can be obtained, and the parameter can be used for subsequent de-embedding of any GSG PAD.
Will be of any length LXThe ABCD parameter of the transmission line is converted into a scattering parameter S, and then the arbitrary length L can be obtainedXThe ABCD parameter of the transmission line is converted into the S parameter.
The S parameters of the two structures respectively obtained by the method can be used for the subsequent de-embedding of other structural parts (such as passive on-chip inductors, transistors and the like) with GSG PAD and transmission lines.
FIGS. 10-17 show the GSG PAD de-embedded length L1Comparison of scattering parameters S (including reverse transmission coefficient S12, forward transmission coefficient S21, input reflection coefficient S11, and output reflection coefficient S22) for (100 μm) pure transmission lines and simulated pure transmission lines.
FIGS. 18-25 show the GSG PAD de-embedded length L2Comparison of scattering parameters S (including reverse transmission coefficient S12, forward transmission coefficient S21, input reflection coefficient S11, and output reflection coefficient S22) for (300 μm) pure transmission lines and simulated pure transmission lines.
FIG. 26 and FIG. 27 are respectively the characteristic impedance Z tested in this embodiment0And simulated characteristic impedance Z0Real part and imaginary part comparison graphs, fig. 28, fig. 29 are the propagation constant γ tested in this example and the simulated propagation constant γ real part and imaginary part comparison graphs, respectively.
Through comparison of tests and simulations, the invention can realize accurate measurement of scattering parameters of transmission lines with any length.
In addition, the invention also discloses a device calibration method, which comprises the following steps:
GSG PAD and any length L are obtained by adopting the scattering parameter measuring methodXA scattering parameter S of the transmission line;
the device of the GSG-transmission line structure is calibrated by the above parameters.
The device applicable to the invention comprises a device on a PCB or a device on a wafer, and the device can be a radio frequency chip, a microwave chip and the like.
Compared with the prior art, the measuring and calibrating method does not need to acquire the characteristic impedance of the transmission line in advance, but the unknown quantities are determined after the calibration is finished. Therefore, the invention can be used for calibrating a Printed Circuit Board (PCB) and a wafer-level radio frequency/microwave chip, and can also extract the characteristic parameters of the transmission line to provide accurate characteristic impedance for a TRL calibration algorithm;
in addition, the test data of the pure transmission lines with different lengths obtained by de-embedding can be used for calibrating the substrate parameters of the PCB or the wafer;
in addition, a large number of levels are usually provided in the silicon process, and the communication among the levels is completed by through holes, and the through holes enable the dimension of the calibration structure to be upgraded from a planar two-dimensional structure to a three-dimensional structure, so that a common open-circuit short-circuit calibration method cannot be used.
According to the technical scheme, the invention has the following beneficial effects:
the invention can realize the measurement of the scattering parameters of the transmission line with any length and the GSG PAD through the scattering parameters of at least two transmission lines with different lengths, has higher measurement precision, greatly improves the flexibility of the measurement of the scattering parameters, and can be widely applied to the calibration of devices.
It will be evident to those skilled in the art that the invention is not limited to the details of the foregoing illustrative embodiments, and that the present invention may be embodied in other specific forms without departing from the spirit or essential attributes thereof. The present embodiments are therefore to be considered in all respects as illustrative and not restrictive, the scope of the invention being indicated by the appended claims rather than by the foregoing description, and all changes which come within the meaning and range of equivalency of the claims are therefore intended to be embraced therein. Any reference sign in a claim should not be construed as limiting the claim concerned.
Furthermore, it should be understood that although the present description refers to embodiments, not every embodiment may contain only a single embodiment, and such description is for clarity only, and those skilled in the art should integrate the description, and the embodiments may be combined as appropriate to form other embodiments understood by those skilled in the art.

Claims (12)

1. A scattering parameter measurement method, characterized in that the measurement method comprises:
preparing N standard structural members including GSG PAD and L lengthNAnd transmission lines which are not equal to each other, wherein N is more than or equal to 2;
measuring scattering parameters S of N standard structural membersN；
Scattering parameter SNConversion to ABCD parameters
Figure FDA0002434424940000011
According to the variable Z1And Y2ABCD matrix for constructing GSG PAD in standard structural component
Figure FDA0002434424940000012
Wherein Z is1＝1/Y1，Y1And Y2Is admittance in an equivalent model of a standard structural member;
according to the variables gamma and Z0Length L in the construction of standard structural membersNABCD matrix of transmission lines
Figure FDA0002434424940000013
Wherein γ is a propagation constant of electromagnetic wave, Z0Is the characteristic impedance of the transmission line;
according to
Figure FDA0002434424940000014
And
Figure FDA0002434424940000015
ABCD matrix for constructing standard structural parts
Figure FDA0002434424940000016
According to
Figure FDA0002434424940000017
Solving for variable Z1、Y2And/or the variables gamma, Z0；
According to the variable Z1、Y2Acquiring ABCD parameters of GSG PAD and/or according to variables gamma and Z0Obtaining an arbitrary length LXABCD parameters of the transmission line;
ABCD parameter and/or arbitrary length L of GSG PADXThe ABCD parameter of the transmission line is converted into a scattering parameter S;
the ABCD matrix analytic expression of the GSG PAD in the standard structural part is as follows:
Figure FDA0002434424940000018
the length of the standard structural member is LNThe ABCD matrix analytic expression of the transmission line of (a) is:
Figure FDA0002434424940000019
2. the scattering parameter measurement method of claim 1, wherein the ABCD matrix analytical expression for the standard structural component is:
Figure FDA0002434424940000021
3. the scattering parameter measurement method of claim 2, wherein in the measurement method, "according to
Figure FDA0002434424940000022
Solving for variable Z1、Y2And/or the variables gamma, Z0The method specifically comprises the following steps:
is unfolded
Figure FDA0002434424940000023
Constructing a nonlinear equation system:
Figure FDA0002434424940000024
wherein Q is A, B, C, D, and M is 1-N;
solving a nonlinear equation system at each frequency point to obtain a variable Z at each frequency point1、Y2And/or the variables gamma, Z0The value of (c).
4. The scattering parameter measurement method of claim 3, wherein the solution of the nonlinear system of equations is performed by a fsolve function in Matlab software.
5. The scattering parameter measurement method of claim 1, wherein in the measurement method, "according to variable Z1、Y2The specific step of obtaining the ABCD parameter of the GSG PAD is as follows:
a variable Z1、Y2Substitution of value of (1)
Figure FDA0002434424940000025
The ABCD parameter of GSG PAD is obtained.
6. The scattering parameter measurement method of claim 1, wherein the measurement method is based on the variables γ and Z0Obtaining an arbitrary length LXABCD parameters of transmission lines ":
the variables gamma and Z0Substitution of value of (1)
Figure FDA0002434424940000026
To obtain any length LXABCD parameters of transmission lines.
7. The method of claim 1, wherein the standard structure is fabricated on a wafer.
8. The method of claim 7, wherein the wafer comprises a radio frequency silicon-based substrate.
9. The scattering parameter measurement method of claim 1, wherein the scattering parameter S of the standard structural memberNMeasured by a vector network analyzer.
10. The method of claim 1, wherein the standard structure comprises a transmission line length L1The first standard structural member and the transmission line have a length L2The second standard structural member of (1) satisfies L1≠L2。
11. A device calibration method, the calibration method comprising:
the method for measuring scattering parameters of any of claims 1-10, the GSG PAD and the arbitrary length L are obtainedXA scattering parameter S of the transmission line;
the device of the GSG-transmission line structure is calibrated by the above parameters.
12. The device calibration method of claim 11, wherein the device is a PCB on board device or a wafer on device.
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