CN111880012A - Method for detecting broadband continuous dielectric characteristic parameters of microwave dielectric substrate - Google Patents

Method for detecting broadband continuous dielectric characteristic parameters of microwave dielectric substrate Download PDF

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CN111880012A
CN111880012A CN202010667847.0A CN202010667847A CN111880012A CN 111880012 A CN111880012 A CN 111880012A CN 202010667847 A CN202010667847 A CN 202010667847A CN 111880012 A CN111880012 A CN 111880012A
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CN111880012B (en
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蔡龙珠
曾一轩
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Southeast University
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R27/00—Arrangements for measuring resistance, reactance, impedance, or electric characteristics derived therefrom
    • G01R27/02—Measuring real or complex resistance, reactance, impedance, or other two-pole characteristics derived therefrom, e.g. time constant
    • G01R27/26—Measuring inductance or capacitance; Measuring quality factor, e.g. by using the resonance method; Measuring loss factor; Measuring dielectric constants ; Measuring impedance or related variables
    • G01R27/2617—Measuring dielectric properties, e.g. constants
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R27/00—Arrangements for measuring resistance, reactance, impedance, or electric characteristics derived therefrom
    • G01R27/02—Measuring real or complex resistance, reactance, impedance, or other two-pole characteristics derived therefrom, e.g. time constant
    • G01R27/26—Measuring inductance or capacitance; Measuring quality factor, e.g. by using the resonance method; Measuring loss factor; Measuring dielectric constants ; Measuring impedance or related variables
    • G01R27/2617—Measuring dielectric properties, e.g. constants
    • G01R27/2635—Sample holders, electrodes or excitation arrangements, e.g. sensors or measuring cells
    • G01R27/2658—Cavities, resonators, free space arrangements, reflexion or interference arrangements
    • G01R27/2664—Transmission line, wave guide (closed or open-ended) or strip - or microstrip line arrangements
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R27/00—Arrangements for measuring resistance, reactance, impedance, or electric characteristics derived therefrom
    • G01R27/02—Measuring real or complex resistance, reactance, impedance, or other two-pole characteristics derived therefrom, e.g. time constant
    • G01R27/26—Measuring inductance or capacitance; Measuring quality factor, e.g. by using the resonance method; Measuring loss factor; Measuring dielectric constants ; Measuring impedance or related variables
    • G01R27/2688—Measuring quality factor or dielectric loss, e.g. loss angle, or power factor
    • G01R27/2694—Measuring dielectric loss, e.g. loss angle, loss factor or power factor

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Abstract

The invention discloses a method for detecting broadband continuous dielectric characteristic parameters of a microwave dielectric substrate, which can be used for establishing a testing device based on two linear wave guide structures, fixing two ends of a material to be tested on the testing device to obtain scattering parameters of the two linear wave guide structures, converting the scattering parameters into corresponding ABCD matrixes to obtain a first ABCD matrix corresponding to a first linear wave guide structure and a second ABCD matrix corresponding to a second linear wave guide structure, calculating an optimized complex propagation constant expression based on the ABCD matrix optimized by double lines to obtain the conductor loss and the radiation loss of the linear wave guide structures, calculating the dielectric loss, determining the dielectric loss tangent of the dielectric substrate to accurately detect the dielectric characteristic parameters such as comprehensive phase number, linear loss, effective dielectric constant, dielectric constant of the dielectric substrate, dielectric loss and dielectric loss tangent of the dielectric substrate, the dielectric characteristic parameters obtained by detection have higher precision.

Description

Method for detecting broadband continuous dielectric characteristic parameters of microwave dielectric substrate
Technical Field
The invention relates to the technical field of dielectric characteristic parameter extraction and test of dielectric substrates, in particular to a method for detecting broadband continuous dielectric characteristic parameters of a microwave dielectric substrate.
Background
In designing Microwave (MW)/millimeter wave (MMW)/terahertz (THz) devices and circuits, it is important to know the dielectric characteristics (dielectric constant and dielectric loss tangent) of the dielectric substrate used. The true situation is that dielectric substrate manufacturers typically provide dielectric information at only a single frequency, such as 1GHz or 10 GHz. Dielectric properties do not change significantly over a small frequency range, but can cause frequency shifts and performance variations in the device. Furthermore, substrate materials from different manufacturers and different batches may also have different dielectric properties. Meanwhile, with the development of material technology, more and more new materials are developed and applied to the field of electromagnetic fields. Therefore, the extraction of dielectric properties in the microwave band has been very important and meaningful, especially for newly developed materials.
Many methods and techniques for extracting dielectric properties have been proposed in the related literature and can be divided into two broad categories. One is a narrow band measurement technique and the other is a wide band measurement technique. Narrow band measurement techniques are primarily based on resonant cavities, which can provide more accurate measurements, but are only applicable to discrete resonance points. Broadband measurement techniques typically rely on the transmission or reflection of electromagnetic waves rather than the use of resonant cavities, and thus can provide broadband and continuous material properties.
At present, a plurality of wires are used for extracting material parameters of a microwave dielectric substrate. However, the microwave dielectric substrate material parameters detected by the methods often have the problems of low precision or low accuracy.
Disclosure of Invention
Aiming at the problems, the invention provides a method for detecting broadband continuous dielectric characteristic parameters of a microwave dielectric substrate.
In order to realize the purpose of the invention, the invention provides a method for detecting the broadband continuous dielectric characteristic parameters of a microwave dielectric substrate, which comprises the following steps:
s10, building a testing device based on the two linear guided wave structures, and fixing two ends of a material to be tested on the testing device through a group of high-frequency microwave connectors; the two ends of the linear guided wave structure are provided with high-frequency microwave connectors so that the testing device is connected with the linear guided wave structure; the two linear guided wave structures comprise a first linear guided wave structure and a second linear guided wave structure, and the length of the first linear guided wave structure is greater than that of the second linear guided wave structure;
s20, respectively testing the two linear guided wave structures by using a vector network analyzer to obtain scattering parameters of the two linear guided wave structures;
s30, converting scattering parameters of the two linear guided wave structures into corresponding ABCD matrixes to obtain a first ABCD matrix corresponding to the first linear guided wave structure and a second ABCD matrix corresponding to the second linear guided wave structure;
s40, calculating according to the first ABCD matrix and the second ABCD matrix to obtain an optimized comprehensive phase number and linear loss, and determining an effective dielectric constant according to a comprehensive phase number-effective dielectric constant equation; the phase number-effective dielectric constant equation records the relationship between the integrated phase number and the effective dielectric constant;
s50, determining the dielectric constant of the dielectric substrate of the material to be measured according to the effective dielectric constant;
s60, obtaining conductor loss and radiation loss of the linear wave guide structure, calculating dielectric loss according to the linear loss, the conductor loss and the radiation loss, and determining dielectric loss tangent of the dielectric substrate according to the dielectric loss, the effective dielectric constant and the dielectric constant of the dielectric substrate.
In one embodiment, the ABCD matrix comprises:
Figure BDA0002581075650000021
wherein A represents a first parameter of the ABCD matrix, B represents a second parameter of the ABCD matrix, C represents a third parameter of the ABCD matrix, D represents a fourth parameter of the ABCD matrix, and S11Representing the input reflection coefficient, S12Representing the reverse transmission coefficient, S21Denotes the forward transmission coefficient, S22Representing the output reflection coefficient, ZcRepresenting the linear characteristic impedance of the linear guided wave structure.
In one embodiment, the synthetic phase calculation formula includes:
Figure BDA0002581075650000022
the calculation formula of the linear loss comprises:
Figure BDA0002581075650000023
wherein β represents the number of integrated phases, α represents the linear loss, and AL1First matrix parameters, D, representing a first ABCD matrixL1Fourth matrix parameter, A, representing the first ABCD matrixS1First matrix parameters, D, representing a second ABCD matrixS1A fourth matrix parameter representing the second ABCD matrix, Re representing the real part, Im representing the imaginary part, L1Denotes the linear length, S, of the first linear waveguide structure1Indicating the linear length of the second linear short waveguide structure.
Specifically, the phase number-effective dielectric constant equation includes:
Figure BDA0002581075650000031
in the formula (I), the compound is shown in the specification,effrepresenting the effective dielectric constant equation, f the operating frequency, c the speed of light.
Specifically, the calculation formula of the dielectric constant of the dielectric substrate comprises:
Figure BDA0002581075650000032
in the formula (I), the compound is shown in the specification,rdenotes the dielectric constant of the dielectric substrate, and q denotes the fill factor of the linear waveguide structure.
In one embodiment, the formula for calculating the dielectric loss comprises:
αd＝α-αc-αr，
the calculation formula of the dielectric loss tangent of the dielectric substrate comprises the following steps:
Figure BDA0002581075650000033
in the formula, alphadDenotes dielectric loss, αcRepresenting conductor loss, αrDenotes the radiation loss, tan denotes the dielectric loss tangent of the dielectric substrate,effdenotes the effective dielectric constant equation, f denotesThe operating frequency, c, represents the speed of light,rdenotes the dielectric constant of the dielectric substrate, and q denotes the fill factor of the linear waveguide structure.
Specifically, the calculation formula of the conductor loss includes:
Figure BDA0002581075650000034
in the formula, RcRepresenting the distributed series resistance, R, of the central signal conductorgRepresenting distributed series resistance of ground plane, ZcThe characteristic impedance of the waveguide structure is represented by the following calculation formula:
Figure BDA0002581075650000035
Figure BDA0002581075650000036
where T is the thickness of the metal conductor, the skin effect resistance
Figure BDA0002581075650000037
σ and μ are skin depth, conductivity of metal conductor, and permeability of free space, respectively, and
Figure BDA0002581075650000041
k0display module
Figure BDA0002581075650000042
Wherein S represents the line width of the central signal conductor, W represents the distance between the central signal conductor and the ground plane, and k0' representation and modulus k0The associated complementary modes, K, represent the first class of perfect elliptic integrals.
Specifically, the formula for calculating the radiation loss includes:
Figure BDA0002581075650000043
Figure BDA0002581075650000044
Figure BDA0002581075650000045
wherein S represents the line width of the central signal conductor, W represents the distance between the central signal conductor and the ground plane, and K (K)0) Representing the first type of complete elliptic integral, superscript' representing the complementary mode.
In one embodiment, the length of the first linear guided wave structure is 2 times or more than 2 times the length of the second linear guided wave structure.
In one embodiment, the fixed installation of the material to be tested in the test device comprises a fixed mode of welding or direct clamping.
The method for detecting the broadband continuous dielectric characteristic parameters of the microwave medium substrate can construct a testing device based on two linear wave guide structures, fix two ends of a material to be tested on the testing device through a group of high-frequency microwave connectors, respectively test the two linear wave guide structures by using a vector network analyzer to obtain scattering parameters of the two linear wave guide structures, convert the scattering parameters into corresponding ABCD matrixes to obtain a first ABCD matrix corresponding to a first linear wave guide structure and a second ABCD matrix corresponding to a second linear wave guide structure, respectively determine the comprehensive phase number and the linear loss according to the first ABCD matrix and the second ABCD matrix, determine the effective dielectric constant according to a phase number and phase number-effective dielectric constant equation, determine the dielectric constant of the medium substrate of the material to be tested according to the effective dielectric constant, and obtain the conductor loss and the radiation loss of the linear wave guide structures, calculating dielectric loss according to the linear loss, the conductor loss and the radiation loss, determining the dielectric loss tangent of the dielectric substrate according to the dielectric loss and the effective dielectric constant, accurately detecting dielectric characteristic parameters such as comprehensive phase number, the linear loss, the effective dielectric constant, the dielectric substrate dielectric constant, the dielectric loss, the dielectric substrate dielectric loss tangent and the like, and establishing and extracting the dielectric constant of the dielectric substraterAnd an ideal model of dielectric loss tangent tan for relieving the error influence caused by the fixed installation process of the microwave connector, so that the detected dielectric characteristic parameter has higher valueThe accuracy of (2).
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FIG. 1 is a flowchart of an embodiment of a method for detecting a broadband continuous dielectric characteristic parameter of a microwave dielectric substrate;
FIG. 2 is a schematic diagram of an ABCD matrix-based test fixture with a two-wire and two-port guided wave structure according to an embodiment;
FIG. 3 is a schematic diagram of an extracted three-dimensional model of dielectric parameters of a dielectric substrate in one embodiment;
FIG. 4 is a top view of a stub structure based on a non-grounded coplanar waveguide in one embodiment;
FIG. 5 is a diagram illustrating the phase number β results derived based on a two-line optimization, long line, short line in one embodiment;
FIG. 6 shows the effective dielectric constant derived from the two-line optimization, long straight line and short straight lineeffA schematic diagram of the results;
FIG. 7 shows the dielectric constant of the dielectric substrate derived based on the double-line optimization, long-line and short-linerA schematic diagram of the results;
FIG. 8 shows the dielectric constant of the dielectric substrate derived based on the bilinear optimization in one embodimentrSchematic diagram of the amplification result of (1);
FIG. 9 shows the total linear loss α, the conductor loss α based on the two-wire optimization method in one embodimentcRadiation loss alpharDielectric loss alphadA schematic diagram of the results;
FIG. 10 is a graph illustrating the dielectric substrate dielectric loss tangent tan derived based on the bi-linear optimization in one embodiment.
Detailed Description
In order to make the objects, technical solutions and advantages of the present application more apparent, the present application is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the present application and are not intended to limit the present application.
Reference herein to "an embodiment" means that a particular feature, structure, or characteristic described in connection with the embodiment can be included in at least one embodiment of the application. The appearances of the phrase in various places in the specification are not necessarily all referring to the same embodiment, nor are separate or alternative embodiments mutually exclusive of other embodiments. It is explicitly and implicitly understood by one skilled in the art that the embodiments described herein can be combined with other embodiments.
Referring to fig. 1, fig. 1 is a flowchart of an embodiment of a method for detecting a broadband continuous dielectric characteristic parameter of a microwave dielectric substrate, including the following steps:
s10, building a testing device based on the two linear guided wave structures, and fixing two ends of a material to be tested on the testing device through a group of high-frequency microwave connectors; the two ends of the linear guided wave structure are provided with high-frequency microwave connectors so that the testing device is connected with the linear guided wave structure; the two linear guided wave structures comprise a first linear guided wave structure and a second linear guided wave structure, and the length of the first linear guided wave structure is greater than that of the second linear guided wave structure;
s20, respectively testing the two linear guided wave structures by using a vector network analyzer to obtain scattering parameters of the two linear guided wave structures;
s30, converting scattering parameters of the two linear guided wave structures into corresponding ABCD matrixes to obtain a first ABCD matrix corresponding to the first linear guided wave structure and a second ABCD matrix corresponding to the second linear guided wave structure;
s40, calculating according to the first ABCD matrix and the second ABCD matrix to obtain an optimized comprehensive phase number and linear loss (such as comprehensive linear loss), and determining an effective dielectric constant according to a comprehensive phase number-effective dielectric constant equation; the phase number-effective dielectric constant equation records the relationship between the integrated phase number and the effective dielectric constant; specifically, the step can obtain an optimized complex propagation constant expression based on the first ABCD matrix and the second ABCD matrix, that is, the total attenuation and the phase number of the linear structure are extracted based on the double-line optimization;
s50, determining the dielectric constant of the dielectric substrate of the material to be measured according to the effective dielectric constant;
s60, obtaining conductor loss and radiation loss of the linear wave guide structure, calculating dielectric loss according to the linear loss, the conductor loss and the radiation loss, and determining dielectric loss tangent of the dielectric substrate according to the dielectric loss, the effective dielectric constant and the dielectric constant of the dielectric substrate.
The material to be measured is a dielectric material to be measured, such as a linear guided wave structure to be measured. The two linear guided wave structures may include a coplanar waveguide structure adapted for ungrounded, microstrip, stripline, or substrate integrated waveguide, among others.
In this embodiment, a test apparatus is composed of two linear microwave guided wave structures (linear guided wave structures) with different lengths, and the results of scattering parameters (S parameters) obtained from the two linear microwave guided wave structures are converted into corresponding ABCD matrices, the ABCD matrices are associated with complex propagation constants, and an optimized complex propagation constant expression is calculated by using an ABCD matrix optimized based on two lines, so that the total attenuation α, the phase number β, and the characteristic impedance Z of the linear guided wave structure can be directly extractedcDielectric constant of dielectric substraterAnd a dielectric loss tangent tan. Compared with a single-wire method, the double-wire optimization method can relieve the error influence caused in the fixed installation process of the microwave connector, and obtain more accurate and continuous dielectric parameters of the broadband dielectric substrate. The method can be applied to the guided wave structures such as ungrounded coplanar waveguide structures, microstrip lines, strip lines, substrate integrated waveguides and the like. In particular, the method is well suited for ungrounded coplanar waveguide structures because the structure is well suited for electroplating certain newly developed dielectric materials (only one electroplating is needed, but multiple electroplating is needed for structures such as microstrip lines), avoiding the high manufacturing cost, difficulty, and consistency errors in conductor thickness and roughness that may be caused by multiple electroplating processes.
The method for detecting the broadband continuous dielectric characteristic parameters of the microwave medium substrate can be used for building a testing device based on two linear guided wave structures, fixing two ends of a material to be tested on the testing device through a group of high-frequency microwave connectors, respectively testing the two linear guided wave structures by using a vector network analyzer to obtain scattering parameters of the two linear guided wave structures, and converting the scattering parameters into corresponding ABCD matrixes to obtain a first linear guided wave junctionConstructing a corresponding first ABCD matrix and a corresponding second ABCD matrix corresponding to a second linear wave guide structure, respectively determining a comprehensive phase number and linear loss according to the first ABCD matrix and the second ABCD matrix, determining an effective dielectric constant according to a phase number and phase number-effective dielectric constant equation, determining a dielectric substrate dielectric constant of a material to be detected according to the effective dielectric constant, obtaining a conductor loss and a radiation loss of the linear wave guide structure, calculating a dielectric loss according to the linear loss, the conductor loss and the radiation loss, determining a dielectric substrate dielectric loss tangent according to the dielectric loss and the effective dielectric constant, accurately detecting dielectric characteristic parameters such as the comprehensive phase number, the linear loss, the effective dielectric constant, the dielectric substrate dielectric constant, the dielectric loss and the dielectric substrate dielectric loss tangent, and establishing and extracting the dielectric substrate dielectric constantrAnd an ideal model of the dielectric loss tangent tan, which is used for relieving the error influence caused by the fixed installation process of the microwave connector, so that the detected dielectric characteristic parameters have higher precision.
In one embodiment, the ABCD matrix comprises:
Figure BDA0002581075650000071
wherein A represents a first parameter of the ABCD matrix, B represents a second parameter of the ABCD matrix, C represents a third parameter of the ABCD matrix, D represents a fourth parameter of the ABCD matrix, and S11Representing the input reflection coefficient, S12Representing the reverse transmission coefficient, S21Denotes the forward transmission coefficient, S22Representing the output reflection coefficient, ZcRepresenting the characteristic impedance of a straight line of linear guided wave structures, such as a first straight guided wave structure and a second straight guided wave structure.
Specifically, a first ABCD matrix corresponding to the first linear guided wave structure is:
Figure BDA0002581075650000072
wherein A isL1First matrix parameters, B, representing a first ABCD matrixL1Second matrix parameters representing the first ABCD matrix, CL1Third moment representing the first ABCD matrixArray parameter, DL1A fourth matrix parameter representing the first ABCD matrix. The second ABCD matrix corresponding to the second linear guided wave structure is as follows:
Figure BDA0002581075650000073
wherein A isS1First matrix parameters, B, representing a second ABCD matrixS1Second matrix parameters representing a second ABCD matrix, CS1Third matrix parameter, D, representing a second ABCD matrixS1A fourth matrix parameter representing a second ABCD matrix. A schematic diagram of a two-port linear wave guide structure and ABCD matrix is shown in fig. 2.
In one embodiment, the synthetic phase calculation formula includes:
Figure BDA0002581075650000074
the calculation formula of the linear loss comprises:
Figure BDA0002581075650000081
wherein β represents the number of integrated phases, α represents the linear loss, and AL1First matrix parameters, D, representing a first ABCD matrixL1Fourth matrix parameter, A, representing the first ABCD matrixS1First matrix parameters, D, representing a second ABCD matrixS1A fourth matrix parameter representing the second ABCD matrix, Re representing the real part, Im representing the imaginary part, L1Denotes the linear length, S, of the first linear waveguide structure1Indicating the linear length of the second linear short waveguide structure.
The above-mentioned phase number β based on the two-line optimization is related to ABCD matrices (e.g., a first ABCD matrix and a second ABCD matrix) of a long straight line (a first linear guided wave structure) and a short straight line (a second linear guided wave structure).
Specifically, the phase number-effective dielectric constant equation includes:
Figure BDA0002581075650000082
in the formula (I), the compound is shown in the specification,effrepresenting the effective dielectric constant equation, f the operating frequency, c the speed of light.
Specifically, the calculation formula of the dielectric constant of the dielectric substrate comprises:
Figure BDA0002581075650000083
in the formula (I), the compound is shown in the specification,rdenotes the dielectric constant of the dielectric substrate, and q denotes the fill factor of the linear waveguide structure.
At this time, there are:
Figure BDA0002581075650000084
specifically, the formula for calculating the dielectric loss includes:
αd＝α-αc-αr，
the calculation formula of the dielectric loss tangent of the dielectric substrate comprises the following steps:
Figure BDA0002581075650000085
in the formula, alphadDenotes dielectric loss, αcRepresenting conductor loss, αrDenotes the radiation loss, tan denotes the dielectric loss tangent of the dielectric substrate,effrepresenting the effective dielectric constant equation, f the operating frequency, c the speed of light,rdenotes the dielectric constant of the dielectric substrate, and q denotes the fill factor of the linear waveguide structure. Wherein the fill factor q, the conductor loss alphacRadiation loss alpharIs associated with a selected structure (e.g., a first linear guided wave structure and a second linear guided wave structure).
In one example, when the non-grounded coplanar waveguide structure is used, the calculation formula of the conductor loss comprises:
Figure BDA0002581075650000091
in the formula, RcRepresenting the characteristic impedance, R, of a linear guided wave structuregDistributed series resistance, Z, representing a linear guided wave structurecRepresenting the characteristic impedance of the waveguide structure.
In particular, the characteristic impedance
Figure BDA0002581075650000092
Distributed series resistance of central signal conductor
Figure BDA0002581075650000093
Figure BDA0002581075650000094
Distributed series resistance of ground plane
Figure BDA0002581075650000095
T is the thickness of the metal conductor, the skin effect resistance
Figure BDA0002581075650000096
σ and μ are skin depth, conductivity of metal conductor, and permeability of free space, respectively, and
Figure BDA0002581075650000097
k0display module
Figure BDA0002581075650000098
Wherein S represents the line width of the central signal conductor, W represents the distance between the central signal conductor and the ground plane, and k0' representation and modulus k0The associated complementary modes, K, represent the first class of perfect elliptic integrals.
In one example, the formula for calculating the radiation loss includes:
Figure BDA0002581075650000099
Figure BDA00025810756500000910
Figure BDA00025810756500000911
wherein S represents the line width of the central signal conductor, W represents the distance between the central signal conductor and the ground plane, and K (K)0) Representing the first type of complete elliptic integral, superscript' representing the complementary mode.
In this example, the radiance factor
Figure BDA00025810756500000912
Wavelength of medium
Figure BDA00025810756500000913
In one embodiment, the length of the first linear guided wave structure is 2 times or more than 2 times the length of the second linear guided wave structure.
The testing device constructed in this embodiment is composed of two linear microwave guided wave structures with different lengths, and the length of the long linear guided wave structure (the first linear guided wave structure) is preferably 2 times or more of the length of the short linear guided wave structure (the second linear guided wave structure), and the scattering parameters of the long linear guided wave structure are tested through the high-frequency microwave connector.
In one embodiment, the fixed installation of the material to be tested in the test device comprises a fixed mode of welding or direct clamping.
In this embodiment, the surface of the material to be measured is attached with metal copper; the fixed installation of the material to be tested in the test device comprises a fixed mode of welding or direct clamping.
Compared with the prior art, the method for detecting the broadband continuous dielectric characteristic parameters of the microwave dielectric substrate has the following technical effects:
1) compared with other methods, such as a wave cascade matrix algorithm, the method is simpler, the test operation is convenient, the parameter extraction precision is high, the method only consists of a simple microwave guided wave structure consisting of two straight lines with different lengths, and the total attenuation, the phase number, the characteristic impedance, the substrate dielectric constant, the dielectric loss tangent and the like of a circuit can be directly extracted;
2) because the method is based on the double-line optimized ABCD matrix to extract parameters, the method can relieve derivation errors caused by connector welding and device manufacturing to a certain extent, and simultaneously considers conductor loss and radiation loss of the structure to obtain accurate and continuous broadband dielectric characteristics;
3) the method realizes the extraction of dielectric parameters of the dielectric substrate based on the ungrounded coplanar waveguide for the first time, is very suitable for electroplating certain newly developed dielectric materials (only one-time electroplating is needed, but structures such as microstrip lines and the like need multiple times of electroplating), and avoids the problems of high manufacturing cost, high difficulty and consistency errors of conductor thickness and roughness possibly caused by multiple electroplating processes;
4) the double-line optimized extraction method is not only suitable for ungrounded coplanar waveguide structures, but also suitable for structures such as microstrip lines, strip lines, substrate integrated waveguides and the like.
In an embodiment, taking the implementation of the extraction of dielectric parameters of a dielectric substrate based on a non-grounded coplanar waveguide as an example, the structure shown in fig. 3 is a three-dimensional model schematic diagram thereof, and is composed of two straight lines (straight line guided wave structures) with different lengths, and fig. 4 is a top view of a short line structure based on a non-grounded coplanar waveguide in an embodiment of the present invention.
As shown in fig. 3 and 4, in the testing apparatus under a group of linear waveguide structures with different lengths shown in this embodiment, the apparatus is fixed at two ends of a material to be tested 2 by high-frequency microwave connectors 1, the material to be tested 2 and the high-frequency microwave connectors 1 may be fixed by welding or directly clamping, and the upper surface of the material to be tested 2 is a metal copper surface 3. Under the test of the test device, an error frame 4 is formed at the joint of the two ends of the material 2 to be tested and the high-frequency microwave connector 1.
The method is experimentally verified by taking a widely-used microwave dielectric material FR4 as a test material. This example was tested by making two ungrounded coplanar waveguide straight line samples of 50 mm and 100 mm length, respectively. The FR4 material is 0.5 mm thick with 18 micron thick copper etched on one side, the signal line width S and the gap W are 1.3 mm and 0.16 mm respectively, and the two SMA coaxial connectors are carefully soldered onto the two straight structures so that they have nearly identical soldering effects, thereby ensuring that their mechanical and electrical properties are close.
Further, the two straight lines thus produced were measured by a Vector Network Analyzer (VNA) N5247A to obtain scattering parameter results of the two straight lines, which were then expressed by the equation
Figure BDA0002581075650000111
Converted into ABCD matrix, the ABCD matrix of long straight line and short straight line are respectively expressed as
Figure BDA0002581075650000112
And
Figure BDA0002581075650000113
further, the ABCD matrix of the long straight line and the short straight line is used for deducing the phase number beta based on the double-line optimization, so that the structure effective dielectric constant is further deducedeffThe equation is:
Figure BDA0002581075650000114
to illustrate the superiority of the two-wire optimization method, the results of the calculation using a single wire are also presented here. Respectively calculating respective phase number beta according to the ABCD matrix of the long straight line and the short straight line, thereby further deducing the effective dielectric constant of each structureeffThe equation used is:
Figure BDA0002581075650000115
phase number beta and effective dielectric constant obtained based on double-line optimization, long straight line and short straight lineeffThe results are shown in FIGS. 5 and 6.
Further, the dielectric constant of the dielectric substrate is utilizedrAnd the resulting effective dielectric constanteffCalculating the medium according to the following relationDielectric constant of substrater：
Figure BDA0002581075650000121
Where q is the fill factor of the selected structure. For the ungrounded coplanar waveguide structure described in fig. 2 and 3, the fill factor q can be calculated by the following equation:
Figure BDA0002581075650000122
where K is the complete elliptic integral of the first class, K'0And k'1Is and a modulus k0And k1The associated complementary mode is given by the following equation:
Figure BDA0002581075650000123
Figure BDA0002581075650000124
Figure BDA0002581075650000125
wherein, S and W are respectively the signal line width and the gap width of the ungrounded coplanar waveguide, and H is the thickness of the dielectric substrate. K (K)/K (K '), K (K) and K' (K) can be calculated by the following equations:
Figure BDA0002581075650000126
Figure BDA0002581075650000127
Figure BDA0002581075650000128
Figure BDA0002581075650000129
Figure BDA00025810756500001210
finally, the dielectric constant of the dielectric substrate is obtained based on double-line optimization, long straight line and short straight line derivationrThe results are shown in FIG. 7, and FIG. 8 shows the dielectric constant of the dielectric substrate obtained by the two-line optimizationrEnlarged view of (a). The dielectric constant of the dielectric substrate at 10GHz obtained based on the double-line optimization, long straight line and short straight line can be knownrThe values were 17.37, 9.95 and 4.37, respectively. Since the supplier supplies the material at 10ghzrIs 4.4, thus extracted based on an optimized two-line algorithmrApparently closer to the reference value, the difference between the two is only-0.03 (0.68%) to-0.07 (1.59%) in an extremely wide frequency band (4 to 20 GHz).
Further, the ABCD matrix of the long straight line and the short straight line is used for deducing the linear loss alpha based on the double-line optimization, and the expression is as follows:
Figure BDA0002581075650000131
establishing a linear loss alpha and a conductor loss alpha based on a two-wire optimizationcRadiation loss alpharDielectric loss alphadCalculating the dielectric loss alpha from the relationship of (A)dAnd deducing the dielectric loss tangent tan of the dielectric substrate, wherein the specific details are as follows:
the dielectric loss αdThe calculation expression of (a) is as follows:
αd＝α-αc-αr
the calculation expression of the dielectric loss tangent tan of the dielectric substrate is as follows:
Figure BDA0002581075650000132
the conductor loss αcThe calculation expression of (a) is as follows:
Figure BDA0002581075650000133
wherein the characteristic impedance
Figure BDA0002581075650000134
Distributed series resistance of central signal conductor
Figure BDA0002581075650000135
Distributed series resistance of ground plane
Figure BDA0002581075650000136
Figure BDA0002581075650000137
T is the thickness of the metal conductor, the skin effect resistance
Figure BDA0002581075650000138
σ and μ are skin depth, conductivity of metal conductor, and permeability of free space, respectively, and
Figure BDA0002581075650000139
the radiation loss αrThe calculation expression of (a) is as follows:
Figure BDA00025810756500001310
wherein the radiation factor
Figure BDA00025810756500001311
Wavelength of medium
Figure BDA00025810756500001312
Finally, the total linear loss alpha and the conductor loss alpha are obtained based on a double-line optimization methodcRadiation loss alpharDielectric loss alphadThe results are shown in FIG. 9, and FIG. 10 is derived based on a two-line optimizationAnd (5) obtaining the dielectric loss tangent value tan of the dielectric substrate. As can be seen from fig. 8, the radiation loss and the conductor loss account for only a small portion of the total loss, and the main source of the loss is the dielectric loss of the substrate, and increases with increasing frequency. As can be seen from fig. 10, the value of tan gradually increased from 0.0186 to 0.0214 between 8 and 20GHz, with a difference of 0.0014 (7%) compared to the 10GHz reference value (0.02) provided by the supplier. The tan value extracted at 10GHz was 0.0199, the difference compared to the reference value was 0.0001 (0.5%). The extraction accuracy below 8GHz becomes relatively poor because at low frequencies the electrical length of the corresponding straight line is too small. The method has higher material parameter extraction precision than other methods commonly used in the literature.
Further, since this example uses SMA coaxial connectors, the dielectric substrate material properties were characterized only at frequencies below 20 GHz. The proposed algorithm is based on quasi-TEM approximation and can achieve the extraction of the properties of dielectric materials at higher frequencies if the quasi-TEM wave assumption is satisfied and good millimeter wave connector (e.g., 2.92mm connector) welding accuracy is achieved.
Further, this example demonstrates the effectiveness of the method in the frequency range below 20GHz, which accurately inverts the complex permittivity of the media substrate with extraction errors of permittivity and dielectric loss tangent of 0.68% (4.37vs 4.4) and 0.5% (0.0199vs 0.02), respectively. The error sources are mainly caused by the fact that the connection and welding of the long and short wires are not identical, and in addition, errors from oxidation and preparation of the metal surface exist. The method is also suitable for other wave guide structures, after differential phase and effective dielectric constant are deduced, various losses are accurately separated by combining the structure size, and the dielectric constant and the dielectric loss tangent value of the dielectric substrate can be extracted.
While the invention has been illustratively described with reference to the results of dielectric parameter extraction and experiments performed on dielectric substrates based on ungrounded coplanar waveguides, as mentioned in the present application, the implementation of the invention is not limited to the above examples, and various modifications made by the method concept and technical solution of the invention are within the scope of the present invention.
Therefore, the method for representing the broadband continuous dielectric characteristic of the microwave medium substrate based on the ABCD matrix with the double-line optimization is simple in structure, easy to implement, high in accuracy and wide in application prospect.
The technical features of the above embodiments can be arbitrarily combined, and for the sake of brevity, all possible combinations of the technical features in the above embodiments are not described, but should be considered as the scope of the present specification as long as there is no contradiction between the combinations of the technical features.
It should be noted that the terms "first \ second \ third" referred to in the embodiments of the present application merely distinguish similar objects, and do not represent a specific ordering for the objects, and it should be understood that "first \ second \ third" may exchange a specific order or sequence when allowed. It should be understood that "first \ second \ third" distinct objects may be interchanged under appropriate circumstances such that the embodiments of the application described herein may be implemented in an order other than those illustrated or described herein.
The terms "comprising" and "having" and any variations thereof in the embodiments of the present application are intended to cover non-exclusive inclusions. For example, a process, method, apparatus, product, or device that comprises a list of steps or modules is not limited to the listed steps or modules but may alternatively include other steps or modules not listed or inherent to such process, method, product, or device.
The above-mentioned embodiments only express several embodiments of the present application, and the description thereof is more specific and detailed, but not construed as limiting the scope of the invention. It should be noted that, for a person skilled in the art, several variations and modifications can be made without departing from the concept of the present application, which falls within the scope of protection of the present application. Therefore, the protection scope of the present patent shall be subject to the appended claims.

Claims (10)

1. A method for detecting broadband continuous dielectric characteristic parameters of a microwave dielectric substrate is characterized by comprising the following steps:
s10, building a testing device based on the two linear guided wave structures, and fixing two ends of a material to be tested on the testing device through a group of high-frequency microwave connectors; the two ends of the linear guided wave structure are provided with high-frequency microwave connectors so that the testing device is connected with the linear guided wave structure; the two linear guided wave structures comprise a first linear guided wave structure and a second linear guided wave structure, and the length of the first linear guided wave structure is greater than that of the second linear guided wave structure;
s20, respectively testing the two linear guided wave structures by using a vector network analyzer to obtain scattering parameters of the two linear guided wave structures;
s30, converting scattering parameters of the two linear guided wave structures into corresponding ABCD matrixes to obtain a first ABCD matrix corresponding to the first linear guided wave structure and a second ABCD matrix corresponding to the second linear guided wave structure;
s40, calculating according to the first ABCD matrix and the second ABCD matrix to obtain an optimized comprehensive phase number and linear loss, and determining an effective dielectric constant according to a comprehensive phase number-effective dielectric constant equation; the phase number-effective dielectric constant equation records the relationship between the integrated phase number and the effective dielectric constant;
s50, determining the dielectric constant of the dielectric substrate of the material to be measured according to the effective dielectric constant;
s60, obtaining conductor loss and radiation loss of the linear wave guide structure, calculating dielectric loss according to the linear loss, the conductor loss and the radiation loss, and determining dielectric loss tangent of the dielectric substrate according to the dielectric loss, the effective dielectric constant and the dielectric constant of the dielectric substrate.
2. The method for detecting the broadband continuous dielectric characteristic parameter of the microwave dielectric substrate according to claim 1, wherein the ABCD matrix comprises:
Figure FDA0002581075640000011
in the formulaA denotes a first parameter of the ABCD matrix, B denotes a second parameter of the ABCD matrix, C denotes a third parameter of the ABCD matrix, D denotes a fourth parameter of the ABCD matrix, S11Representing the input reflection coefficient, S12Representing the reverse transmission coefficient, S21Denotes the forward transmission coefficient, S22Representing the output reflection coefficient, ZcRepresenting the linear characteristic impedance of the linear guided wave structure.
3. The method for detecting the broadband continuous dielectric characteristic parameter of the microwave dielectric substrate according to claim 1, wherein the comprehensive phase calculation formula comprises:
Figure FDA0002581075640000021
the calculation formula of the linear loss comprises:
Figure FDA0002581075640000022
wherein β represents the number of integrated phases, α represents the linear loss, and AL1First matrix parameters, D, representing a first ABCD matrixL1Fourth matrix parameter, A, representing the first ABCD matrixS1First matrix parameters, D, representing a second ABCD matrixS1A fourth matrix parameter representing the second ABCD matrix, Re representing the real part, Im representing the imaginary part, L1Denotes the linear length, S, of the first linear waveguide structure1Indicating the linear length of the second linear short waveguide structure.
4. The method for detecting the broadband continuous dielectric characteristic parameter of the microwave dielectric substrate as claimed in claim 3, wherein the equation of phase number-effective dielectric constant includes:
Figure FDA0002581075640000023
in the formula (I), the compound is shown in the specification,effequation representing effective dielectric constantF denotes the operating frequency and c denotes the speed of light.
5. The method for detecting the broadband continuous dielectric characteristic parameter of the microwave dielectric substrate as claimed in claim 4, wherein the formula for calculating the dielectric constant of the dielectric substrate comprises:
Figure FDA0002581075640000024
in the formula (I), the compound is shown in the specification,rdenotes the dielectric constant of the dielectric substrate, and q denotes the fill factor of the linear waveguide structure.
6. The method for detecting the broadband continuous dielectric characteristic parameter of the microwave dielectric substrate according to claim 1, wherein the formula for calculating the dielectric loss comprises:
αd＝α-αc-αr，
the calculation formula of the dielectric loss tangent of the dielectric substrate comprises the following steps:
Figure FDA0002581075640000025
in the formula, alphadDenotes dielectric loss, αcRepresenting conductor loss, αrDenotes the radiation loss, tan denotes the dielectric loss tangent of the dielectric substrate,effrepresenting the effective dielectric constant equation, f the operating frequency, c the speed of light,rdenotes the dielectric constant of the dielectric substrate, and q denotes the fill factor of the linear waveguide structure.
7. The method for detecting the broadband continuous dielectric characteristic parameter of the microwave dielectric substrate according to claim 6, wherein the calculation formula of the conductor loss comprises:
Figure FDA0002581075640000031
in the formula, RcRepresenting the distributed series resistance, R, of the central signal conductorgRepresenting distributed series resistance of ground plane, ZcThe characteristic impedance of the waveguide structure is represented by the following calculation formula:
Figure FDA0002581075640000032
Figure FDA0002581075640000033
where T is the thickness of the metal conductor, the skin effect resistance
Figure FDA0002581075640000034
σ and μ are skin depth, conductivity of metal conductor, and permeability of free space, respectively, and
Figure FDA0002581075640000035
k0display module
Figure FDA0002581075640000036
Wherein S represents the line width of the central signal conductor, W represents the distance between the central signal conductor and the ground plane, and k0' representation and modulus k0The associated complementary modes, K, represent the first class of perfect elliptic integrals.
8. The method for detecting the broadband continuous dielectric characteristic parameter of the microwave dielectric substrate according to claim 6, wherein the formula for calculating the radiation loss comprises:
Figure FDA0002581075640000037
Figure FDA0002581075640000038
Figure FDA0002581075640000039
where superscript' denotes the complementary mode.
9. The method according to claim 1, wherein the length of the first linear guided wave structure is 2 times or more the length of the second linear guided wave structure.
10. The method for detecting the broadband continuous dielectric characteristic parameter of the microwave dielectric substrate as claimed in claim 1, wherein the fixing and installation of the material to be tested in the testing device comprises a fixing mode of welding or direct clamping.
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