CN109581069B - Complex dielectric constant calculation method of microwave material under high temperature and wide frequency - Google Patents
Complex dielectric constant calculation method of microwave material under high temperature and wide frequency Download PDFInfo
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Abstract
The embodiment of the invention provides a method for calculating a complex dielectric constant of a microwave material under high-temperature broadband, which comprises the following steps: s1, acquiring microwave test data at a test temperature and a test frequency range, and calculating the forward two-port impedance of the microstrip line covered with the heat insulation cushion layer structure by using a forward transmission reflection method based on the microwave test data and the microstrip line two-port network covered with the heat insulation cushion layer structure; s2, calculating the reverse two-port impedance of the microstrip line covered with the heat insulation cushion layer structure when the microstrip line is covered by the microwave material to be measured by using a variational capacitance calculation method; s3, based on the equivalence relation between the forward two-port impedance and the reverse two-port impedance of the microstrip line covered with the heat insulation cushion layer structure, the complex dielectric constant of the microwave material to be tested in the test temperature and test frequency range is solved. The embodiment of the invention can accurately calculate the complex dielectric constant of the microwave material under high temperature and broadband states, and provides reliable data support for the application of the high temperature and broadband microwave material.
Description
Technical Field
The invention relates to the technical field of microwave testing, in particular to a complex dielectric constant calculation method of a microwave material under high temperature and broadband.
Background
With the rapid development of scientific and technological technology and communication technology, microwave materials are widely applied in many fields such as radar navigation, aerospace, microwave communication, national defense and military industry, electronic technology, new materials and the like. However, in the process of using the dielectric material, the temperature of the dielectric material is often increased, and the frequency band of the surrounding environment is often changed. The increase of temperature and the change of environmental frequency band bring about the change of complex dielectric constant of the dielectric material and further influence the accuracy of the test result. Therefore, it is very important to accurately and efficiently measure the complex dielectric constant of the dielectric material under the conditions of high temperature and wide frequency band.
Because the microstrip line has simple structure, convenient processing and wider transmission frequency band, the microstrip line method is often selected in the actual process of measuring the complex dielectric constant. At present, when a microstrip line is used for measuring the complex dielectric constant of a medium, the complex dielectric constant of a microwave material can be measured only under the condition of normal temperature, and a microstrip line measuring clamp is needed to fix a sample to be measured, namely the sample to be measured is needed to be in direct contact with the microstrip line.
However, when high temperature measurement of a sample to be tested is performed, the sample needs to be heated to a higher temperature, and measurement result inaccuracy and even damage of a measurement clamp can be caused. Therefore, the traditional microstrip line method is not suitable for measuring the complex dielectric constant of the microwave material at high temperature. Therefore, it is necessary to perform a high-temperature microwave test on the microwave material by changing the structure type of the microstrip line clamp. Then the traditional algorithm for measuring the complex dielectric constant by the microstrip line method is not applicable any more, which can cause larger deviation of the calculation result and even serious errors.
Disclosure of Invention
In order to overcome the above problems or at least partially solve the above problems, the present invention provides a method for calculating the complex dielectric constant of a microwave material at a high temperature and a wide frequency band, so as to better perform an accurate calculation of the complex dielectric constant of the microwave material at a high temperature and in a frequency conversion state.
The invention provides a complex dielectric constant calculation method of a microwave material under high temperature and broadband, which comprises the following steps:
s1, acquiring microwave test data at a test temperature and a test frequency range, and calculating the forward two-port impedance of the microstrip line covered with the heat insulation cushion layer structure by using a forward transmission reflection method based on the microwave test data and the two-port network of the microstrip line covered with the heat insulation cushion layer structure;
s2, calculating the reverse port impedance of the microstrip line covered with the heat insulation cushion layer structure by using a variational capacitance calculation method;
and S3, solving the complex dielectric constant of the microwave material to be tested in the test temperature and test frequency range based on the equivalent relation between the forward port impedance and the reverse port impedance of the microstrip line covered with the heat insulation cushion layer structure.
Wherein the step of S2 further comprises: and calculating the capacitance of the microstrip line covered with the heat insulation cushion structure relative to the microstrip line capacitance of the complex dielectric constant of the microwave material to be detected after the microwave material to be detected is added to the microstrip line covered with the heat insulation cushion structure in the microstrip line testing process by using an inverse variation component capacitance method, and calculating the inverse two-port impedance of the microstrip line covered with the heat insulation cushion structure based on the microstrip line capacitance and the transformation relation between the impedance and the capacitance.
The step of calculating the capacitance of the microstrip line covered with the heat insulation cushion structure with respect to the complex dielectric constant of the microwave material to be tested after the microwave material to be tested is added to the microstrip line covered with the heat insulation cushion structure in the microstrip line testing process specifically includes:
after the microwave material to be detected is added to the microstrip line covered with the heat insulation cushion structure, potential functions and boundary conditions corresponding to each layer of lamination of the microstrip line covered with the heat insulation cushion structure are determined, Fourier transformation is carried out on the potential functions, a capacitance value with a differential form is converted and solved according to the Pasteval theorem, and the microstrip line capacitance of the microstrip line covered with the heat insulation cushion structure relative to the complex dielectric constant of the microwave material to be detected is obtained.
Wherein the step of determining the boundary condition specifically comprises:
if the thickness of the microwave material to be tested is increased in the high-temperature testing process, calculating the thickness of the microwave material to be tested according to the following formula:
t＝t0+Temp×ρ×t0；
in the formula, t0The thickness of the microwave material to be tested is represented under the normal temperature condition, Temp represents the testing temperature, and rho represents the expansion coefficient of the microwave material to be tested.
The heat insulation cushion layer is specifically an air layer or a heat insulation medium layer.
The complex dielectric constant calculation method of the microwave material under the high temperature and the wide frequency provided by the invention is based on microwave test data in a high temperature and wide frequency test process, and respectively utilizes a forward transmission reflection method, a variable division capacitance calculation method and an equivalent relation of forward and reverse two-port impedances of a microstrip line to calculate the complex dielectric constant of the microwave material to be tested under the test temperature and the test frequency range, so that the complex dielectric constant of the microwave material under the high temperature and wide frequency state can be accurately calculated, and reliable data support is provided for the application of the microwave material.
Drawings
FIG. 1 is a schematic flow chart illustrating a method for calculating a complex dielectric constant of a microwave material at a high temperature and a wide frequency according to an embodiment of the present invention;
fig. 2 is a schematic diagram of a theoretical model of a microstrip line two-port network in a method for calculating a complex dielectric constant of a microwave material under high-temperature and wide-frequency conditions according to an embodiment of the present invention;
fig. 3 is a schematic cross-sectional view of a capacitor with a thermal insulating pad layer added in a method for calculating a complex dielectric constant of a microwave material under high temperature and broadband according to an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention clearer, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. All other embodiments, which can be obtained by a person skilled in the art without any inventive step based on the embodiments of the present invention, are within the scope of the present invention.
As an embodiment of the present invention, the present embodiment provides a method for calculating a complex dielectric constant of a microwave material under a high temperature and a wide frequency band, and referring to fig. 1, a schematic flow chart of the method for calculating a complex dielectric constant of a microwave material under a high temperature and a wide frequency band of the present invention includes:
s101, microwave test data under a test temperature and a test frequency range are obtained, and forward two-port impedance of the microstrip line covered with the heat insulation cushion layer structure is calculated by utilizing a forward transmission reflection method based on the microwave test data and the two-port network of the microstrip line covered with the heat insulation cushion layer structure.
It can be understood that, first, in the course of performing a microwave test of a microwave material to be tested, microwave test data at a test temperature and a test frequency range are acquired. And then, based on the microwave test data and the two-port network of the microstrip line covered with the heat insulation cushion layer structure, performing transmission reflection method calculation to obtain the impedance of the two-port microstrip line clamp, namely the forward two-port impedance of the microstrip line covered with the heat insulation cushion layer structure.
It should be noted that, for convenience of description, the microstrip line coated with the thermal insulation pad structure may be simply referred to as a microstrip line hereinafter.
Fig. 2 is a schematic diagram of a two-port microstrip line network, which is a theoretical model schematic diagram of a two-port microstrip line network in a complex dielectric constant calculation method for a microwave material under a high-temperature broadband according to an embodiment of the present invention. Electromagnetic wave signals are input from a port 201 and output from a port 202, wherein (i) the electromagnetic wave signals indicate no-load areas of the microstrip lines, and (ii) the electromagnetic wave signals indicate areas of the microstrip lines where samples are placed, and (l) the electromagnetic wave signals indicate the areas of the microstrip lines where the samples are placed0And (c) indicating the width of the no-load area, and l indicating the width of the sample, namely the microwave material to be detected. The reflection constant at the interface is represented by R, and the microwave test data by S, including S11And S21. Wherein S11Representing the input reflection coefficient, S21Representing the forward transmission coefficient, the scattering parameter T can be obtained from the cascaded network as follows:
in the formula, k0The propagation constants of the regions (i) and (iii) are shown, and k is a propagation constant in the sample region.
Meanwhile, solving a formula and a transformation relation between the scattering parameters T and the microwave test data S according to the scattering parameters:
the relationship between the obtained microwave test data S and the reflection coefficient R and the propagation constant is as follows:
finally, according to the reflection coefficient R and the microstrip line forward two-port impedance ZcThe transformation relation of (1) backward-pushing the microstrip line forward two-port impedance Zc1：
And S102, solving the reverse two-port impedance of the microstrip line covered with the heat insulation cushion layer structure by using a variational solution capacitance method.
It can be understood that, in this step, on the basis of assuming that the parameters of the microstrip line, the added thermal insulation cushion layer and the complex dielectric constant of the microwave material to be measured are known, the expression C of the microstrip line capacitance of the microstrip line clamp with respect to the complex dielectric constant of the microwave material to be measured is obtained by using a variational capacitance calculation method (step C)r3). And, combining the transformation relationship between impedance and capacitance, according to the expression C (of microstrip line capacitance)r3) Calculating the expression Z of the reverse two-port impedance of the microstrip line with respect to the complex dielectric constant of the microwave material to be measuredc2(r3)。
Optionally, when calculating the microstrip line reverse two-port impedance according to step S102, a variable-division capacitance method may be first used to calculate a microstrip line capacitance of the microstrip line clamp with respect to the complex dielectric constant of the microwave material to be measured after adding the thermal insulation cushion layer and the microwave material to be measured in the microstrip line testing process, and then calculate the microstrip line reverse two-port impedance based on the microstrip line capacitance and the transformation relationship between the impedance and the capacitance.
S103, solving the complex dielectric constant of the microwave material to be tested in the test temperature and test frequency range based on the equivalent relation between the forward two-port impedance and the reverse two-port impedance of the microstrip line covered with the heat insulation cushion layer structure.
It can be understood that, on the basis of theoretical calculation, the impedance values of the microstrip lines obtained by the forward solution and the backward solution are equal, that is, the impedance of the forward port of the microstrip line is equal to the impedance of the backward port of the microstrip line:
Zc2(r3)＝Zc1。
the complex dielectric constant of the microwave material to be measured in the test temperature and test frequency range can be calculatedr3。
The measuring steps of the high-temperature broadband complex dielectric constant of the dielectric material can be simplified and expressed as follows:
placing the medium to be measured, namely the microwave material to be measured, on the microstrip line with the heat insulation powder, and measuring S at the moment11Parameter and S21Calculating two-port impedance Z by using parameters and applying transmission reflection method theoryc1；
Calculating the port impedance Z of the microstrip line covered with the material to be measured and the heat insulation cushion layer by using a variational methodc2(r3) And calculating the complex dielectric constant Z of the microwave material to be tested in the test temperature and test frequency rangec2(r3)＝Zc1。
According to the method for calculating the complex dielectric constant of the microwave material under the high-temperature broadband, provided by the embodiment of the invention, based on microwave test data in a high-temperature broadband test process, a forward transmission reflection method and a reverse variation capacitance calculation method are respectively utilized, and the equivalent relation of forward and reverse two-port impedance of a microstrip line covered with a heat insulation cushion layer structure is utilized to calculate the complex dielectric constant of the microwave material to be measured under the test temperature and the test frequency range, so that the complex dielectric constant of the microwave material can be accurately calculated under the high-temperature and frequency conversion states, and reliable data support is provided for the application of the microwave material.
Optionally, after the heat insulation cushion layer and the microwave material to be tested are added in the microstrip line testing process according to the calculation of each embodiment, the microstrip line resistance of the microstrip line covered with the heat insulation cushion layer structure and related to the complex dielectric constant of the microwave material to be tested may be converted into a mode of obtaining the capacitance of the microstrip line:
the microstrip line fixture with the heat-insulating layer medium structure has the following impedance-capacitance conversion relation, namely the microstrip line reverse two-port impedance Z of the microstrip line fixture with the heat-insulating layer medium structure relative to the complex dielectric constant of the microwave material to be measuredc2(r)：
Wherein c represents the speed of light, 3X 108m/s，C(r3) Microstrip line capacitance, C, for placing sample to be measured and heat-insulating powder0Representing the capacitance of the air microstrip line.
The capacitance of an air microstrip line can be directly obtained by the following equation:
C0＝1/cZ0
wherein the air microstrip line impedance can be directly expressed by the following formula:
in the formula, w represents the microstrip line conduction band width, and h represents the dielectric layer height.
After adding the heat insulation powder and the material to be measured, determining the transformation relation between the microstrip line capacitance with the heat insulation layer dielectric structure and the potential function and the intermediate variable in the solving process according to the following dielectric capacitance solving formula:
in the formula, Q represents a unit-length charge on a microstrip line conduction band with a thermal insulation layer dielectric structure, and the expression is as follows:
in the formula, ρ (x) represents a charge distribution function.
The charge distribution function is a heuristic function, chosen so that it is an even function, and is smallest at the center of the conduction band and largest on both sides. In one embodiment, the charge distribution function is chosen as follows:
fig. 3 is a schematic cross-sectional view of a capacitor with a thermal insulation pad layer added in a method for calculating a complex dielectric constant of a microwave material under high temperature and broadband according to an embodiment of the present invention, in which a layer 301 represents a microstrip line dielectric layer, a layer 302 represents a thermal insulation pad layer, a layer 303 represents a measured microwave material layer, and a layer 304 represents an air layer. Then, the capacitance is solved according to the variational method, and the solved potential function is as follows:
in the formula (I), the compound is shown in the specification,
represents the potential function, ρ (x) represents the charge distribution function, and (y-h) represents the dirac function, which represents the complex permittivity for each layer to be solved.
And then, carrying out Fourier transform on the potential function, solving a formula according to the dielectric capacitance, solving a conversion relation between an intermediate variable and each potential function, boundary conditions and the complex dielectric constant of the microwave material to be detected in the process, and simultaneously obtaining the microstrip line capacitance of the microstrip line clamp with the heat insulation layer dielectric structure relative to the complex dielectric constant of the microwave material to be detected according to the Pasteval theorem.
It can be understood that the potential function solving formula is subjected to fourier transform, and the potential function in the area of 301 layer is solved according to the difference between the potential function and the boundary condition after the thermal insulation pad layer and the microwave material to be measured are covered. Namely, after a layer of heat insulation cushion layer and a microwave material to be measured are added, the original potential function boundary condition with the Laplace operator and the solving area are changed. And (3) carrying out test calculation and measurement process correction by adopting a quasi-static method principle.
From the above equation, it can be known that in 4-layer media, the fourier transform is performed on the potential function at the same time, and the general solution is:
in region 1, the potential function is generally solved as:
in region 2, the potential function is generally solved as:
in region 3, the potential function is generally solved as:
in the 4 region, the potential function is generally solved as:
wherein the content of the first and second substances,
is that
After fourier transformation.
Where h denotes a 301 layer material thickness, d denotes a 302 layer material thickness, t denotes a 303 layer material thickness,0representing the value of the dielectric constant in vacuum.
Wherein, the material expands under high temperature, and the t value is as follows:
t＝t0+Temp×ρ×t0。
wherein, t0The thickness of the microwave material to be tested under the normal temperature condition is shown, Temp shows the testing temperature, and rho shows the expansion coefficient of the microwave material to be tested.
And simultaneously determining potential functions and boundary conditions corresponding to each layer of the laminated layers of the microstrip line clamp with the thermal insulation layer medium structure after the thermal insulation cushion layer and the microwave material to be detected are added.
It can be understood that after the thermal insulation cushion layer is added and the microwave material to be measured is placed, each potential function of the microstrip line and the boundary conditions corresponding to each potential function in different layers are changed:
wherein the content of the first and second substances,r1representing the complex permittivity values of layer 301,r2representing the complex permittivity values of layer 302,r3representing the complex permittivity values of layer 303,r4the complex permittivity values of 304 layers are expressed, and after the boundary conditions are substituted into the general solution of the potential function, the following can be obtained:
wherein:
and finally, obtaining the following expression of the microstrip line capacitance covered with the dielectric material on the complex dielectric constant of the microwave material to be detected:
wherein:
before the complex permittivity calculation of the above embodiment is performed, the microwave test data at the test temperature and the test frequency needs to be measured by using the corresponding test device.
In addition, it should be understood by those skilled in the art that the terms "comprises," "comprising," or any other variation thereof, in the specification of the present invention, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising an … …" does not exclude the presence of other identical elements in a process, method, article, or apparatus that comprises the element.
In the description of the present invention, numerous specific details are set forth. However, it is understood that embodiments of the invention may be practiced without these specific details. In some instances, well-known methods, structures and techniques have not been shown in detail in order not to obscure an understanding of this description. Similarly, it should be appreciated that in the foregoing description of exemplary embodiments of the invention, various features of the invention are sometimes grouped together in a single embodiment, figure, or description thereof for the purpose of streamlining the disclosure and aiding in the understanding of one or more of the various inventive aspects.
However, the disclosed method should not be interpreted as reflecting an intention that: that the invention as claimed requires more features than are expressly recited in each claim. Rather, as the following claims reflect, inventive aspects lie in less than all features of a single foregoing disclosed embodiment. Thus, the claims following the detailed description are hereby expressly incorporated into this detailed description, with each claim standing on its own as a separate embodiment of this invention.
Finally, it should be noted that: the above examples are only intended to illustrate the technical solution of the present invention, but not to limit it; although the invention has been described in detail with reference to the foregoing embodiments, it will be understood by those skilled in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; and such modifications or substitutions do not depart from the spirit and scope of the corresponding technical solutions of the embodiments of the present invention.
Claims (3)
1. A method for calculating the complex dielectric constant of a microwave material under high temperature and broadband conditions is characterized by comprising the following steps:
s1, acquiring microwave test data at a test temperature and a test frequency range, and calculating the forward two-port impedance of the microstrip line covered with the heat insulation cushion layer structure by using a forward transmission reflection method based on the microwave test data and the two-port network of the microstrip line covered with the heat insulation cushion layer structure;
s2, calculating the reverse port impedance of the microstrip line covered with the heat insulation cushion layer structure by using a variational capacitance calculation method;
s3, solving the complex dielectric constant of the microwave material to be tested in the test temperature and test frequency range based on the equivalent relation between the forward two-port impedance and the reverse two-port impedance of the microstrip line covered with the heat insulation cushion layer structure;
wherein the step of S2 further comprises:
calculating the capacitance of the microstrip line covered with the heat insulation cushion structure relative to the microstrip line with the complex dielectric constant of the microwave material to be detected after the microwave material to be detected is added to the microstrip line covered with the heat insulation cushion structure in the microstrip line testing process by using a reverse variation component capacitance calculating method, and calculating the reverse two-port impedance of the microstrip line covered with the heat insulation cushion structure based on the capacitance of the microstrip line and the transformation relation between the impedance and the capacitance;
the step of calculating the capacitance of the microstrip line covered with the heat insulation cushion structure with respect to the complex dielectric constant of the microwave material to be tested after the microwave material to be tested is added to the microstrip line covered with the heat insulation cushion structure in the microstrip line testing process specifically comprises the following steps:
after the microwave material to be detected is added to the microstrip line covered with the heat insulation cushion structure, potential functions and boundary conditions corresponding to each layer of lamination of the microstrip line covered with the heat insulation cushion structure are determined, Fourier transformation is carried out on the potential functions, a capacitance value with a differential form is converted and solved according to the Pasteval theorem, and the microstrip line capacitance of the microstrip line covered with the heat insulation cushion structure relative to the complex dielectric constant of the microwave material to be detected is obtained.
2. The method according to claim 1, wherein the step of determining the boundary condition specifically comprises:
if the thickness of the microwave material to be tested is increased in the high-temperature testing process, calculating the thickness of the microwave material to be tested according to the following formula:
t＝t0+Temp×ρ×t0；
in the formula, t0The thickness of the microwave material to be tested is represented under the normal temperature condition, Temp represents the testing temperature, and rho represents the expansion coefficient of the microwave material to be tested.
3. Method according to any one of claims 1-2, characterized in that the insulating blanket is in particular a layer of air or a layer of insulating medium.
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| CN111157580A (en) * | 2020-01-10 | 2020-05-15 | 青岛兴仪电子设备有限责任公司 | High-temperature material electromagnetic parameter measurement system and method based on fixture de-embedding |
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