CN110609248A - Coaxial resonant cavity calibration method and system based on multiple reference samples - Google Patents
Coaxial resonant cavity calibration method and system based on multiple reference samples Download PDFInfo
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Abstract
The invention provides a method and a system for calibrating a coaxial resonant cavity based on multiple reference samples, wherein a vector network analyzer and the coaxial resonant cavity are connected through a connecting cable, a cavity is excited to obtain a resonance curve, and the resonance frequency and the quality factor of the cavity are obtained; loading a first reference sample with a certain dielectric constant, and recording the variation of the resonant frequency relative to the resonant frequency and the quality factor of the cavity; loading another second reference sample with the dielectric constant of the second reference sample, and recording the variation of the resonant frequency relative to the resonant frequency and the quality factor of the cavity; solving the constant according to the relation among the dielectric constant, the resonance frequency and the quality factor variable quantity, and completing the solution of the calibration constant; and loading a sample to be tested, recording the variation of the resonant frequency relative to the resonant frequency and the quality factor of the cavity, and combining the calibration constant to obtain the dielectric constant and the loss tangent of the sample to be tested so as to finish the calibration of the coaxial resonant cavity.
Description
Technical Field
The disclosure belongs to, and particularly relates to a coaxial resonant cavity calibration method and system based on multiple reference samples.
Background
The statements in this section merely provide background information related to the present disclosure and may not necessarily constitute prior art.
Microwave dielectric materials have been widely used in various fields of microwaves as electromagnetic wave transmission media, and systems such as microwave communication, satellite communication, missile guidance, electronic countermeasure, radar navigation, remote sensing, remote measurement and the like have largely used microwave dielectric materials. The dielectric constant of a dielectric material characterizes the interaction of the material with an electromagnetic field. The dielectric constant test has more and more important significance with the wide application of dielectric materials. Compared with other methods, the material dielectric constant testing method based on the coaxial resonant cavity has the advantages of high testing precision, capability of testing a plurality of frequency points at one time, convenience in testing and the like.
The basic principle of the coaxial resonant cavity material testing method is to invert the dielectric constant of the material by utilizing the resonant frequency change before and after loading of the dielectric material, and the calibration method is the key point of realizing high-precision testing of the coaxial resonant cavity. However, according to the knowledge of the inventor, a dielectric constant inversion formula is deduced based on the terminal capacitance equivalence principle of the coaxial resonant cavity at present, for the coaxial resonant cavity, a sample area is located outside an open end surface, an electromagnetic field of the area belongs to a radiation field, and an electromagnetic field expression is required to be accurately written, so that the test precision is relatively difficult, the test precision is relatively low, and particularly under a high-frequency test, the capacitance equivalence method has relatively large error, so that the dielectric constant test precision adopting the calibration technology cannot reach 2%.
Disclosure of Invention
The invention provides a method and a system for calibrating a coaxial resonant cavity based on multiple reference samples, which aim to solve the problems and adopt a quasi-static equivalent principle to realize accurate calibration of the coaxial resonant cavity by utilizing multiple reference samples for multiple tests on the premise of not increasing any hardware cost, thereby improving the extraction precision of the dielectric constant.
According to some embodiments, the following technical scheme is adopted in the disclosure:
a coaxial resonant cavity calibration method based on multiple reference samples comprises the following steps:
connecting the vector network analyzer and the coaxial resonant cavity through a connecting cable, exciting the cavity to obtain a resonant curve, and obtaining the resonant frequency and the quality factor of the cavity;
loading a first reference sample with a certain dielectric constant, and recording the variation of the resonant frequency relative to the resonant frequency and the quality factor of the cavity;
loading another second reference sample with the dielectric constant of the second reference sample, and recording the variation of the resonant frequency relative to the resonant frequency and the quality factor of the cavity;
solving the constant according to the relation among the dielectric constant, the resonance frequency and the quality factor variable quantity, and completing the solution of the calibration constant;
and loading a sample to be tested, recording the variation of the resonant frequency relative to the resonant frequency and the quality factor of the cavity, and combining the calibration constant to obtain the dielectric constant and the loss tangent of the sample to be tested so as to finish the calibration of the coaxial resonant cavity.
A coaxial resonant cavity calibration method based on multiple reference samples comprises the following steps:
receiving the resonant frequency and the quality factor of the cavity measured by the coaxial resonant cavity;
receiving the variation of the resonant frequency and the quality factor of the first reference sample with a known dielectric constant relative to the cavity;
receiving a change in resonant frequency and quality factor of a known dielectric constant second reference sample relative to the cavity;
solving the constant according to the relation among the dielectric constant, the resonance frequency and the quality factor variable quantity, and completing the solution of the calibration constant;
and receiving the variation of the resonant frequency and the quality factor of the sample to be measured relative to the cavity, and combining the calibration constant to obtain the dielectric constant and the loss tangent of the sample to be measured so as to finish the calibration of the coaxial resonant cavity.
By way of further limitation, the relationship between the dielectric constant and the amount of change in the resonant frequency and the quality factor is:
wherein f is0Indicating the resonant frequency of the cavity, af the resonant frequency offset after loading the sample to be measured,representing the amount of quality factor shift after loading the sample,. epsilon. 'representing the real part of the dielectric constant,. epsilon.' representing the imaginary part of the dielectric constant, RsThe impedance of the metal surface of the cavity is shown, and A, gamma and G are constants related to the gap of the open end of the cavity and the gap of the sample and the open end.
As a further limitation, the number of reference samples may also be increased.
As a further limitation, the purity of the reference sample is greater than the set value. The higher the purity of the reference sample, the more accurate the complex dielectric constant, and the better the calibration effect.
As a further limitation, the difference between the complex dielectric constant of the reference sample and the complex dielectric constant of the sample to be measured is less than a set value. The closer the complex dielectric constant of the sample to be tested is to the first reference sample and the second reference sample, the better the calibration effect is, and the more accurate the dielectric constant is in testing.
A multi-reference sample based coaxial cavity calibration system comprising:
the coaxial resonant cavity is used for bearing a sample;
the vector network analyzer is used for generating an excitation signal and receiving a return signal of the coaxial resonant cavity;
a processor configured to: receiving the resonant frequency and the quality factor of the cavity measured by the coaxial resonant cavity;
receiving the variation of the resonant frequency and the quality factor of the first reference sample with a known dielectric constant relative to the cavity;
receiving a change in resonant frequency and quality factor of a known dielectric constant second reference sample relative to the cavity;
solving the constant according to the relation among the dielectric constant, the resonance frequency and the quality factor variable quantity, and completing the solution of the calibration constant;
and receiving the variation of the resonant frequency and the quality factor of the sample to be measured relative to the cavity, and combining the calibration constant to obtain the dielectric constant and the loss tangent of the sample to be measured so as to finish the calibration of the coaxial resonant cavity.
The processor further includes:
a receiving parameter module configured to receive variations in resonant frequency and quality factor of the first reference sample, the second reference sample, or/and the sample under test with respect to the cavity, for which the dielectric constant is known;
the calculation module is configured to solve the constant according to the relation among the dielectric constant, the resonant frequency and the quality factor variable quantity, and the solution of the calibration constant is completed; and (4) combining the calibration constant to obtain the dielectric constant and the loss tangent of the sample to be measured, and completing the calibration of the coaxial resonant cavity.
A computer readable storage medium having stored therein a plurality of instructions adapted to be loaded by a processor of a terminal device and to perform a method of multi-reference sample based coaxial cavity calibration.
A terminal device comprising a processor and a computer readable storage medium, the processor being configured to implement instructions; the computer readable storage medium is used for storing a plurality of instructions, and the instructions are suitable for being loaded by a processor and executing the coaxial resonant cavity calibration method based on the multi-reference sample.
Compared with the prior art, the beneficial effect of this disclosure is:
the method starts from a quasi-static model for calibration, and the dielectric constant test precision after calibration is higher and can reach 1%;
the method is suitable for a resonant cavity material testing system which is built by utilizing a vector network analyzer and a scalar network analyzer;
the method and the device are applicable to calibration of multiple resonant frequency points of the coaxial resonant cavity.
Drawings
The accompanying drawings, which are included to provide a further understanding of the disclosure, illustrate embodiments of the disclosure and together with the description serve to explain the disclosure and are not to limit the disclosure.
FIG. 1 is a schematic diagram of a material testing scenario by a coaxial resonant cavity method.
The specific implementation mode is as follows:
the present disclosure is further described with reference to the following drawings and examples.
It should be noted that the following detailed description is exemplary and is intended to provide further explanation of the disclosure. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this disclosure belongs.
It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of example embodiments according to the present disclosure. As used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, and it should be understood that when the terms "comprises" and/or "comprising" are used in this specification, they specify the presence of stated features, steps, operations, devices, components, and/or combinations thereof, unless the context clearly indicates otherwise.
In the present disclosure, terms such as "upper", "lower", "left", "right", "front", "rear", "vertical", "horizontal", "side", "bottom", and the like indicate orientations or positional relationships based on those shown in the drawings, and are only relational terms determined for convenience in describing structural relationships of the parts or elements of the present disclosure, and do not refer to any parts or elements of the present disclosure, and are not to be construed as limiting the present disclosure.
In the present disclosure, terms such as "fixedly connected", "connected", and the like are to be understood in a broad sense, and mean either a fixed connection or an integrally connected or detachable connection; may be directly connected or indirectly connected through an intermediate. The specific meanings of the above terms in the present disclosure can be determined on a case-by-case basis by persons skilled in the relevant art or technicians, and are not to be construed as limitations of the present disclosure.
Fig. 1 is a schematic diagram showing a typical material testing scenario of a coaxial resonant cavity method, wherein a vector network analyzer is used for generating and receiving signals, a resonant cavity is excited to generate a resonant curve, the resonant curve comprises resonant frequency and quality factor of the current test signal, the dielectric constant and loss tangent are inverted according to changes of the resonant frequency and the quality factor before and after a sample to be tested is placed, and the coaxial resonant cavity calibration is completed by finding out the transformation of the resonant frequency and the quality factor and turning off the dielectric constant and the loss tangent of the sample to be tested, so that the calibration method is closely related to the coaxial resonant cavity inversion algorithm.
In the traditional method, a capacitance equivalent principle is adopted, an open end of a coaxial resonant cavity is taken as an open circuit device with a terminal loaded with capacitance, and after derivation, a dielectric constant solving formula can be expressed as follows:
wherein, Y0Characteristic admittance, omega, of a coaxial cavity, representing the cavity1For placing a sample to be measured and then corresponding to the resonance frequency1For the phase constant after the sample is placed, CfCapacitance of the inner edge of the coaxial waveguide at the open end of the coaxial resonant cavity, depending on the dimensions of the coaxial resonant cavity and the medium filled therein, C0Indicating that the static fringe capacitance is constant, LeffThe equivalent cavity length of the resonant cavity.
As can be seen from equation (1), it is desired to solve the dielectric constant εrThe expression (C) must be known for three parameters C to be measured in the formula0、Cf、LeffThe method comprises the steps of respectively measuring three different samples with known dielectric constants in a working frequency band by using a coaxial resonant cavity, obtaining the resonant frequency of each working mode, and driving the resonant frequency and the dielectric constant of the three samples into a formula (1) to form three parameters C to be measured0、Cf、LeffThe equations can be solved by simultaneously solving the three equations, and the prior art deduces a dielectric constant inversion formula on the basis of the equivalent principle of the terminal capacitance of the coaxial resonant cavity, so that the test precision is low after the calibration technology is adopted, particularly the calibration technologyUnder high-frequency test, the capacitance equivalent method has larger error, so that the dielectric constant test precision by adopting the calibration technology is less than 2 percent.
The invention provides a coaxial resonant cavity calibration method based on multiple reference samples, which adopts a quasi-static equivalent principle, realizes accurate calibration of a coaxial resonant cavity by utilizing multiple reference samples for multiple tests on the premise of not increasing any hardware cost, and improves the extraction precision of dielectric constants. To obtain the relationship between dielectric constant and frequency and quality factor, an accurate representation of the electromagnetic field in the integrated region is required.
However, for the coaxial resonant cavity, the sample area is located outside the open end surface, the electromagnetic field in the area belongs to the radiation field, and it is difficult to accurately write the electromagnetic field expression, so that when the perturbation method is used to solve the complex dielectric constant, in order to avoid solving the radiation field problem, the quasi-static model analysis is combined with the perturbation principle to solve the problem, and the relationship between the dielectric constant and the resonant frequency and the quality factor variation can be obtained through derivation:
wherein f is0Indicating the resonant frequency of the cavity, af the resonant frequency offset after loading the sample to be measured,representing the amount of quality factor shift after loading the sample,. epsilon. 'representing the real part of the dielectric constant,. epsilon.' representing the imaginary part of the dielectric constant, RsThe impedance of the metal surface of the cavity is shown, and in this example, 377 Ω is taken, and a, Γ, and G are constants related to the gap at the open end of the cavity, the gap between the sample and the open end, and the like. Therefore, the real part and the imaginary part of the dielectric constant are required, the constants a, Γ, and G need to be solved, and the specific calibration principle is as follows:
at a dielectric constant and a loss angleThe known reference sample 1 is used as the sample to be measured, and the relative complex dielectric constant thereof can be expressed as epsilon1＝ε′1+jε″1The resonance frequency and the quality factor value are calculated from the measurement result of the amplitude-frequency response curve of the sample, and the offset amount deltaf of the frequency and the quality factor of the reference sample 1 can be calculated by taking the resonance frequency and the quality factor of the air measurement result as reference1、Δ(1/2Q1) The following formulas (2) and (3) can be taken:
the reference sample 2 with known dielectric constant and loss tangent is used as the sample to be measured, and the relative complex dielectric constant is expressed as epsilon2＝ε′2+jε″2Calculating the deviation delta f of the resonant frequency and the quality factor value through the measurement result of the amplitude-frequency response curve of the sample2And Δ (1/2Q)2) The resonance frequency and the quality factor of the air measurement result are used as references, and the offset of the frequency and the quality factor of the reference sample 2 can be calculated and obtained by substituting the following equations (2) and (3):
solving the constants by simultaneous (4), (5), (6) and (7) can obtain:
and (5) bringing the formulas (8), (9) and (10) into the formulas (4) and (5) to obtain the dielectric constant and the loss tangent of the sample to be measured, and completing the calibration of the coaxial resonant cavity.
The coaxial cavity calibration process is performed as follows:
step 1, firstly, the connection between the receiving equipment and the resonant cavity is carried out according to the signal generation shown in figure 1, the resonant cavity is excited to obtain a resonant curve, and the resonant frequency f of the cavity is obtained0And quality factor Q0；
Step 2, loading the dielectric constant to be epsilon1＝ε′1+jε″1With reference to sample 1, the resonant frequency was recorded relative to the resonant frequency f of the cavity obtained in step 10And quality factor Q0Amount of change Δ f of1And
step 3, loading the dielectric constant to be epsilon2＝ε′2+jε″2With reference to sample 2, the resonant frequency was recorded relative to the resonant frequency f of the cavity obtained in step 10And quality factor Q0Amount of change Δ f of2And
step 4, the known data obtained in the steps 1, 2 and 3 are brought into the formulas (8), (9) and (10), constants A, gamma and G are solved, and the solution of the calibration constants is completed;
loading a sample to be tested, setting the dielectric constant of the sample to be tested to be epsilon '+ j epsilon', and recording the resonant frequency f relative to the resonant frequency f of the cavity obtained in the step 10And quality factor Q0Amount of change Δ f andthe calculation results A, gamma and G of the step (4) are taken into the formulas (2) and (3) to finishThe real parts of the dielectric constants ε' and ε ".
In the calibration process, the higher the purity and the more accurate the complex dielectric constant of the reference sample 1 and the reference sample 2 are, the better the calibration effect is.
The closer the complex dielectric constant of the sample to be tested is to air, the reference sample 1 and the reference sample 2, the better the calibration effect is, and the more accurate the dielectric constant is in the test.
The above description is only a preferred embodiment of the present disclosure and is not intended to limit the present disclosure, and various modifications and changes may be made to the present disclosure by those skilled in the art. Any modification, equivalent replacement, improvement and the like made within the spirit and principle of the present disclosure should be included in the protection scope of the present disclosure.
Although the present disclosure has been described with reference to specific embodiments, it should be understood that the scope of the present disclosure is not limited thereto, and those skilled in the art will appreciate that various modifications and changes can be made without departing from the spirit and scope of the present disclosure.
Claims (10)
1. A coaxial resonant cavity calibration method based on multiple reference samples is characterized by comprising the following steps: the method comprises the following steps:
connecting the vector network analyzer and the coaxial resonant cavity through a connecting cable, exciting the cavity to obtain a resonant curve, and obtaining the resonant frequency and the quality factor of the cavity;
loading a first reference sample with a certain dielectric constant, and recording the variation of the resonant frequency relative to the resonant frequency and the quality factor of the cavity;
loading another second reference sample with the dielectric constant of the second reference sample, and recording the variation of the resonant frequency relative to the resonant frequency and the quality factor of the cavity;
solving the constant according to the relation among the dielectric constant, the resonance frequency and the quality factor variable quantity, and completing the solution of the calibration constant;
and loading a sample to be tested, recording the variation of the resonant frequency relative to the resonant frequency and the quality factor of the cavity, and combining the calibration constant to obtain the dielectric constant and the loss tangent of the sample to be tested so as to finish the calibration of the coaxial resonant cavity.
2. A coaxial resonant cavity calibration method based on multiple reference samples is characterized by comprising the following steps: the method comprises the following steps:
receiving the resonant frequency and the quality factor of the cavity measured by the coaxial resonant cavity;
receiving the variation of the resonant frequency and the quality factor of the first reference sample with a known dielectric constant relative to the cavity;
receiving a change in resonant frequency and quality factor of a known dielectric constant second reference sample relative to the cavity;
solving the constant according to the relation among the dielectric constant, the resonance frequency and the quality factor variable quantity, and completing the solution of the calibration constant;
and receiving the variation of the resonant frequency and the quality factor of the sample to be measured relative to the cavity, and combining the calibration constant to obtain the dielectric constant and the loss tangent of the sample to be measured so as to finish the calibration of the coaxial resonant cavity.
3. A method according to claim 1 or 2, wherein the method comprises the following steps: the relationship between the dielectric constant and the variation of the resonant frequency and the quality factor is:
wherein f is0Indicating the resonant frequency of the cavity, af the resonant frequency offset after loading the sample to be measured,denotes the amount of quality factor shift after loading the sample,. epsilon.' denotes the real part of the dielectric constant,. epsilon. "" denotes the imaginary part of the dielectric constant,Rsthe impedance of the metal surface of the cavity is shown, and A, gamma and G are constants related to the gap of the open end of the cavity and the gap of the sample and the open end.
4. A method according to claim 1 or 2, wherein the method comprises the following steps: the number of reference samples can be increased.
5. A method according to claim 1 or 2, wherein the method comprises the following steps: the purity of the reference sample is greater than the set value.
6. A method according to claim 1 or 2, wherein the method comprises the following steps: the difference between the complex dielectric constant of the reference sample and the complex dielectric constant of the sample to be measured is less than a set value.
7. A coaxial resonant cavity calibration system based on multiple reference samples is characterized in that: the method comprises the following steps:
the coaxial resonant cavity is used for bearing a sample;
the vector network analyzer is used for generating an excitation signal and receiving a return signal of the coaxial resonant cavity;
a processor configured to: receiving the resonant frequency and the quality factor of the cavity measured by the coaxial resonant cavity;
receiving the variation of the resonant frequency and the quality factor of the first reference sample with a known dielectric constant relative to the cavity;
receiving a change in resonant frequency and quality factor of a known dielectric constant second reference sample relative to the cavity;
solving the constant according to the relation among the dielectric constant, the resonance frequency and the quality factor variable quantity, and completing the solution of the calibration constant;
and receiving the variation of the resonant frequency and the quality factor of the sample to be measured relative to the cavity, and combining the calibration constant to obtain the dielectric constant and the loss tangent of the sample to be measured so as to finish the calibration of the coaxial resonant cavity.
8. The multi-reference sample based coaxial cavity calibration system of claim 7, wherein: the processor further includes:
a receiving parameter module configured to receive variations in resonant frequency and quality factor of the first reference sample, the second reference sample, or/and the sample under test with respect to the cavity, for which the dielectric constant is known;
the calculation module is configured to solve the constant according to the relation among the dielectric constant, the resonant frequency and the quality factor variable quantity, and the solution of the calibration constant is completed; and (4) combining the calibration constant to obtain the dielectric constant and the loss tangent of the sample to be measured, and completing the calibration of the coaxial resonant cavity.
9. A computer-readable storage medium characterized by: a plurality of instructions stored therein, the instructions adapted to be loaded by a processor of a terminal device and to perform a method for multi-reference sample based coaxial cavity calibration according to any one of claims 2-6.
10. A terminal device is characterized in that: the system comprises a processor and a computer readable storage medium, wherein the processor is used for realizing instructions; a computer readable storage medium storing a plurality of instructions adapted to be loaded by a processor and to perform a method of multi-reference sample based coaxial cavity calibration according to any one of claims 2 to 6.
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Application publication date: 20191224 |