CN111856150B - Error correction method for frequency-dependent change of quasi-optical cavity dielectric constant test - Google Patents
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- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
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Abstract
The invention discloses a correction method for error along with frequency change in a quasi-optical cavity dielectric constant test, which belongs to the field of detection and can solve the problem of error along with frequency change in the quasi-optical cavity dielectric constant test, and comprises the following steps: analyzing Gaussian beam phase distribution in the optical cavity; obtaining actual phase distribution of the upper surface of the sample and an expression of an electric field and a magnetic field according to boundary condition relation of the upper surface of the sample to be detected, namely an electromagnetic field at the interface of the air and a medium area; considering the longitudinal field component of the electric field in the quasi-optical cavity, and simultaneously, listing the transverse field component and the longitudinal field component of the electric field in the quasi-optical cavity into the calculation step; the formula is carried in for calculation.
Description
Technical Field
The invention belongs to the field of detection, and particularly relates to a frequency-dependent error correction method for a quasi-optical cavity dielectric constant test.
Background
The statements herein merely provide background information related to the present disclosure and may not necessarily constitute prior art.
For testing dielectric properties of materials, the currently commonly used testing methods mainly include a plate capacitance method, a network parameter method, a resonance method, a free space method, a quasi-optical cavity method and the like. The quasi-optical cavity method has the advantages of simple operation, good mode purification effect and strong test adaptability. The quasi-optical cavity method has two structures of a quasi-optical cavity with a semi-symmetrical structure (a plano-concave cavity) and a quasi-optical cavity with a symmetrical structure (a double-ball cavity), and the structure schematic diagram is shown in figure 1. The flat concave cavity has the advantages of convenient sample loading, low processing cost and the like, and is widely used. The structure of the quasi-optical cavity test system is schematically shown in FIG. 2.
The inventor discovers that on one hand, the dielectric constant of a tested sample is unknown and cannot estimate the size of a quarter of the medium wavelength, and on the other hand, the test frequency range of the quasi-optical cavity is extremely wide, and the test cannot meet the matching of the thickness along with the change of the frequency in the wide frequency range. In a quasi-optical cavity test system, the thickness of a sample to be tested is usually a fixed value, and when the thickness does not meet one quarter of the medium wavelength, the test result can generate errors; the equiphase surface in the quasi-optical cavity is not a plane vertical to the z-axis, but a curved surface with a certain radian and a small included angle with the z-axis. The equiphase graph is shown in fig. 3. Since the sample surface is a plane and the equiphase surface is a curved surface, a point at the axis cannot represent the field of the whole material surface when boundary surface matching is performed, and errors are introduced. The included angle between the equiphase surface curve and the sample surface plane is smaller and smaller along with the increase of the frequency, so that the error phenomenon of sinusoidal fluctuation of the dielectric constant test result is avoided, the air gap between the equiphase surface and the sample surface is corrected according to the prior patent, and the inventor considers that the correction cannot solve the error phenomenon.
Disclosure of Invention
Aiming at the defects existing in the prior art, the invention aims to provide a correction method for the error of the dielectric constant test of the quasi-optical cavity along with the change of frequency.
In order to achieve the above object, the present invention is realized by the following technical scheme:
in a first aspect, the present invention provides a method for correcting error of a quasi-optical cavity dielectric constant test along with frequency change, including the following steps:
analyzing Gaussian beam phase distribution in the optical cavity;
obtaining actual phase distribution of the upper surface of the sample and an expression of an electric field and a magnetic field according to boundary condition relation of the upper surface of the sample to be detected, namely an electromagnetic field at the interface of the air and a medium area;
considering the longitudinal field component of the electric field in the quasi-optical cavity, and simultaneously, listing the transverse field component and the longitudinal field component of the electric field in the quasi-optical cavity into the calculation step;
the formula is carried in for calculation.
The technical scheme of the invention has the following beneficial effects:
in the past, although the quasi-optical cavity test system has higher precision compared with a network parameter method and the like, the extremely high precision condition of the test precision is ensured to be that the thickness of a sample is equal to odd times of the quarter dielectric wavelength during test, the thickness of the sample cannot be estimated during engineering test of unknown dielectric materials, and meanwhile, during broadband internal test, the quarter dielectric wavelength is a frequency variable, and the thickness of the test sample cannot be changed along with the change of the test frequency, so that the test error of the broadband internal dielectric constant is increased. The invention can solve the problem that the sample thickness does not meet the calculation result error introduced by the system theory when the quarter-medium wavelength matching is tested, thereby realizing the high-precision test of the broadband quasi-optical cavity.
Drawings
The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the invention.
Figure 1a is a schematic diagram of a quasi-optical cavity with a semi-symmetrical structure in the background of the invention,
figure 1b is a schematic diagram of a symmetrical structured quasi-optical cavity in the background of the invention,
figure 2 is a schematic diagram of a quasi-optical cavity test system in the background of the invention,
figure 3 is an equiphase curve x-plane and z-plane diagram of the background of the invention,
figure 4 is a 10mm inner equiphase plane plot on a 20GHz mirror in one or more embodiments of the invention,
figure 5 is a 10mm inner equiphase plane plot on a 40GHz mirror in one or more embodiments of the invention,
figure 6 is a 10mm inner equiphase plane plot on an 80GHz plane mirror in one or more embodiments of the invention,
figure 7 is a graph of 15-50GHz quartz dielectric constant test result data in one or more embodiments of the invention,
figure 8 is a graph of Ex field components as a function of frequency in one or more embodiments of the invention,
fig. 9 is a graph of a power line in one or more embodiments of the invention.
The mutual spacing or dimensions are exaggerated for the purpose of showing the positions of the various parts, and the schematic illustrations are used for illustration only.
Detailed Description
It should be noted that the following detailed description is illustrative and is intended to provide further explanation of the invention. 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 invention 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 exemplary embodiments according to the present invention. As used herein, the singular forms also are intended to include the plural forms unless the present invention clearly dictates otherwise, and furthermore, it should be understood that when the terms "comprise" and/or "include" are used in this specification, they specify the presence of stated features, steps, operations, devices, components, and/or combinations thereof;
as described in the background art, the invention aims to provide a correction method for frequency-dependent error of quasi-optical cavity dielectric constant test, which can solve the problem of frequency-dependent error of quasi-optical cavity dielectric constant test.
Examples
In an exemplary implementation manner of the present invention, the present embodiment provides a method for correcting error of a quasi-optical cavity dielectric constant test along with frequency variation, which is mainly used for correcting error of a wideband quasi-optical cavity dielectric constant test result error regularity, analyzing by using a quasi-optical cavity field theory derived by a complex point source theory, correcting error amplitude by considering influence of a longitudinal field component, and correcting phase error by using a corresponding relation between a dielectric test result frequency variation phenomenon and theory.
Specifically, the method comprises the following steps:
1) Analyzing Gaussian beam phase distribution in the optical cavity;
2) According to the matching relation of the electromagnetic field boundary conditions at the interface of the air and the medium area on the upper surface of the sample to be detected, the actual phase distribution of the upper surface of the sample and the electric field and magnetic field intensity are obtained;
3) Meanwhile, the transverse field component and the longitudinal field component of the electric field in the quasi-optical cavity are listed in a dielectric constant calculation step;
4) And carrying out formula calculation to calculate the dielectric constant.
When the Gaussian beam phase distribution in the optical cavity is aligned by adopting the beam theory for analysis, the quasi-optical cavity size and the sample thickness of the sample are determined, and a graph of the electric field at the interface of the sample and the air along with the frequency is drawn according to the calculation result.
The correction method is suitable for flat concave cavities and double concave cavities.
Said step 1) comprises the steps of:
1) Adopting a beam theory to aim at Gaussian beam phase distribution in an optical cavity for analysis;
2) The phase expression of Gaussian beams is obtained by beam theory and wave equation:
it will be appreciated by those skilled in the art that it is common knowledge in the art to analyze the gaussian beam phase distribution in an optical cavity, and that the calculation methods and calculation steps are only listed here and are not listed.
Said step 3) comprises the steps of:
the quasi-optical cavity field theory deduced by the complex point source theory is utilized for analysis, the influence of the longitudinal field component is considered for error amplitude correction, and the phase error correction is carried out through the corresponding relation between the frequency change phenomenon of the dielectric test result and the theory.
It will be appreciated by those skilled in the art that the theory of multiple point sources is common general knowledge in the art, and that the steps for performing specific calculations using the theory are not listed together.
The gaussian beam theory mainly refers to that the transverse amplitude of electromagnetic waves in an optical cavity meets gaussian beam function distribution, is not a strict mathematical solution of the electromagnetic waves, but is a reasonable approximation of the spatial distribution of the electromagnetic waves when the electromagnetic waves meet certain conditions. The approximation introduces very small errors and can greatly simplify the field solution complexity, so that the method is widely applied to practical problems. The transverse boundary condition in Gaussian beam theory does not influence the distribution of beams, and is matched with the open structure of the quasi-optical cavity, so that the quasi-optical cavity can be well applied to a quasi-optical cavity system.
The Gaussian beam theory solves the problem of the open boundary condition of the quasi-optical cavity, and the paraxial approximation condition is applied to the analysis of the field inside the cavity. Analyzing Gaussian beam phase distribution in the optical cavity, including quasi-optical cavity open boundary condition analysis and cavity internal field analysis; the problem of the quasi-optical cavity open boundary condition is analyzed by using a beam wave theory, and the analysis is performed by using paraxial approximate conditions and combining the beam wave theory when the field inside the cavity is analyzed.
When the paraxial approximation is used, the distribution of the field along the z-axis in the collimating optical cavity is assumed to be superimposed by plane waves having a small angle with the z-axis.
And analyzing Gaussian beam phase distribution in the optical cavity, including resonance problem analysis, wherein standing wave solution is required to be obtained for the field in the resonant cavity, and a main mode standing wave field formula in the flat concave cavity is finally obtained by applying scalar fluctuation theory under the condition of meeting paraxial approximation.
Under the condition of meeting paraxial approximation, a scalar fluctuation theory is applied to finally obtain a main mode standing wave field formula in the flat concave cavity:
wherein E is x For the transverse electric field component, H y Is the transverse magnetic field component, j is the complex unit, w 0 The wave beam is Gaussian, w (z) is the beam radius at z, ρ is a transverse variable, k is a wave number, phi is Guan Canliang with z, R (z) is a wave front curvature radius, ε is a dielectric constant, μ is a dielectric permeability, and z is a longitudinal variable;
it can be seen that only the transverse field component E is used in the formula X Or H y The calculation of the amount in the z-direction is lacking.
Based on the prior knowledge, a person skilled in the art can calculate the z-direction component of the field by using gaussian beam theory under the condition of knowing the field distribution, and the specific principle thereof will not be described here.
It should be noted that, in the step 3), after the longitudinal field component is listed in the calculation step, the phase correction factor is obtained by combining the test data result; and selecting a typical frequency point, matching the thickness of the sample with a frequency point corresponding to one quarter and one half of the medium wavelength, analyzing a transverse field and a longitudinal field, and matching at the interface of the medium and air to obtain an amplitude correction factor.
On the basis of the test result of the traditional method, the test result of the dielectric constant in the broadband range is corrected, the error of the test result when the thickness of the sample is not matched with the quarter-wavelength dielectric is eliminated, and the high-precision dielectric performance test of the dielectric constant of the quasi-optical cavity is realized.
In a specific implementation scenario, for example, taking a polytetrafluoroethylene sample with a thickness of 3.53mm as an example, when the quasi-optical cavity is sized and the thickness of the sample is fixed, a graph of the electric field at the interface between the sample and air is plotted as shown in fig. 8, and the abscissa is the frequency. From the electric field graph and the fluctuation of the test result, it can be seen that when the transverse electric field Ex takes the maximum value (positive and negative represent the field direction), namely, the corresponding quarter wavelength, the dielectric constant test result is the central axis value, namely, no amplitude fluctuation exists, the test result is the most accurate, and the maximum error occurs in the test result when the electric field amplitude is 0.
The plot of the power line in the xz plane is shown in fig. 9. The tangential direction of the electric field lines represents the direction of the electric field, and the field strength of the electric field is maximum when the thickness of the sample is equal to an odd multiple of the quarter-medium wavelength, and the electric field is mainly the transverse electric field when the tangential direction of the electric line lines is close to a straight line parallel to the z-axis, and corresponds to the place where the electric line lines are most dense. When the thickness of the sample is equal to an integral multiple of one half of the medium wavelength, the electric field is transverse only on the axis, and other position power lines are close to be perpendicular to the surface of the sample, although the power lines are sparse at the moment, namely the electric field value is small, and the longitudinal field component of the whole surface of the sample cannot be ignored at the moment.
The accuracy of error analysis sources can be determined by combining the power line curve graph with the test data curve, and the periodic variation rule of dielectric property can be seen by analyzing the field component derived from the complex point source theory. Combining the test data result to obtain a phase correction factor; and selecting a typical frequency point, matching the thickness of the sample with a frequency point corresponding to one quarter and one half of the medium wavelength, analyzing a transverse field and a longitudinal field, and matching at the interface of the medium and air to obtain an amplitude correction factor.
If the conventional calculation method only considering the transverse field component is adopted, the graphs of the equiphase surfaces of 20GHz, 40GHz and 80GHz are shown in fig. 4 to 6, respectively, and the equiphase surfaces at the interface of the sample and the air are analyzed to change along with the frequency, so that the equiphase surfaces only slightly change along with the frequency, and the change direction rule is not consistent with the change rule of the dielectric constant test result in the broadband.
It can be seen that the magnitude of the equiphase surface variation is small in the range of 20-80GHz, i.e. the degree of matching of the equiphase surface of the sample surface with the sample hardly changes with frequency, and thus the air gap introduced by the mismatch hardly changes with frequency, and when the sample thickness t is fixed (e.g. 3.5mm is taken, i.e. z=3.5), the radius of curvature of the equiphase surface at the sample surface hardly changes with frequency. And the actual test results dielectric calculations fluctuate over a range of frequency values.
The results of the test polytetrafluoroethylene dielectric constant calculations are shown in the graph below, with the relative dielectric constant on the ordinate and frequency (in GHz) on the abscissa. The calculation result adopts an error correction formula for the mismatch between the equiphase surface and the sample surface, and the problem of frequency variation error cannot be solved. In the scalar fluctuation theory, the transverse electric field only has the Ex direction, no longitudinal field component, and the difference exists between the transverse electric field and the actual electric field in the cavity, and if analysis is carried out from the field theory, the analysis cannot be carried out. The corrected result curve is shown in fig. 7.
The vector theory (complex point source theory) gives standing wave field solution in the quasi-optical cavity, but the transverse field Ex is still utilized for matching when the sample is matched with the air interface field, so that the error of the broadband test settlement result is not solved. I.e. the test result is most accurate when the thickness of the tested sample meets the quarter medium wavelength. Aiming at the test error problem, the invention starts from the quasi-optical cavity internal field theory, considers the influence factors of the longitudinal field components, and corrects the broadband test result, thereby eliminating the broadband dielectric constant test error.
The above description is only of the preferred embodiments of the present invention and is not intended to limit the present invention, but various modifications and variations can be made to the present invention by those skilled in the art. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (7)
1. The error correction method for the dielectric constant test of the quasi-optical cavity along with the frequency change is characterized by comprising the following steps:
analyzing Gaussian beam phase distribution in the optical cavity;
adopting a beam theory to aim at Gaussian beam phase distribution in an optical cavity for analysis;
the phase expression of Gaussian beams is obtained by beam theory and wave equation:
obtaining actual phase distribution of the upper surface of the sample and an expression of an electric field and a magnetic field according to boundary condition relation of the upper surface of the sample to be detected, namely an electromagnetic field at the interface of the air and a medium area;
considering the longitudinal field component of the electric field in the quasi-optical cavity, and simultaneously, listing the transverse field component and the longitudinal field component of the electric field in the quasi-optical cavity into the calculation step;
the main mode standing wave field formula in the flat concave cavity is as follows:
wherein E is x For the transverse electric field component, H y Is the transverse magnetic field component, j is the complex unit, w 0 The wave beam is Gaussian, w (z) is the beam radius at z, ρ is a transverse variable, k is a wave number, phi is Guan Canliang with z, R (z) is a wave front curvature radius, ε is a dielectric constant, μ is a dielectric permeability, and z is a longitudinal variable;
carrying out calculation of dielectric constant by taking the formula into the formula;
after the longitudinal field component is listed in the calculation step, a phase correction factor is obtained by combining the test data result; selecting a typical frequency point, matching the thickness of a sample with a frequency point corresponding to one quarter and one half of the medium wavelength, analyzing a transverse field and a longitudinal field, and matching at the interface of the medium and air to obtain an amplitude correction factor;
when considering the longitudinal field component of the electric field in the quasi-optical cavity, the quasi-optical cavity field theory deduced by the complex point source theory is utilized to analyze, the influence of the longitudinal field component is considered to correct the error amplitude, and the phase error correction is carried out through the corresponding relation between the frequency change phenomenon of the dielectric test result and the theory.
2. The method for correcting error along with frequency variation in a quasi-optical cavity dielectric constant test according to claim 1, wherein a beam theory is adopted when Gaussian beam phase distribution in an optical cavity is aligned for analysis, the quasi-optical cavity size and the sample thickness of a sample are determined, and a graph of electric field along with frequency variation at an interface between the sample and air is drawn according to a calculation result.
3. The method of claim 1, wherein the correction method is applicable to both flat-cavity and double-cavity.
4. The method for correcting error of frequency variation in dielectric constant test of quasi-optical cavity according to claim 1, wherein when the Gaussian beam phase distribution in the optical cavity is analyzed, including quasi-optical cavity open boundary condition analysis and cavity internal field analysis; the problem of the quasi-optical cavity open boundary condition is analyzed by using a beam wave theory, and the analysis is performed by using paraxial approximate conditions and combining the beam wave theory when the field inside the cavity is analyzed.
5. The method of correcting frequency dependent error in a quasi-optical cavity dielectric constant test of claim 4, wherein said paraxial approximation is used to assume that the distribution of the field along the z-axis in the quasi-optical cavity is formed by superimposing plane waves having a small angle with the z-axis.
6. The method for correcting error of frequency variation in dielectric constant test of quasi-optical cavity according to claim 1, wherein the analysis of Gaussian beam phase distribution in the optical cavity is performed by analyzing Gaussian beam phase distribution in the optical cavity, and further comprising resonance problem analysis, wherein standing wave solution is needed to be obtained for the field in the resonant cavity, and a main mode standing wave field formula in the flat cavity is finally obtained by applying scalar fluctuation theory under the condition of meeting paraxial approximation.
7. The method for correcting frequency variation error in quasi-optical cavity dielectric constant test of claim 1, wherein the typical frequency point is 20GHz, 40GHz or 80GHz.
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