Complex dielectric constant testing method and system based on TMmn0 mode cylindrical cavity

Abstract

The invention discloses a complex dielectric constant testing method and system based on a TMmn0 mode cylindrical cavity, and the method comprises the steps: enabling the cross section of an actually-loaded to-be-tested sample to be approximate to the cross section of an equivalent sample, obtaining a parameter a related to electric field integration in a TMmn0 mode, and calculating a self-defined parameter k related to resonant frequency based on a; modeling the test fixture, performing parameter scanning on the test fixture loaded with the to-be-tested sample near different TMmn0 working mode resonant frequencies, and constructing a fitting curve between a dielectric constant real part and k; obtaining a dielectric constant real part based on k and a fitting curve between the dielectric constant real part and k; a complex permittivity is obtained based on the permittivity real part. The method has the advantages of dense test frequency points in a broadband and high test precision of a low-loss material, and effectively solves the problems of mode excitation, identification and test pain points in high-frequency application of a traditional TM0n0 mode cylindrical cavity.

Description

Technical Field

[0001] The present invention relates to the fields of radio frequency application and microwave testing, and in particular to a complex dielectric constant testing method and system based on a TMmn0 mode cylindrical cavity. Background Art

[0002] Dielectric materials are the medium for electromagnetic wave propagation and are widely used in microwave circuits, antennas, radars and other fields. The microwave propagation characteristics of materials mainly include two parameters: complex dielectric constant and complex magnetic permeability. Therefore, accurate measurement of the complex dielectric constant of materials is of great significance to the design and performance prediction of microwave systems. However, with the accelerated commercialization of 5G systems, low-loss materials are widely used, which brings higher requirements for the accurate measurement of the microwave performance of low-loss materials, which is challenging for current testing technology.

[0003] The current mainstream complex dielectric constant methods mainly include network parameter method and resonance method, such as Figure 1 As shown. However, the application scenarios of these two methods are not the same, and each has its own advantages and disadvantages; the network parameter method has the advantages of broadband testing and continuous frequency testing, but the large error in testing low-loss materials (tanδ≤0.01) is the biggest drawback; on the contrary, the resonance method uses the high quality factor Q of the microwave resonant cavity to have a higher sensitivity to the change of the quality factor Q of the loaded / unloaded resonant cavity, so the resonant cavity method has a natural advantage in testing low-loss dielectric materials. However, the quality factor Q is defined at the resonant frequency, which means that this method can only be tested at the resonant frequency of a resonant cavity. The resonant mode determines the resonant frequency of this resonant cavity, and the resonant frequency of the resonant mode is discontinuous, so the cavity perturbation can only provide a complex dielectric constant at a discrete frequency point.

[0004] In 5G applications, it is usually required to provide the complex dielectric constant of the dielectric material to be tested at multiple frequency points; in order to save costs, single-cavity multi-mode technology is widely used in the resonant cavity perturbation method. However, the working mode used in the traditional cylindrical cavity test fixture is TM0n0 mode. As the number of working modes increases (the resonant frequency will increase accordingly), the frequency distribution of the mixed mode will become particularly dense, such as Figure 2 As shown, this creates great obstacles to the stimulation, identification and testing of the TM0n0 working mode, which also greatly affects the application of high-order TM0n0 working modes, that is, the TM0n0 mode cylindrical cavity test fixture has essential defects in broadband test applications. Summary of the invention

[0005] In order to solve the problem that the existing TM0n0 mode cylindrical cavity test fixture has essential defects in broadband test applications, the present invention proposes a complex dielectric constant test method based on the TMmn0 mode cylindrical cavity, comprising:

[0006] The cross section of the actually loaded sample to be tested is approximated to the cross section of the equivalent sample, and the custom parameter a for the electric field integral in the TMmn0 mode is obtained;

[0007] The test fixture is modeled, and the test fixture loaded with the sample to be tested is scanned near the resonant frequency of different TMmn0 working modes to construct a fitting curve between the real part of the dielectric constant and the custom parameter k related to the resonant frequency;

[0008] Calculating a custom parameter k related to the resonance frequency based on the resonance frequencies of the front and rear resonance cavities of the sample to be tested and the custom parameter a related to the electric field integral;

[0009] The complex dielectric constant is obtained based on the custom parameter k related to the resonant frequency and a fitting curve between the real part of the dielectric constant and the custom parameter k related to the resonant frequency.

[0010] Optionally, the cross section of the actually loaded sample to be tested is approximated to the cross section of the equivalent sample, and a custom parameter a for electric field integration in the TMmn0 mode is obtained, including:

[0011] The cross section and loading position of the equivalent sample are used to approximate the cross section and loading position of the actual loaded sample to be tested, and the electric field component formula is obtained;

[0012] Substitute the electric field component formula into the calculation formula of the custom parameter a for the electric field integral to obtain the custom parameter a for the electric field integral.

[0013] Optionally, the calculation formula for the custom parameter a regarding the electric field integral is as follows:

[0014]

[0015] In the formula, a TMmn0 is the value of the custom parameter a for the electric field integral in the TMmn0 mode of the cylindrical resonant cavity, J m (k c ρ) is the m-order Bessel function, is the polar angle of the cylindrical coordinates, m is the order of the Bessel function, θ is the polar angle of the center axis of the cross section of the sample to be tested, β is the radian of the equivalent cross section of the sample to be tested, l 0 is the radial length of the equivalent cross section of the sample to be tested, l 2 is the end radius of the equivalent cross section of the sample to be tested, ρ is the radial coordinate of the cylindrical coordinates, k c =p mn / R,P mn is the nth root of the m-order Bessel function, h is the height of the cylindrical cavity, z is the height coordinate of the cylindrical coordinates, R is the inner diameter of the cylindrical cavity, n is the serial number of the Bessel function root, E 0is the mode electric field when not disturbed, V is the resonator volume, V s is the volume of the sample to be tested, and E is the mode electric field.

[0016] Optionally, the custom parameter k related to the resonant frequency is calculated as follows:

[0017]

[0018] In the formula, f 0 is the original resonant frequency of the resonant cavity, f 1 is the resonant frequency of the resonant cavity after being disturbed.

[0019] Optionally, obtaining the complex dielectric constant based on the custom parameter k related to the resonant frequency and a fitting curve between the real part of the dielectric constant and the custom parameter k related to the resonant frequency includes:

[0020] Obtaining the real part of the dielectric constant based on the custom parameter k related to the resonant frequency and a fitting curve between the real part of the dielectric constant and the custom parameter k related to the resonant frequency;

[0021] Based on the real part of the dielectric constant and the loss tangent calculation formula, a loss tangent value is obtained;

[0022] The complex dielectric constant is calculated based on the loss tangent value in combination with the real part of the dielectric constant.

[0023] Optionally, the real part of the dielectric constant is calculated as follows:

[0024]

[0025] In the formula, ε r ' is the real part of the dielectric constant, L 0 is the depolarization factor of the sample to be tested in the electromagnetic field.

[0026] Optionally, the loss tangent value is calculated as follows:

[0027]

[0028] Where tanδ is the loss tangent, ε r " is the imaginary part of the complex dielectric constant, f 0 is the original resonant frequency of the resonant cavity, f 1 is the resonant frequency of the resonant cavity after being disturbed, Q 0 is the original quality factor of the resonant cavity, Q 1 is the quality factor of the resonant cavity after disturbance, ε r ' is the real part of the dielectric constant of the perturbation material, ε r " is the imaginary part of the dielectric constant of the perturbation material.

[0029] Optionally, the complex dielectric constant is calculated as follows:

[0030] ε r =ε' r -jε" r =ε' r (1-jtanδ)

[0031] In the formula, ε r is the complex dielectric constant, and j represents the imaginary part.

[0032] On the other hand, the present application also provides a complex dielectric constant testing system based on a TMmn0 mode cylindrical cavity, comprising:

[0033] The first parameter calculation module is used to approximate the cross section of the actually loaded sample to be tested to the cross section of the equivalent sample, and obtain a custom parameter a about the electric field integral in the TMmn0 mode;

[0034] A relationship building module is used to model the test fixture, scan the test fixture loaded with the sample to be tested near the resonant frequency of different TMmn0 working modes, and build a fitting curve between the real part of the dielectric constant and the custom parameter k about the resonant frequency;

[0035] A second parameter calculation module, used to calculate a custom parameter k related to the resonance frequency based on the resonance frequency of the front and rear resonance cavities of the sample to be tested and the custom parameter a related to the electric field integral;

[0036] The complex permittivity calculation module is used to obtain the complex permittivity based on the user-defined parameter k related to the resonant frequency and a fitting curve between the real part of the permittivity and the user-defined parameter k related to the resonant frequency.

[0037] Optionally, the first parameter calculation module is specifically used for:

[0038] The cross section and loading position of the equivalent sample are used to approximate the cross section and loading position of the actual loaded sample to be tested, and the electric field component formula is obtained;

[0039] Substitute the electric field component formula into the calculation formula of the custom parameter a for the electric field integral to obtain the custom parameter a for the electric field integral.

[0040] Optionally, the calculation formula for the custom parameter a regarding the electric field integral is as follows:

[0041]

[0042] In the formula, a TMmn0 is the value of the custom parameter a for the electric field integral in the TMmn0 mode of the cylindrical resonant cavity, J m (kc ρ) is the m-order Bessel function, is the polar angle of the cylindrical coordinates, m is the order of the Bessel function, θ is the polar angle of the center axis of the cross section of the sample to be tested, β is the radian of the equivalent cross section of the sample to be tested, l 0 is the radial length of the equivalent cross section of the sample to be tested, l 2 is the end radius of the equivalent cross section of the sample to be tested, ρ is the radial coordinate of the cylindrical coordinates, k c =p mn / R,P mn is the nth root of the m-order Bessel function, h is the height of the cylindrical cavity, z is the height coordinate of the cylindrical coordinates, R is the inner diameter of the cylindrical cavity, n is the serial number of the Bessel function root, E 0 is the mode electric field when not disturbed, V is the resonator volume, V s is the volume of the sample to be tested, and E is the mode electric field.

[0043] Optionally, the custom parameter k related to the resonant frequency is calculated as follows:

[0044]

[0045] In the formula, f 0 is the original resonant frequency of the resonant cavity, f 1 is the resonant frequency of the resonant cavity after being disturbed.

[0046] Optionally, the complex dielectric constant calculation module is specifically used for:

[0047] Obtaining the real part of the dielectric constant based on the custom parameter k related to the resonant frequency and a fitting curve between the real part of the dielectric constant and the custom parameter k related to the resonant frequency;

[0048] Based on the real part of the dielectric constant and the loss tangent calculation formula, a loss tangent value is obtained;

[0049] The complex dielectric constant is calculated based on the loss tangent value in combination with the real part of the dielectric constant.

[0050] Optionally, the real part calculation module calculates the real part of the dielectric constant according to the following formula:

[0051]

[0052] In the formula, ε r ' is the real part of the dielectric constant, L 0 is the depolarization factor of the sample to be tested in the electromagnetic field.

[0053] Optionally, the loss tangent value is calculated as follows:

[0054]

[0055] Where tanδ is the loss tangent, ε r " is the imaginary part of the complex dielectric constant, f 0 is the original resonant frequency of the resonant cavity, f 1 is the resonant frequency of the resonant cavity after being disturbed, Q 0 is the original quality factor of the resonant cavity, Q 1 is the quality factor of the resonant cavity after disturbance, ε r ' is the real part of the dielectric constant of the perturbation material, ε r " is the imaginary part of the dielectric constant of the perturbation material.

[0056] Optionally, the complex dielectric constant is calculated as follows:

[0057] ε r =ε' r -jε" r =ε' r (1-jtanδ)

[0058] In the formula, ε r is the complex dielectric constant, and j represents the imaginary part.

[0059] In another aspect, the present application further provides an electronic device, comprising: at least one processor and a memory; the memory and the processor are connected via a bus;

[0060] The memory is used to store one or more programs;

[0061] When the one or more programs are executed by the at least one processor, the complex dielectric constant testing method based on the TMmn0 mode cylindrical cavity as described above is implemented.

[0062] On the other hand, the present application also provides a readable storage medium having an execution program stored thereon, and when the execution program is executed, the complex dielectric constant testing method based on the TMmn0 mode cylindrical cavity as described above is implemented.

[0063] Compared with the prior art, the present invention has the following beneficial effects:

[0064] The present invention provides a complex dielectric constant test method based on a TMmn0 mode cylindrical cavity, including: approximating the cross section of the actually loaded sample to be tested to the cross section of an equivalent sample, obtaining a custom parameter a about the electric field integral in the TMmn0 mode, and calculating a custom parameter k about the resonant frequency based on the custom parameter a about the electric field integral; modeling the test fixture, scanning the test fixture loaded with the sample to be tested near the resonant frequency of different TMmn0 working modes, respectively, constructing a fitting curve between the real part of the dielectric constant and the custom parameter k about the resonant frequency; based on the fitting curve between the custom parameter k about the resonant frequency and the real part of the dielectric constant and the custom parameter k about the resonant frequency, obtaining the real part of the dielectric constant; based on the real part of the dielectric constant, obtaining the complex dielectric constant. The present invention has the advantages of dense test frequency points in a wide band and high test accuracy of low-loss materials, and can effectively solve the pain points of mode excitation, identification and testing in high-frequency applications of traditional TM0n0 mode cylindrical cavities. Since the total mode order of the TMmn0 mode is larger, a smaller test fixture can be used and higher frequency testing can be achieved, which not only greatly saves fixture costs but also greatly expands the application space of the resonant cavity method. BRIEF DESCRIPTION OF THE DRAWINGS

[0065] Figure 1 It is the mainstream classification of complex dielectric constant test methods;

[0066] Figure 2 Frequency distribution of TM mode of a cylindrical cavity;

[0067] Figure 3 It is a flow chart of the complex dielectric constant testing method based on the TMmn0 mode cylindrical cavity of the present invention;

[0068] Figure 4 (a) is a cross-section (rectangle) of an actual sample of the present invention and a schematic diagram of the loading position;

[0069] Figure 4 (b) is a cross-section (fan-shaped) diagram of an equivalent sample of the present invention and a schematic diagram of the loading position;

[0070] Figure 5 ε is obtained by fitting a TMmn0 cylindrical cavity test fixture of the present invention. r 'The implicit relationship diagram with k;

[0071] Figure 6 (a) is a top view of the cylindrical cavity test fixture of the present invention;

[0072] Figure 6 (b) is a side view of the cylindrical cavity test fixture of the present invention;

[0073] Figure 7A test fixture loaded with a sample to be tested and connected to a vector network analyzer according to the present invention;

[0074] Figure 8 The figure is a schematic diagram of the structure of an electronic device of the present invention. DETAILED DESCRIPTION

[0075] The frequency distribution of the cylindrical cavity TMmn0 mode is richer, and the selectivity of suitable high-order working modes is more. Therefore, the purpose of the present invention is to propose a complex dielectric constant test method, and it is suitable for a TMmn0 mode cylindrical cavity test fixture, which can effectively solve the excitation, identification and test pain points of the traditional TM0n0 mode cylindrical cavity in high-frequency applications, and provide a new solution for broadband testing of low-loss dielectric materials; this solution, at the same test frequency, because the total mode order of the TMmn0 mode is larger, a smaller test fixture can be implemented, and a higher frequency test can be achieved, which can not only greatly save the fixture cost, but also greatly expand the application space of the resonant cavity method.

[0076] In order to better understand the present invention, the content of the present invention is further described below in conjunction with the accompanying drawings and embodiments.

[0077] Embodiment 1:

[0078] A complex dielectric constant test method based on TMmn0 mode cylindrical cavity, such as Figure 3 As shown, including:

[0079] Step S1: approximating the cross section of the actually loaded sample to be tested to the cross section of the equivalent sample, obtaining a custom parameter a about the electric field integral in the TMmn0 mode, and calculating a custom parameter k about the resonant frequency based on the custom parameter a about the electric field integral;

[0080] Step S2: Modeling the test fixture, scanning the test fixture loaded with the sample to be tested near the resonant frequency of different TMmn0 working modes, and constructing a fitting curve between the real part of the dielectric constant and the custom parameter k about the resonant frequency;

[0081] Step S3: obtaining the real part of the dielectric constant based on the custom parameter k related to the resonant frequency and a fitting curve between the real part of the dielectric constant and the custom parameter k related to the resonant frequency;

[0082] Step S4: Calculate the complex dielectric constant based on the real part of the dielectric constant.

[0083] The present invention provides a complex dielectric constant testing method based on a TMmn0 mode cylindrical cavity. The method has the advantages of dense testing frequency points in a wide frequency band and high testing accuracy for low-loss materials.

[0084] Before introducing the solution of the present invention, the principle that the method can be implemented is first introduced:

[0085] The analytical formula for the complex dielectric constant test of the cavity perturbation method is derived from Maxwell's equations. The analytical formula without any approximation is shown in (1).

[0086]

[0087] Wherein, μ, ε, ω, E, H and V are the complex permeability, complex permittivity, complex resonant frequency, mode electric field, mode magnetic field and resonator volume of the perturbed dielectric material, respectively. Subscript 0 represents the state without perturbation. For E 0 The conjugate electric field, H 0 * H 0 The conjugate magnetic field of . In order to simplify and facilitate application, the perturbation method is introduced here to make two approximations:

[0088] 1. In the entire space of the resonant cavity V 0 Because the introduced disturbance is very weak, it can be considered that the field before and after the disturbance is unchanged. Therefore, the field E,H of the perturbed cavity in the denominator on the right side of equation (1) can be expressed as the field E of the original cavity. 0 , H 0 approximate.

[0089] 2. Replace the denominator ω on the left side of equation (1) with ω 0 approximate.

[0090] After approximation, we get (2)

[0091]

[0092] Integration region V of the right numerator s is the space of material perturbation. From V in equation (1) 0 Change to V s The reason is that V s The dielectric constant change (Δε) and magnetic permeability change (Δμ) in the area outside the region are both 0.

[0093] When the dielectric constant change (Δε) is very small, and this paper only focuses on the test of non-magnetic materials, Δμ = 0, and formula (2) is simplified to obtain:

[0094]

[0095] The study shows that the electric field E in the perturbed material can still be considered a constant and can be expressed as a quasi-static field, which is consistent with the electric field E in the original cavity. 0 There is a functional relationship between them, and the parameter that usually establishes this relationship is the depolarization factor L 0and the complex dielectric constant ε of the perturbative material r , expressed by the following relationship:

[0096]

[0097] Among them, ε r =ε' r -jε" r =ε' r (1-jtanδ); depolarization factor L 0 It is a dimensionless quantity, which is related to the shape of the sample to be tested, its own material properties and the external electric field. Since the test object of this work is a low-loss material (tanδ≤0.01), this means that the loss tangent tanδ is less than 1% of the real part of the dielectric constant. The loss tangent has little effect on the electric field of the perturbed material, and it is reasonable to ignore its influence here; therefore, ε r ≈ε' r Simplifying (3), we get:

[0098]

[0099] When the resonant cavity resonates, the stored electrical energy is equal to the magnetic energy. Further expansion gives

[0100]

[0101] In the formula, f 0 is the original resonant frequency of the resonant cavity, f 1 is the resonant frequency of the resonant cavity after being disturbed, Q 0 is the original quality factor of the resonant cavity, Q 1 is the quality factor of the resonant cavity after disturbance, ε r ' is the real part of the dielectric constant of the perturbation material, ε r " is the imaginary part of the dielectric constant of the perturbation material.

[0102] definition

[0103]

[0104] Where a is a custom integral about the electric field, and k is a custom function about the resonant frequency.

[0105] Simplifying (6), we get

[0106]

[0107] Where tanδ is the loss tangent of the perturbation material.

[0108] Formulas (8) and (9) are the test formulas for the complex dielectric constant. (9) shows that it is not necessary to know the depolarization factor to extract the loss tangent, provided that the real part of the dielectric constant ε is first obtained. r '.

[0109] Therefore, the core of the present invention is to first obtain the real part of the dielectric constant by the following numerical method, and then solve the loss tangent value by formula (9). The solution steps are as follows:

[0110] Step S1: approximate the cross section of the actually loaded sample to be tested to the cross section of the equivalent sample, obtain the custom parameter a about the electric field integral in the TMmn0 mode, and calculate the custom parameter k about the resonant frequency based on the custom parameter a about the electric field integral, including:

[0111] The cross section and loading position of the equivalent sample are used to approximate the cross section and loading position of the actual loaded sample to be tested, and the electric field component formula is obtained;

[0112] Substitute the electric field component formula into the calculation formula of the custom parameter a for the electric field integral to obtain the custom parameter a for the electric field integral;

[0113] The custom parameter k regarding the resonance frequency is calculated based on the custom parameter a regarding the electric field integral and a calculation formula for the custom parameter k regarding the resonance frequency.

[0114] Step S1 specifically includes:

[0115] The custom parameter a for the electric field integral is obtained by the following analytical method:

[0116] ① Make the following approximation for the cross section of the actually loaded sample to be tested: Figure 4 As shown, Figure 4 (a) represents the cross section (rectangle) of the actual sample and the loading position, Figure 4 (b) represents the cross-section (sector) of the equivalent sample and the loading position (applicable to TMmn0 mode), and it is necessary to ensure that the actual cross-sectional area = the equivalent cross-sectional area.

[0117] ②The formula for the TMmn0 mode electric field component of the cylindrical resonant cavity is as follows:

[0118]

[0119] Among them, ρ, z is the three directions of cylindrical coordinates; m, n, p represent the three coordinate directions of the cylindrical cavity, ρ, The number of resonances of z; E 0 is the normalized electric field strength; J m (x) is the m-th order Bessel function; k c =p mn / R,Pmn is the nth root of the m-th order Bessel function, and R is the radius of the cylindrical cavity.

[0120] Substituting formula (10) into formula (7), we can obtain the custom parameter a for the electric field integral in the TMmn0 mode, namely:

[0121]

[0122] In the formula, is the value of the custom parameter a for the electric field integral in the TMmn0 mode of the cylindrical resonant cavity, J m (k c ρ) is the m-order Bessel function, is the polar angle of the cylindrical coordinates, m is the order of the Bessel function, θ is the polar angle of the center axis of the cross section of the sample to be tested, β is the radian of the equivalent cross section of the sample to be tested, l 0 is the radial length of the equivalent cross section of the sample to be tested, l 2 is the end radius of the equivalent cross section of the sample to be tested, ρ is the radial coordinate of the cylindrical coordinates, k c =p mn / R (where Pmn is the nth root of the m-order Bessel function), h is the height of the cylindrical cavity, z is the height coordinate of the cylindrical coordinates, R is the inner diameter of the cylindrical cavity, n is the serial number of the Bessel function root, E 0 is the mode electric field when not disturbed, V is the resonator volume, V s is the volume of the sample to be tested, and E is the mode electric field.

[0123] Derived from this, we get the parameter a is a definite integral of the Bessel function on the radial ρ. The integral formula of this form is as follows:

[0124]

[0125]

[0126] In the formula, x is the independent variable, J' m (k c x) is the Bessel function J m (k c x), J m (k c x) is the Bessel function, J m-1 (x) is the m-1 order Bessel function with respect to the independent variable x, J m+1 (x) is the m+1 order Bessel function with respect to the independent variable x, J' m (x) is the derivative of the m-th order Bessel function with respect to the independent variable x.

[0127] With the above integral formula, the custom parameter a for the electric field integral can be solved smoothly, and the result is a constant.

[0128] Step S2 models the test fixture, scans the test fixture loaded with the sample to be tested near the resonant frequency of different TMmn0 working modes, and constructs a fitting curve between the real part of the dielectric constant and the custom parameter k about the resonant frequency. The specific implementation steps are as follows:

[0129] The test fixture was modeled using the electromagnetic simulation software ANSYS HFSS. Only the real dielectric constant of the material to be tested was used as a variable. The samples to be tested (1≤ε r '≤10, step size 0.1, tanδ=0) test fixture is used for multiple parameter sweeps to establish ε r The sample data of the fitting curve between ' and k can be referred to Figure 5 .

[0130] Step S3: Calculate the custom parameter k about the resonant frequency based on the resonant frequency of the front and rear resonant cavities of the sample to be tested and the custom parameter a about the electric field integral. The specific implementation steps are as follows:

[0131] The cylindrical cavity test fixture is manufactured according to the specifications of the simulation design, such as Figure 6 (a) and Figure 6 (b), dimensions are as follows (mm): θ = 54°, x 0 =70,y 0 =50,l 1 =10.05,w 1 =0.55,l 2 =45, d=240, h=15. Among them, SMA Adaptor is SMA coaxial probe, MUT is the sample to be tested, and then the resonant frequency f of the resonant cavity before and after loading the sample to be tested is tested. 0 and f, and substitute the custom parameter a for the electric field integral calculated in step 1 to obtain the value of parameter k.

[0132] Step S4: obtaining the complex dielectric constant based on the custom parameter k related to the resonant frequency and a fitting curve between the real part of the dielectric constant and the custom parameter k related to the resonant frequency, including:

[0133] Obtaining the real part of the dielectric constant based on the custom parameter k related to the resonant frequency and a fitting curve between the real part of the dielectric constant and the custom parameter k related to the resonant frequency;

[0134] Based on the real part of the dielectric constant and the loss tangent calculation formula, a loss tangent value is obtained;

[0135] The complex dielectric constant is calculated based on the loss tangent value in combination with the real part of the dielectric constant.

[0136] The specific implementation steps of step S4 are as follows:

[0137] By ε r The real part of the dielectric constant of the material to be tested can be obtained by the implicit relationship between ' and k.

[0138] The real part of the dielectric constant is calculated as follows:

[0139]

[0140] In the formula, ε r ' is the real part of the dielectric constant, L 0 is the depolarization factor of the sample to be tested in the electromagnetic field.

[0141] Substitute the real part of the dielectric constant obtained in the previous step into formula (9) to obtain the loss tangent value of the material to be tested;

[0142] The loss tangent value is calculated as follows:

[0143]

[0144] Where tanδ is the loss tangent, ε r " is the imaginary part of the complex dielectric constant, f 0 is the original resonant frequency of the resonant cavity, f 1 is the resonant frequency of the resonant cavity after being disturbed, Q 0 is the original quality factor of the resonant cavity, Q 1 is the quality factor of the resonant cavity after disturbance, ε r ' is the real part of the dielectric constant of the perturbation material, ε r " is the imaginary part of the dielectric constant of the perturbation material.

[0145] The complex dielectric constant is calculated based on the loss tangent value of the material under test and the real part of the dielectric constant.

[0146] The complex dielectric constant is calculated as follows:

[0147] ε r =ε' r -jε" r =ε' r (1-jtanδ)

[0148] In the formula, ε r is the complex dielectric constant, and j represents the imaginary part.

[0149] The advantages of the test method proposed by the present invention are:

[0150] 1. The influence of the depolarization factor is considered, and the modified analytical formulas (8) and (9) are proposed, which is conducive to improving the test accuracy;

[0151] 2. A clever numerical solution method for the complex dielectric constant is proposed, which avoids the extremely complicated analytical solution of the depolarization factor and considers it as an intermediate variable;

[0152] 3. The proposed method for solving the complex dielectric constant breaks through the barrier of using the TMmn0 mode as the working mode, making the new TMmn0 mode cylindrical resonant cavity truly applicable. This test fixture is very suitable for broadband testing of low-loss materials, improving the test bandwidth of the resonant cavity, while also reducing the volume of the test fixture and reducing manufacturing costs.

[0153] Example 2

[0154] The specific implementation scheme of the present invention will be described in detail below with reference to the accompanying drawings.

[0155] The present invention is designed as Figure 7 The test fixture shown, based on which a total of 8 TMmn0 resonance modes are selected as working modes, namely TM330, TM430, TM440, TM540, TM640, TM740, TM840 and TM460, and the resonant frequencies of these working modes are 5.17, 5.72, 7.01, 7.55, 8.07, 8.61, 9.13 and 9.55 GHz, respectively, which are densely distributed in the test frequency band of 5-10 GHz.

[0156] First, using step 1 in the test method, a custom parameter a for electric field integral under different working modes of the test fixture is obtained.

[0157] Then, use step 2 of the test method to obtain the ε of the test fixture in different working modes. r 'The implicit relationship with k.

[0158] Then, the test fixture is manufactured for actual measurement, such as Figure 6 As shown; and use step 3 in the test method to obtain the custom parameter k about the resonant frequency of the sample to be tested (MUT).

[0159] Finally, the loss tangent value and the complex dielectric constant of the sample under test (MUT) are obtained using step 4 of the test method.

[0160] Three commonly used medium samples were used for the actual measurement verification of the test method proposed in the present invention. The test results are shown in Tables 1 and 2:

[0161] Table 1 Test results of the actual dielectric constants of the three samples to be tested

[0162]

[0163] Table 2 Test results of loss tangent of three samples to be tested

[0164]

[0165]

[0166] The results show that this method can achieve the acquisition of complex dielectric constants at relatively dense frequency points within 5-10 GHz, and has good test accuracy.

[0167] Example 3

[0168] The present invention based on the same inventive concept also provides a complex dielectric constant testing system based on a TMmn0 mode cylindrical cavity, comprising:

[0169] The first parameter calculation module is used to approximate the cross section of the actually loaded sample to be tested to the cross section of the equivalent sample, and obtain a custom parameter a about the electric field integral in the TMmn0 mode;

[0170] A relationship building module is used to model the test fixture through ANSYS HFSS, scan the test fixture loaded with the sample to be tested near the resonant frequency of different TMmn0 working modes, and build a fitting curve between the real part of the dielectric constant and the custom parameter k about the resonant frequency;

[0171] A second parameter calculation module, used to calculate a custom parameter k related to the resonance frequency based on the resonance frequency of the front and rear resonance cavities of the sample to be tested and the custom parameter a related to the electric field integral;

[0172] The complex permittivity calculation module is used to obtain the complex permittivity based on the user-defined parameter k related to the resonant frequency and a fitting curve between the real part of the permittivity and the user-defined parameter k related to the resonant frequency.

[0173] Optionally, the first parameter calculation module is specifically used for:

[0174] The cross section and loading position of the equivalent sample are used to approximate the cross section and loading position of the actual loaded sample to be tested, and the electric field component formula is obtained;

[0175] Substitute the electric field component formula into the calculation formula of the custom parameter a for the electric field integral to obtain the custom parameter a for the electric field integral.

[0176] Optionally, the calculation formula for the custom parameter a regarding the electric field integral is as follows:

[0177]

[0178] In the formula, a TMmn0 is the value of the custom parameter a for the electric field integral in the TMmn0 mode of the cylindrical resonant cavity, J m (k c ρ) is the m-order Bessel function, is the polar angle of the cylindrical coordinates, m is the order of the Bessel function, θ is the polar angle of the center axis of the cross section of the sample to be tested, β is the radian of the equivalent cross section of the sample to be tested, l 0 is the radial length of the equivalent cross section of the sample to be tested, l 2 is the end radius of the equivalent cross section of the sample to be tested, ρ is the radial coordinate of the cylindrical coordinates, k c =p mn / R(where P mn is the nth root of the m-order Bessel function), h is the height of the cylindrical cavity, z is the height coordinate of the cylindrical coordinates, R is the inner diameter of the cylindrical cavity, and E is the mode electric field.

[0179] Optionally, the custom parameter k related to the resonant frequency is calculated as follows:

[0180]

[0181] In the formula, f 0 is the original resonant frequency of the resonant cavity, f 1 is the resonant frequency of the resonant cavity after being disturbed.

[0182] Optionally, the complex dielectric constant calculation module is specifically used for:

[0183] Obtaining the real part of the dielectric constant based on the custom parameter k related to the resonant frequency and a fitting curve between the real part of the dielectric constant and the custom parameter k related to the resonant frequency;

[0184] Based on the real part of the dielectric constant and the loss tangent calculation formula, a loss tangent value is obtained;

[0185] The complex dielectric constant is calculated based on the loss tangent value in combination with the real part of the dielectric constant.

[0186] Optionally, the real part calculation module calculates the real part of the dielectric constant according to the following formula:

[0187]

[0188] In the formula, ε r ' is the real part of the dielectric constant, L 0 is the depolarization factor of the sample to be tested in the electromagnetic field.

[0189] Optionally, the loss tangent value is calculated as follows:

[0190]

[0191] Where tanδ is the loss tangent, ε r " is the imaginary part of the complex dielectric constant, f 0 is the original resonant frequency of the resonant cavity, f 1 is the resonant frequency of the resonant cavity after being disturbed, Q 0 is the original quality factor of the resonant cavity, Q 1 is the quality factor of the resonant cavity after disturbance, ε r ' is the real part of the dielectric constant of the perturbation material, ε r " is the imaginary part of the dielectric constant of the perturbation material.

[0192] Optionally, the complex dielectric constant is calculated as follows:

[0193] ε r =ε' r -jε" r =ε' r (1-jtanδ)

[0194] In the formula, ε r is the complex dielectric constant, and j represents the imaginary part.

[0195] Example 4

[0196] like Figure 8 As shown, the present invention also provides an electronic device, which may be a computer device, a single-chip device, an intelligent mobile device, etc. The electronic device in this embodiment may include a processor, a memory, a transceiver component, etc. The memory, the processor, and the transceiver component are connected via a bus; the memory may be used to store an execution program, and an exemplary execution program may include instructions; the processor is used to execute the instructions stored in the memory. The memory may also be used to store data, which may be called and / or modified when the instructions are executed.

[0197] The processor may be a central processing unit (CPU), or other general-purpose processors, digital signal processors (DSP), application-specific integrated circuits (ASIC), field-programmable gate arrays (FPGA) or other programmable logic devices, discrete gates or transistor logic devices, discrete hardware components, etc. It is the computing core and control core of the terminal, which is suitable for implementing one or more instructions, specifically suitable for loading and executing one or more instructions in a storage medium to implement the corresponding method flow or corresponding function, so as to implement the steps of a complex dielectric constant testing method based on a TMmn0 mode cylindrical cavity in the above-mentioned embodiment.

[0198] Example 5

[0199] Based on the same inventive concept, the present invention also provides a readable storage medium, specifically an electronic device readable storage medium (Memory), which is a memory device in an electronic device for storing programs and data. It can be understood that the storage medium here can include both a built-in storage medium in an electronic device and an extended storage medium supported by the electronic device. The storage medium provides a storage space, which stores the operating system of the terminal. In addition, one or more instructions suitable for being loaded and executed by a processor are also stored in the storage space, and these instructions can be one or more execution programs (including program codes). It should be noted that the storage medium here can be a high-speed RAM memory or a non-volatile memory, such as at least one disk memory. The processor loads and executes one or more instructions stored in the storage medium, which can implement the steps of a complex dielectric constant test method based on a TMmn0 mode cylindrical cavity in the above embodiment.

[0200] Those skilled in the art will appreciate that embodiments of the present invention may be provided as methods, systems, or computer program products. Therefore, the present invention may take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Moreover, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0201] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0202] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0203] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0204] The above are merely embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention are included in the scope of the claims of the present invention to be approved.

Claims

1. A complex dielectric constant test method based on TMmn0 mode cylindrical cavity, characterized in that: include: The cross section of the actually loaded sample to be tested is approximated to the cross section of the equivalent sample, and the custom parameter a for the electric field integral in the TMmn0 mode is obtained; The test fixture is modeled, and the test fixture loaded with the sample to be tested is scanned near the resonant frequency of different TMmn0 working modes to construct a fitting curve between the real part of the dielectric constant and the custom parameter k related to the resonant frequency; Calculating a custom parameter k related to the resonance frequency based on the resonance frequencies of the front and rear resonance cavities of the sample to be tested and the custom parameter a related to the electric field integral; The complex dielectric constant is obtained based on the custom parameter k related to the resonant frequency and a fitting curve between the real part of the dielectric constant and the custom parameter k related to the resonant frequency.

2. The method according to claim 1, characterized in that The cross section of the actually loaded sample to be tested is approximated to the cross section of the equivalent sample, and the custom parameter a for the electric field integral in the TMmn0 mode is obtained, including: The cross section and loading position of the equivalent sample are used to approximate the cross section and loading position of the actual loaded sample to be tested, and the electric field component formula is obtained; Substitute the electric field component formula into the calculation formula of the custom parameter a for the electric field integral to obtain the custom parameter a for the electric field integral.

3. The method according to claim 2, characterized in that The calculation formula for the custom parameter a of the electric field integral is as follows: In the formula, is the value of the custom parameter a for the electric field integral in the TMmn0 mode of the cylindrical resonant cavity, J m (k c ρ) is the m-order Bessel function, is the polar angle of the cylindrical coordinates, m is the order of the Bessel function, θ is the polar angle of the center axis of the cross section of the sample to be tested, β is the arc of the equivalent cross section of the sample to be tested, l0 is the radial length of the equivalent cross section of the sample to be tested, l2 is the end radius of the equivalent cross section of the sample to be tested, ρ is the radial coordinate of the cylindrical coordinates, k c =p mn R, P mn is the nth root of the m-th order Bessel function, h is the height of the cylindrical cavity, z is the height coordinate of the cylindrical coordinates, R is the inner diameter of the cylindrical cavity, n is the number of the Bessel function root, E0 is the mode electric field when it is not disturbed, V is the resonator volume, V s is the volume of the sample to be tested, and E is the mode electric field.

4. The method according to claim 3, characterized in that The custom parameter k is calculated as follows: Where f0 is the original resonant frequency of the resonant cavity, and f1 is the resonant frequency of the resonant cavity after being disturbed.

5. The method according to claim 1, characterized in that The step of obtaining the complex dielectric constant based on the custom parameter k related to the resonant frequency and a fitting curve between the real part of the dielectric constant and the custom parameter k related to the resonant frequency comprises: Obtaining the real part of the dielectric constant based on the custom parameter k related to the resonant frequency and a fitting curve between the real part of the dielectric constant and the custom parameter k related to the resonant frequency; Based on the real part of the dielectric constant and the loss tangent calculation formula, a loss tangent value is obtained; The complex dielectric constant is calculated based on the loss tangent value in combination with the real part of the dielectric constant.

6. The method according to claim 5, characterized in that The real part of the dielectric constant is calculated as follows: In the formula, ε r ' is the real part of the dielectric constant, and L0 is the depolarization factor of the sample to be tested in the electromagnetic field.

7. The method according to claim 6, characterized in that The loss tangent value is calculated as follows: Where tanδ is the loss tangent, ε r " is the imaginary part of the complex dielectric constant, f0 is the original resonant frequency of the resonant cavity, f1 is the resonant frequency of the resonant cavity after being disturbed, Q0 is the original quality factor of the resonant cavity, Q1 is the quality factor of the resonant cavity after being disturbed, ε r ' is the real part of the dielectric constant of the perturbation material, ε r " is the imaginary part of the dielectric constant of the perturbation material.

8. The method according to claim 7, characterized in that The complex dielectric constant is calculated as follows: e r =e r '-je r "=e" r '(1-jtanδ) In the formula, ε r is the complex dielectric constant, and j represents the imaginary part.

9. A complex dielectric constant test system based on TMmn0 mode cylindrical cavity, characterized in that: include: The first parameter calculation module is used to approximate the cross section of the actually loaded sample to be tested to the cross section of the equivalent sample, and obtain a custom parameter a about the electric field integral in the TMmn0 mode; A relationship building module is used to model the test fixture, scan the test fixture loaded with the sample to be tested near the resonant frequency of different TMmn0 working modes, and build a fitting curve between the real part of the dielectric constant and the custom parameter k about the resonant frequency; A second parameter calculation module, used to calculate a custom parameter k related to the resonance frequency based on the resonance frequency of the front and rear resonance cavities of the sample to be tested and the custom parameter a related to the electric field integral; The complex permittivity calculation module is used to obtain the complex permittivity based on the user-defined parameter k related to the resonant frequency and a fitting curve between the real part of the permittivity and the user-defined parameter k related to the resonant frequency.

10. An electronic device, characterized in that: include: at least one processor and memory; The memory and the processor are connected via a bus; The memory is used to store one or more programs; When the one or more programs are executed by the at least one processor, the complex dielectric constant testing method based on the TMmn0 mode cylindrical cavity as described in any one of claims 1 to 8 is implemented.

11. A readable storage medium, characterized in that: An execution program is stored thereon, and when the execution program is executed, the complex dielectric constant testing method based on the TMmn0 mode cylindrical cavity as described in any one of claims 1 to 8 is implemented.

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