Design method of complex dielectric constant sensor based on coupled mode theory

Abstract

The invention discloses a complex dielectric constant sensor design method based on a coupling mode theory, and belongs to the technical field of material dielectric property research. The method comprises the following steps: S1, listing a kinetic equation of coupling between electromagnetic modes containing fitting parameters according to a measurement frequency range and a system structure; s2, listing an electromagnetic energy conservation equation in the system according to a Maxwell equation set; s3, according to an undetermined coefficient method, obtaining a relation including fitting parameters between a system scattering coefficient and a medium complex dielectric constant; and S4, determining residual fitting parameters by measuring a standard medium, performing computer simulation and the like to obtain a relationship between the scattering coefficient of the system and the complex dielectric constant of the medium. According to the complex dielectric constant sensor design method based on the coupling mode theory, the universal complex dielectric constant sensor design method is provided from the first principle, and the design of the complex dielectric constant sensor can be effectively guided through the method.

Description

Technical Field

[0001] The invention belongs to the technical field of material dielectric property research, and relates to a complex dielectric constant sensor design method based on coupled mode theory. Background Art

[0002] The complex dielectric constant is an important parameter for describing the electromagnetic properties of materials. It consists of real and imaginary parts, which respectively reflect the material's storage capacity and loss characteristics for electromagnetic energy. The accurate measurement of the complex dielectric constant is of great significance in many fields, such as microwave technology, communication engineering, materials science, biomedicine, and food industry. In particular, in the application of new material research and development, wireless sensor technology, and electromagnetic wave absorption materials, the measurement of the complex dielectric constant is an indispensable technical foundation.

[0003] With the continuous growth of technological demands, the research and development of complex dielectric constant sensors has gradually become a research hotspot. However, existing complex dielectric constant measurement technologies face many challenges in terms of sensitivity, accuracy, frequency coverage, and adaptability to complex environments. For example, although the traditional coaxial probe method, resonant cavity method, and free space method work well under certain conditions, they often have limitations in measuring complex materials, tiny samples, or application scenarios that require real-time monitoring. The shortcomings of these technologies limit the further development of complex dielectric constant measurement technology.

[0004] At present, the design methods of complex dielectric constant sensors are mostly based on empirical formulas or experimental fitting, lacking systematic and theoretical guidance. This design method not only has a long development cycle, but also has difficulty adapting to the needs of different application scenarios. In contrast, starting from the first principles and designing sensors through theoretical models can achieve higher design efficiency and performance optimization, which has significant advantages.

[0005] Coupled mode theory is a powerful tool for analyzing and designing structures such as waveguides and resonators. It has been widely used in the fields of photonics and microwave technology. By describing the energy exchange between different modes, the theory provides a clear physical picture and mathematical tools, which is suitable for in-depth research on complex electromagnetic phenomena. Introducing coupled mode theory into the design of complex dielectric constant sensors can effectively establish the precise connection between sensor structural parameters and measurement performance, thereby providing systematic theoretical guidance for sensor design.

[0006] The complex dielectric constant sensor design method based on coupled mode theory can not only significantly improve the design efficiency, but also can be applied to the design of various types of sensors. The promotion of this method is expected to promote the further development of complex dielectric constant measurement technology and provide strong support for the research and development of new sensors. Summary of the invention

[0007] In view of this, the purpose of the present invention is to provide a design method for a complex dielectric constant sensor based on coupled mode theory. The dynamic equation and the electromagnetic energy conservation equation are written according to the measurement frequency range and the system structure, the two equations are simplified by the method of undetermined coefficients, and finally the fitting parameters are determined by calibration or computer simulation to obtain the relationship between the system scattering coefficient and the complex dielectric constant of the medium.

[0008] In order to achieve the above object, the present invention provides the following technical solutions:

[0009] A method for designing a complex dielectric constant sensor based on coupled mode theory comprises the following steps:

[0010] S1: Write the dynamic equations of coupling between electromagnetic modes including fitting parameters according to the measurement frequency range and system structure;

[0011] S2: Write the conservation equations of electromagnetic energy in the system based on Maxwell's equations;

[0012] S3: The relationship between the system scattering coefficient and the medium complex dielectric constant including the fitting parameters is obtained according to the method of undetermined coefficients;

[0013] S4: Determine the remaining fitting parameters using measurement of standard media, computer simulation, etc., and obtain the relationship between the system scattering coefficient and the complex dielectric constant of the medium.

[0014] Optionally, the system structure includes a resonant structure; and there may be at least one resonant mode in the resonant structure within the measurement frequency range.

[0015] Optionally, the electromagnetic energy in the resonant structure may enter and exit through a radiation channel; and the radiation channel may contain at least one radiation mode within the measurement frequency range.

[0016] The S1 is specifically:

[0017] S11: determining the number of resonant modes in the resonant structure according to the measurement frequency range and the system structure;

[0018] S12: Determine the number of radiation modes in the radiation channel according to the measurement frequency range and the system structure;

[0019] S13: The number of resonant modes and the number of radiation modes are listed to write the dynamic equations of the coupling between electromagnetic modes including the fitting parameters, and the fitting parameters are used to describe the coupling strength between the resonant modes, between the radiation modes, and between the resonant mode and the radiation mode;

[0020] S14: Simplify the equation according to the measurement frequency range and the system structure, eliminate redundant fitting parameters, and obtain the relationship between part or all of the complex dielectric constant of the medium and the resonant frequency of the resonant mode.

[0021] The S2 is specifically:

[0022] Write down the conservation equation of electromagnetic energy in the system. Specifically, the growth rate of electromagnetic energy in the system over time plus the electromagnetic energy discharged from the radiation channel per unit time plus the electromagnetic energy lost in the dielectric per unit time plus the electromagnetic energy input into the system in other ways per unit time is equal to zero.

[0023] The S3 is specifically:

[0024] By making the corresponding terms in the kinetic equation obtained by S1 and the energy conservation equation obtained by S2 equal, the relationship between part or all of the complex dielectric constant of the medium and the fitting parameters is obtained, and further the relationship between the system scattering coefficient and the complex dielectric constant of the medium is obtained.

[0025] The S4 is specifically:

[0026] The remaining fitting parameters are determined by measuring standard media, computer simulation, etc., and the relationship between the system scattering coefficient and the complex dielectric constant of the medium is obtained.

[0027] The beneficial effects of the present invention are:

[0028] In view of the problems that most design methods of traditional complex dielectric constant sensors are based on empirical formulas or experimental fitting, lack systematic and theoretical guidance, have a long development cycle, and are difficult to adapt to the needs of different application scenarios, a design method for complex dielectric constant sensors based on coupled mode theory is provided. Based on this method, a variety of complex dielectric constant sensors based on scattering parameters can be designed. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] In order to more clearly illustrate the technical solution of the present invention, the present invention will be described in detail below with reference to the accompanying drawings, and an embodiment in which the resonant structure is a rectangular resonant cavity and the radiation channel is a waveguide eigenmode is given, wherein:

[0030] Figure 1 This is a flow chart of a design method for a complex dielectric constant sensor based on coupled mode theory;

[0031] Figure 2 This is the schematic diagram of the complex dielectric constant sensor;

[0032] Figure 3 A three-dimensional model diagram of an embodiment of the present invention;

[0033] Figure 4 A schematic diagram of an embodiment of the present invention;

[0034] Figure 5 The relative dielectric constant (ε r ) is the internal electric field distribution diagram of a lossless medium with a resonant frequency of 3;

[0035] Figure 6 is the transmission coefficient (S) of an embodiment of the present invention 21 ) The resonant frequency varies with the lossless medium ε r changing relationships;

[0036] Figure 7 This is an embodiment of the present invention. 21 Amplitude varies with ε r The relationship between the change of dielectric loss tangent (tanδ) of 3;

[0037] Figure 8 This is an embodiment of the present invention. 21 The resonant frequency of the lossless medium ε r changing relationships;

[0038] Fig. 9 The resonant frequency S of an embodiment of the present invention is 21 Amplitude varies with ε r The relationship between the change of tanδ of the medium of 3.

[0039] The corresponding relationship between the reference numerals and the component names is as follows:

[0040] Resonant structure 1, radiation channel 2. DETAILED DESCRIPTION

[0041] Hereinafter, exemplary embodiments of the present invention will be described in conjunction with the accompanying drawings. For the sake of clarity and conciseness, not all features of the actual implementation are described in the specification. However, it should be understood that many implementation-specific decisions must be made in the process of developing any such actual implementation in order to achieve the specific goals of the developer, for example, to meet those restrictions related to the system and business, and these restrictions may vary from implementation to implementation. In addition, it should be understood that although the development work may be very complex and time-consuming, it is only a routine task for those skilled in the art who benefit from the content of the present invention. Here, it should also be noted that in order to avoid obscuring the present invention due to unnecessary details, only the device structure and / or processing steps closely related to the scheme according to the present invention are shown in the accompanying drawings, and other details that are not very relevant to the present invention are omitted.

[0042] Figure 1 This is a flow chart of a complex dielectric constant sensor design method based on coupled mode theory. Figure 1 As shown, the method comprises the following steps:

[0043] S1: Write the dynamic equations of coupling between electromagnetic modes including fitting parameters according to the measurement frequency range and system structure;

[0044] S2: Write the conservation equations of electromagnetic energy in the system based on Maxwell's equations;

[0045] S3: The relationship between the system scattering coefficient and the medium complex dielectric constant including the fitting parameters is obtained according to the method of undetermined coefficients;

[0046] S4: Determine the remaining fitting parameters using measurement of standard media, computer simulation, etc., and obtain the relationship between the system scattering coefficient and the complex dielectric constant of the medium.

[0047] Figure 2 This is the schematic diagram of the complex dielectric constant sensor, where Port includes ports in a physical sense as well as ports in an abstract sense, and electromagnetic energy enters and exits the resonant structure 1 through a radiation channel 2 introduced through Port1, Port2, Port... Specific embodiments

[0049] Design of the complex dielectric constant sensor of rectangular waveguide cuboid resonant cavity:

[0050] Figure 3 The figure is a three-dimensional model diagram of this embodiment. The inner dimensions of the rectangular waveguide are 72.14mm×200mm×8.6mm; the inner dimensions of the rectangular parallelepiped resonant cavity are 72.14mm×70mm×10mm; the rectangular waveguide and the rectangular parallelepiped resonant cavity are coupled through a slit of 72.14mm×1mm×2.03mm; the medium to be measured fills the entire rectangular parallelepiped resonant cavity. The entire sensor is mirror-symmetric about the slit, with the rectangular parallelepiped resonant cavity serving as the resonant structure 1.

[0051] Figure 4 The schematic diagram of this embodiment is shown in FIG. 2 , where the rectangular parallelepiped resonant cavity is used as the resonant structure, and the eigenmode in the rectangular waveguide is used as the radiation channel 2. The mode amplitude of the energy input from the waveguide port is represented by S i+ The mode amplitude of the energy output from the waveguide port is represented by S i -, where i is the port number; the coupling coefficients between the waveguide mode and the resonant cavity mode are represented by K and D; and the mode amplitude in the resonant cavity is represented by |a>. These amplitudes are normalized so that their inner product is energy, as<a|a> represents the energy in the resonant cavity.

[0052] S1: Write the dynamic equations of electromagnetic mode coupling including fitting parameters according to the measurement frequency range and system structure

[0053] The measurement frequency range is selected to be 2.5 to 5.5 GHz. For simplicity, the case where there is only one transmission mode in the rectangular waveguide and only one resonance mode in the rectangular resonant cavity is analyzed.

[0054] The dynamics equation of this system is written as follows

[0055]

[0056] |s - >=C|s + >+D|a>

[0057] where ω 0 Indicates the resonant frequency of the resonant mode after the resonant cavity is filled with the medium to be measured. 1 / τ e and 1 / τ 0 They correspond to radiation loss and dielectric loss respectively. C is the direct scattering matrix between the two ports of the waveguide without resonant cavity coupling.

[0058] According to the system symmetry and energy conservation, we can simplify it and get

[0059]

[0060] According to the energy conservation analysis, the zero input response of the system is |S + >=(0 0) T , can be obtained

[0061]

[0062] Through time reversal transformation, we can get K = D and CD * = -D, we can further get

[0063]

[0064] For an input frequency of ω |S + >, the steady-state solution of the system dynamics equation is

[0065]

[0066] Bring it into |S - >=C|S + >+D|a> can be obtained

[0067]

[0068] So the scattering matrix of the system is

[0069]

[0070] The transmission coefficient is

[0071]

[0072] When the input frequency ω=ω 0 When S 21 A resonance valley appears.

[0073] Figure 5 For this example, ε is measured r The internal electric field distribution diagram of the lossless medium with a value of 3 at the resonant frequency shows that the electromagnetic energy input at one end is completely reflected.

[0074] Figure 6 For this embodiment S 21 With lossless medium ε r According to the measurement frequency range and system structure, ω 0 and the ε of the medium in the resonant cavity r The relationship between

[0075]

[0076] Where μ is the magnetic permeability of the medium, ε is the dielectric constant of the medium, and ε 0 is the dielectric constant of vacuum. Simplifying, we get

[0077]

[0078] S2: Write the electromagnetic energy conservation equations in the system based on Maxwell's equations

[0079] The differential form of Poyting's theorem is

[0080]

[0081] For non-magnetic media, the electric field and magnetic field energy in the system are the same, and the constitutive relation of the electromagnetic field is introduced to obtain

[0082]

[0083] Where ε = ε 0 ε r Then, integrating the area Ω in the entire resonant cavity, we can get

[0084]

[0085] S3: The relationship between the system scattering coefficient and the medium complex dielectric constant including the fitting parameters is obtained according to the method of undetermined coefficients

[0086] For zero input response, the energy conservation equation for this system can also be written as

[0087]

[0088] Combine it with Lianli Kede

[0089]

[0090] Further, according to Available

[0091]

[0092] And because tanδ=σ / (ωε), We can get ω=ω 0 Department

[0093]

[0094] Figure 7 For this embodiment S 21 Amplitude varies with ε r The relationship between the change of tanδ of the medium of 3 can be seen 0 Does not change with tanδ, f 0 =ω 0 / (2π)=3.025GHz. But ω=ω 0 S 21 It increases with the increase of tanδ.

[0095] S4: Determine the fitting parameters through calibration or computer simulation to obtain the relationship between the system scattering coefficient and the complex dielectric constant of the medium

[0096] Determine ε r and ω 0 The relationship between:

[0097] Figure 8 For this embodiment S 21 Omega 0 With lossless medium ε r The dots are the results of numerical simulation, and the gray solid line is

[0098]

[0099] The constant term added at the end can effectively improve the curve fitting effect. Based on this, we can get ε r and ω 0 The relationship between

[0100]

[0101] in The unit is GHz.

[0102] Determine ω=ω 0 tanδ and S 21 The relationship between:

[0103] Fig. 9 For this embodiment f 0 =ω 0 / (2π)=3.025GHz, S 21 Amplitude varies with εr The square points are the results of numerical simulation, and the gray solid line is

[0104]

[0105] From this, we can get tanδ and S 21 The relationship between

[0106]

[0107] In summary, the medium to be tested ε is obtained r , tanδ and the transmission coefficient amplitude S in the scattering coefficient amplitude 21 and the resonant frequency ω 0 The relationship between them completes the design of the sensor.

[0108] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit them. Although the present invention is described in detail with reference to the embodiments, it is understood by those skilled in the art that other embodiments can be envisioned within the scope of the present invention described thereby. In addition, it should be noted that the language used in this specification is mainly selected for the purpose of readability and teaching, rather than for the purpose of explaining or limiting the subject matter of the present invention. Therefore, many modifications and changes are obvious to those of ordinary skill in the art without departing from the scope and spirit of the appended claims. For the scope of the present invention, the disclosure made to the present invention is illustrative rather than restrictive, and the scope of the present invention is defined by the appended claims.

Claims

1. A design method for a complex dielectric constant sensor based on coupled mode theory, characterized in that: The following steps are involved: S1: Write the dynamic equations of coupling between electromagnetic modes including fitting parameters according to the measurement frequency range and system structure; S2: Write the conservation equations of electromagnetic energy in the system based on Maxwell's equations; S3: The relationship between the system scattering coefficient and the medium complex dielectric constant including the fitting parameters is obtained according to the method of undetermined coefficients; S4: Determine the remaining fitting parameters using measurement of standard media, computer simulation, etc., and obtain the relationship between the system scattering coefficient and the complex dielectric constant of the medium.

2. The method for designing a complex dielectric constant sensor based on coupled mode theory according to claim 1, characterized in that: The system structure includes a resonant structure; There may be at least one resonant mode in the resonant structure within the measurement frequency range.

3. The resonant structure according to claim 2, characterized in that: The electromagnetic energy in the resonant structure can enter and exit through the radiation channel; The radiation channel contains no less than one radiation mode within the measurement frequency range.

4. A method for designing a complex dielectric constant sensor based on coupled mode theory according to claims 1 to 3, characterized in that: The S1 is specifically: S11: determining the number of resonant modes in the resonant structure according to the measurement frequency range and the system structure; S12: Determine the number of radiation modes in the radiation channel according to the measurement frequency range and the system structure; S13: The number of resonant modes and the number of radiation modes are listed to write the dynamic equations of the coupling between electromagnetic modes including the fitting parameters, and the fitting parameters are used to describe the coupling strength between the resonant modes, between the radiation modes, and between the resonant mode and the radiation mode; S14: Simplify the equation according to the measurement frequency range and the system structure, eliminate redundant fitting parameters, and obtain the relationship between part or all of the complex dielectric constant of the medium and the resonant frequency of the resonant mode.

5. A method for designing a complex dielectric constant sensor based on coupled mode theory according to claims 1 to 3, characterized in that: The S2 is specifically: Write down the conservation equation of electromagnetic energy in the system. Specifically, the growth rate of electromagnetic energy in the system over time plus the electromagnetic energy discharged from the radiation channel per unit time plus the electromagnetic energy lost in the dielectric per unit time plus the electromagnetic energy input into the system in other ways per unit time is equal to zero.

6. A method for designing a complex dielectric constant sensor based on coupled mode theory according to claims 1 to 3, characterized in that: The S3 is specifically: By making the corresponding terms in the kinetic equation obtained by S1 and the energy conservation equation obtained by S2 equal, the relationship between part or all of the complex dielectric constant of the medium and the fitting parameters is obtained, and further the relationship between the system scattering coefficient and the complex dielectric constant of the medium is obtained.

7. A method for designing a complex dielectric constant sensor based on coupled mode theory according to claims 1 to 3, characterized in that: The S4 is specifically: The remaining fitting parameters are determined by measuring standard media, computer simulation, etc., and the relationship between the system scattering coefficient and the complex dielectric constant of the medium is obtained.

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