A method for calculating characteristic impedance of asymmetric transverse electromagnetic wave transmission chamber

Abstract

The application belongs to the field of electromagnetic compatibility, and particularly relates to a characteristic impedance calculation method of an asymmetric transverse electromagnetic cell (ATEM cell) based on a static field theory. First, a simplified modeling is performed on a middle cross section of a main transmission section of the ATEM cell, and then according to basic principles of electromagnetic fields, positive and negative charge distributions of inner and outer conductors under electrostatic field conditions are calculated. Then, the capacitance of the cross section is calculated according to the calculated charge amount, and finally, the characteristic impedance of the middle cross section of the main transmission section of the ATEM cell is calculated by using a characteristic impedance formula of a lossless transmission line. The characteristic impedance of the middle cross section of the main transmission section of the ATEM cell obtained by the method has a small error compared with the actually tested characteristic impedance, and has practical engineering application significance.

Description

Technical Field

[0001] This invention belongs to the research field of electromagnetic wave transmission chambers, specifically involving a method for calculating the characteristic impedance of an asymmetric transverse electromagnetic wave transmission chamber based on static field theory. Background Technology

[0002] With the rapid development of information and electronic technology, the electromagnetic environment is becoming increasingly complex, leading to more severe electromagnetic compatibility (EMC) issues for electronic equipment and a growing demand for testing radiated emissions and immunity. Transverse electromagnetic cell (TEM cell), as a relatively low-cost testing device, is widely used in the field of EMC, often for radiated emission testing and electric field probe calibration. As an improvement over the TEM cell, the asymmetric transverse electromagnetic cell (ATEM cell) offers a larger usable testing space.

[0003] Whether it's a TEM cell or an ATEM cell, it is essentially a section of a two-conductor transmission line that operates in TEM mode. The basic principle is to generate TEM waves between the inner and outer conductor plates of the TEM / ATEM cell.

[0004] As shown in Figure 5, the electromagnetic field distribution inside is similar to that of the coaxial line. The field distribution is relatively uniform, and the electric field value can be calculated conveniently and accurately. Therefore, it can be used for measurement, testing and other applications.

[0005] Currently, for the characteristic impedance of TEM cells, due to their structural symmetry, the empirical formula is relatively accurate for calculation. However, for ATEM cells, whose cross-section is asymmetrical, the results calculated by the empirical formula have a larger error. Summary of the Invention

[0006] The technical problem solved by the present invention: The purpose of the present invention is to address the problems in the background art mentioned above by proposing a precise measurement method for ATEM cells with asymmetrical cross-sections.

[0007] The technical solution of this invention: This invention discloses a method comprising the following steps: First, a simplified model of the cross-section in the middle of the main transmission section of the ATEM cell is performed, and a static field approximation is applied to the field distribution of the cross-section.

[0008] Then, the charge distribution across the cross section is calculated using the matrix method.

[0009] Then, the distributed capacitance of the cross-section is calculated based on the charge distribution of the cross-section.

[0010] Finally, the characteristic impedance is calculated based on the distributed capacitance of the cross-section.

[0011] Furthermore, the following steps are included:

[0012] S1. The inner and outer conductors of the cross-section in the middle of the main transmission section of the ATEM cell are modeled as a filament structure, and the charge is distributed on the filament structure according to a certain rule. It is assumed that the charge distribution on the model conforms to the static field theory.

[0013] S2. Based on the static field approximation theory, calculate the positive and negative charge distribution of the inner and outer conductors of the cross section under electrostatic field conditions;

[0014] S3. Divide the inner and outer conductors of the cross section into grids, and assume that the charge of each segment is concentrated at the midpoint of each grid segment. Use the static field scalar potential formula to calculate the charge value and polarity at the midpoint of each grid segment on the inner and outer conductors. Calculate the distributed capacitance of the cross section based on the calculated charge distribution.

[0015] S4. Based on the distributed capacitance of the cross section, the characteristic impedance of the cross section in the middle of the main transmission section of the ATEM cell is calculated using the characteristic impedance formula of a lossless transmission line.

[0016] Furthermore, the scalar potential formula is as follows:

[0017] (1)

[0018] (2)

[0019] In the formula, r ( x , y () represents the coordinates of the potential observation point, that is, the coordinates of the point where the potential is to be determined. r ’ ( x , y ) represents the coordinates of the charge source point, that is, each charge distribution point (each Δ). L The coordinates of the midpoint of the segment. G ( r, r ’ () represents the Green's function in a static field;

[0020] The formula for calculating scalar potential under discrete conditions is:

[0021] (3)

[0022] In the formula, S represents the midpoint of each grid of the inner and outer conductors, S i Let S represent the i-th point. i The charge at the point is ρi .

[0023] 4. The method for calculating the characteristic impedance of an asymmetric transverse electromagnetic wave transmission chamber, as described above, is characterized by:

[0024] This represents the scalar potential contribution of the charge on the i-th conductor segment to the j-th point; where,

[0025]

[0026] When i≠j

[0027]

[0028] When i=j

[0029]

[0030] Furthermore, the formula for calculating the charge distribution is as follows: ,in,

[0031]

[0032] In the formula,

[0033] , ,

[0034] Furthermore, after calculating the capacitance using the capacitance calculation formula, the impedance is then obtained using the characteristic impedance calculation formula for lossless transmission lines.

[0035] Furthermore, the capacitance calculation formula In the formula, Q Indicates the amount of charge in the inner or outer conductor. U This indicates the voltage between the inner and outer conductors.

[0036] Furthermore, the formula for calculating the characteristic impedance of the lossless transmission line is as follows: ;

[0037] In the formula, μ0 is the free magnetic permeability and ε0 is the dielectric constant.

[0038] Compared with the prior art, the present invention, employing the above technical solution, has the following technical effects:

[0039] 1. The present invention aims to solve the problem of calculating the characteristic impedance of ATEM cells and improve the universality of the characteristic impedance calculation method. The present invention is also applicable to the calculation of the characteristic impedance of TEM cells.

[0040] 2. Since the present invention obtains the characteristic impedance by solving the charge distribution using a numerical algorithm, the specific structure of the cross-section has been considered through modeling during the process of solving the charge distribution. Therefore, the symmetry of the cross-section does not need to be considered in subsequent calculations. Compared with existing empirical formulas, the method proposed in this invention is simple to calculate, has strong algorithm versatility, and has small error. The effectiveness of the calculation method has been verified by time-domain impedance testing. Attached Figure Description

[0041] Figure 1 This is a flowchart of the calculation method of the present invention;

[0042] Figure 2 This is a 3D model of the ATEM cell;

[0043] Figure 3 This is a cross-section of the middle part of the main transmission section of the ATEM cell;

[0044] Figure 4 It is a numerical calculation model of the cross-section of the middle part of the main transmission section of the ATEM cell.

[0045] Figure 5 These are cross-sectional field distribution diagrams of the coaxial line, TEM cell, and ATEM cell;

[0046] Figure 6 It is a method for optimizing numerical calculation models in local areas. Detailed Implementation

[0047] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0048] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings:

[0049] (1) Model simplification

[0050] like Figure 1 The image shown is a 3D view of the ATEM cell. Figure 4 As shown, for ease of calculation, the cross-sectional structure of the main transmission section of the ATEM cell is simplified to the structure shown in Figure 2. Charged thin metal wires are used to replace the inner and outer conductors, and the inner and outer conductors are arranged according to a length of Δ... L Mesh the data as shown in Figure 3 for subsequent numerical calculations, assuming that the inner and outer conductors are divided into N grids of length Δ. LA small segment. The length and width of the cross-section are both L, the width of the inner conductor is Lx, C1 represents the outer conductor, and C2 represents the inner conductor.

[0051] (2) Algorithm Design

[0052] Static Field Basic Theory 1. Calculating Scalar Points

[0053] According to the fundamental theory of static fields, the scalar potential can be calculated using formula (1).

[0054] (1)

[0055] (2)

[0056] in, r ( x , y () represents the coordinates of the potential observation point, that is, the coordinates of the point where the potential is to be determined. r ’ ( x , y ) represents the coordinates of the charge source point, that is, each charge distribution point (each Δ). L The coordinates of the midpoint of the segment. G ( r, r ’ ) represents the Green's function under static field. Formula (1) shows that the potential at a certain point is actually determined by all charges in that space.

[0057] Design of computational methods based on static field theory

[0058] Let S represent the midpoint of each grid on the inner and outer conductors. i Let S represent the i-th point. i The charge at the point is ρ i According to formula (1), the formula for calculating the scalar potential under discrete conditions is as follows (3):

[0059] (3)

[0060] in, (4)

[0061] For ease of subsequent matrix calculations, we define it using formula (4). This represents the contribution of the charge on the i-th conductor segment to the scalar potential at the j-th point.

[0062] When i=j, assume that the charge is uniformly distributed on a short conductor of length ΔL, as follows: Figure 6 S i The gray stripes represent uniformly distributed charges.

[0063] (5)

[0064] because Inside ρ i This is the unknown quantity to be solved, therefore it needs to be separated. According to formulas (4) and (5), formula (6) can be obtained.

[0065] (6)

[0066] When i≠j

[0067] (7)

[0068] When i=j

[0069] (8)

[0070] Therefore, N independent equations can be obtained, as shown in formula (9).

[0071] make:

[0072] , ,

[0073] Then we have:

[0074] (9)

[0075] therefore:

[0076] (10)

[0077] In the formula, γ is the charge at each point to be solved, Φ is the potential at each point, and B is the relation matrix.

[0078] The charge distribution can be calculated using formula (10) based on the known potential information.

[0079] And based on this, the capacitance is calculated according to formula (11). C , Q Indicates the amount of charge in the inner or outer conductor. U This indicates the voltage between the inner and outer conductors.

[0080] (11)

[0081] After calculating the capacitance, the impedance Zc can be calculated according to the characteristic impedance calculation formula (12) for lossless transmission lines, where μ0 and ε0 are the vacuum permeability and dielectric constant, respectively.

[0082] (12)

[0083] Example:

[0084] Taking the 1.2m × 1.2m ATEM cell developed in our laboratory as an example, the calculated and measured values ​​of the characteristic impedance of the middle section of the main transmission segment are as follows:

[0085]

[0086] Through the examples, the time-domain reflection test was conducted, and the result of the time-domain reflection test was used as the accurate value to demonstrate the correctness of the algorithm in calculating the characteristic impedance of the asymmetric transverse electromagnetic wave transmission chamber.

[0087] The above examples are merely preferred embodiments of the present invention and are not intended to limit the invention. This method is applicable not only to the calculation of the characteristic impedance of an ATEM cell but also to the calculation of the characteristic impedance of a TEM cell. For those skilled in the art, the present invention can be modified and varied in various ways. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method of calculating the characteristic impedance of an asymmetric TEM transmission cell, characterized by: The method comprises the following steps of: First, a cross section in the middle of the main transmission section of the ATEM cell is simplified modeled, the cross section field distribution is approximated by a static field, then the charge distribution of the cross section is calculated based on the matrix method, then the distributed capacitance of the cross section is calculated according to the charge distribution of the cross section, and finally the characteristic impedance is calculated according to the distributed capacitance of the cross section; The method comprises the following steps of: S1. The inner and outer conductors of the cross section in the middle of the main transmission section of the ATEM cell are modeled as filament structures, charges are regularly distributed on the filament structures, and it is assumed that the charge distribution on the model conforms to the static field theory; S2. Based on the static field approximation theory, the positive and negative charge distributions of the inner and outer conductors of the cross section under the electrostatic field condition are calculated; S3. The inner and outer conductors of the cross section are meshed, and it is assumed that the charge of each segment is concentratedly distributed at the midpoint of each mesh segment, the scalar potential formula of the static field is used to calculate the charge value and polarity at the midpoint of each mesh segment of the inner and outer conductors, and the distributed capacitance of the cross section is calculated according to the calculated charge distribution; S4. According to the distributed capacitance of the cross section, the characteristic impedance formula of the lossless transmission line is used to calculate the cross section characteristic impedance in the middle of the main transmission section of the ATEM cell.

2. The method of claim 1, wherein: The scalar potential formula is: ； (1) ； (2) In the formula, r x y represents the coordinates of the potential observation point, i.e. the coordinates of the point where the potential is sought, r ’ x y represents the coordinates of the charge source point, i.e. the coordinates of each charge distribution point (the midpoint of each L G r, r ’ represents the Green function under static field;​​​​​​ The scalar potential calculation formula under the discrete condition is: ； (3) In the formula, S represents the midpoint of each mesh of the inner and outer conductors, S i represents the i-th point, and it is assumed that the charge of the point S i is ρ i .

3. The characteristic impedance calculation method of the asymmetric transverse electromagnetic wave transmission cell according to claim 2, characterized in that: Qi,j represents the scalar potential contribution of the charge on the ith segment of conductor to the jth point; wherein, ； When i≠j, ； When i=j, 。 4. The method of claim 3, wherein: The charge distribution calculation formula is wherein, ； In the formula, ， , 。 5. The method of claim 1-4, wherein: After the capacitance is calculated by the capacitance calculation formula, the impedance is obtained according to the characteristic impedance calculation formula of the lossless transmission line.

6. The characteristic impedance calculation method of the asymmetric transverse electromagnetic wave transmission cell according to claim 5, characterized in that: The capacitance calculation formula ; wherein, Q represents the inner conductor or outer conductor charge amount, U represents the inner and outer conductor voltage.

7. The method of claim 6, wherein: The characteristic impedance calculation formula of the lossless transmission line is ; In the formula, μ0 is the vacuum permeability, and ε0 is the dielectric constant.

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