CN111208171A - Method for judging transmittance performance based on electromagnetic periodic structure impedance characteristic - Google Patents

Method for judging transmittance performance based on electromagnetic periodic structure impedance characteristic Download PDF

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CN111208171A
CN111208171A CN202010029077.7A CN202010029077A CN111208171A CN 111208171 A CN111208171 A CN 111208171A CN 202010029077 A CN202010029077 A CN 202010029077A CN 111208171 A CN111208171 A CN 111208171A
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transmittance
impedance
periodic structure
electromagnetic periodic
electromagnetic
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郭敏
付云起
桑迪
陈强
郑月军
林沂
袁方
郭田田
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National University of Defense Technology
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    • G01N27/02Investigating or analysing materials by the use of electric, electrochemical, or magnetic means by investigating impedance

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Abstract

The invention provides a simple method for judging transmittance performance based on the impedance characteristic of an electromagnetic periodic structure. The technical scheme is as follows: preferably, a plurality of curve values of typical transmittance are drawn under a normalized real part and imaginary part coordinate system of impedance, and a plane is divided into intervals with different transmittance values for judging the transmittance of the electromagnetic periodic structure. And marking the normalized impedance value of the electromagnetic periodic structure on a circular graph with different transmittances to obtain the transmittance of the electromagnetic periodic structure. The invention converts the calculation between the impedance characteristic and the transmittance into an intuitive method of the mark reading in the coordinate system, simplifies the workload, and can be more conveniently applied to the design of electromagnetic periodic structures with different transmittances.

Description

Method for judging transmittance performance based on electromagnetic periodic structure impedance characteristic
Technical Field
The invention belongs to the technical field of electromagnetic materials, and particularly relates to an electromagnetic periodic structure design with different transmittance performances.
Background
The electromagnetic periodic structure is as follows: the frequency selective surface, the circuit simulation wave absorber, the metamaterial wave absorber and the like are effective means for realizing the regulation and control of the spatial electromagnetic wave. Have been widely used in radar and communication systems. The electromagnetic periodic structure with high transmittance can be used in the fields of antenna covers and the like, and the electromagnetic periodic structure with low transmittance can be widely used in the fields of electromagnetic protection, electromagnetic shielding and the like. Therefore, designing electromagnetic periodic structures with different transmittance coefficients is an important research and development direction in the microwave field.
The core of designing the electromagnetic periodic structure with different transmittances is to design the impedance characteristics of the electromagnetic periodic structure, and the different impedance characteristics correspond to the different transmittances. There is a direct link between the impedance characteristic and the transmittance characteristic of the electromagnetic periodic structure, and the expression thereof has been disclosed in reference 1 (m.guo, z.sun, d.sang.x.jia, and y.fu, "Design of Frequency-Selective reflectors Based on central nervous system bound-StripResonator," IEEE Access, vol.7, pp.24964-24970,2019.). However, extensive analysis and study were not conducted, and only a summary expression that the larger the impedance value, the higher the transmittance was given qualitatively was. Nor does it give a range of values for designing electromagnetic periodic structures with different transmittances and their impedance characteristics. Although reference two (q.chen, d.sang.g., m.guo, and y.fu, "minor Frequency-Selective radar With a Wide transmission band Using Circular helical reactor," IEEE Transactions on Antennas and amplification, vol.67, pp.1045,2019.) discloses that the real and imaginary parts of the normalized impedance may form an elliptic curve in a plane when the transmittance is fixed at two specific fixed values. However, the curve characteristics disclosed in the article are greatly different from the actual curve characteristics, and no analytical expression of the curve is given.
In order to improve the efficiency of designing electromagnetic periodic structures with different transmittances, an urgent need exists to deeply study the direct relationship between the impedance characteristic and the transmittance of the electromagnetic periodic structure and provide a simple method for judging the transmittance characteristic based on the impedance characteristic of the electromagnetic periodic structure.
Disclosure of Invention
The invention aims to provide a simple method for judging the transmittance performance based on the impedance characteristic of an electromagnetic periodic structure, which can accurately, efficiently and directly establish the relationship between the transmittance and the impedance characteristic of the electromagnetic periodic structure. According to the method, the transmittance of the electromagnetic periodic structure can be obtained by marking the normalized impedance value of the electromagnetic periodic structure on the circular graphs with different transmittances. The method converts the calculation between the impedance characteristic and the transmittance into an intuitive method of the mark reading in the coordinate system, simplifies the workload, and can be more conveniently applied to the design of electromagnetic periodic structures with different transmittances.
The invention adopts the technical scheme that a method for judging the transmittance performance based on the impedance characteristic of an electromagnetic periodic structure comprises the following steps:
setting the impedance value Z of a known electromagnetic periodic structurepAnd Z isp=Rp+jXp;RpAnd XpThe real and imaginary parts of the impedance values, respectively;
and normalizing the impedance value, wherein the normalization formula is as follows:
Figure BDA0002363615010000011
wherein Z is0Is the wave impedance of free space;
drawing a plurality of circular curves with the transmittance corresponding to T under the normalized real part and imaginary part coordinate systems of the impedance, wherein the expression of the circular curves is as follows:
Figure BDA0002363615010000021
wherein the content of the first and second substances,
Figure BDA0002363615010000022
is the abscissa axis variable of the coordinate system and represents the value of the real impedance part of the normalized electromagnetic periodic structure,
Figure BDA0002363615010000023
the variable of the ordinate axis of the coordinate system represents the value of the impedance imaginary part of the normalized electromagnetic periodic structure; r0Radius ═ T/2(1-T)
Figure BDA0002363615010000024
The value of T is determined according to the actual situation;
impedance value ZpIn the area under the coordinate system, the corresponding transmittance T is the transmittance of the electromagnetic periodic structure.
The invention has the following beneficial effects: when the transmittance of various electromagnetic periodic structures is calculated, the transmittance circular graph (namely, the circular curve corresponding to the transmittance T) is drawn only once, and the electromagnetic periodic structures can be repeatedly used. Therefore, the method for judging the transmittance through the impedance characteristics is simple, convenient, easy and efficient. According to the invention, the transmittance values T with different quantities are selected, and the transmittance T with different densities corresponding to the circular curve can be drawn, so that the transmittance with different precision requirements can be obtained. Therefore, the method has wide application prospect in the field of electromagnetic periodic structure analysis and design.
Drawings
FIG. 1 is a circular plot of transmission T in normalized real and imaginary coordinate systems of impedance;
fig. 2 is a circular curve with 70%, 80%, 90% transmittance T in normalized real and imaginary impedance coordinates;
fig. 3 is a circular curve at a transmittance T of 40%, 50%, 60% in normalized real and imaginary impedance coordinates;
fig. 4 is a circular curve at 10%, 20%, 30% transmittance T in normalized real and imaginary impedance coordinates;
FIG. 5 is a schematic diagram of the principle of a simple method for designing transmittance.
Detailed Description
The invention is further illustrated below with reference to the figures and tables.
It should be noted that, in the normalized real and imaginary coordinate systems of the impedance, the shape corresponding to the curve with transmittance T given by the present invention is a circular curve, not an elliptic curve. Meanwhile, the invention also provides an analytical expression of the curve, and the conclusion is finally proved in the text. The core idea of the invention is to draw a plurality of curve values of typical transmittance under a normalized real part and imaginary part coordinate system of impedance, and divide a plane into intervals with different transmittance values for judging the transmittance of the electromagnetic periodic structure.
FIG. 1 is a circular plot of transmission T in normalized real and imaginary coordinate systems of impedance; the expression of this curve satisfies the expression provided in the summary of the invention. The abscissa in the figure represents the real part of the impedance of the normalized electromagnetic periodic structure and the ordinate represents the imaginary part of the impedance of the normalized electromagnetic periodic structure; the circles drawn by the dotted lines represent the corresponding circular curves when the transmittance is T, and the regions indicated by the grid lines represent
Figure BDA0002363615010000026
The real part of the impedance of the electromagnetic periodic structure must be greater than or equal to zero, so that the region is not considered when the transmittance is judged.
Fig. 2 is a circular curve with 70%, 80%, 90% transmittance T in normalized real and imaginary impedance coordinates; fig. 3 is a circular curve with a transmittance T of 40%, 50%, 60% in normalized real and imaginary impedance coordinates; fig. 4 is a circular plot of transmission T at 10%, 20%, 30% in normalized real and imaginary impedance coordinates. FIGS. 2, 3 and 4 are graphs for determining transmittance intervals, which are graphs obtained by plotting normalized impedance coordinates of electromagnetic periodic structures
Figure BDA0002363615010000025
The transmittance is marked in the coordinate system, which is the transmittance range of the corresponding section. For example: in FIG. 3, according to
Figure BDA0002363615010000031
In the region, 50% is obtained<T<60 percent; in FIG. 4, according to
Figure BDA0002363615010000032
In the region where 0 is obtained<T<10%。
By using the idea of the invention, a simple method for designing the transmittance is provided under the condition of low precision requirement. For any transmittance T, it can be plotted as an impedance circle in the normalized impedance coordinate system, as shown in fig. 1. The impedance artwork may be represented as an approximate rectangle having a long side equal to the diameter of the impedance circle and a short side Rrm=R0+ r, as shown in fig. 5, using a rectangle with three sides tangent to the impedance circle; the coordinate abscissa of the rightmost end of the rectangle is Rrm(ii) a The vertical coordinates of the upper end and the lower end of the rectangle are +/-
Figure BDA0002363615010000033
The design rule of the method is as follows: if the design transmittance requirement is greater than T,
Figure BDA0002363615010000034
or
Figure BDA0002363615010000035
And (4) finishing.
The following demonstrates that the proof process of the transmittance T curve expression given by the present invention under the normalized real and imaginary coordinate systems is described as follows:
the transmittance and transmission coefficient formulas of the known electromagnetic periodic structure are as follows:
T=S21 2
substituting the formula (3) of reference one mentioned in the background of the invention into the above formula yields the following formula:
Figure BDA0002363615010000036
the curve represented by the above expression is known as ellipse by using the second referenceA circle, an ellipse is circular if the major axis of the ellipse is equal to the minor axis. Order to
Figure BDA0002363615010000037
The major axis of the ellipse can be found to be
Figure BDA0002363615010000038
Order to
Figure BDA0002363615010000039
The minor axis of the ellipse can be found to be
Figure BDA00023636150100000310
Thus, the transmittance T curve is proved to be a circular curve.

Claims (2)

1. A method for judging transmittance performance based on the impedance characteristic of electromagnetic periodic structure, known as the impedance value Z of electromagnetic periodic structurepAnd Z isp=Rp+jXp;RpAnd XpThe real and imaginary parts of the impedance values, respectively;
it is characterized in that the preparation method is characterized in that,
the impedance values are normalized using the following equation:
Figure FDA0002363613000000011
wherein Z is0Is the wave impedance of free space;
drawing a plurality of circular curves with the transmittance corresponding to T under the normalized real part and imaginary part coordinate systems of the impedance, wherein the expression of the circular curves is as follows:
Figure FDA0002363613000000012
wherein the content of the first and second substances,
Figure FDA0002363613000000013
representing the impedance of the normalized electromagnetic periodic structure as a function of the axis of abscissa of the above-mentioned coordinate systemThe value of the real part is,
Figure FDA0002363613000000014
the variable of the ordinate axis of the coordinate system represents the value of the impedance imaginary part of the normalized electromagnetic periodic structure; r0Radius ═ T/2(1-T)
Figure FDA0002363613000000015
The value of T is determined according to the actual situation;
impedance value ZpIn the area under the coordinate system, the corresponding transmittance T is the transmittance of the electromagnetic periodic structure.
2. A method for designing the transmittance of the impedance characteristic of an electromagnetic periodic structure is characterized in that,
if the design transmittance requirement is greater than T, then
Figure FDA0002363613000000016
Or
Figure FDA0002363613000000017
Then the method is finished;
wherein R isrm=R0+r,R0=T/2(1-T),
Figure FDA0002363613000000018
Figure FDA0002363613000000019
Is the real part of the impedance characteristic of the electromagnetic periodic structure;
Figure FDA00023636130000000110
the imaginary part of the impedance characteristic of the electromagnetic periodic structure.
CN202010029077.7A 2020-01-12 2020-01-12 Method for judging transmittance performance based on electromagnetic periodic structure impedance characteristic Pending CN111208171A (en)

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CN107102617A (en) * 2017-06-26 2017-08-29 北京艾利特科技有限公司 A kind of high-precision spatial elliptic curve Real-time Interpolation
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