CN110247194A - The upper transmittance prediction technique and system of the double-deck bandpass-type frequency selecting structures - Google Patents

The upper transmittance prediction technique and system of the double-deck bandpass-type frequency selecting structures Download PDF

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CN110247194A
CN110247194A CN201910514565.4A CN201910514565A CN110247194A CN 110247194 A CN110247194 A CN 110247194A CN 201910514565 A CN201910514565 A CN 201910514565A CN 110247194 A CN110247194 A CN 110247194A
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黄敏杰
刘虎
武哲
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Beihang University
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    • H01Q15/0013—Devices acting selectively as reflecting surface, as diffracting or as refracting device, e.g. frequency filtering or angular spatial filtering devices said selective devices working as frequency-selective reflecting surfaces, e.g. FSS, dichroic plates, surfaces being partly transmissive and reflective
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Abstract

The invention discloses the upper transmittance prediction techniques and system of a kind of double-deck bandpass-type frequency selecting structures.This method comprises: obtaining electromagnetism wave parameter and medium parameter；Electromagnetism wave parameter includes wave vector in the frequency and vacuum of plane of incidence electromagnetic wave, and medium parameter includes the dielectric constant of each layer overwrite media and the dielectric constant and magnetic conductivity of magnetic conductivity, the dielectric constant of each layer intermediate medium and magnetic conductivity and each layer substrate dielectric；Wave vector normal component and mould admittance are determined according to electromagnetism wave parameter and medium parameter；Objective function is generated according to wave vector normal component and mould admittance；The minimum of calculating target function；The upper transmittance of the double-deck bandpass-type frequency selecting structures is determined according to the minimum of objective function.Using method and system of the invention, having can be in such a way that the upper transmittance of the double-deck bandpass-type frequency selecting structures quickly selects coated by dielectric, so that it is determined that being easiest to the advantages of realizing the medium arrangement form that design performance requires.

Description

Transmission rate upper limit prediction method and system of double-layer band-pass type frequency selection structure
Technical Field
The invention relates to the technical field of communication and electromagnetic filtering, in particular to a method and a system for predicting the upper limit of transmissivity of a double-layer band-pass frequency selection structure.
Background
Frequency Selective Surface (FSS) is widely used in electromagnetic filters of various Frequency bands. In-band transmittance is an important design criterion in the design of a bandpass FSS element such as a radome. It is generally required that the higher the in-band transmittance is, the better the in-band transmittance is, and the lower the out-of-band transmittance is, and the transmittance rapidly decreases away from the central band.
The transmission characteristics of the dual-layer FSS are close to the requirements of people for ideal frequency selection characteristics, and therefore, people have attracted much interest, and although the frequency selection characteristics of the dual-layer FSS are close to the ideal situation, the difficulty is that the in-band transmittance is difficult to improve. At present, the transmittance of the double-layer band-pass type frequency selective structure is researched to be more focused on predicting the transmittance, but the transmittance prediction cannot provide the optimization direction of the design of the double-layer band-pass type frequency selective structure. How to design a high-quality medium loading mode, meet the design performance requirement and improve the in-band transmittance is a problem to be solved urgently by research workers.
Disclosure of Invention
The invention aims to provide a method and a system for predicting the upper limit of the transmissivity of a double-layer band-pass type frequency selection structure, which have the advantages that the upper limit of the transmissivity of the double-layer band-pass type frequency selection structure can be used for quickly selecting a medium loading mode, so that the medium arrangement form which meets the design performance requirement most easily is determined.
In order to achieve the purpose, the invention provides the following scheme:
a method for predicting the upper limit of the transmissivity of a double-layer band-pass type frequency selective structure comprises the following steps:
the double-layer band-pass type frequency selection structure is positioned in a vacuum environment; starting from the electromagnetic wave irradiation side, the double-layer band-pass type frequency selective structure sequentially comprises M layers of covering media, a first frequency selective surface, N layers of middle media, a second frequency selective surface and L layers of substrate media;
acquiring electromagnetic wave parameters and medium parameters; the electromagnetic wave parameters comprise the frequency of an incident plane electromagnetic wave and a vacuum medium wave vector, and the medium parameters comprise the dielectric constant and the magnetic permeability of each layer of covering medium, the dielectric constant and the magnetic permeability of each layer of intermediate medium and the dielectric constant and the magnetic permeability of each layer of substrate medium;
determining a wave vector normal component and a mode admittance according to the electromagnetic wave parameters and the medium parameters;
generating a target function according to the normal component of the wave vector and the mode admittance;
calculating a minimum value of the objective function;
and determining the upper limit of the transmissivity of the double-layer band-pass type frequency selection structure according to the minimum value of the objective function.
Optionally, determining a normal component of a wave vector and a mode admittance according to the electromagnetic wave parameter and the medium parameter specifically includes:
determining the incident electromagnetic wave angular frequency omega by adopting a formula omega-2 pi f according to the frequency f of the incident plane electromagnetic wave;
according to the incident frequency f, using a formulaDetermining an electromagnetic wave propagation constant k in an i-th layer medium(i)(ii) a Wherein epsilon(i)Is the dielectric constant of the ith layer of dielectric; mu.s(i)The magnetic permeability of the ith layer of medium;
according to the vacuum medium wave vectorUsing a formulaDetermining the tangential component of the wave vector in vacuumWherein a coordinate z-axis is established along the thickness direction of the medium of the double-layer bandpass type frequency selective structure,is a z coordinate direction vector;
according to the propagation constant k of electromagnetic wave in the i-th layer medium(i)And the tangential component of the wave vector in the vacuumUsing a formulaDetermining the normal component gamma of the wave vector in the i-th layer medium(i)(ii) a Wherein k istIs the tangential component of the wave vector in said vacuumThe mold of (4); im (·) denotes taking the imaginary part of the complex number;
according to the normal component gamma of the wave vector in the ith layer of medium(i)By the formulaDetermining mode admittance in ith layer of mediaWherein r represents the polarization state; TE polarization represents transverse electric field polarization; TM polarization represents transverse magnetic field polarization.
Optionally, generating an objective function according to the normal component of the wave vector and the mode admittance specifically includes:
according to normal component gamma of wave vector in n layer medium(n)And mode admittance in the n-th layer of dielectricDetermining a transmission matrix; the transmission matrix comprises a first transmission matrix, a second transmission matrix and a third transmission matrix;
determining coefficients of the objective function according to the transmission matrix;
and generating an objective function according to the coefficient of the objective function.
Optionally, the normal component gamma is determined according to the wave vector in the n-th layer medium(n)And mode admittance in the n-th layer of dielectricDetermining a transmission matrix specifically comprises:
calculating a first transmission matrix according to the following formula
Calculating a second transmission matrix according to the following formula
Calculating a third transmission matrix Γ according to the following equation(m,n)：
In the formula, znIs the z coordinate, gamma, of the interface of the nth medium when counting from the incident side of the planar electromagnetic wave(n+1)ξ, the normal component of the wave vector in the n +1 th layer medium(n+1)Is the mode admittance in the (n + 1) th layer of medium, I is an identity matrix, and m and n are natural numbers;
determining the coefficient of the objective function according to the transmission matrix, specifically comprising:
according to b1＝-juMBΩC12A calculating coefficients b of the objective function F (x, y)1；
According to b2＝-juBΩCM12A calculating coefficients b of the objective function F (x, y)2；
According to c ═ Γ11A calculating the coefficient c of the objective function F (x, y);
wherein,
Γ＝Γ(0,M+N+L+1)，
ΓMB＝Γ(M+1,M+N+L+1)，
ΓB＝Γ(M+N+1,M+N+L+1)，
wherein M represents the total number of covering dielectric layers, N represents the total number of intermediate dielectric layers, L represents the total number of substrate dielectric layers, and omegaC12Represents the matrix omegaCElement of row 1, column 2, ΩCM12Represents the matrix omegaCMElement of row 1 and column 2, Γ11The elements of the matrix Γ row 1 and column 1, ΩM12Represents the matrix omegaMElement of row 1, column 2, ΩM22Represents the matrix omegaMElement of row 2, column 2, zMIs the z coordinate, gamma, of the M-th medium interface when counting from the incident side of the planar electromagnetic wave(M+1)Is the normal component of wave vector in the M +1 th layer medium, gammaMB,11Representation matrix rMBElement of row 1, column 1, ΓMB,21Representation matrix rMBElement of row 2 and column 1, ΓB,11Representation matrix rBElement of row 1, column 1, ΓB,21Representation matrix rBElement of row 2, column 1, γ(M+N+1)Is the normal component of wave vector, z, in the M + N +1 th layer mediumM+NIs the z coordinate of the M + N medium interface when the counting is started from the incident side of the plane electromagnetic wave;
generating an objective function according to the coefficients of the objective function, specifically comprising:
according to the coefficient b1、b2And c generating an objective function F (x, y) ═ xy + b1x+b2y+c。
The invention also provides a system for predicting the upper limit of the transmissivity of the double-layer band-pass frequency selection structure, which comprises the following components:
the parameter acquisition module is used for acquiring electromagnetic wave parameters and medium parameters; the electromagnetic wave parameters comprise the frequency of an incident plane electromagnetic wave and a vacuum medium wave vector, and the medium parameters comprise the dielectric constant and the magnetic permeability of each layer of covering medium, the dielectric constant and the magnetic permeability of each layer of intermediate medium and the dielectric constant and the magnetic permeability of each layer of substrate medium;
the wave vector normal component and mode admittance calculating module is used for determining the wave vector normal component and the mode admittance according to the electromagnetic wave parameters and the medium parameters;
the target function generating module is used for generating a target function according to the normal component of the wave vector and the mode admittance;
the target function minimum value calculation module is used for calculating the minimum value of the target function;
and the transmissivity upper limit determining module is used for determining the transmissivity upper limit of the double-layer band-pass type frequency selection structure according to the minimum value of the objective function.
Optionally, the wave vector normal component and mode admittance calculating module specifically includes:
the incident electromagnetic wave angular frequency calculation unit is used for determining the incident electromagnetic wave angular frequency omega by adopting a formula omega-2 pi f according to the frequency f of the incident plane electromagnetic wave;
an electromagnetic wave propagation constant calculation module for adopting a formula according to the incident frequency fDetermining an electromagnetic wave propagation constant k in an i-th layer medium(i)(ii) a Wherein epsilon(i)Is the dielectric constant of the ith layer of dielectric; mu.s(i)The magnetic permeability of the ith layer of medium;
a tangential component calculation module of wave vector in vacuum for calculating the tangential component of wave vector in vacuumUsing a formulaDetermining the tangential component of the wave vector in vacuumWherein a coordinate z-axis is established along the thickness direction of the medium of the double-layer bandpass type frequency selective structure,is a z coordinate direction vector;
a wave vector normal component calculation module for calculating the normal component of the wave vector according to the propagation constant k of the electromagnetic wave in the ith layer of medium(i)And the tangential component of the wave vector in the vacuumUsing a formulaDetermining the normal component gamma of the wave vector in the i-th layer medium(i)(ii) a Wherein k istIs the tangential component of the wave vector in said vacuumThe mold of (4); im (·) denotes taking the imaginary part of the complex number;
a mode admittance calculating unit for calculating a normal component gamma according to the wave vector in the ith layer of medium(i)By the formulaDetermining mode admittance in ith layer of mediaWherein r represents the polarization state; TE polarization represents transverse electric field polarization; TM polarization represents transverse magnetic field polarization.
Optionally, the objective function generating module specifically includes:
a transmission matrix generating unit for generating a normal component gamma according to a wave vector in the nth layer medium(n)And mode admittance in the n-th layer of dielectricDetermining a transmission matrix; the transmission matrix comprises a first transmission matrix, a second transmission matrix and a third transmission matrix;
an objective function coefficient calculation unit for determining the coefficient of the objective function according to the transmission matrix;
and the target function generating unit is used for generating a target function according to the coefficient of the target function.
Optionally, the transmission matrix generating unit specifically includes:
a first transmission matrix generation subunit for calculating a first transmission matrix according to the following formula
A second transmission matrix generation subunit for calculating a second transmission matrix according to the following formula
A third transmission matrix generation subunit for calculating a third transmission according to the following formulaInput matrix gamma(m,n)：
In the formula, znIs the z coordinate, gamma, of the interface of the nth medium when counting from the incident side of the planar electromagnetic wave(n+1)ξ, the normal component of the wave vector in the n +1 th layer medium(n+1)Is the mode admittance in the (n + 1) th layer of medium, I is an identity matrix, and m and n are natural numbers;
the objective function coefficient calculating unit specifically includes:
coefficient b1A calculation subunit for calculating according to b1＝-juMBΩC12A calculating coefficients b of the objective function F (x, y)1；
Coefficient b2A calculation subunit for calculating according to b2＝-juBΩCM12A calculating coefficients b of the objective function F (x, y)2；
A coefficient c calculation subunit for calculating a coefficient based on c ═ Γ11A calculating the coefficient c of the objective function F (x, y);
wherein,
Γ＝Γ(0,M+N+L+1)，
ΓMB＝Γ(M+1,M+N+L+1)，
ΓB＝Γ(M+N+1,M+N+L+1)，
wherein M represents the total number of covering dielectric layers, N represents the total number of intermediate dielectric layers, L represents the total number of substrate dielectric layers, and omegaC12Represents the matrix omegaCElement of row 1, column 2, ΩCM12Represents the matrix omegaCMElement of row 1 and column 2, Γ11The elements of the matrix Γ row 1 and column 1, ΩM12Represents the matrix omegaMElement of row 1, column 2, ΩM22Represents the matrix omegaMElement of row 2, column 2, zMIs the z coordinate, gamma, of the M-th medium interface when counting from the incident side of the planar electromagnetic wave(M+1)Is the normal component of wave vector in the M +1 th layer medium, gammaMB,11Representation matrix rMBElement of row 1, column 1, ΓMB,21Representation matrix rMBElement of row 2 and column 1, ΓB,11Representation matrix rBElement of row 1, column 1, ΓB,21Representation matrix rBElement of row 2, column 1, γ(M+N+1)Is the normal component of wave vector, z, in the M + N +1 th layer mediumM+NIs the z coordinate of the M + N medium interface when the counting is started from the incident side of the plane electromagnetic wave;
the objective function generation unit specifically includes:
an objective function generation subunit for generating an objective function based on the coefficient b1、b2And c generating an objective function F (x, y) ═ xy + b1x+b2y+c。
Optionally, the transmittance upper limit determining module specifically includes:
a transmittance upper limit calculation unit for calculating a transmittance upper limit according to the objective function F (x, y) ═ xy + b1x+b2Minimum value min (| F |) of y + c by adopting a formulaCalculating the upper limit T of the transmissivity of the double-layer band-pass frequency selection structuretopWhere | F | is the modulus of the objective function F (x, y) and | a | is the modulus of a.
Compared with the prior art, the invention has the beneficial effects that:
the invention provides a method and a system for predicting the upper limit of transmissivity of a double-layer band-pass type frequency selection structure, which can determine the upper limit of the transmissivity of the double-layer band-pass type frequency selection structure by acquiring the frequency of incident plane electromagnetic waves, wave vectors in vacuum, the dielectric constant and the magnetic permeability of a covering medium, the dielectric constant and the magnetic permeability of an intermediate medium and the dielectric constant and the magnetic permeability of a substrate medium, thereby showing that the double-layer band-pass type frequency selection structure has an upper limit of the transmissivity irrelevant to a frequency selection surface FSS and a unit array shape, rapidly selecting a medium loading mode and a given electromagnetic wave irradiation mode by utilizing the upper limit of the transmissivity of the double-layer band-pass type frequency selection structure, designing the maximum value of the transmissivity which can be reached by an array and a unit array, determining a medium arrangement mode which most easily realizes design performance requirements, and avoiding the proposal of, the problem that the optimization direction of the double-layer band-pass type frequency selection structure design cannot be given only through the calculation of the transmissivity in the prior art is solved.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings without inventive exercise.
FIG. 1 is a flowchart of a method for predicting an upper limit of transmittance of a dual-layer bandpass frequency selective structure according to an embodiment of the present invention;
FIG. 2 is a diagram of an upper-limit transmittance prediction system for a dual-layer bandpass frequency selective structure according to an embodiment of the present invention;
FIG. 3 is a schematic cross-sectional view of a frequency selective structure of a dual-layer array according to an embodiment of the present invention;
FIG. 4 is an equivalent transmission line model of a dual-layer array frequency selective structure according to an embodiment of the present invention;
FIG. 5 is a cross-sectional view of another dual-layer array frequency selective structure according to an embodiment of the present invention;
FIG. 6 is a schematic diagram of an FSS array configuration in accordance with an embodiment of the present invention;
FIG. 7 is a graph of transmittance versus 0 degrees incident angle for an example of the present invention;
FIG. 8 is a graph showing transmittance contrast under irradiation of TE polarized electromagnetic waves at an incident angle of 60 degrees in the example of the present invention;
FIG. 9 is a graph showing transmittance contrast under irradiation of a TM polarized electromagnetic wave at an incident angle of 60 degrees in an example of the present invention;
FIG. 10 is a graph showing the transmittance of TE polarized electromagnetic waves at an incident angle of 15 degrees in accordance with an embodiment of the present invention;
FIG. 11 is a schematic diagram of another FSS array configuration in accordance with an embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The invention aims to provide a method and a system for predicting the upper limit of the transmissivity of a double-layer band-pass type frequency selection structure, which have the advantages that the upper limit of the transmissivity of the double-layer band-pass type frequency selection structure can be used for quickly selecting a medium loading mode, so that the medium arrangement form which meets the design performance requirement most easily is determined.
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in further detail below.
Examples
Fig. 1 is a flowchart of a method for predicting an upper limit of transmittance of a dual-layer bandpass frequency selective structure according to an embodiment of the present invention, as shown in fig. 1, the method for predicting an upper limit of transmittance of a dual-layer bandpass frequency selective structure is provided, and the dual-layer bandpass frequency selective structure is located in a vacuum environment; the double-layer band-pass type frequency selection structure sequentially comprises an M layer of covering medium, a first frequency selection surface, an N layer of middle medium layer, a second frequency selection surface and an L layer of substrate medium layer from bottom to top; the planar electromagnetic wave is incident to the double-layer band-pass type frequency selection structure from the lower surface of the covering medium.
Establishing a coordinate system according to the double-layer band-pass frequency selection structure and the plane electromagnetic wave irradiation direction; the z axis of the coordinate system takes the thickness direction of the frequency selective structure and points to the transmission side from the incident side of the electromagnetic wave; the x axis and the y axis of the coordinate system are parallel to the medium interface of the frequency selection structure, and the origin is taken on the lower surface of the first layer of covering medium on the incident side.
A method for predicting the upper limit of the transmissivity of a double-layer band-pass frequency selection structure comprises the following specific steps:
step 101: acquiring electromagnetic wave parameters and medium parameters; the electromagnetic wave parameters comprise the frequency of an incident plane electromagnetic wave and a vacuum medium wave vector, and the medium parameters comprise the dielectric constant and the magnetic permeability of each layer of covering medium, the dielectric constant and the magnetic permeability of each layer of intermediate medium and the dielectric constant and the magnetic permeability of each layer of substrate medium.
Step 102: and determining the normal component of the wave vector and the mode admittance according to the electromagnetic wave parameters and the medium parameters. The method specifically comprises the following steps:
determining the angular frequency omega of the incident electromagnetic wave by adopting a formula omega-2 pi f according to the frequency f of the incident plane electromagnetic wave;
according to the incident frequency f, using the formulaDetermining an electromagnetic wave propagation constant k in an i-th layer medium(i)(ii) a Wherein epsilon(i)Is the dielectric constant of the ith layer of dielectric; mu.s(i)The magnetic permeability of the ith layer of medium; wherein i is more than or equal to 1 and less than or equal to M + N + L.
According to the vector of medium wave in vacuumUsing a formulaDetermining the tangential component of the wave vector in vacuumWherein a coordinate z-axis is established along the thickness direction of the medium of the double-layer bandpass type frequency selective structure,is a z coordinate direction vector.
According to the propagation constant k of electromagnetic wave in the i-th layer medium(i)And tangential component of wave vector in vacuumUsing a formulaDetermining the normal component gamma of the wave vector in the i-th layer medium(i)(ii) a Wherein k istIs the tangential component of the wave vector in vacuumThe mold of (4); im (·) denotes taking the imaginary part of the complex number.
According to normal component gamma of wave vector in ith layer medium(i)By the formulaDetermining mode admittance in ith layer of mediaWherein r represents the polarization state; TE polarization represents transverse electric field polarization; TM polarization represents transverse magnetic field polarization.
Step 103: and generating an objective function according to the normal component of the wave vector and the mode admittance. The method specifically comprises the following steps:
calculating a first transmission matrix according to the following formula
Calculating a second transmission matrix according to the following formula
Calculating a third transmission matrix Γ according to the following equation(m,n)：
In the formula, znIs the z coordinate, gamma, of the interface of the nth medium when counting from the incident side of the planar electromagnetic wave(n+1)ξ, the normal component of the wave vector in the n +1 th layer medium(n+1)Is the mode admittance in the (N + 1) th layer of medium, I is an identity matrix, M and N are natural numbers, wherein M is more than or equal to 1 and less than or equal to M + N + L, and N is more than or equal to 1 and less than or equal to M + N + L.
According to b1＝-juMBΩC12A calculating the coefficients b of the objective function F (x, y)1；
According to b2＝-juBΩCM12A calculating the coefficients b of the objective function F (x, y)2；
According to c ═ Γ11A calculating the coefficient c of the target function F (x, y);
wherein,
Γ＝Γ(0,M+N+L+1)，
ΓMB＝Γ(M+1,M+N+L+1)，
ΓB＝Γ(M+N+1,M+N+L+1)，
wherein M represents the total number of covering dielectric layers, N represents the total number of intermediate dielectric layers, L represents the total number of substrate dielectric layers, and ΩC12Represents the matrix omegaCElement of row 1, column 2, ΩCM12Represents the matrix omegaCMElement of row 1 and column 2, Γ11The elements of the matrix Γ row 1 and column 1, ΩM12Represents the matrix omegaMElement of row 1, column 2, ΩM22Represents the matrix omegaMElement of row 2, column 2, zMIs the z coordinate, gamma, of the M-th medium interface when counting from the incident side of the planar electromagnetic wave(M+1)Is the normal component of wave vector in the M +1 th layer medium, gammaMB,11Representation matrix rMBElement of row 1, column 1, ΓMB,21Representation matrix rMBElement of row 2 and column 1, ΓB,11Representation matrix rBElement of row 1, column 1, ΓB,21Representation matrix rBElement of row 2, column 1, γ(M+N+1)Is the normal component of wave vector, z, in the M + N +1 th layer mediumM+NIs the z coordinate of the interface of the M + N medium when counting from the incident side of the plane electromagnetic wave.
According to the coefficient b1、b2And c generating an objective function F (x, y) ═ xy + b1x+b2y+c。
Step 104: the minimum value min (| F |) of the target function is calculated.
Step 105: and determining the upper limit of the transmissivity of the double-layer band-pass type frequency selection structure according to the minimum value of the objective function.
According to the target function F (x, y) ═ xy + b1x+b2The minimum value min (| F |) of y + c adopts a formulaCalculating the upper limit T of the transmissivity of the double-layer band-pass frequency selection structuretopWhere | F | is the modulus of the objective function F (x, y) and | a | is the modulus of a.
Fig. 2 is a structural diagram of a transmittance upper limit prediction system of a dual-layer bandpass frequency selective structure according to an embodiment of the present invention, and as shown in fig. 2, the transmittance upper limit prediction system of the dual-layer bandpass frequency selective structure includes:
a parameter obtaining module 201, configured to obtain electromagnetic wave parameters and medium parameters; the electromagnetic wave parameters comprise the frequency of an incident plane electromagnetic wave and a vacuum medium wave vector, and the medium parameters comprise the dielectric constant and the magnetic permeability of each layer of covering medium, the dielectric constant and the magnetic permeability of each layer of intermediate medium and the dielectric constant and the magnetic permeability of each layer of substrate medium.
And a wave vector normal component and mode admittance calculation module 202, configured to determine a wave vector normal component and a mode admittance according to the electromagnetic wave parameter and the medium parameter.
The wave vector normal component and mode admittance calculating module 202 specifically includes:
the incident electromagnetic wave angular frequency calculation unit is used for determining the incident electromagnetic wave angular frequency omega by adopting a formula omega-2 pi f according to the frequency f of the incident plane electromagnetic wave;
an electromagnetic wave propagation constant calculation module for adopting a formula according to the incident frequency fDetermining an electromagnetic wave propagation constant k in an i-th layer medium(i)(ii) a Wherein epsilon(i)Is the dielectric constant of the ith layer of dielectric; mu.s(i)The magnetic permeability of the ith layer of medium;
a tangential component calculation module of wave vector in vacuum for calculating the tangential component of wave vector in vacuumUsing a formulaDetermining the tangential component of the wave vector in vacuumWherein a coordinate z-axis is established along the thickness direction of the medium of the double-layer bandpass type frequency selective structure,is a z coordinate direction vector;
a wave vector normal component calculation module for calculating the normal component of the wave vector according to the propagation constant k of the electromagnetic wave in the ith layer of medium(i)And tangential component of wave vector in vacuumUsing a formulaDetermining the normal component gamma of the wave vector in the i-th layer medium(i)(ii) a Wherein k istIs the tangential component of the wave vector in vacuumThe mold of (4); im (·) denotes taking the imaginary part of the complex number;
a mode admittance calculating unit for calculating a normal component gamma according to a wave vector in the ith layer medium(i)By the formulaDetermining mode admittance in ith layer of mediaWherein r represents the polarization state; TE polarization represents transverse electric field polarization; TM polarization represents transverse magnetic field polarization.
And an objective function generating module 203, configured to generate an objective function according to the normal component of the wave vector and the mode admittance.
The objective function generating module 203 specifically includes:
a transmission matrix generating unit for generating a normal component gamma according to a wave vector in the nth layer medium(n)And mode admittance in the n-th layer of dielectricDetermining a transmission matrix; the transmission matrices include a first transmission matrix, a second transmission matrix, and a third transmission matrix.
The transmission matrix generating unit specifically includes:
a first transmission matrix generation subunit for calculating a first transmission matrix according to the following formula
A second transmission matrix generation subunit for calculating a second transmission matrix according to the following formula
A third transmission matrix generation subunit for calculating a third transmission matrix Γ according to the following formula(m,n)：
In the formula, znIs the z coordinate, gamma, of the interface of the nth medium when counting from the incident side of the planar electromagnetic wave(n+1)ξ, the normal component of the wave vector in the n +1 th layer medium(n+1)Is the mode admittance in the (n + 1) th layer of medium, I is an identity matrix, and m and n are natural numbers.
And the objective function coefficient calculating unit is used for determining the coefficient of the objective function according to the transmission matrix.
The objective function coefficient calculating unit specifically includes:
coefficient b1A calculation subunit for calculating according to b1＝-juMBΩC12A calculating the coefficients b of the objective function F (x, y)1。
Coefficient b2A calculation subunit for calculating according to b2＝-juBΩCM12A calculating the coefficients b of the objective function F (x, y)2。
A coefficient c calculation subunit for calculating a coefficient based on c ═ Γ11A calculates the coefficient c of the objective function F (x, y).
Wherein,
Γ＝Γ(0,M+N+L+1)，
ΓMB＝Γ(M+1,M+N+L+1)，
ΓB＝Γ(M+N+1,M+N+L+1)，
wherein M represents the total number of covering dielectric layers, N represents the total number of intermediate dielectric layers, L represents the total number of substrate dielectric layers, and omegaC12Represents the matrix omegaCElement of row 1, column 2, ΩCM12Represents the matrix omegaCMElement of row 1 and column 2, Γ11The elements of the matrix Γ row 1 and column 1, ΩM12Represents the matrix omegaMElement of row 1, column 2, ΩM22Represents the matrix omegaMElement of row 2, column 2, zMIs the z coordinate, gamma, of the M-th medium interface when counting from the incident side of the planar electromagnetic wave(M+1)Is the normal component of wave vector in the M +1 th layer medium, gammaMB,11Representation matrix rMBElement of row 1, column 1, ΓMB,21Representation matrix rMBElement of row 2 and column 1, ΓB,11Representation matrix rBElement of row 1, column 1, ΓB,21Representation matrix rBElement of row 2, column 1, γ(M+N+1)Is the normal component of wave vector, z, in the M + N +1 th layer mediumM+NIs the z coordinate of the interface of the M + N medium when counting from the incident side of the plane electromagnetic wave.
And the target function generating unit is used for generating the target function according to the coefficient of the target function.
The objective function generation unit specifically includes:
an objective function generation subunit for generating an objective function based on the coefficient b1、b2And c generating an objective function F (x, y) ═ xy + b1x+b2y+c。
And an objective function minimum value calculating module 204, configured to calculate a minimum value min (| F |) of the objective function.
And the upper transmittance limit determining module 205 is used for determining the upper transmittance limit of the double-layer bandpass type frequency selection structure according to the minimum value of the objective function.
The transmittance upper limit determining module 205 specifically includes:
a transmittance upper limit calculation unit for calculating a transmittance upper limit according to the objective function F (x, y) ═ xy + b1x+b2Minimum value min (| F |) of y + c by adopting a formulaCalculating the upper limit T of the transmissivity of the double-layer band-pass frequency selection structuretopWherein | F |Being the modulus of the objective function F (x, y), a is the modulus of a.
Fig. 3 is a schematic cross-sectional view of a two-layer array frequency selective structure having M layers of a cover medium, N layers of an intermediate medium, and L layers of a substrate medium, as shown in fig. 3, with a first frequency selective surface FSS array disposed between the cover medium and the intermediate medium, and a second frequency selective surface FSS array disposed between the intermediate medium and the substrate medium. In FIG. 3, the lowest side and the uppermost side are both vacuum, the z-axis of the coordinate axis is along the thickness direction of the medium, and the z-coordinate of the interface from bottom to top is z0～zM+N+LLet the dielectric constant and permeability of the i-th layer of medium be epsilon(i)And mu(i)(ii) a Let the incident plane electromagnetic wave frequency be f and the incident direction vector be
FIG. 4 is an equivalent transmission line model of a frequency selective structure of a double-layer array, where the equivalent inductance and capacitance parameters of the first FSS array are (L)1,C1) The equivalent inductance and capacitance parameters of the second FSS array are (L)2,C2) The equivalent impedance of the ith layer of medium is Zi。
FIG. 5 is a schematic cross-sectional view of another dual-layer array frequency selective structure for use in verifying the accuracy of the proposed method, the dual-layer array frequency selective structure comprising 1 covering dielectric layer, 3 intermediate dielectric layers and 1 substrate dielectric layer; FIG. 6 is a schematic diagram of a frequency selective surface FSS array structure corresponding to the double-layer array frequency selective structure in FIG. 5, the two layers of frequency selective surface FSS arrays are the same and are obtained by etching circular rings with an inner radius of 3.6mm and a slit width of 0.5mm on copper foil, and circular ring units are arranged in a square shape and have a spacing of 10 mm; in the figure epsilonrAnd tan δ represent the relative dielectric constant and the tangent loss of the medium, respectively.
As shown in fig. 7, fig. 7 is a comparison between the transmittance obtained by the transadmittance calculation and the sample test and the upper limit of the transmittance provided by the present invention under the incident angle of 0 degree in the double-layer array frequency selective structure shown in fig. 5, and it can be seen that neither the transmittance calculation result nor the test result exceeds the upper limit of the transmittance provided by the present invention.
As shown in fig. 8, fig. 8 is a comparison between the transmittance obtained by the transadmittance calculation and the sample test under the irradiation of the TE polarized electromagnetic wave at the incident angle of 60 degrees of the double-layer array frequency selective structure shown in fig. 5 and the transmittance upper limit given by the present invention, from which it can be seen that neither the calculation result nor the test result of the transmittance exceeds the transmittance upper limit given by the present invention.
As shown in fig. 9, fig. 9 is a comparison between the transmittance obtained by the transadmittance calculation and the sample test under the irradiation of the TM polarized electromagnetic wave at the incidence angle of 60 degrees of the double-layer array frequency selective structure shown in fig. 5 and the transmittance upper limit given by the present invention, from which it can be seen that neither the calculation result nor the test result of the transmittance exceeds the transmittance upper limit given by the present invention.
As shown in fig. 10, fig. 10 is a comparison of the transmittance obtained by the mutual admittance method calculation and Finite Element Method (FEM) calculation under the irradiation of TE polarized electromagnetic waves at an incident angle of 15 degrees when the frequency selective surface FSS array is replaced by the closely arranged square ring units as shown in fig. 11, and the transmittance upper limit given by the present invention can be approximated by the reasonable design of the array units.
The invention discloses a rapid prediction method for the upper limit of the transmissivity of a double-layer band-pass frequency selective structure, which is based on a theoretical method for accurately solving the problem of electromagnetic scattering of a planar periodic structure and deduces a calculation method for the upper limit of the transmissivity of the double-layer band-pass frequency selective structure; according to the design characteristics of the finite large frequency selection structure, the electrical property of the finite large frequency selection structure is generally inherited from a planar infinite frequency selection structure, so that the upper limit of the transmissivity can be used for rapidly estimating the possible transmissivity of the double-layer band-pass type frequency selection structure in engineering, and guiding the design optimization direction of the double-layer band-pass type frequency selection structure or avoiding poor medium loading mode design.
By adopting the method for calculating the upper limit of the transmissivity of the double-layer band-pass frequency selection structure, the upper limit of the transmissivity and the equivalent capacitance and inductance parameters (L) of the array1，C1) And (L)2，C2) Regardless, therefore, regardless of the incident design array, the field transmission (the ratio of the transmitted field amplitude to the incident field amplitude) of the two-layer frequency selective structure cannot be higher than the upper transmission limit, as long as the layers of the medium are unchanged and the incident electromagnetic wave form is unchanged.
The field transmittance upper limit of the double-layer band-pass type frequency selective structure provided by the invention can be popularized to the situation of an array with limited thickness, and is irrelevant to the internal structural characteristics of the array, and the internal structural characteristics comprise: whether there are ideal conductors and whether there is a dielectric embedded inside the limited thickness array.
The principles and embodiments of the present invention have been described herein using specific examples, which are provided only to help understand the method and the core concept of the present invention; meanwhile, for a person skilled in the art, according to the idea of the present invention, the specific embodiments and the application range may be changed. In summary, this summary should not be construed to limit the present invention.

Claims (10)

1. A method for predicting the upper limit of the transmissivity of a double-layer band-pass type frequency selective structure is characterized by comprising the following steps:
the double-layer band-pass type frequency selection structure is positioned in a vacuum environment; starting from the electromagnetic wave irradiation side, the double-layer band-pass type frequency selective structure sequentially comprises M layers of covering media, a first frequency selective surface, N layers of middle media, a second frequency selective surface and L layers of substrate media;
acquiring electromagnetic wave parameters and medium parameters; the electromagnetic wave parameters comprise the frequency of an incident plane electromagnetic wave and a vacuum medium wave vector, and the medium parameters comprise the dielectric constant and the magnetic permeability of each layer of covering medium, the dielectric constant and the magnetic permeability of each layer of intermediate medium and the dielectric constant and the magnetic permeability of each layer of substrate medium;
determining a wave vector normal component and a mode admittance according to the electromagnetic wave parameters and the medium parameters;
generating a target function according to the normal component of the wave vector and the mode admittance;
calculating a minimum value of the objective function;
and determining the upper limit of the transmissivity of the double-layer band-pass type frequency selection structure according to the minimum value of the objective function.
2. The method for predicting the upper limit of the transmittance of the double-layer bandpass frequency selective structure according to claim 1, wherein the determining the normal component of the wave vector and the mode admittance according to the electromagnetic wave parameter and the medium parameter specifically comprises:
determining the incident electromagnetic wave angular frequency omega by adopting a formula omega-2 pi f according to the frequency f of the incident plane electromagnetic wave;
according to the incident frequency f, using a formulaDetermining an electromagnetic wave propagation constant k in an i-th layer medium(i)(ii) a Wherein epsilon(i)Is the dielectric constant of the ith layer of dielectric; mu.s(i)The magnetic permeability of the ith layer of medium;
according to the vacuum medium wave vectorUsing a formulaDetermining the tangential component of the wave vector in vacuumWherein a coordinate z-axis is established along the thickness direction of the medium of the double-layer bandpass type frequency selective structure,is a z coordinate direction vector;
according to the propagation constant k of electromagnetic wave in the i-th layer medium(i)And the tangential component of the wave vector in the vacuumUsing a formulaAnd Im (gamma)(i)) Determining the normal component gamma of the wave vector in the ith layer of medium to be less than or equal to 0(i)(ii) a Wherein k istIs the tangential component of the wave vector in said vacuumThe mold of (4); im (·) denotes taking the imaginary part of the complex number;
according to the normal component gamma of the wave vector in the ith layer of medium(i)By the formulaDetermining mode admittance in ith layer of mediaWherein r represents the polarization state; TE polarization represents transverse electric field polarization; TM polarization represents transverse magnetic field polarization.
3. The method for predicting the upper limit of transmittance of the dual-layer bandpass frequency selective structure according to claim 2, wherein generating an objective function according to the normal component of the wave vector and the mode admittance specifically comprises:
according to normal component gamma of wave vector in n layer medium(n)And mode admittance in the n-th layer of dielectricDetermining a transmission matrix; the transmission matrix comprises a first transmission matrix, a second transmission matrix and a third transmission matrix;
determining coefficients of the objective function according to the transmission matrix;
and generating an objective function according to the coefficient of the objective function.
4. The method of predicting the upper limit of transmittance of a double-layer bandpass type frequency selective structure according to claim 3,
according to normal component gamma of wave vector in n layer medium(n)And mode admittance in the n-th layer of dielectricDetermining a transmission matrix specifically comprises:
calculating a first transmission matrix according to the following formula
Calculating a second transmission matrix according to the following formula
Calculating a third transmission matrix Γ according to the following equation(m,n)：
In the formula, znIs the z coordinate, gamma, of the interface of the nth medium when counting from the incident side of the planar electromagnetic wave(n+1)ξ, the normal component of the wave vector in the n +1 th layer medium(n+1)Is the mode admittance in the (n + 1) th layer of medium, I is an identity matrix, and m and n are natural numbers;
determining the coefficient of the objective function according to the transmission matrix, specifically comprising:
according to b1＝-juMBΩC12A calculating coefficients b of the objective function F (x, y)1；
According to b2＝-juBΩCM12A calculating coefficients b of the objective function F (x, y)2；
According to c ═ Γ11A calculating the coefficient c of the objective function F (x, y);
wherein,
Γ＝Γ(0,M+N+L+1)，
ΓMB＝Γ(M+1,M+N+L+1)，
ΓB＝Γ(M+N+1,M+N+L+1)，
wherein M represents the total number of covering dielectric layers, N represents the total number of intermediate dielectric layers, L represents the total number of substrate dielectric layers, and omegaC12Represents the matrix omegaCElement of row 1, column 2, ΩCM12Represents the matrix omegaCMElement of row 1 and column 2, Γ11The elements of the matrix Γ row 1 and column 1, ΩM12Represents the matrix omegaMElement of row 1, column 2, ΩM22Represents the matrix omegaMElement of row 2, column 2, zMIs the z coordinate, gamma, of the M-th medium interface when counting from the incident side of the planar electromagnetic wave(M+1)Is the normal component of wave vector in the M +1 th layer medium, gammaMB,11Representation matrix rMBElement of row 1, column 1, ΓMB,21Representation matrix rMBElement of row 2 and column 1, ΓB,11Representation matrix rBElement of row 1, column 1, ΓB,21Representation matrix rBElement of row 2, column 1, γ(M+N+1)Is the normal component of wave vector, z, in the M + N +1 th layer mediumM+NIs the z coordinate of the M + N medium interface when the counting is started from the incident side of the plane electromagnetic wave;
generating an objective function according to the coefficients of the objective function, specifically comprising:
according to the coefficient b1、b2And c generating an objective function F (x, y) ═ xy + b1x+b2y+c。
5. The method for predicting the upper limit of the transmittance of the double-layer bandpass frequency selective structure according to claim 4, wherein the determining the upper limit of the transmittance of the double-layer bandpass frequency selective structure according to the minimum value of the objective function specifically comprises:
according to the target function F (x, y) ═ xy + b1x+b2Minimum value min (| F |) of y + c by adopting a formulaCalculating the upper limit T of the transmissivity of the double-layer band-pass frequency selection structuretopWhere | F | is the modulus of the objective function F (x, y) and | a | is the modulus of a.
6. A transmittance upper limit prediction system for a two-layer bandpass type frequency selective structure, comprising:
the parameter acquisition module is used for acquiring electromagnetic wave parameters and medium parameters; the electromagnetic wave parameters comprise the frequency of an incident plane electromagnetic wave and a vacuum medium wave vector, and the medium parameters comprise the dielectric constant and the magnetic permeability of each layer of covering medium, the dielectric constant and the magnetic permeability of each layer of intermediate medium and the dielectric constant and the magnetic permeability of each layer of substrate medium;
the wave vector normal component and mode admittance calculating module is used for determining the wave vector normal component and the mode admittance according to the electromagnetic wave parameters and the medium parameters;
the target function generating module is used for generating a target function according to the normal component of the wave vector and the mode admittance;
the target function minimum value calculation module is used for calculating the minimum value of the target function;
and the transmissivity upper limit determining module is used for determining the transmissivity upper limit of the double-layer band-pass type frequency selection structure according to the minimum value of the objective function.
7. The transmittance upper limit prediction system of the double-layer bandpass frequency selective structure according to claim 6, wherein the wave vector normal component and mode admittance calculation module specifically includes:
the incident electromagnetic wave angular frequency calculation unit is used for determining the incident electromagnetic wave angular frequency omega by adopting a formula omega-2 pi f according to the frequency f of the incident plane electromagnetic wave;
an electromagnetic wave propagation constant calculation module for adopting a common mode according to the incident frequency fFormula (II)Determining an electromagnetic wave propagation constant k in an i-th layer medium(i)(ii) a Wherein epsilon(i)Is the dielectric constant of the ith layer of dielectric; mu.s(i)The magnetic permeability of the ith layer of medium;
a tangential component calculation module of wave vector in vacuum for calculating the tangential component of wave vector in vacuumUsing a formulaDetermining the tangential component of the wave vector in vacuumWherein a coordinate z-axis is established along the thickness direction of the medium of the double-layer bandpass type frequency selective structure,is a z coordinate direction vector;
a wave vector normal component calculation module for calculating the normal component of the wave vector according to the propagation constant k of the electromagnetic wave in the ith layer of medium(i)And the tangential component of the wave vector in the vacuumUsing a formulaAnd Im (gamma)(i)) Determining the normal component gamma of the wave vector in the ith layer of medium to be less than or equal to 0(i)(ii) a Wherein k istIs the tangential component of the wave vector in said vacuumThe mold of (4); im (·) denotes taking the imaginary part of the complex number;
die guideA nano-computing unit for calculating the normal component gamma according to the wave vector in the ith layer of medium(i)By the formulaDetermining mode admittance in ith layer of mediaWherein r represents the polarization state; TE polarization represents transverse electric field polarization; TM polarization represents transverse magnetic field polarization.
8. The transmittance upper limit prediction system of the double-layer bandpass type frequency selection structure according to claim 7, wherein the objective function generation module specifically includes:
a transmission matrix generating unit for generating a normal component gamma according to a wave vector in the nth layer medium(n)And mode admittance in the n-th layer of dielectricDetermining a transmission matrix; the transmission matrix comprises a first transmission matrix, a second transmission matrix and a third transmission matrix;
an objective function coefficient calculation unit for determining the coefficient of the objective function according to the transmission matrix;
and the target function generating unit is used for generating a target function according to the coefficient of the target function.
9. The upper limit transmission prediction system of a two-layer bandpass frequency selective structure according to claim 8,
the transmission matrix generating unit specifically includes:
a first transmission matrix generation subunit for calculating a first transmission matrix according to the following formula
A second transmission matrix generation subunit for calculating a second transmission matrix according to the following formula
A third transmission matrix generation subunit for calculating a third transmission matrix Γ according to the following formula(m,n)：
In the formula, znIs the z coordinate, gamma, of the interface of the nth medium when counting from the incident side of the planar electromagnetic wave(n+1)ξ, the normal component of the wave vector in the n +1 th layer medium(n+1)Is the mode admittance in the (n + 1) th layer of medium, I is an identity matrix, and m and n are natural numbers;
the objective function coefficient calculating unit specifically includes:
coefficient b1A calculation subunit for calculating according to b1＝-juMBΩC12A calculating coefficients b of the objective function F (x, y)1；
Coefficient b2A calculation subunit for calculating according to b2＝-juBΩCM12A calculating coefficients b of the objective function F (x, y)2；
A coefficient c calculation subunit for calculating a coefficient based on c ═ Γ11A calculating the coefficient c of the objective function F (x, y);
wherein,
Γ＝Γ(0,M+N+L+1)，
ΓMB＝Γ(M+1,M+N+L+1)，
ΓB＝Γ(M+N+1,M+N+L+1)，
wherein M represents the total number of covering dielectric layers, N represents the total number of intermediate dielectric layers, L represents the total number of substrate dielectric layers, and omegaC12Represents the matrix omegaCElement of row 1, column 2, ΩCM12Represents the matrix omegaCMElement of row 1 and column 2, Γ11The elements of the matrix Γ row 1 and column 1, ΩM12Represents the matrix omegaMElement of row 1, column 2, ΩM22Represents the matrix omegaMElement of row 2, column 2, zMIs the z coordinate, gamma, of the M-th medium interface when counting from the incident side of the planar electromagnetic wave(M+1)Is the normal component of wave vector in the M +1 th layer medium, gammaMB,11Representation matrix rMBLine 1, no1 column of elements, ΓMB,21Representation matrix rMBElement of row 2 and column 1, ΓB,11Representation matrix rBElement of row 1, column 1, ΓB,21Representation matrix rBElement of row 2, column 1, γ(M+N+1)Is the normal component of wave vector, z, in the M + N +1 th layer mediumM+NIs the z coordinate of the M + N medium interface when the counting is started from the incident side of the plane electromagnetic wave;
the objective function generation unit specifically includes:
an objective function generation subunit for generating an objective function based on the coefficient b1、b2And c generating an objective function F (x, y) ═ xy + b1x+b2y+c。
10. The transmittance upper limit prediction system of the double-layer bandpass type frequency selective structure according to claim 9, wherein the transmittance upper limit determination module specifically includes:
a transmittance upper limit calculation unit for calculating a transmittance upper limit according to the objective function F (x, y) ═ xy + b1x+b2Minimum value min (| F |) of y + c by adopting a formulaCalculating the upper limit T of the transmissivity of the double-layer band-pass frequency selection structuretopWhere | F | is the modulus of the objective function F (x, y) and | a | is the modulus of a.
CN201910514565.4A 2019-06-14 2019-06-14 The upper transmittance prediction technique and system of the double-deck bandpass-type frequency selecting structures Pending CN110247194A (en)

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Application publication date: 20190917