CN108182336A - The computational methods of phased array antenna directional diagram under plasma sheath - Google Patents
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Abstract
The invention discloses a kind of computational methods of phased array antenna directional diagram under plasma sheath, determine basic module and the spatial position of phased array antenna array element, establish the computation model of phased array antenna under plasma sheath；Calculate the transmission coefficient of parallel polarization electromagnetic wave and vertical polarization electromagnetic wave Jing Guo plasma sheath；The port feed current of each array element of phased array antenna is set, obtains the mutual coupling matrix between each array element, the port current of each array element when calculating actual transmission under the influence of plasma sheath, calculates the electromagnetic field of the near field region of each array element；It obtains phased array antenna near field and passes through the electric field complex vector after plasma sheath；Coherent superposition processing is carried out to the far-field region radiation field of each array element, obtains the far-field pattern of phased array antenna under plasma sheath.The present invention considers the influence of mutual coupling of the plasma sheath to phased array antenna between each array element, and the accurate far region radiation field for solving phased array antenna under plasma sheath, calculating process is simple, and workload is small.
Description
Technical field
The invention belongs to field of antenna, are related to a kind of computational methods of phased array antenna directional diagram under plasma sheath, fit
For practical engineering application.
Background technology
When spacecraft is with hypersonic reentry, with air shock wave severe friction occurs for aircraft stationary point, makes sky
Gas temperature and pressure steeply rises, and gas molecule is caused to ionize, and generates one layer of plasma sheath for being wrapped in aircraft.Deng
Containing a large amount of free electron in ion sheath, by reflecting the electromagnetism to communicate with sink effect deep fades Spacecraft TT＆C
Signal even results in signal transmission interruption, generates " communicate black barrier " phenomenon.
In order to overcome the problems, such as this, have aerospace expert propose using repeater satellite come alleviate " barrier ".Its basic ideas is
According to plasma sheath electron density distribution feature, antenna is mounted on the weaker aircraft tail portion of plasma sheath, from leeward
It is transmitted towards space-based repeater satellite, the repeated satellite of signal is forwarded to ground control station again, avoids huge when directly communicating over the ground
Big signal energy attenuation, achievees the purpose that alleviate " black barrier ".The transmission distance of signal is the increase in using the cost of trunking method
From with space attenuation amount.Phased array antenna can be easily achieved extremely narrow wave beam and very high gain, be replaced using phased array antenna
For traditional omnidirectional's single antenna, antenna beam is directed toward by position and attitude information with reference to aircraft by beam-forming technology
Repeater satellite improves signal transmission quality, inhibits communication " black barrier " phenomenon.
But plasma sheath is a kind of complex permittivity medium for having consumption dispersion, and with very strong non-homogeneous point
Cloth characteristic has a certain impact to phase array antenna beam synthetic effect and beam-pointing accuracy tool.It is mainly shown as following two
Point：(1) plasma sheath generates stronger refraction action to the electromagnetic wave of aerial radiation, leads to electromagnetic wave on different directions angle
Additional propagation path difference is larger, leads to the distortion of far field coherent superposition；(2) plasma sheath generates strongly anti-to electromagnetic wave
The effect of penetrating, so as to change the mutual coupling between the impedance operator of bay and increase array element；Lead to antenna in far field
Directional diagram changes, and eventually leads to the reduction of antenna radiation performance.Plasma sheath and phased array antenna radiated electromagnetic wave it
Between interact sufficiently complex, therefore phased array antenna in far-field pattern is difficult to obtain under plasma sheath, and there is an urgent need for a kind of fast
Phased array antenna patterns calculating method under speed, accurate acquisition plasma sheath.
Invention content
To solve the above-mentioned problems, the present invention provides a kind of calculating side of phased array antenna directional diagram under plasma sheath
Method, considers the influence of mutual coupling of the plasma sheath to phased array antenna between each array element, accurately solves phased under plasma sheath
The far region radiation field of array antenna, calculating process is simple, and workload is small, solves the problems, such as of the existing technology.
The technical solution adopted in the present invention is the computational methods of phased array antenna directional diagram under a kind of plasma sheath,
Specifically follow the steps below：
Step 1：According to requirement of engineering, basic module and the spatial position of phased array antenna array element are determined, according to plasma
The spatial distribution characteristic of sheath parameter establishes the computation model of phased array antenna under plasma sheath；
Step 2：Using Transmission line analogy, transmission coefficient of the parallel polarization electromagnetic wave Jing Guo plasma sheath is calculated
T||The transmission coefficient t of % and vertical polarization electromagnetic wave Jing Guo plasma sheath⊥%；
Step 3：The amplitude and phase of the port feed current of each array element of phased array antenna are set, it is soft by Electromagnetic Simulation
Mutual coupling matrix under the influence of part acquisition plasma sheath between each array element, the port electricity of each array element when calculating actual transmission
Stream calculates the electromagnetic field of the near field region of each array element；
Step 4：The electromagnetic field of the near field region of each array element is decomposed, obtains the parallel polarization of incident plasma sheath
Component and perpendicular polarisation components substitute into parallel and field strength attenuation and phase delay of the vertical polarization electromagnetic wave Jing Guo plasma sheath
The factor obtains phased array antenna near field and passes through the electric field complex vector after plasma sheath；
Step 5：Coherent superposition processing is carried out to the far-field region radiation field of each array element, phase under plasma sheath is calculated
Control the far-field pattern of array antenna.
The present invention is further characterized in that, further, in the step 1, establishes phased array antenna under plasma sheath
Computation model, specially：Equipped with N=Nx×NyOn a certain plane, spacing is d in the x-direction for a identical radiation element installationx, along y
Direction spacing is dy, the coordinate position of the mn unit is：
According to the electron density change curve of plasma sheath, with adjacent uniform plasma thin layer simulate non-homogeneous grade from
Sub- sheath, n-th layer plasma characteristics frequencies omegap,nIt is calculated according to formula (1)：
Wherein, e is electron charge, neFor the electron density of n-th layer plasma, meFor electron mass, ε0For free space
Dielectric constant；
N-th layer relative dielectric constantIt is calculated according to formula (2)：
Wherein, ω is incoming electromagnetic wave frequency rate, and ν is the collision frequency of plasma, and n is the plasma number of plies, and j represents multiple
The unit of number imaginary part.
Further, in the step 3, the electromagnetic field of the near field region of each array element is calculated, specially：Take the mn array element
Exciting current isImnRepresent the mn array element feed amplitude, βmnThe mn array element current feed phase is represented, is passed through
Mutual coupling matrix under the influence of electromagnetic simulation software CST acquisition plasma sheaths between each array element, the mn array element port are practical
Port current during transmittingIt is calculated according to formula (5)：
Wherein, Smn,pqRepresent the mutual coupling coefficient of the q array element of pth to the mn array element,Represent the excitation of q array element of pth
Electric current；
The mn array element directional diagram is taken to beThe then electromagnetic field E of the near field region of the mn array elementmnAccording to formula (6)
It calculates：
Wherein, k is free space wave number,It is unit vector of the coordinate origin to far field point, R is array element to coordinate origin
Distance,It is position vector of the array element to coordinate origin, θ represents pitch angle,Represent azimuth.
Further, in the step 4, phased array antenna near field pass through plasma sheath after electric field complex vector meter
It calculates, specially：
Wherein,The electric field complex vector after plasma sheath is passed through for phased array antenna near field,It is unit
Vector parallel polarized wave,It is unit vector vertically polarized wave,It is the parallel polarized wave of each array element radiation,It is the vertically polarized wave of each array element radiation；T||(θ) is parallel polarization electromagnetic wave by the multiple saturating of plasma sheath
Penetrate coefficient,It is affixture machine of the vertical polarization electromagnetic wave Jing Guo plasma sheath.
Further, in the step 5, the far-field pattern of phased array antenna is calculated, specially：
Wherein,It is the parallel polarized wave phased array antenna pattern in phased array antenna far field,It is phase
Control the vertically polarized wave phased array antenna pattern in array antenna far field.
The invention has the advantages that it has the following advantages：
1) port current of phased array antenna each array-element antenna in actual transmission is calculated, it is accurate to consider plasma sheath
The influence of mutual coupling to phased array antenna between each array element calculates antenna radiation pattern.
2) by calculating field strength attenuation and phase delay of the electromagnetic wave Jing Guo plasma sheath because subnumber is to free space electricity
Field vector amendment, obtains phased array antenna near field and the electric field after plasma sheath is passed through to swear again, and vector superposed obtain is carried out in far field
Phased array antenna directional diagram under plasma sheath is obtained, is not required to it is to be understood that the operating mode of plasma sheath set internal antenna and radiation are special
Property, you can the complex process that lossy media influences phased array antenna is solved, reduces the complexity and workload of calculating.This hair
Each step of bright computational methods is all based on stringent theory, and theoretic preciseness ensure that the accuracy of result of calculation.
Description of the drawings
In order to illustrate more clearly about the embodiment of the present invention or technical scheme of the prior art, to embodiment or will show below
There is attached drawing needed in technology description to be briefly described, it should be apparent that, the accompanying drawings in the following description is only this
Some embodiments of invention, for those of ordinary skill in the art, without creative efforts, can be with
Other attached drawings are obtained according to these attached drawings.
Fig. 1 is the flow diagram of the present invention；
Fig. 2 is the hierarchical mode of the plasma sheath of double gauss distribution；
Fig. 3 is the computation model of phased array antenna under plasma sheath；
Fig. 4 is the equivalent transmission line computation model for being layered plasma sheath；
Fig. 5 a are the basic structure of array element；
Fig. 5 b are the layouts of Planar Phased Array Antenna；
Fig. 6 a be antenna beam be directed toward angle be 10 ° when plasma sheath under phased array antenna directional diagram；
Fig. 6 b be antenna beam be directed toward angle be 20 ° when plasma sheath under phased array antenna directional diagram；
Fig. 7 is that antenna beam is directed toward theoretical calculation and Electromagnetic Simulation of the present invention when angle is 20 ° and calculates antenna pattern comparison.
Specific embodiment
Below in conjunction with the drawings and specific embodiments, the present invention is further elaborated.It should be appreciated that the embodiment
It is merely to illustrate the present invention rather than limits the scope of the invention.In addition, it should also be understood that, having read of the invention describe
After content, those skilled in the art can make the present invention various changes or modification, and such equivalent forms equally fall within this Shen
The protection domain please limited.
As shown in Figure 1, the invention discloses a kind of computational methods of phased array antenna directional diagram under plasma sheath, specifically
It follows the steps below：
Step 1：According to requirement of engineering, phased array antenna basic parameter is determined, basic module and space bit including array element
It puts, according to the spatial distribution characteristic of plasma sheath parameter, establishes the hierarchical mode of plasma sheath, and then establish plasma sheath
The computation model of the lower phased array antenna of set；
Equipped with N=Nx×NyOn a certain plane, spacing is d in the x-direction for a identical radiation element installationx, spacing in the y-direction
For dy, the coordinate position of the mn unit is：
According to plasma sheath electron density Ne change curves, with adjacent uniform plasma thin layer simulate non-homogeneous grade from
Sub- sheath, builds the hierarchical mode of non-homogeneous plasma sheath, such as Fig. 2, Ne in figurepeakFor peak electron density.Determine wait from
The characteristic frequency ω of the thickness d of sub- sheath, plasma number of plies n and n-th layer plasmap,n：
Wherein, e electron charges, neFor the electron density of n-th layer plasma, meFor electron mass, ε0It is situated between for free space
Electric constant.
N-th layer relative dielectric constantIt is calculated according to formula (2)：
Wherein, ω be incoming electromagnetic wave frequency rate, ωp,nFor n-th layer plasma characteristics frequency, ν is the collision of plasma
Frequency, n are the plasma number of plies, and j represents the unit of imaginary part.
The computation model of phased array antenna under plasma sheath is established, as shown in figure 3.
Step 2：Using Transmission line analogy, parallel and transmission of the vertical polarization electromagnetic wave Jing Guo plasma sheath is calculated
Coefficient；
Such as Fig. 4, using Transmission line analogy, transmission coefficient of the parallel polarization electromagnetic wave Jing Guo plasma sheath is calculated
With transmission coefficient of the vertical polarization electromagnetic wave Jing Guo plasma sheath
Wherein,WithRespectively parallel polarized wave and vertically polarized wave are in the equivalent wave impedance of free space, k0For certainly
By space propagation constant, θ0Represent electromagnetic wave with angle, θ0Incident plasma sheath, L represent electromagnetic wave pass through etc. plasma sheaths set
Afterwards along the propagation distance perpendicular to direction of wave traveldnFor the thickness of n-th layer plasma, θnFor n-th layer
The birefringence angle of plasma.
For n-th layer, parallel polarized wave characteristic wave impedance isAnd vertically polarized wave characteristic wave impedance isA, B, C, D are respectively the total transmission matrix of networkElement, i.e.,：
Wherein,Transmission matrix of the sum for the n-th layer of N layers of plasma sheath is represented, for parallel polarized waveIt can
To be expressed as：
For vertically polarized waveIt is represented by：Wherein,For n-th layer etc.
The propagation constant of gas ions uniform transmission line upper ripple,Intrinsic wave impedance for n-th layer plasma；
Step 3：The each array element port feed current amplitude of phased array antenna and phase are set, obtained by electromagnetic simulation software
Mutual coupling matrix under the influence of plasma sheath between each array element, the port electricity of each array-element antenna when calculating actual transmission
Stream calculates the electromagnetic field of the near field region of each array element；
The mn array element exciting currents are taken to beImnRepresent the mn array element feed amplitude, βmnRepresent mn
A array element current feed phase, the mutual coupling between each array element under the influence of plasma sheath strengthen, and pass through electromagnetic simulation software CST
Mutual coupling matrix under the influence of acquisition plasma sheath between each array element；Port current during the mn array element port actual transmission
For the sum of feed excitation and adjacent cells scattering excitation, both considered feed current during array element transmitting, at the same consider etc. from
The sensing electric current of mutual coupling under the influence of sub- sheath between each array element of phased array antenna is specifically shown in formula (5)：
Wherein, Smn,pqRepresent the mutual coupling coefficient of the q array element of pth to the mn array element,Represent the excitation of q array element of pth
Electric current.
The mn array element directional diagram is taken to beThe then electromagnetic field E of its near field region radiationmnIt is represented by：
Wherein, k is free space wave number, and rr is unit vector of the coordinate origin to far field point, and R is array element to coordinate origin
Distance,It is position vector of the array element to coordinate origin；θ represents pitch angle,Represent azimuth.
Step 4：The electromagnetic field of the near field region of each array element is decomposed, obtains the parallel polarization of incident plasma sheath
Component and perpendicular polarisation components substitute into parallel and field strength attenuation and phase delay of the vertical polarization electromagnetic wave Jing Guo plasma sheath
The factor obtains phased array antenna near field and passes through the electric field complex vector after plasma sheath
Wherein,It is unit vector parallel polarized wave,It is unit vector vertically polarized wave,It is each array element
The parallel polarized wave of radiation,It is the vertically polarized wave of each array element radiation；T||(θ) is that parallel polarization electromagnetic wave passes through
The affixture machine of plasma sheath, T⊥(θ) is affixture machine of the vertical polarization electromagnetic wave Jing Guo plasma sheath, by step
2 are calculated.
Step 5：Coherent superposition processing is carried out to the far-field region radiation field of each array element, the remote of phased array antenna is calculated
Field pattern；
Wherein,It is the parallel polarized wave phased array antenna pattern in phased array antenna far field,It is phase
Control the vertically polarized wave phased array antenna pattern in array antenna far field.
Embodiment
Design 4 × 4 rectangular microband paste antenna arrays.The basic knot of array element with non-central coaxial feeding
Structure as shown in Figure 5 a, the width 36.14mm of conductor patch in figure, the thickness 1.524mm of dielectric substrate, the feed placement of coaxial line
5.1mm；As shown in Figure 5 b, the working frequency of phased array antenna is 2.3GHz to the layout of Planar Phased Array Antenna, substrate it is opposite
Dielectric constant and loss angle tangent are respectively 3 and 0.0013.Adjacent array element is half-wavelength in x and y directions spacing, is being calculated
In, plasma sheath parameter peak electron density NepeakTake 1017/m3, the collision frequency v of plasma takes 1GHz, plasma
Thickness takes 6cm, is divided into 30 layers.By adjusting the mn array element current feed phase β of phased array antennamn, obtain antenna beam and be directed toward angle
When being 10 °, 20 °, phased array antenna directional diagram under plasma sheath, as shown in Fig. 6 a-6b.
In order to verify the correctness of analytic method of the present invention, it would be desirable to the calculated results and CST electricity more of the present invention
Magnetic simulation result.Fig. 7 provides antenna beam and is directed toward antenna pattern comparison result when angle is 20 °, it can be seen that reason of the invention
It coincide by result of calculation and Electromagnetic Simulation result, illustrates this computational methods correctness.
Above description and examples, only preferred embodiment of the invention, do not form any limitation of the invention, it is clear that right
It, all may be in the original based on the present invention after the content of present invention and design principle has been understood for one of skill in the art
In the case of reason and structure, carry out in form and the various modifications and variations in details, but these are based on inventive concept
Modifications and variations are still within the scope of the claims of the present invention.
Claims (5)
1. the computational methods of phased array antenna directional diagram under a kind of plasma sheath, which is characterized in that specifically according to following steps
It carries out：
Step 1：According to requirement of engineering, basic module and the spatial position of phased array antenna array element are determined, according to plasma sheath
The spatial distribution characteristic of parameter establishes the computation model of phased array antenna under plasma sheath；
Step 2：Using Transmission line analogy, transmission coefficient t of the parallel polarization electromagnetic wave Jing Guo plasma sheath is calculated||% and
Transmission coefficient t of the vertical polarization electromagnetic wave Jing Guo plasma sheath⊥%；
Step 3：The amplitude and phase of the port feed current of each array element of phased array antenna are set, obtained by electromagnetic simulation software
Mutual coupling matrix under the influence of plasma sheath between each array element, the port current of each array element when calculating actual transmission, meter
Calculate the electromagnetic field of the near field region of each array element；
Step 4：The electromagnetic field of the near field region of each array element is decomposed, obtains the parallel polarization component of incident plasma sheath
And perpendicular polarisation components, substitute into field strength attenuation Jing Guo plasma sheath of parallel and vertical polarization electromagnetic wave and phase delay because
Son obtains phased array antenna near field and passes through the electric field complex vector after plasma sheath；
Step 5：Coherent superposition processing is carried out to the far-field region radiation field of each array element, phased array under plasma sheath is calculated
The far-field pattern of antenna.
2. the computational methods of phased array antenna directional diagram, feature exist under a kind of plasma sheath according to claim 1
In in the step 1, establishing the computation model of phased array antenna under plasma sheath, specially：Equipped with N=Nx×NyIt is a identical
Radiation element is installed on a certain plane, and spacing is d in the x-directionx, spacing is d in the y-directiony, the coordinate position of the mn unit is：
According to the electron density change curve of plasma sheath, non-homogeneous plasma sheath is simulated with adjacent uniform plasma thin layer
Set, n-th layer plasma characteristics frequencies omegap,nIt is calculated according to formula (1)：
Wherein, e is electron charge, neFor the electron density of n-th layer plasma, meFor electron mass, ε0For free space dielectric
Constant；
N-th layer relative dielectric constant εn% is calculated according to formula (2)：
Wherein, ω is incoming electromagnetic wave frequency rate, and ν is the collision frequency of plasma, and n is the plasma number of plies, and j represents plural void
The unit in portion.
3. the computational methods of phased array antenna directional diagram, feature exist under a kind of plasma sheath according to claim 1
In in the step 3, calculating the electromagnetic field of the near field region of each array element, specially：The mn array element exciting current is taken to beImnRepresent the mn array element feed amplitude, βmnThe mn array element current feed phase is represented, it is soft by Electromagnetic Simulation
Part CST obtains the mutual coupling matrix between each array element under the influence of plasma sheath, port during the mn array element port actual transmission
Electric currentIt is calculated according to formula (5)：
Wherein, Smn,pqRepresent the mutual coupling coefficient of the q array element of pth to the mn array element,Represent the exciting current of q array element of pth；
The mn array element directional diagram is taken to beThe then electromagnetic field E of the near field region of the mn array elementmnIt is calculated according to formula (6)：
Wherein, k is free space wave number,Unit vector of the coordinate origin to far field point, R be array element to coordinate origin away from
From,It is position vector of the array element to coordinate origin, θ represents pitch angle,Represent azimuth.
4. the computational methods of phased array antenna directional diagram, feature exist under a kind of plasma sheath according to claim 1
In, in the step 4, phased array antenna near field pass through plasma sheath after electric field complex vector calculating, specially：
Wherein,The electric field complex vector after plasma sheath is passed through for phased array antenna near field,It is unit vector
Parallel polarized wave,It is unit vector vertically polarized wave,It is the parallel polarized wave of each array element radiation,It is
The vertically polarized wave of each array element radiation；T||(θ) is affixture machine of the parallel polarization electromagnetic wave Jing Guo plasma sheath, T⊥
(θ) is affixture machine of the vertical polarization electromagnetic wave Jing Guo plasma sheath.
5. the computational methods of phased array antenna directional diagram, feature exist under a kind of plasma sheath according to claim 1
In in the step 5, calculating the far-field pattern of phased array antenna, specially：
Wherein,It is the parallel polarized wave phased array antenna pattern in phased array antenna far field,It is phased array
The vertically polarized wave phased array antenna pattern of Antenna Far Field.
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| CN111405577A (en) * | 2020-02-28 | 2020-07-10 | 成都信息工程大学 | Antenna position layout method for full-duplex cognitive radio |
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