CN107958107A - Radio-frequency powers of the UHF with limit single resonance electronically small antenna obtains and balance method - Google Patents

Radio-frequency powers of the UHF with limit single resonance electronically small antenna obtains and balance method Download PDF

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CN107958107A
CN107958107A CN201711132785.8A CN201711132785A CN107958107A CN 107958107 A CN107958107 A CN 107958107A CN 201711132785 A CN201711132785 A CN 201711132785A CN 107958107 A CN107958107 A CN 107958107A
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mrow
msub
mfrac
msubsup
msup
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胡圣波
宋小伟
韦姗姗
舒恒
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Guizhou Education University
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Guizhou Education University
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/30—Circuit design
    • G06F30/36—Circuit design at the analogue level
    • G06F30/367—Design verification, e.g. using simulation, simulation program with integrated circuit emphasis [SPICE], direct methods or relaxation methods
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/30—Circuit design
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2111/00—Details relating to CAD techniques
    • G06F2111/10—Numerical modelling

Abstract

The invention discloses a kind of radio-frequency power acquisitions of UHF with limit single resonance electronically small antenna and balance method, comprise the following steps：Build antenna scattering model, calculating antenna scattering and absorption cross section, calculate with limit antenna scattering and absorbed power, with the balance between limit antenna scattering and absorbed power.The present invention is based on classical dipole antenna equivalent-circuit model, it is theoretical using antenna scattering, construct a kind of band limit single resonance electronically small antenna scattering equivalent-circuit model, the relation between the beamwidth of antenna and resonant frequency is analyzed, foundation is provided for the design and optimization of backscatter communications system electronically small antenna.

Description

Radio-frequency powers of the UHF with limit single resonance electronically small antenna obtains and balance method
Technical field
The present invention relates to a kind of radio-frequency power acquisitions of UHF with limit single resonance electronically small antenna and balance method, belong to electronics Field of communication technology.
Background technology
For using backscatter communications come passive RFID system, for intelligent wireless sensing system, undertake radio frequency work( The critical piece that rate obtains is scattering object-antenna.Generally, for these application scenarios, it is always desirable to maximize antenna and obtain Take the absorbed power in radio-frequency power, still, constrained by the conservation of energy and system causality, day line absorption and scattered power it Between balance and control nature receive significant attention.In view of backscatter communications system more by the way of Resonance scattering, And since resonance manner needs to introduce the larger capacitive reactance of larger induction reactance counteracting antenna itself, so that the beamwidth of antenna will become Must be narrower, radiation efficiency will also decrease.
The content of the invention
The technical problems to be solved by the invention are that providing a kind of radio-frequency powers of UHF with limit single resonance electronically small antenna obtains Take and balance method, analyze the relation between the beamwidth of antenna and resonant frequency, be the design of backscatter communications system electronically small antenna Foundation is provided with optimization.
In order to solve the above technical problems, the technical solution adopted by the present invention is as follows：
Radio-frequency powers of the UHF with limit single resonance electronically small antenna obtains and balance method, this method comprise the following steps：
(1) antenna scattering model is built：
A, collision matrix model：Introduce the antenna scattering matrix of the single port based on sphere vector wave spread：
In formula, in-field and radiation field sphere vector wave expansion coefficient are all the vectors of ∞ × 1, i.e. a=(a1,a2,…)T With b=(b1,b2,…)T, u and v are respectively incidence and send signal；Γ is reflectance factor, and R is that nth elements are Rn1 × ∞ Matrix, T is that nth elements are TnThe matrix of ∞ × 1, S is ∞ × ∞ matrixes, and m rows, the n-th column element are Sm×n, and S=I+ 2T, I are unit matrixs；
B, dipole antenna circuit model：The corresponding radiation resistance of dipole antennaIncluding Scatter resistance RscatWith absorption resistance Re [Z], wherein, wave impedance η0=R1, antenna feed impedance is：
Reflectance factor is expressed as：
Γ (ω)=(Z (ω)-R0)/(Z(ω)+R0)
(2) antenna scattering and absorption cross section are calculated：
The power of dipole antenna obtains sectional area, scattering resonance state transmission matrix T diagonal elements T11(k) approximate representation For：
In formula, knFor S11(k) zero point in positive half-plane, * represent conjugation；
(3) band limit antenna scattering and absorbed power are calculated：It is λ for centre wavelength0, wavelength interval is Λ=[λ1,λ2] Band limit antenna, absorbs and scattering efficiency is then respectively defined as：
In formula, λ0=λ1+λ2/2；
(4) with the balance between limit antenna scattering and absorbed power：
In formula,For the ratio between absorbed power and its maximum,For scattered power and its maximum The ratio between value,For the ratio between absorbed power and scattered power,It is absorbed power and acquisition power ratio.
Radio-frequency powers of the above-mentioned UHF with limit single resonance electronically small antenna obtains and balance method, it is preferred that in step (2), Work as k0During a ＜ ＜ 1, ignore the higher modes of dipole antenna, and D ≈ 1.5；Consider simplest situation, i.e., only single zero Point k1, at the same time, it is contemplated that σext(k) and σscat(k) expansion is respectively σext(k)=O (k2) and σs(k)=O (k4), select k1= j/(a-CR0c0),
Radio-frequency powers of the foregoing UHF with limit single resonance electronically small antenna obtains and balance method, it is preferred that in step (1), Generally there is single resonance structure in view of dipole antenna, the electronically small antenna equivalent-circuit model proposed with reference to Chu and Collin, In the case where radius is the TM ripple spherical modes of a, dipole antenna is described with RLC equivalent-circuit models, in the TM ripple spheres that radius is a Under pattern, L=μ0A, C=ε0A, ω=kc0,Wherein, ε0、μ0、c0And η0It is freely respectively Space medium dielectric constant microwave medium, magnetic conductivity, the light velocity and wave impedance.
Beneficial effect of the present invention：Compared with prior art, dipole antenna equivalent-circuit model of the present invention based on classics, It is theoretical using antenna scattering, a kind of band limit single resonance electronically small antenna scattering equivalent-circuit model is constructed, analyzes the beamwidth of antenna Relation between resonant frequency, gives with the relation between limit single resonance day line absorption, scattering resonance state and frequency, have studied The ratio between the ratio between the ratio between absorbed power and its maximum, scattered power and its maximum, absorbed power and scattered power, absorbed power With obtaining the relation between power ratio and resonant frequency, provided for the design and optimization of backscatter communications system electronically small antenna Foundation.This method can be generalized to other fields of employing wireless sensing network, including Aeronautics and Astronautics, environmental monitoring, Modern Agriculture Industry etc..
Brief description of the drawings
Fig. 1 is the collision matrix model schematic of the present invention；
Fig. 2 is the RLC equivalent-circuit model schematic diagrames of the present invention；
Fig. 3 is relation schematic diagram between absorption efficiency and resonant frequency of the invention；
Fig. 4 is relation schematic diagram between the scattering efficiency of the present invention and resonant frequency；
Fig. 5 isThe relation schematic diagram between resonant frequency；
Fig. 6 isThe relation schematic diagram between resonant frequency；
Fig. 7 isThe relation schematic diagram between resonant frequency；
Fig. 8 isThe relation schematic diagram between resonant frequency；
The present invention is further illustrated with reference to the accompanying drawings and detailed description.
Embodiment
Embodiment 1：Comprise the following steps：
1.1 structure antenna scattering models
(1) collision matrix model
Introduce the antenna scattering matrix of the single port based on sphere vector wave spread：
In formula, in-field and radiation field sphere vector wave expansion coefficient are all the vectors of ∞ × 1, i.e. a=(a1,a2,…)T With b=(b1,b2,…)T, u and v are respectively incidence and send signal；Γ is reflectance factor, and R is that nth elements are Rn1 × ∞ Matrix, T is that nth elements are TnThe matrix of ∞ × 1, and S is ∞ × ∞ matrixes, and m rows, the n-th column element are Sm×n, and S =I+2T[21], I is unit matrix, as shown in Figure 1.
(2) dipole antenna circuit model
Generally there is single resonance structure in view of dipole antenna, the electronically small antenna proposed with reference to Chu and Collin is equivalent Circuit model, in the case where radius is the TM ripple spherical modes of a, dipole antenna can be retouched with the RLC equivalent-circuit models shown in Fig. 2 State.
In the case where radius is the TM ripple spherical modes of a, L=μ0A, C=ε0A, ω=kc0, Wherein, ε0、μ0、c0And η0It is free space medium dielectric constant microwave medium, magnetic conductivity, the light velocity and wave impedance respectively.
Under this equivalent-circuit model, the corresponding radiation resistance of dipole antennaIncluding Scatter resistance RscatWith absorption resistance Re [Z].Wherein, wave impedance η0=R1.And antenna feed impedance is：
Reflectance factor can be expressed as：
Γ (ω)=(Z (ω)-R0)/(Z(ω)+R0) (3)
1.2 antenna scatterings and absorption cross section
Work as k0During a ＜ ＜ 1, the higher modes of dipole antenna, and D ≈ 1.5 can be ignored.In this way, dipole antenna Power obtains sectional area, scattering resonance state available transmission matrix T diagonal elements T11(k) approximate representation is：
In formula, T11(k) be transmission matrix T diagonal element.
In view of S=I+2T, S can be first determined11(k).By | Γ |=| S11| know, S can be determined by reflectance factor11(k), But due to reflectance factor and S11(k) amplitude is the same, and the function of a unit amplitude is only differed between them, therefore, can use half The Blaschke product representations S of analytical function in plane11(k), i.e.,：
In formula, knFor S11(k) zero point in positive half-plane, * represent conjugation.
For ease of analysis, simplest situation is considered, i.e., only single zero point k1.At the same time, it is contemplated that σext(k) and σscat (k) expansion is respectively σext(k)=O (k2) and σs(k)=O (k4), convolution (4), can select k1=j/ (a-CR0c0), from And S11(k) can be approximately：
1.3 band limit antenna scatterings and absorbed power
It is λ for centre wavelength0, wavelength interval is Λ=[λ1,λ2] band limit antenna, absorb and scattering efficiency can then divide It is not defined as：
In formula, λ0=λ1+λ2/2
By foregoing electronically small antenna resonant frequency and the relation of maximum bandwidth, in 500-1200MHz resonant frequency ranges, work as a Respectively 3/60 π meters, 3/50 π meters, when the band limit beamwidth of antenna is set to 200kHz, 400kHz,WithWith resonant frequency Relation respectively as shown in Figures 3 and 4.1.4 with the balance between limit antenna scattering and absorbed power
To study with the equilibrium relation between the absorption of limit resonant antenna and scattered power, by foregoing dipole antenna circuit mould Type, gives resonant frequency range WfoIn the range of the beamwidth of antenna, four parameters can be defined respectively as, i.e., absorbed power with it most The ratio between big valueThe ratio between scattered power and its maximumThe ratio between absorbed power and scattered powerAbsorbed power is with obtaining power ratioIt can be expressed as：
As aforementioned parameters, antenna resonant frequency scope is set to 500-1200MHz, and the beamwidth of antenna is set to 200kHz, 400kHz,Relation between resonant frequency is as illustrated in Figures 5 and 6.From Fig. 5 and Fig. 6 is as it can be seen that the beamwidth of antenna pairWithHave little to no effect, and increase with resonant frequency, the two Ratio is reduced.Trace it to its cause, be, resonant frequency is smaller, and reciprocal wave numbers value is bigger so that the two ratios with frequency increase and Reduce.
The ratio between absorbed power and scattered powerAbsorbed power is with obtaining power ratioWith resonant frequency it Between relation then as shown in FIG. 7 and 8.From Fig. 7 and 8,WithIncrease with resonant frequency increase and bandwidth and subtract It is few,Totally level off to 1, andThen level off to 0.5, it is consistent with the variation tendency of sectional area.

Claims (3)

  1. Radio-frequency powers of the 1.UHF with limit single resonance electronically small antenna obtains and balance method, it is characterised in that comprises the following steps：
    (1) antenna scattering model is built：
    A, collision matrix model：The antenna scattering matrix of single port based on sphere vector wave spread：
    <mrow> <mfenced open = "(" close = ")"> <mtable> <mtr> <mtd> <mi>&amp;Gamma;</mi> </mtd> <mtd> <mi>R</mi> </mtd> </mtr> <mtr> <mtd> <mi>T</mi> </mtd> <mtd> <mi>S</mi> </mtd> </mtr> </mtable> </mfenced> <mfenced open = "(" close = ")"> <mtable> <mtr> <mtd> <mi>u</mi> </mtd> </mtr> <mtr> <mtd> <mi>a</mi> </mtd> </mtr> </mtable> </mfenced> <mo>=</mo> <mfenced open = "(" close = ")"> <mtable> <mtr> <mtd> <mi>v</mi> </mtd> </mtr> <mtr> <mtd> <mi>b</mi> </mtd> </mtr> </mtable> </mfenced> </mrow>
    In formula, in-field and radiation field sphere vector wave expansion coefficient are all the vectors of ∞ × 1, i.e. a=(a1,a2,…)TAnd b= (b1,b2,…)T, u and v are respectively incidence and send signal；Γ is reflectance factor, and R is that nth elements are Rn1 × ∞ square Battle array, T is that nth elements are TnThe matrix of ∞ × 1, S is ∞ × ∞ matrixes, and m rows, the n-th column element are Sm×n, and S=I+2T, I It is unit matrix；
    B, dipole antenna circuit model：The corresponding radiation resistance of dipole antennaIncluding scattering Resistance RscatWith absorption resistance Re [Z], wherein, wave impedance η0=R1, antenna feed impedance is：
    <mrow> <mi>Z</mi> <mo>=</mo> <msub> <mi>j&amp;omega;L</mi> <mn>1</mn> </msub> <mo>+</mo> <mfrac> <mn>1</mn> <mrow> <mi>j</mi> <mi>&amp;omega;</mi> <mi>C</mi> </mrow> </mfrac> <mo>+</mo> <mfrac> <mrow> <mi>j</mi> <mi>&amp;omega;</mi> <mi>L</mi> </mrow> <mrow> <mn>1</mn> <mo>+</mo> <mi>j</mi> <mi>&amp;omega;</mi> <mi>L</mi> <mo>/</mo> <msub> <mi>&amp;eta;</mi> <mn>0</mn> </msub> </mrow> </mfrac> </mrow>
    Reflectance factor is：
    Γ (ω)=(Z (ω)-R0)/(Z(ω)+R0)
    (2) antenna scattering and absorption cross section are calculated：
    The power of dipole antenna obtains sectional area, scattering resonance state transmission matrix T diagonal elements T11(k) approximate representation is：
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    <mrow> <msub> <mi>&amp;sigma;</mi> <mrow> <mi>a</mi> <mi>b</mi> <mi>s</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <mn>3</mn> <mi>&amp;pi;</mi> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <msup> <mrow> <mo>|</mo> <mrow> <mi>&amp;Gamma;</mi> <mrow> <mo>(</mo> <mrow> <msub> <mi>kc</mi> <mn>0</mn> </msub> </mrow> <mo>)</mo> </mrow> </mrow> <mo>|</mo> </mrow> <mn>2</mn> </msup> <mo>)</mo> </mrow> </mrow> <mrow> <mn>2</mn> <msup> <mi>k</mi> <mn>2</mn> </msup> </mrow> </mfrac> </mrow>
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    In formula, knFor S11(k) zero point in positive half-plane, * represent conjugation
    (3) band limit antenna scattering and absorbed power are calculated：It is λ for centre wavelength0, wavelength interval is Λ=[λ1,λ2] band limit Antenna, absorbs and scattering efficiency is respectively defined as：
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    <mrow> <msubsup> <mi>&amp;eta;</mi> <mrow> <mi>s</mi> <mi>c</mi> <mi>a</mi> <mi>t</mi> </mrow> <mi>&amp;Lambda;</mi> </msubsup> <mo>=</mo> <mn>1</mn> <mo>-</mo> <msubsup> <mi>&amp;eta;</mi> <mrow> <mi>a</mi> <mi>b</mi> <mi>s</mi> </mrow> <mi>&amp;Lambda;</mi> </msubsup> </mrow>
    In formula, λ0=λ1+λ2/2；
    (4) with the balance between limit antenna scattering and absorbed power：
    <mrow> <mfrac> <msubsup> <mi>P</mi> <mrow> <mi>a</mi> <mi>b</mi> <mi>s</mi> </mrow> <mi>&amp;Lambda;</mi> </msubsup> <mrow> <munder> <mi>max</mi> <msub> <mi>W</mi> <mrow> <mi>f</mi> <mi>a</mi> </mrow> </msub> </munder> <mrow> <mo>(</mo> <msubsup> <mi>P</mi> <mrow> <mi>a</mi> <mi>b</mi> <mi>s</mi> </mrow> <mi>&amp;Lambda;</mi> </msubsup> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <msubsup> <mo>&amp;Integral;</mo> <msub> <mi>k</mi> <mn>1</mn> </msub> <msub> <mi>k</mi> <mn>2</mn> </msub> </msubsup> <mfrac> <mrow> <mn>3</mn> <mi>&amp;pi;</mi> </mrow> <mn>2</mn> </mfrac> <mo>&amp;CenterDot;</mo> <mfrac> <mrow> <mn>1</mn> <mo>-</mo> <msup> <mrow> <mo>|</mo> <mi>&amp;Gamma;</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>|</mo> </mrow> <mn>2</mn> </msup> </mrow> <msup> <mi>k</mi> <mn>4</mn> </msup> </mfrac> <mi>d</mi> <mi>k</mi> </mrow> <mrow> <munder> <mi>max</mi> <msub> <mi>W</mi> <mrow> <mi>f</mi> <mi>a</mi> </mrow> </msub> </munder> <mrow> <mo>(</mo> <msubsup> <mo>&amp;Integral;</mo> <msub> <mi>k</mi> <mn>1</mn> </msub> <msub> <mi>k</mi> <mn>2</mn> </msub> </msubsup> <mfrac> <mrow> <mn>3</mn> <mi>&amp;pi;</mi> </mrow> <mn>2</mn> </mfrac> <mo>&amp;CenterDot;</mo> <mfrac> <mrow> <mn>1</mn> <mo>-</mo> <msup> <mrow> <mo>|</mo> <mi>&amp;Gamma;</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>|</mo> </mrow> <mn>2</mn> </msup> </mrow> <msup> <mi>k</mi> <mn>4</mn> </msup> </mfrac> <mi>d</mi> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </mfrac> </mrow>
    <mrow> <mfrac> <msubsup> <mi>P</mi> <mrow> <mi>s</mi> <mi>c</mi> <mi>a</mi> <mi>t</mi> </mrow> <mi>&amp;Lambda;</mi> </msubsup> <mrow> <munder> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> <msub> <mi>W</mi> <mrow> <mi>f</mi> <mi>o</mi> </mrow> </msub> </munder> <mrow> <mo>(</mo> <msubsup> <mi>P</mi> <mrow> <mi>s</mi> <mi>c</mi> <mi>a</mi> <mi>t</mi> </mrow> <mi>&amp;Lambda;</mi> </msubsup> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <msubsup> <mo>&amp;Integral;</mo> <msub> <mi>k</mi> <mn>1</mn> </msub> <msub> <mi>k</mi> <mn>2</mn> </msub> </msubsup> <mrow> <mo>(</mo> <mo>-</mo> <mn>6</mn> <mi>&amp;pi;</mi> <mo>)</mo> </mrow> <mo>&amp;CenterDot;</mo> <mfrac> <mrow> <mi>Re</mi> <mo>{</mo> <msub> <mi>T</mi> <mn>11</mn> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>}</mo> </mrow> <msup> <mi>k</mi> <mn>4</mn> </msup> </mfrac> <mi>d</mi> <mi>k</mi> <mo>-</mo> <msubsup> <mo>&amp;Integral;</mo> <msub> <mi>k</mi> <mn>1</mn> </msub> <msub> <mi>k</mi> <mn>1</mn> </msub> </msubsup> <mfrac> <mrow> <mn>3</mn> <mi>&amp;pi;</mi> </mrow> <mn>2</mn> </mfrac> <mo>&amp;CenterDot;</mo> <mfrac> <mrow> <mn>1</mn> <mo>-</mo> <msup> <mrow> <mo>|</mo> <mi>&amp;Gamma;</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>|</mo> </mrow> <mn>2</mn> </msup> </mrow> <msup> <mi>k</mi> <mn>4</mn> </msup> </mfrac> <mi>d</mi> <mi>k</mi> </mrow> <mrow> <munder> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> <msub> <mi>W</mi> <mrow> <mi>f</mi> <mi>o</mi> </mrow> </msub> </munder> <mrow> <mo>(</mo> <msubsup> <mo>&amp;Integral;</mo> <msub> <mi>k</mi> <mn>1</mn> </msub> <msub> <mi>k</mi> <mn>2</mn> </msub> </msubsup> <mo>(</mo> <mrow> <mo>-</mo> <mn>6</mn> <mi>&amp;pi;</mi> </mrow> <mo>)</mo> <mo>&amp;CenterDot;</mo> <mfrac> <mrow> <mi>Re</mi> <mo>{</mo> <msub> <mi>T</mi> <mn>11</mn> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>}</mo> </mrow> <msup> <mi>k</mi> <mn>4</mn> </msup> </mfrac> <mi>d</mi> <mi>k</mi> <mo>-</mo> <msubsup> <mo>&amp;Integral;</mo> <msub> <mi>k</mi> <mn>1</mn> </msub> <msub> <mi>k</mi> <mn>1</mn> </msub> </msubsup> <mfrac> <mrow> <mn>3</mn> <mi>&amp;pi;</mi> </mrow> <mn>2</mn> </mfrac> <mo>&amp;CenterDot;</mo> <mfrac> <mrow> <mn>1</mn> <mo>-</mo> <msup> <mrow> <mo>|</mo> <mi>&amp;Gamma;</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>|</mo> </mrow> <mn>2</mn> </msup> </mrow> <msup> <mi>k</mi> <mn>4</mn> </msup> </mfrac> <mi>d</mi> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </mfrac> </mrow>
    <mrow> <mfrac> <msubsup> <mi>P</mi> <mrow> <mi>a</mi> <mi>b</mi> <mi>s</mi> </mrow> <mi>&amp;Lambda;</mi> </msubsup> <msubsup> <mi>P</mi> <mrow> <mi>s</mi> <mi>c</mi> <mi>a</mi> <mi>t</mi> </mrow> <mi>A</mi> </msubsup> </mfrac> <mo>=</mo> <mfrac> <mrow> <msubsup> <mo>&amp;Integral;</mo> <msub> <mi>k</mi> <mn>1</mn> </msub> <msub> <mi>k</mi> <mn>1</mn> </msub> </msubsup> <mfrac> <mrow> <mn>3</mn> <mi>&amp;pi;</mi> </mrow> <mn>2</mn> </mfrac> <mo>&amp;CenterDot;</mo> <mfrac> <mrow> <mn>1</mn> <mo>-</mo> <msup> <mrow> <mo>|</mo> <mi>&amp;Gamma;</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>|</mo> </mrow> <mn>2</mn> </msup> </mrow> <msup> <mi>k</mi> <mn>4</mn> </msup> </mfrac> <mi>d</mi> <mi>k</mi> </mrow> <mrow> <msubsup> <mo>&amp;Integral;</mo> <msub> <mi>k</mi> <mn>1</mn> </msub> <msub> <mi>k</mi> <mn>2</mn> </msub> </msubsup> <mrow> <mo>(</mo> <mo>-</mo> <mn>6</mn> <mi>&amp;pi;</mi> <mo>)</mo> </mrow> <mo>&amp;CenterDot;</mo> <mfrac> <mrow> <mi>Re</mi> <mo>{</mo> <msub> <mi>T</mi> <mn>11</mn> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>}</mo> </mrow> <msup> <mi>k</mi> <mn>4</mn> </msup> </mfrac> <mi>d</mi> <mi>k</mi> <mo>-</mo> <msubsup> <mo>&amp;Integral;</mo> <msub> <mi>k</mi> <mn>1</mn> </msub> <msub> <mi>k</mi> <mn>1</mn> </msub> </msubsup> <mfrac> <mrow> <mn>3</mn> <mi>&amp;pi;</mi> </mrow> <mn>2</mn> </mfrac> <mo>&amp;CenterDot;</mo> <mfrac> <mrow> <mn>1</mn> <mo>-</mo> <msup> <mrow> <mo>|</mo> <mi>&amp;Gamma;</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>|</mo> </mrow> <mn>2</mn> </msup> </mrow> <msup> <mi>k</mi> <mn>4</mn> </msup> </mfrac> <mi>d</mi> <mi>k</mi> </mrow> </mfrac> </mrow>
    <mrow> <mfrac> <msubsup> <mi>P</mi> <mrow> <mi>a</mi> <mi>b</mi> <mi>s</mi> </mrow> <mi>&amp;Lambda;</mi> </msubsup> <msubsup> <mi>P</mi> <mrow> <mi>e</mi> <mi>x</mi> <mi>t</mi> </mrow> <mi>&amp;Lambda;</mi> </msubsup> </mfrac> <mo>=</mo> <mfrac> <mrow> <msubsup> <mo>&amp;Integral;</mo> <msub> <mi>k</mi> <mn>1</mn> </msub> <msub> <mi>k</mi> <mn>1</mn> </msub> </msubsup> <mfrac> <mrow> <mn>3</mn> <mi>&amp;pi;</mi> </mrow> <mn>2</mn> </mfrac> <mo>&amp;CenterDot;</mo> <mfrac> <mrow> <mn>1</mn> <mo>-</mo> <msup> <mrow> <mo>|</mo> <mi>&amp;Gamma;</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>|</mo> </mrow> <mn>2</mn> </msup> </mrow> <msup> <mi>k</mi> <mn>4</mn> </msup> </mfrac> <mi>d</mi> <mi>k</mi> </mrow> <mrow> <msubsup> <mo>&amp;Integral;</mo> <msub> <mi>k</mi> <mn>1</mn> </msub> <msub> <mi>k</mi> <mn>2</mn> </msub> </msubsup> <mrow> <mo>(</mo> <mo>-</mo> <mn>6</mn> <mi>&amp;pi;</mi> <mo>)</mo> </mrow> <mo>&amp;CenterDot;</mo> <mfrac> <mrow> <mi>Re</mi> <mo>{</mo> <msub> <mi>T</mi> <mn>11</mn> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>}</mo> </mrow> <msup> <mi>k</mi> <mn>4</mn> </msup> </mfrac> <mi>d</mi> <mi>k</mi> </mrow> </mfrac> </mrow>
    In formula,For the ratio between absorbed power and its maximum,For scattered power and its maximum it Than,For the ratio between absorbed power and scattered power,It is absorbed power and acquisition power ratio.
  2. 2. radio-frequency powers of the UHF according to claim 1 with limit single resonance electronically small antenna obtains and balance method, its feature It is：In step (2), work as k0During a ＜ ＜ 1, ignore the higher modes of dipole antenna, and D ≈ 1.5；Consider simplest feelings Shape, i.e., only single zero point k1, at the same time, it is contemplated that σext(k) and σscat(k) expansion is respectively σext(k)=O (k2) and σs(k) =O (k4), select k1=j/ (a-CR0c0),
  3. 3. radio-frequency powers of the UHF according to claim 1 with limit single resonance electronically small antenna obtains and balance method, its feature It is：In step (1), it is contemplated that dipole antenna generally has single resonance structure, the electric small day proposed with reference to Chu and Collin Line equivalent-circuit model, in the case where radius is the TM ripple spherical modes of a, dipole antenna is described with RLC equivalent-circuit models, half Footpath is L=μ under the TM ripple spherical modes of a0A, C=ε0A, ω=kc0,Wherein, ε0、μ0、c0 And η0It is free space medium dielectric constant microwave medium, magnetic conductivity, the light velocity and wave impedance respectively.
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