Antenna parameters. Definition, general considerations and fundamental parameters

Transcription

1 Antenna parameters Definition, general considerations and fundamental parameters Departamento de Señales, Sistemas y Radiocomunicaciones Universidad olitécnica de Madrid Manuel Sierra Castañer mscastaner@gr.ssr.upm.es Outline Radiation fundaments Fundamental parameters of antennas o Input impedance o Radiation patterns o Gain o olariation Friis Formula Antenna noise temperature

2 Radiation of a current source he simplest radiation source is a liner electric element placed in a isotropic, homogeneous, infinity and lossless medium.. r A r k Ar Jr k k A J Escalar equation for J Since the scalar source can be considered an infinitesimal point source the problem has spherical symmetry and the solution is: J I ds dv dl ds x Idl, y r d r dr da dr k A J Solving the equation for J = (no sources), there are two independent solutions: jkr e hysical problem for the A r C Outwardly travelling wave radiation problem A r C r jk e r r Inwardly travelling wave Solving the equation for non ero J C J dv 4 Idl Radiation of a current source he fields produced by a source element are: H A Replacing ẑ jkr e A Idlrˆ cos ˆ sen E H 4 r j If k r>> (r>>) terms /r are more significant than /r or /r 3 ˆ ˆ Idlsen H ra A r jk e r 4r r jidl jk ˆ sen k jk E rˆ cos 3 k r r r r he power density (oynting vector), depends on /r (spherical wave) and it is calculated as: k sen * S Re EH r I dl 3 r jk r jk r e 3 r jkr e H jk ˆ Idlsen 4r jkr e E jk Idlsen ˆ 4r Radiated fields: E r, H r, E H 4

3 Radiation of an antenna A real antenna has a current distribution supposed to be formed by infinites elements dv of current J situated in a point r. Each infinites elements dv of current J in a point in the space will generate a differential of potential magnetic vector da da r jk r r e 4 r r JrdV x Jr dv j r r r r' r y For the total radiated potential will be the superposition. jk rr jk r r Jre Js r e A r Ar dv 4 ds S V rr 4 r r A r 4 jk r r I r e dl L r r Volume Surface Wire Antenna (diameter << ) 5 Far field properties An antenna radiates, in far field: he radiated electromagnetic wave is propagated radially in all the space directions. he dependence of E and H with r is always one of a spherical wave e -jkr /r. he field decreases with the distance as /r. he field E and H depend with and because the spherical wave is not homogeneous. o analye its variation, it is employed the spherical coordinates system. rˆ, x y 6

4 Far field properties he radiation fields of any antenna fulfil these general properties: he radiated spherical wave behave locally as a plane wave: a fixed direction (,): E rˆ E H H rˆ E H x he fields E and H do not have radial components: Ar ( ) Ar r A A Er Hr E jr Ar E ja E H E ja E H r y he power density that transport the wave decrease as /r. If the medium have no losses, it is defined: * S ReE H Er,, Er,, rˆ 7 Fundamental parameters of radiation Before we saw how to determine, from the Maxwell equations, the radiated electric and magnetic fields of an antenna. Actual field expressions are more complex, so for the antenna characteriation we use parameters that can be measured and are easier to analyse. he measured parameters of an antenna follow the IEEE standard. hose parameters allow to consider the antenna as ablackboxand calculate the parameters of a radio communication link. he most important parameters are: Input impedance Radiation pattern Gain olariation 8

5 arameters of an antenna: Impedance Feeding a linear antenna with a harmonic generator of frequency f, we can define a circuit model: From the input terminals Input impedance is generally a complex number that varies with the frequency Input reflection coefficient Z antenna V I Z R jx antenna antenna antenna ransmission line Generally, reactance X antenna (f)=, at the frequency of resonance ransmitter ransmitting antenna Z Z ant ant Z Z * g g 9 Impedance parameters he real part of the input impedance antenna is the sum of the loss resistance (associate to the energy that is dissipated) and the radiated resistance (associate to the radiated energy). Radiation efficiency radiated radiation rad input Rlosses Rradation Others alternative parameters to the input impedance, more easy to measure in the high frequency range are: Return losses (db): VSWR: RL(dB) log ref inc log R VSWR Available power of the transmitter and transmitted to the antenna: inc 8 V R g g trans inc ref inc VSWR MAX should be RL 9.5 db % of power loss

6 arameters of an antenna: Radiation pattern In the far field Radiation pattern of electric field F olariation pattern ê ê(,)= polariation pattern ==free space impedance jk r e H jk ˆ Idlsen 4 r jk r e E j k Idlsen ˆ 4 r When we feed the antenna with a voltage V, it is generated a current distribution (give by the Maxwell equations) that produce an electromagnetic radiation characteried by the fields E and H. Radiation parameters: radiation pattern It is defined as a graphic representation of the radiation properties of an antenna in function of space angular coordinates. lot patterns of: field : arg arg, E C, E X, etc power : <S> = power density, Gain, Directivity. he formats that have the patterns are : Absolute patterns: it plots the fields or power density for a delivered power to the antenna and a constant distance. Relative patterns: like the previous ones but normalied in relation to the maximum value of the plotted function. In this case the plot are in logarithmic scale (db). So, the power and fields plots coincide because: S log log S max E E max

7 attern types Depending the application of the antenna, we classify: Isotropic (quasi-isotropic) Omnidirectional: Directional in one plane and isotropic in the other (symmetry revolution pattern). Directional: concentrate fundamentally the radiation in a small angular cone:» encil beam: conic beam (f.e. for point to point communication)» Fan beam (f.e. base station mobile communication sectorial antennas)» Contour beam, typical for adjusted coverage in DBS systems» Beamforming, typical for security radar» Multibeam (several main lobes) Multi-pattern: several simultaneous patterns depending on the feeding input. Reconfigurable beamwidth antennas: when we can control the radiation pattern by a remote control depending on the communication system. Interesting for antennas in satellites. Adaptative antennas: when the radiation pattern is instantaneously adapted to the radioelectric environment. 3 3D patterns DIRECIVE AERN OMNIDIRECIONAL AERN, E E, max y ISOROIC AERN Z DIOLE / y X 4

8 D patterns OLAR LOS AND BEAMWIDH DEFINIION between half power points (at 3 db) HBW= Half-ower Beamwidth Normalied field pattern Normalied power pattern Normalied pattern in [db] 5 Radiation pattern parameters Lobe: portion of the radiation pattern bounded by regions of relatively weak radiation intensity (nulls) Major or main lobe: radiation lobe containing the direction of maximum radiation. Minor lobes: any lobe except a major lobe. Side lobes: a radiation lobe in any direction other than the intended lobe. Usually is adjacent to the main lobe. Back lobe: a radiation lobe whose axis draws an angle of aprox. 8º with respect to the antenna s main lobe. Side lobe level: ratio of the power density in the lobe in question to that of the major lobe Front to back ratio Half power beamwidth (HBW), first null beamwidth (FNBW) Side lobe Minor lobes Main lobe BW first null i BW -3dB Side lobe level (S.L.L.) Radiation pattern D in db. Cartesian plot 6

9 Radiation pattern: principal planes For linearly polaried directive antennas it is usually enough the characteriation of radiation pattern in main planes: E-plane: the plane containing the electrical field vector and the direction of maximum radiation (YZ) H-plane: the plane containing the magnetic field vector and the direction of maximum radiation (XZ) y x 7 ridimensional representation 3D patterns in (u,v) coordinates u sincos v sin sin db db 8

10 Bidimensional representation D patterns in (u,v) coordinates u sincos v sin sin 9 Radiation pattern planes: olar and Cartesian representation E i. max( E) 8 EdB i i i deg olar (Linear) Cartesian (db)

11 Examples of contour patterns Multibeam pattern of contour beam DBS antenna from HISASA satellite. antenna VA-GOV pattern (multipattern antenna) form HISASA satellite. Radiation intensity Is the radiated power by solid angle in a determined direction. Represents the capacity that have an antenna to radiate the energy in this direction. Solid angle: Zone of the space included by a succession of radial lines with vertex in centre of a sphere. Its unit is steradian (solid angle that includes a spherical surface r with a radius r). U, da r sindd d sindd r r Radiation intensity: is the radiated power by solid angle unit. Sr,, da r Sr,, d r da r sin d r d

12 Directivity Directivity: D(,) Represent the capacity that has the antenna to concentrate the radiation intensity in a particular direction. he ratio of the radiation intensity in a given direction from the antenna to the radiation intensity of an isotropic antenna that radiated the equivalent total power averaged over all the directions. U U, U, Sr,, D, 4 4r U Isotropic radiated radiated he total radiated power of an antenna: rad U, d r 4 S r,, sin dd Maximum directivity: D. Directivity in maximum radiation direction. It is always greater than ( dbi). In dbi: log D. U, isotropic 4 radiated 3 Gain and Efficiency Absolute gain: G(,), is the ratio of the intensity, in a given direction, to the radiation intensity that would be obtained if the power accepted by the antenna were radiated isotropically. Maximum gain: G, gain in maximum radiation direction It can be lower than ( dbi) In dbi: log G. Antenna Efficiency: it is the relation between gain and directivity radiated G R D G, D, R in G, U 4, Sr,, in 4r in 4

13 Gain and Efficiency E.I.R..: Equivalent Isotropic Radiated ower he EIR is a figure of merit of the combined transmitter antenna. If we divide it by 4r (sphere area), we obtain the power density at a distance r. he EIR curves are plotted in dbw.,,, EIR G D in rad, in, G EIR Sr,, W / m 4r 4r 5 arameters of an individual antenna: polariation pattern Another important element in the radiation pattern of the antenna is the polariation, that comes from its unitary vector. (, ) ˆ ˆ e eˆ, cos( (, )) sin( (, )) j he shape and the orientation of the polariation ellipse depends on the amplitude relation and the phases between the electric field components. 6

14 olariation type he polariation, that we generally achieved, is never perfectly circular of perfectly linear, but elliptic. So this implies that an antenna radiated with a desired polariation, which have an undesired orthogonal polariation. his is why we say Copolar component (C) (for the desired field polariation) and Cross polar component (X) (for the field polariation orthogonal to C). Right hand circular polariation Horiontal linear polariation 7 olariation: Co-polar and Cross-polar plots E, E, E, E, E C, û cp E X, û xp E C and X components: x Linear polariation: Ludwig 3 rd definition for linear components (co polar on y-axes) EC, E, sin E, cos E, E, cos E, sin X Circular polariation: ERHC, ELHC, E, je, E, je, e j j e x E y E E y 8

15 ypical C-X plots of a terrestrial station 9 olariation Loss Factor (LF) Any field can be discomposes as a sum of two orthogonal components and to the direction of propagation to each other. When a radio communication is settled down, the receiving antenna only couples the component of coincident incident field with its polariation. he polariation loss factor (LF) is defined like the fraction of power that transports the incident wave in the polariation of the receiving antenna. his factor is calculated as the scalar product of the unitary vectors of polariation from the transmitting and receiving antenna in the link direction., ˆ, LF eˆ e R Dipoles LF = LF = cos p LF = 3

16 olariation Loss Factor (LF) Examples: Linear polariation: a change of in the polariation orientation, causes small losses in the copolar coupling. LF=cos ( p ) Circular polariation: perfect coupling (LF=) if the turn sense in polariation of the transmitting and receiving antenna are the same. Uncoupling (LF decreasing towards ) if they are in contrary sense. For linear(transmitter antenna) and circular polariation(receiver antenna): LF=/ (-3dB) 3 Dual polariation Nowadays because the saturation of the radio bands, the use of antennas of high polariation purity allow to duplicate the capacity of a band using both polariation, transmitting and receiving channels that occupy the same band on two orthogonal polariations. his is done for example in the fixed service by satellite, transmitting and receiving simultaneously orthogonal linear polariations. In order to avoid interferences between orthogonal channels, the radiation level crosspolar of the antennas do not have to be more than -35 db. We notice that the previous requirement also conditions the position (adjustment) of the polariation axes in the terrestrial station. A misalignment of in the axis direction of polariation reference (maximum admitted variation in terrestrial stations) cause small losses in the copolar coupling but coupled -35 db of crosspolar component. log log cos º.dB cos 89º 35.dB 3

17 Bandwidth It is the frequency range where the characteristic parameters (input impedance, reflection coefficient, radiation pattern, gain, ) fulfil specifications. For the narrow band antennas (resonant antennas) it is usually defined in % of the resonance frequency. For the broadband antennas, it is defined as the relation between the upper frequency of the band to the lower one, for example :, : etc. Reflection coefficient (Input impedance) for a Reflection coefficient (Input impedance) for a wide bandwidth antenna narrow bandwidth antenna he antennas that are over a : relation for a certain specification (impedance ) they are designed based on angles and they receive the name of antennas independent of the frequency. 33 Circuital model of an antenna in reception In an antenna, reciprocity Z ir = Z i Available power of the receiving antenna: Z ir available 8 V R ca ir V c.a Z Z L Input power at receiver: received IL R L available R Receiving Antenna Receiver Reflection coefficient (Z o =Z ir ): R Z Z L ir * ir Z Z L 34

18 Absorption equivalent area If we consider the antenna as an aperture that get energy from the incident electromagnetic wave, we can define an equivalent antenna area (or effective area) as the relation between the available power at the antenna and the power density of the incident wave. available, Ae, S,, S i, Z i =Z o =Z L available Z L Z o Z i It is demonstrate that: * his definition consider perfect coupling (LF=) in polariation between the incident wave and the antenna. Ae, G, Aemax G 4 4 Reception pattern is identical to the transmission one Relation between the gain and the physical area for aperture antennas: A emax r a A aper G 4 A r a aperture a : Aperture efficiency ( ).5,.8 i 35 Friis Formulas: ropagation in free space In all radiocomunication systems, we need to establish a power balance between the transmitter and the receiver to calculate the needed power in the transmitter that allows to reach a minimum level of signal in the receiver, that is above the noise floor. Friis formula allows to calculate the insertion losses of a radiolink as a function function of the transmission parameters for achantenna, associated with the directions that which one see the other (olariation Loss Factor (LF)). hese insertion losses are define as the ratio between the delivered power at the receiver DR and the available power at the transmitter A. 36

19 ransmission equation: Friis Formulas Using the definitions of power gain and the mismatches of the impedance in x and R x, a balance link can be made in conditions of free space. his equation is what it is defined as Friis Formula: DR A x x eˆ eˆ,, t t R r r G,, 4 R G R t t R r r R Alternative Friis Formula:,, ˆ ˆ S A e e DR i e R R 37 Loss Factors Radiolink insertion loss in db: Uncoupling polariation losses (LF): Unmatched impedance losses: Free space propagation losses: (relation with spherical behaviour of the transmitted wave). ower gain: Delivered Rx log Available x G ( db) y G ( db), ê log ê R, log R log 4R log R Radiolink losses or Friis Formulas: ˆ ˆ G db e er GR db R Delivered Rx log log log,, log Available x 38

20 Antenna noise temperature When a power balance is studied in a radiolink, not only the signal level is important also the noise that reach the receiver. All the bodies with a temperature different from K give incoherent radiation (noise). he antenna catches the radiation of all the bodies that surround it through their radiation pattern and put it as an available noise power N AR at the receiving antenna input. Being N AR, the power of noise available in the antenna considering no losses, its noise temperature is defined as: k, Boltman cste. =.38-3 (J/K) Nyquist Formula B f, noise bandwidth (H) a, antenna noise temperature (K) N AR a k B f 39 Antenna noise temperature Based on brightness temperature B (,) associated to the noise radiation that impinges on the antenna for the (,) direction, the antenna temperature a is obtained as: a 4 B, f, 4 f, d d a 4 B, f, d he antenna noise temperature a depends on the antenna orientation in the atmosphere and of the frequency work. 4

21 ypical values of a (MF, HF y VHF) Maximum ropical Zones Antenna temperature [ K] Atmospheric noise associated to the rays/s D C A Cosmic noise oles Minimum Frequency [MH] MF and HF: Noise temperature Isolines of atmospheric noise at MH in db refers to K a B 4 ypical values of a (MF, HF y VHF) Noise from industrial type: a log 9 Commercial one Residential one Rural one eaceful rural one Galactic noise (medium) (medio) f ( MH) Industrial type noise 4

22 ypical values of a (Microwave band) Antenna temperature [ K] Cosmic noise Background noise Atmospheric gas absorption Narrow beam antennas pointing with the main lobe at an elevation over the horion with clear atmosphere (without considering ground contribution) he atmospheric attenuation produce by the rain, the fog, etc. increase the antenna temperature as: L a m ( m, medium value of the atmosphere temperature and L additional atmosphere attenuation. Elevation angle Atmosphere attenuation L Additional noise temperature of the antenna Frequency [GH] Noise temperature in microwave frequency ypical increase in the microwave range 43