WIRELESS COMMUNICATIONSCOMMUNICATION REQUIRES ENERGY AND POWERCIRCUIT PROPERTIES OF ANTENNASL17-1WIRELESS COMMUNICATIONSRANGEArm’sLength<100 m<100 kmGlobalCosmicACTIVEPills, hearing aids, computer peripheralsWireless phones, remote controllers, computer linksRadio, television, cell phones, UWB, 802.11Ham radio, communications satellites, radar, lidarRadio & optical interplanetary communications, radar, lidarPASSIVEFaucets, CD’s, thermometers, Cameras, doorsMultispectral remote sensingWeather satellitesRadio & optical astronomyL17-2COMMUNICATION REQUIRES ENERGY AND POWERTypical receivers need: Eb> ~10-20Joules/bitReceived power required: Prec= MbpsEb[Watts](Mbpsis data rate, bits/sec)L17-3Transmitted Intensity: I(θ,φ,r) [W/m2]I(θ,φ,r)area =(r dθ)(r sin θ dφ)dΩ steradiansIsotropic:φrxzθRADIATED POWERFor isotropic radiation: I(θ,φ,r) = PR/4πr2[Wm-2]Total power radiated [W]Steradian: unit of solid angledθ, dφ: units of radians.Spheres: span 4π steradiansPR= I(θ,φ,r) r2 sinθ dθ dφdΩ (steradians)200ππ∫∫main beambacklobessidelobesAntenna pattern:I(θ,φ,r)L17-4ANTENNA GAIN G(θ,φ)Intensity at receiver:I(θ,φ,r) = G(θ,φ) (PR/4πr2 ) [Wm-2] Gain over Isotropic, G(θ,φ):Intensity actually radiated [Wm-2]Intensity if PRwere radiated isotropicallyG(θ,φ) = I(θ,φ,r)_ (PR/4πr2)backlobessidelobesG(θ,φ)Isotropic gainL17-5HOW TO INCREASE ANTENNA GAIN G(θ,φ)?Focus the energyLensesMirrorsPhasingPhotographs illustrating lenses, mirrors, and phasing removed due to copyright restrictions.L17-6I(θ,φ,r) = Gt(θ,φ) (PR/4πr2 ) [ W/m2 ] Power Received from a particular directionAntenna Effective Area and GainIntensity radiated in a particular directionPrec= I(θ,φ) A(θ,φ) [W]A(θ,φ) = G(θ,φ) (λ2/4π) [m2]Power Received from a particular directionPrec= PtGtGr(λ/4πr)2[W] ⇒ “reciprocity”ANTENNA EFFECTIVE AREA Ae(θ,φ)[m2]L17-7CIRCUIT PROPERTIES OF ANTENNASThevenin voltage VThis induced by incoming wavesReactive elements are tuned outMaximum power extractable from the antenna:When transmitting:When receiving:Equivalent circuit of antennaVThRr+-i(t)+-v(t)jXReactanceThevenin voltage sourceRadiation resistancePower radiated = PRPR= <i2(t)>Rr[W] Prec= <(VTh(t)/2)2>/RrVThRr+-RrL17-8SUMMARYWireless communications are ubiquitousM [bps] = Prec/Eb= IAe/Eb= PtGtGr(λ/4πr)2/Eb = data rateAr= Gr(λ2/4π) = Antenna effective area [m2]Antennas have Thevenin equivalent circuits, radiation resistanceBoost antenna gain using lenses, mirrors, or phasingEb> ~10-20[J] at the receiver (see footnote 39 on p360)G(θ,φ) = I(θ,φ,r) / (Pt/4πr2) = Antenna gain over isotropicL17-9EXAMPLE – INTERSTELLAR COMM.πππ= θφ θθφ⇒ θφΩ=ππ∫∫ ∫22RadRad200 4PP G(,) rsin d d G(,)d 44rdΩ steradiansΩBGoGoΩB= 4π⇒Go= 4π/ΩBΩBis the “beam solid angle”θBis “antenna beamwidth”Best microwave antennas: θB≅ 1 arc min = (1/60)o(1/57) radians ≅ 2-12radGo= 4π/ΩB≅ 23/2-24≅ 227≅ 108(or 80 dB)Strongest transmitters ~ 106WattsNearest stars ~1 light year = 3×107sec × 3×108m/s ≅ 1016 m−λ=≅ ≅ππ2 688 215radrec t r232P10 10 10 0.03P G G 10 [W] [J/s]44 r 10 10 10Data rate R ≅ Prec[J/s] / 10-20[J/bit] = 10-15/10-20= 105bits/secMIT OpenCourseWare http://ocw.mit.edu 6.013 Electromagnetics and Applications Spring 2009 For information about citing these materials or our Terms of Use, visit:
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