04 Spherical Waves

III. Spherical Waves and RadiationAntennas radiate spherical waves into free spaceReceiving antennas, reciprocity, path gain and path lossNoise as a limit to receptionRay model for antennas above a plane earth and in a street canyonCylindrical waves

2002 by H. L. Bertoni

Radio Channel Encompasses Cables, Antennas and Environment Between Transmitter impresses information onto the voltage of a high power RF carrier for transmission through the air - called modulationReceiver extracts the information from the voltage of a low power received signal - called demodulation


Examples of Different Cellular Antennas


PCS Antennas


Base Station Antennas


Antennas Radiate Electromagnetic WavesEM waves have:Electric field E (V/m)Magnetic field H (A/m)E and HPerpendicular to each other and to direction of propagation - PolarizationAmplitude depends on direction of propagation - Radiation PatternTransmitting AntennaEH


Spherical Waves Radiated by AntennasI: terminal CurrentZ: constant with units of ohms: 120Radial Power Flux

Antenna pattern = For large r, localized current sources radiate fields in the form of Spherical Wavesz


Power Radiation Pattern Power density radiated by antenna P(q) = ExH* watts/m2Poynting vector in the radial directionP(q)q


Omnidirectional Antennas


Parabolic Reflector Antenna


Horn Antennas


Log Periodic Dipole Array


Dual Polarization Patch Antenna


Total Radiated PowerPT is independent of r, as required byconservation of power.

Normalization for is:


Antenna Gain and Radiation Resistance for No Resistive LossDirective gain = g(q,f)= |f (q,f)|2 andAntenna gain = G = Max. value of g(q,f)If isotropic antennas could exist, then |f (q,f)|2 = 1, G = 1

Radiation Resistance Rr = effective resistance seen at antenna terminals


Antenna Directivity, Gain, Efficiency


Short (Hertzian) Dipole Antenna


Half Wave Dipole AntennaThe radiated field can be written:


Summary of Antenna RadiationRadiation in free space takes the form of spherical wavesE, H and r form a right hand systemField amplitudes vary as 1/r to conserve powerPower varies as 1/r2, and varies with direction from the antennaDirection dependence gives the directivity and gain of the antennaRadiation resistance is the terminal representation of the radiated power


Receiving Antennas and ReciprocityFor a linear two-port V1 =Z11I1 + Z12I2 V2 =Z21I1 + Z22I2Reciprocity Z12 = Z21If I2 = 0, V2 = Z12I1 ~ 1/r

For r large,

|Z12|

Circuit Relation for Radiation into Free Space


Received Power and Path Loss RatioI2


Effective Area of Receiving AntennaEffective Area = Ae


Effective Area for a Hertzian DipoleFor matched termination


Effective Area for a Hertzian Dipole - cont.


Path Gain and Path Loss in Free Space


Path Gain in dB for Antennas in Free Space


Summary of Antennas as ReceiversDirective properties of antennas is the same for reception and transmissionEffective area for reception Ae = gl2/4pFor matched terminations, same power is received no matter which antenna is the transmitterPath gain PG = PR/PT < 1Path loss PL = 1/PG > 1


Noise Limit on Received PowerMinimum power for reception set by noise and interferenceNoise power set by temperature T, Boltzmans constant k and bandwidth Df of receiver: N = kTDf For analog system, received power PR must be at least 10N For digital systems, the maximum capacity C (bits/s) in presence of white noise is given by the limit


Sources of Thermal Noise


Thermal Noise Power N

Boltsmans constant = k =1.38x10-23 watts/(Hz oK)System temperature = TS oKBandwidth = Df HzFor TS = 300o K and Df = 30x103 HzN = 1.24x10-16 watts(N)dB = -159.1 dBw = -129.1 dBmNoise figure of receiver amplifier F ~ 5 dBEffective noise = N + FFor the example, N + F = -124.1 dBm


WalkAbout Phones

Frequency band450 MHz = 0.667 mBand width12.5 kHzThermal noise 4x10-18 mW /Hz5x10-14 mW-133 dBmReceiver noise figure5 dB typicalSNR for reception10 dB for FMMinimum received power2x10-12 mW-118 dBmTransmitted power500 mW27 dBmMaximum allowed path loss(PTr)dB - (PRec)dB145 dBMinimum path gainPRec /PTr = 10-14.53.2x10-15Antenna gain / Antenna heightAssume 0 dB1.6 m


Maximum Range WalkAbouts in Free Space


Summary of NoiseNoise and interference set the limit on the minimum received power for signal detectionThermal noise can be generated in all parts of the communications systemMiracle of radio is that signals ~ 10-12 mW can be detected


Ground and Buildings Influence Radio PropagationReflection and transmission at ground, wallsDiffraction at building corners and edgesDiffraction PathTransmission Reflection


Two Ray Model for Antennas Over Flat Earth(Antennas are Assumed to be Isotropic)


Reflection Coefficients at Plane Earth Vertical (TM) and Horizontal (TE) Polarizations


Path Gain vs. Antenna Separation(h1 = 8.7 m and h2 = 1.8 m)


Sherman Island/Rural


Sherman Island Measurements vs. Theory


Flat Earth Path Loss Dependence for Large R


Path Gain of Two Ray Model


Maximum Range for WalkAbouts on Flat Earth


Fresnel Zone Gives Region of PropagationFresnel zone is ellipsoid about ray connecting source and receiver and such that r2-r1 =l/2Ray fields propagates within Fresnel zoneObjects placed outside Fresnel zone generate new rays, but have only small effect on direct ray fieldsObjects placed inside Fresnel zone change field of direct ray


Fresnel Zone Interpretation of Break Point


Regression Fits to the 2-Ray Model on Either Side of the Break Point


Six Ray Model to Account for ReflectionsFrom Buildings Along the StreetEach ray seen from above represents two rayswhen viewed from the side:

1. Ray propagating directly from Tx to Rx2. Ray reflected from ground


Six Ray Model of the Street Canyon


Six Ray Model for Street Canyonf = 900 MHz, h1= 10 m, h2= 1.8 m, w = 30 m, zT = zR = 8 m


Received Signal on LOS Route f = 1937 MHz, hBS= 3.2 m, hm = 1.6 mTelesis Technology Laboratories, Experimental License Progress Report to the FCC, August, 1991.


Summary of Ray Models forLine-of-Sight (LOS) ConditionsRay models describes ground reflection for antennas above the earthPresence of earth changes the range dependence from 1/R2 to 1/R4 Propagation in a street canyon causes fluctuations on top of the two ray modelFresnel zone identifies the region in space through which fields propagate


Cylindrical Waves Due to Line Source


04 Spherical Waves

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