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Polytechnic University© 2002 by H. L. Bertoni1 III. Spherical Waves and Radiation Antennas radiate spherical waves into free space Receiving antennas, reciprocity, path gain and path loss Noise as a limit to reception Ray model for antennas above a plane earth and in a street canyon Cylindrical waves

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Polytechnic University© 2002 by H. L. Bertoni2 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 modulation Receiver extracts the information from the voltage of a low power received signal - called demodulation Information Tx Information Rx Cable Transmitting Antenna Receiving Antenna Radio Channel

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Polytechnic University© 2002 by H. L. Bertoni3 Examples of Different Cellular Antennas Full wave monopole above ground plane /2 /4 Half wave dipole /2 Dipole in corner reflector

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Polytechnic University© 2002 by H. L. Bertoni4 PCS Antennas

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Polytechnic University© 2002 by H. L. Bertoni5 Base Station Antennas

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Polytechnic University© 2002 by H. L. Bertoni6 Antennas Radiate Electromagnetic Waves EM waves have: –Electric field E (V/m) –Magnetic field H (A/m) E and H –Perpendicular to each other and to direction of propagation - Polarization –Amplitude depends on direction of propagation - Radiation Pattern Transmitting Antenna Cable E H

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Polytechnic University© 2002 by H. L. Bertoni7 Spherical Waves Radiated by Antennas I terminal Current Z constant with units of ohms 120 Radial Power Flux Antenna pattern = For large r, localized current sources radiate fields in the form of Spherical Waves z x y r I

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Polytechnic University© 2002 by H. L. Bertoni8 Power Radiation Pattern Power density radiated by antenna P( ) = E x H* watts/m 2 Poynting vector in the radial direction P()P()

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Polytechnic University© 2002 by H. L. Bertoni9 Omnidirectional Antennas

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Polytechnic University© 2002 by H. L. Bertoni10 Parabolic Reflector Antenna

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Polytechnic University© 2002 by H. L. Bertoni11 Horn Antennas

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Polytechnic University© 2002 by H. L. Bertoni12 Log Periodic Dipole Array

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Polytechnic University© 2002 by H. L. Bertoni13 Dual Polarization Patch Antenna

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Polytechnic University© 2002 by H. L. Bertoni14 Total Radiated Power P T is independent of r, as required by conservation of power. Normalization for is: dA r

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Polytechnic University© 2002 by H. L. Bertoni15 Antenna Gain and Radiation Resistance for No Resistive Loss Directive gain = g ( )= |f ( )| 2 and Antenna gain = G = Max. value of g( If isotropic antennas could exist, then |f ( )| 2 = 1, G = 1 Radiation Resistance R r = effective resistance seen at antenna terminals

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Polytechnic University© 2002 by H. L. Bertoni16 Antenna Directivity, Gain, Efficiency

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Polytechnic University© 2002 by H. L. Bertoni17 Short (Hertzian) Dipole Antenna L<< r z I (z)I (z) z I

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Polytechnic University© 2002 by H. L. Bertoni18 Half Wave Dipole Antenna r I z I (z)I (z) /4 /4 The radiated field can be written:

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Polytechnic University© 2002 by H. L. Bertoni19 Summary of Antenna Radiation Radiation in free space takes the form of spherical waves E, H and r form a right hand system Field amplitudes vary as 1/r to conserve power Power varies as 1/r 2, and varies with direction from the antenna Direction dependence gives the directivity and gain of the antenna Radiation resistance is the terminal representation of the radiated power

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Polytechnic University© 2002 by H. L. Bertoni20 Receiving Antennas and Reciprocity For a linear two-port V 1 =Z 11 I 1 + Z 12 I 2 V 2 =Z 21 I 1 + Z 22 I 2 Reciprocity Z 12 = Z 21 If I 2 = 0, V 2 = Z 12 I 1 ~ 1/r For r large, |Z 12 | << |Z 11 |, |Z 22 | +V1-+V1- +V2-+V2- r I1I1 I2I2 Equivalent Circuit Z 11 -Z 12 Z 22 -Z 12 Z 12 V1V1 I1I1 V2V2 I2I2

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Polytechnic University© 2002 by H. L. Bertoni21 Circuit Relation for Radiation into Free Space Z 11 -Z 12 Z 22 -Z 12 Z 12 +V1-+V1- I1I1 +V2-+V2- (open circuit) V 1 = Z 11 I 1 V 2 = V OC = Z 12 I 1

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Polytechnic University© 2002 by H. L. Bertoni22 Received Power and Path Loss Ratio I2I2 Z 11 -Z 12 Z 22 -Z 12 Z 22 * +V1-+V1- I1I1 +V2-+V2- Z 12 Matched Load R r2 - jX 2 V

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Polytechnic University© 2002 by H. L. Bertoni23 Effective Area of Receiving Antenna Effective Area = A e PTPT Z * 11 A e1 Z * 22 PTPT A e2

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Polytechnic University© 2002 by H. L. Bertoni24 Effective Area for a Hertzian Dipole z L<< r I I (z)I (z) For matched termination or Z 11 Z 11 * + V oc - R R + V oc - + V oc /2 -

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Polytechnic University© 2002 by H. L. Bertoni25 Effective Area for a Hertzian Dipole - cont.

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Polytechnic University© 2002 by H. L. Bertoni26 Path Gain and Path Loss in Free Space

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Polytechnic University© 2002 by H. L. Bertoni27 Path Gain in dB for Antennas in Free Space Slope=20 -32.4 -52.4 -72.4 -92.4 r =1r =1r =10r =100r =1000 f GH = 1 PG dB

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Polytechnic University© 2002 by H. L. Bertoni28 Summary of Antennas as Receivers Directive properties of antennas is the same for reception and transmission Effective area for reception A e = g 2 /4 For matched terminations, same power is received no matter which antenna is the transmitter Path gain PG = P R /P T < 1 Path loss PL = 1/PG > 1

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Polytechnic University© 2002 by H. L. Bertoni29 Noise Limit on Received Power Minimum power for reception set by noise and interference Noise power set by temperature T, Boltzman’s constant k and bandwidth f of receiver: N = kT f For analog system, received power P R must be at least 10N For digital systems, the maximum capacity C (bits/s) in presence of white noise is given by the limit

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Polytechnic University© 2002 by H. L. Bertoni30 Sources of Thermal Noise Sky Temp ~5 o -150 o K Ground Temp ~300 o K Physical Temp of Antenna T AP Physical Temp of Line = T L Temp of Receiver T R TATA

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Polytechnic University© 2002 by H. L. Bertoni31 Thermal Noise Power N –Boltsman’s constant = k =1.38x10 -23 watts/(Hz o K) –System temperature = T S o K –Bandwidth = f Hz –For T S = 300 o K and f = 30x10 3 Hz N = 1.24x10 -16 watts (N) dB = -159.1 dBw = -129.1 dBm –Noise figure of receiver amplifier F ~ 5 dB –Effective noise = N + F For the example, N + F = -124.1 dBm

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Polytechnic University© 2002 by H. L. Bertoni32 WalkAbout Phones Frequency band450 MHz = 0.667 m Band width12.5 kHz Thermal noise 4x10 -18 mW /Hz5x10 -14 mW-133 dBm Receiver noise figure5 dB typical SNR for reception10 dB for FM Minimum received power2x10 -12 mW-118 dBm Transmitted power500 mW27 dBm Maximum allowed path loss(P Tr ) dB - (P Rec ) dB 145 dB Minimum path gainP Rec /P Tr = 10 -14.5 3.2x10 -15 Antenna gain / Antenna heightAssume 0 dB1.6 m

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Polytechnic University© 2002 by H. L. Bertoni33 Maximum Range WalkAbouts in Free Space

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Polytechnic University© 2002 by H. L. Bertoni34 Summary of Noise Noise and interference set the limit on the minimum received power for signal detection Thermal noise can be generated in all parts of the communications system Miracle of radio is that signals ~ 10 -12 mW can be detected

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Polytechnic University© 2002 by H. L. Bertoni35 Ground and Buildings Influence Radio Propagation Reflection and transmission at ground, walls Diffraction at building corners and edges Diffraction Path Transmission Reflection

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Polytechnic University© 2002 by H. L. Bertoni36 Two Ray Model for Antennas Over Flat Earth (Antennas are Assumed to be Isotropic) r1r1 r2r2 R h1h1 h2h2 Antenna Image

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Polytechnic University© 2002 by H. L. Bertoni37 Reflection Coefficients at Plane Earth Vertical (TM) and Horizontal (TE) Polarizations 1 Incident Angle , degree 0102030405060708090 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Horiz. Pol. r =15-j0.1 Vert. Pol. r =15-j0.1

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Polytechnic University© 2002 by H. L. Bertoni38 Path Gain vs. Antenna Separation (h 1 = 8.7 m and h 2 = 1.8 m) 10 0 1 2 3 -110 -100 -90 -80 -70 -60 -50 -40 Distance (m) Path Gain (dB) Vertical pol. Horizontal pol Brewster’s angle f = 900MHz

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Polytechnic University© 2002 by H. L. Bertoni39 Sherman Island/Rural

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Polytechnic University© 2002 by H. L. Bertoni40 Sherman Island Measurements vs. Theory

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Polytechnic University© 2002 by H. L. Bertoni41 Flat Earth Path Loss Dependence for Large R

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Polytechnic University© 2002 by H. L. Bertoni42 Path Gain of Two Ray Model

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Polytechnic University© 2002 by H. L. Bertoni43 Maximum Range for WalkAbouts on Flat Earth

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Polytechnic University© 2002 by H. L. Bertoni44 Fresnel Zone Gives Region of Propagation Fresnel zone is ellipsoid about ray connecting source and receiver and such that r 2 -r 1 = /2 –Ray fields propagates within Fresnel zone –Objects placed outside Fresnel zone generate new rays, but have only small effect on direct ray fields –Objects placed inside Fresnel zone change field of direct ray r2r2 r1r1 r 2 - r 1 = /2

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Polytechnic University© 2002 by H. L. Bertoni45 Fresnel Zone Interpretation of Break Point r1r1 r2r2 RBRB Fresnel zone ( r 2 - r 1 =

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Polytechnic University© 2002 by H. L. Bertoni46 Regression Fits to the 2-Ray Model on Either Side of the Break Point 10 0 10 1 10 2 10 3 -120 -110 -100 -90 -80 -70 -60 -50 Distance (m) Path Gain (dB ) n 1 =1.3 n 2 =3.6 f=1850MHz h 1 =8.7 h 2 =1.6 Model: 2ray, r =15 RBRB

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Polytechnic University© 2002 by H. L. Bertoni47 Six Ray Model to Account for Reflections From Buildings Along the Street Each ray seen from above represents two rays when viewed from the side: 1. Ray propagating directly from Tx to Rx 2. Ray reflected from ground zTzT zRzR pp R0R0 w Top view of street canyon showing relevant rays RbRb RaRa

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Polytechnic University© 2002 by H. L. Bertoni48 Six Ray Model of the Street Canyon

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Polytechnic University© 2002 by H. L. Bertoni49 10 1 10 2 10 3 10 4 -140 -130 -120 -110 -100 -90 -80 -70 -60 -50 -40 Distance (m) Received Power (dBW) 2 ray model 6 ray model Six Ray Model for Street Canyon f = 900 MHz, h 1 = 10 m, h 2 = 1.8 m, w = 30 m, z T = z R = 8 m

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Polytechnic University© 2002 by H. L. Bertoni50 Received Signal on LOS Route f = 1937 MHz, h BS = 3.2 m, h m = 1.6 m Telesis Technology Laboratories, Experimental License Progress Report to the FCC, August, 1991.

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Polytechnic University© 2002 by H. L. Bertoni51 Summary of Ray Models for Line-of-Sight (LOS) Conditions Ray models describes ground reflection for antennas above the earth Presence of earth changes the range dependence from 1/R 2 to 1/R 4 Propagation in a street canyon causes fluctuations on top of the two ray model Fresnel zone identifies the region in space through which fields propagate

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Polytechnic University© 2002 by H. L. Bertoni52 Cylindrical Waves Due to Line Source y z x Line Source

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