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Published byAubrie McCoy Modified over 3 years ago

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ALLAH ALLAH

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Compiled by :Engr.Muhammad Waseem( MS Telecommunication,England,BS.(ssuet)). Assistant Professor, Telecom Eng.Deptt. Sir Syed University of Engineering & Technology, Karachi, Pakistan. Email ID:engrmwaseem@gmail.com Office: CF-02,FFT-10

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The free Space propagation model is used to predict received signal strength when the transmitter and receiver have a clear,unobstructed line of sight path between them. Satellite Communication systems and microwave line of sight radio links typically undergo free space propagation.

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The free space model predicts that received power decays as a function of the T-R separation distance raised to some power. The free space power received by a receiver antenna which is separated from a radiating transmitter antenna by a distance d, is given by the Friis free space equation,

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In the above equation Pt is the transmitted power, Pr(d) is the received power which is a function of the T-R separation, Gt is transmitter antenna gain, Gr is the receiver antenna gain, d is the T-R separation distance in meters, L is the system loss factor not related to propagation(L ˃ 1 or L=1), λ is the wavelength in meters

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The gain of an antenna can also be related to its effectiv e aperture, Ae, by G= 4πAe/ λ. λ The effective aperture Ae is related to the physical size of the antenna,and λ is related to the carrier frequency by λ=c/f =2πc/ ωc,where f is the carrier frequency in Hertz, ωc is the frequency in radians per second, and c is the speed of light given in meters/second.

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The values of Pt and Pr must be expressed in the same units, Gt and Gr are dimensionless quantities. The miscellaneous losses L (L ˃ 1) are usually due to transmission line attenuation, filter losses, antenna losses in the communication system. A value L=1 indicates no loss in the system hardware.

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The Friis free space equation indicates that the received power falls off as the square of the T-R separation distance. This implies that the received power decays with distance at a rate of 20dB/decade.

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An isotopic radiator is an ideal antenna which radiates power with unit gain uniformly in all directions, and is often used to reference antenna gains in wireless systems. The effective isotropic radiated power (EIRP) is defined as EIRP=Pt.Gt and represents the maximum radiated power available from a transmitter in the direction of maximum antenna gain, as compared to an isotropic radiator.

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In Practice, Effective Radiated Power(ERP) is used instead of EIRP to denote the maximum radiated power as compared to a half wave dipole antenna(instead of isotropic antenna ).Since a dipole antenna has a gain of 1.64( 2.15 dB above an isotrope), the ERP will be 2.15dB smaller than the EIRP for the same transmission system.

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In practice, antenna gains are given in units of dBi( dB gain with respect to an isotropic antenna) or dBd( dB gain with respect to a half wave dipole).

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Path Loss: It represents signal attenuation as a positive quantity measured in dB, is defined as the difference (in dB) between the effective transmitted power and the received power, and may or not may include the effect of the antenna gains.

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The path loss for the free space model when the antenna gains are included is given by PL(dB)=10 log(Pt/Pr)=-10log [ GtGr

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When the antenna gains are excluded, the antennas are assumed to have unity gains, and path loss is given by

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If a transmitter produces 50 W of power, express the transmit power in units of (a) dBm, and (b) dBW. If 50 W is applied to a unity gain antenna with a 900 MHZ carrier frequency, find the received power in dBm at a free space distance of 100 m from the antenna.What is Pr(10)?Assume using gain for the receiver antenna.

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Given: Transmitter Power, Pt=50W Carrier Frequency, fc=900MHz (a) Transmitter Power, Pt(dBm)=10 Log[Pt(mW)/(1mW)] =10 Log[501000] =47.0dBm

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(b) Transmitter power, Pt(dBW)=10Log[Pt(W)/(1W)] =10 Log[50]=17.0dBW The received power can be determined by using the following equation.

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Pr=[50(1)(1)(1/3)(1/3)] / [(4π)(4π)(100)(100)(1)] Pr= Pr(dBm)=10Log Pr(mW) =10Log( ) = -24.5dBm

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The received power at 10 Km can be expressed in terms of dBm using Pr(10km)=Pr(100)+20log[do/d] ( where do=100 and d=10km) Pr(10km)=Pr(100)+20log[do/d] = -24.5dBm-40dB =-64.5dBm

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THANKS TO ALLAH TALA

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