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8/13/2019 Lecture 5 Path Loss
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PATH LOSS
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Definition of Path Loss
Path loss includes all of the lossy effectsassociated with distance
Transmitter
TransmitPower,Pt
Feeder LossLt
Receiver
ReceivedPower,Pr
Feeder LossLr
Antenna GainGt
Antenna GainGr
Path LossL
Pti Pri
[Saunders,`99]
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Motivation Need path loss to determine range of operation (using a
link budget)
This module considers two cases, Free space Flat earth
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Received Power The power appearing at the receiver input terminals is
All gains Gand lossesLare expressed as power ratiosand the powers are in Watts
rt
rtt
r
LLL
GGP
P =
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dBm and dBW Powers may also be expressed in
dBm, the number of dB the power exceeds 1 milliwatt dBW, the number of dB the power exceeds 1 Watt.
Watts
PP
r
r 310 10
(in Watts)log10dBm)(in
!
=
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EIRP The effective isotropic radiated power (EIRP) is
The effective isotropic receivedpower is
t
tt
ti
L
GPP =
L
EIRP
G
LPP
r
rr
ri ==
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Antenna GainsAntenna gain may be expressed in dBi or dBd
dBi: maximum radiated power relative to an isotropic antenna dBd: maximum radiated power relative to a half-wave dipole
antenna
A half-wave dipole has a peak gain of 2.15 dBi
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Path LossThe path loss is the ratio of the EIRP to theeffective isotropic received power
Path loss is independent of system parametersexcept for the antenna radiation pattern The pattern determines which parts of the environment
are illuminated
ri
ti
P
PL =
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Free-Space Path Loss In the far-field of the transmit antenna, the free-space path
loss is given by
The far-field is any distance dfrom the antenna, such that2
22
)4(!
" dL =
!!
>>>>>> dDdD
d and,,2
2
whereDis the largest dimension of the antenna.
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Power and Electric Field
The peak power flux density (W/m2) in free space:
This holds in the neighborhood (but far field) oftransmitters on towers
!=
!=
===
377120
44
22
2
22
EE
E
dL
GP
d
EIRPP
t
ttd
"
#""
where |E|= envelope of the electric field in V/m
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Effective Aperture
Antenna gain may be expressed in terms ofeffective aperture,Ae
For aperture antennas, such as dishantennas, , where is the antenna
efficiency and Ais the area of the apertureThe aperture intercepts the power flux density
2
4
!
"e
AG =
edri APP =
!AAe = !
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Flat Earth (2-Ray) Model
If there is a line-of-sight (LOS) path, then the secondstrongest path is the ground bounce
LOS
GroundBounce
Transmitter
Receiver
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Typical Relative Dimensions
d>>ht, d>>hr for a typical mobile communicationsgeometry
LOS
Ground
Bounce
Transmitter
Receiver
hthr
d
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Field Near Transmitter
Let the field at a distance doin the neighborhood of, butalso in the far field of, the transmit antenna be E(do,t) , and
its envelope beEo
Assuming the transmitter is high enough,
The field at some other distance d>dois
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o
ot
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dL
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d
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c
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Low Grazing Angle
At such a low (grazing) angle of incidence (!=afew degrees), the reflection coefficient is -1 for
horizontal polarization
Transmitter
Receiver
! !
#= 1
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Field at Receiver
The direct and bounce paths add coherently
d
ht hr
d
d1 d2
21
),(),(),(
ddd
tdEtdEtdETOT
!!+!!=!!
!!"!=
#= 1
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Long Baseline Effects
Since dis so large,
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A Trick
Pull an exponential with half the phase out to make a sine
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Field Envelope at Receiver
Recall d>dThe envelope of the field is then
Can show that , and
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cdd
ddEE
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Power Received
Making the substitutions yields
The power received isd
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TOT
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Flat Earth Path Loss
Recalling
gives
The flat earth path loss is therefore
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2
2
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tt E
dL
GP=
4
22
dL
hhGGPP
t
rtrtt
ri =
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rthh
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10 100 1000 10000
Path Length, d(m)
10
100
1000
PathLoss(dB)
Propagation path lossLp (dB) with distance over a flat reflecting surface;
hb = 7.5 m, hm = 1.5 m, fc = 1800 MHz.
Lp =
c
4d
24sin2
2hbhm
cd
1
6
1
1
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In reality, the earths surface is curved and rough, and the signal
strength typically decays with the inverse power of the distance,
and the received power is
p= kt
d
where k is a constant of proportionality. Expressed in units of dBm,
the received power is
p (dBm) = 10log10(k) +t (dBm) 10log10(d)
is called the path loss exponent. Typical values of are have been
determined by empirical measurements for a variety of areas
Terrain Free Space 2Open Area 4.35
North American Suburban 3.84North American Urban (Philadelphia) 3.68North American Urban (Newark) 4.31Japanese Urban (Tokyo) 3.05
7
1
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Using a Reference Power Measurement
Suppose that a reference measurement ofreceived power,Po, is taken at some point in the
far field of the antenna
Then the power taken at some more distant pointmay be expressed relative to the reference
power:
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ori
d
dPP !
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Summary
Free space path loss depends only on distance andwavelength, and falls off as 1/d2
Flat earth path loss depends also on the antenna heights, and falls off as 1/d4 Has a pretty good fit to urban and suburban environments, even
though it is an idealization, derived only for horizontal polarization
The power of d is called the path loss exponent For mobile comm, this exponent is typically between 3.5
and 4
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References
[Saunders,`99] Simon R. Saunders,Antennasand Propagation for Wireless Communication
Systems, John Wiley and Sons, LTD, 1999.
[Rapp, 96] T.S. Rappaport, WirelessCommunications, Prentice Hall, 1996
[Lee, 98] W.C.Y. Lee, Mobile CommunicationsEngineering, McGraw-Hill, 1998