Lecture 5 Path Loss

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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!""#$%&

'


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!"#$%$&$'%('#)%$&( *+ ,-.&$'/

*+0 ,)%$&1'%2"3($'%/

*+4 ,)%$&1'%2"3($'%/


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!"# $%!!"&


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!"# !"$


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!""#$%&'()*+,-*#$%".,$""./ !""#$%".0,1(23#3*423,52,3&'()#*(+#$%6#*4+2%(1,+$(5)2+37'8#9:8(,""

;429#$,1,$362+6#11)2:8(+8(*=(*=862+12021#$".57

[email protected]+A2*B4**=@&&6667)2332+$2*7-85&,+*#-123&")5&C8$02+*


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!""#$%&'()*+,-*#$%".,$""./!"#$%&'(

0$*123#%(+2,)452621,52,$#$7(*7462+82528439:".;*461#-162,""1#?#?*12?,;2,??*,+*#$%6#*19:;A43#$7(*7462+,$";(8*#78B#$%*1,*)B,3,-*4+439::C%#5#$%,$4(*7(*7462+439C:::;A=

D232+2$-2E.2??2+F2*C1**7E&&666=)2??2+$2*=-4;&,+*#-82?&");&G4$52+*:


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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

!! 1204

2

2

o

ot

tt E

dL

GP=

!!"

#$$%

&'(

)*+

,-=

c

dt

d

dEtdE

c

oo.cos),(


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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,

!"

!#$

!%

!&'

((

)

*

++

,

-.=

!"

!#$

!%

!&'

./

!"

!#$

!%

!&'

00.

!"

!#$

!%

!&'

0=

12

345

6 0.0012

345

6 00.

12

345

6 00.1

2

345

6 0.

1234

56 00.1

234

56 0.

1Re

Re

ReRe),(

c

ddj

c

dtj

oo

c

dtj

c

dtj

oo

cdtj

oocdtj

oo

cc

cc

cc

eed

dE

ee

d

dE

ed

dEe

d

dEtdE

77

77

77

ddd

111!

""!

"


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A Trick

Pull an exponential with half the phase out to make a sine

!"

!#$

!%

!&'

(()

*++,

-./

012

3 4544=

!"

!#

$

!%

!&

'

(((

)

*

+++

,

-5

./

012

3 4544./

012

3 445

./

012

3 45445.

/

012

3 4544

./

012

3 4544./

012

3 445

c

ddjee

d

dE

j

eejee

d

dE

c

c

ddj

c

dtj

oo

c

ddj

c

ddj

c

ddj

c

dtj

oo

cc

cc

cc

2sinRe

2

22Re

2

22

2

6

66

66

66


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Field Envelope at Receiver

Recall d>dThe envelope of the field is then

Can show that , and

!!"#$$

%& '(

)*+, -.--=

cdd

ddEE

c

oo

TOT

2sin2 /

d

hhdd

rt2

!"#""

!"

#$%

& '('')**

+

,--.

/!"

#$%

& '(''

c

dd

c

ddcc

22sin 00


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Power Received

Making the substitutions yields

The power received isd

hh

d

dE

E rtoo

TOT

!

"22=

!!"

#

$$%

&

!!

"

#

$$

%

&==

'

(

' 4120

22

rTOT

edri

GEAPP


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Flat Earth Path Loss

Recalling

gives

The flat earth path loss is therefore

!! 1204

2

2

o

ot

tt E

dL

GP=

4

22

dL

hhGGPP

t

rtrtt

ri =

22

4

rthh

dL =


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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:

n

o

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

Lecture 5 Path Loss

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