Definition of Path Loss Path Loss

[Pages:4]Path Loss

Instructor: M. A. Ingram ECE 4823

Definition of Path Loss

Path loss includes all of the lossy effects associated with distance and the interaction of the propagating wave with the objects in the environment between the antennas

Antenna Gain

Transmit

Gt

Power, Pt

Pti

Antenna Gain

Gr

Received

Pri

Power, Pr

Transmitter

Feeder Loss Lt

Path Loss L

Receiver

Feeder Loss Lr

[Saunders,`99]

Motivation

Need path loss to determine range of operation (using a link budget)

This module considers two cases,

Free space Flat earth

Received Power

The power appearing at the receiver input terminals

is

Pr

=

Pt Gt Gr Lt LLr

All gains G and losses L are expressed as power ratios and the powers are in Watts

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.

Pr

(in

dBm)

= 10 log10

Pr (in Watts) 10-3Watts

EIRP

The effective isotropic radiated power

(EIRP) is

Pti

=

Pt Gt Lt

The effective isotropic received power is

Pri

=

Pr Lr Gr

Antenna Gains

Antenna 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

Path Loss

The path loss is the ratio of the EIRP to the effective isotropic received power

L = Pti Pri

Path loss is independent of system parameters except for the antenna radiation pattern

The pattern determines which parts of the environment are illuminated

Free-Space Path Loss

In the far-field of the transmit antenna, the freespace path loss is given by

L

=

(4 )2 2

d

2

The far-field is any distance d from the antenna, such

that

d >> 2D2 , d >> D, and d >>

where D is the largest dimension of the antenna.

Power and Electric Field

The peak power flux density in free space:

2

Pd

=

EIRP 4d 2

=

Pt Gt Lt 4d 2

=

E

2

2

E

E

= 120 = 377

where |E| = envelope of the electric field in V/m

This holds in the neighborhood (but far field) of transmitters on towers

Effective Aperture

Antenna gain may be expressed in

terms of effective aperture, Ae

G

=

4Ae 2

The aperture intercepts the power flux

density

Pri = Pd Ae

Flat Earth (2-Ray) Model

If there is a line-of-sight (LOS) path, then the second strongest path is the ground bounce

Transmitter

LOS

Ground Bounce

Receiver

Typical Relative Dimensions

d>>ht, d>>hr for a typical mobile communications geometry

Transmitter

ht

LOS

Ground Bounce

Receiver

hr

d

Field Near Transmitter

Let the field at a distance do in the neighborhood of, but also in the far field of, the transmit antenna be E(do,t) , and its envelope be Eo

Assuming the transmitter is high enough,

PtGt Lt 4do2

=

Eo 2 120

The field at some other distance d>do is

E (d , t )

=

Eo d o d

cosc

t

-

d c

Low Grazing Angle

At such a low (grazing) angle of incidence (=a few degrees), the reflection coefficient is -1 for horizontal polarization

Transmitter

= - 1

Receiver

Field at Receiver

The direct and bounce paths add coherently ETOT (d, t) = E(d, t) - E(d, t) d = d1+ d2

d'

ht

d1''

= -1

d2''

hr

d

Long Baseline Effects

1 11

Since d is so large,

d d d

E(d,t)

=

Eo d o d

Ree

jc

t

-

d c

-

Eo d o d

Re

e

j

c

t

-

d c

Eo d o

Ree

jc

t

-

d c

-

e

j

c

t

-

d c

d

=

Eo d o d

Ree

jc

t

-

d c

e

j

c

d

-d c

-1

A Trick

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

Eodo d

Ree e 2 j

c

t

-

d c

j

c

d

-d 2c

e j

c

d

-d 2c

j

- e-

j

c

d

-d 2c

2j

=

2Eodo d

Ree e j

c

t

-

d c

j

c

d

-d 2c

j

sin

c

d

- d 2c

Field Envelope at Receiver

Recall d''>d' The envelope of the field is then

ETOT

=

2Eodo d

sinc

d

- d 2c

Can show that d - d 2hthr , and d

sin

c

d

- 2c

d

c

d

- 2c

d

Flat Earth Path Loss

Recalling

PtGt Lt 4do2

=

Eo 2 120

gives

Pri

=

PtGtGr ht2hr2 Lt d 4

The flat earth path loss is therefore

L

=

d4 ht2 hr2

Power Received

Making the substitutions yields

ETOT

= 2Eodo d

2ht hr d

The power received is

Pri

=

Pd

Ae

=

2

ETOT 120

Gr 2 4

Summary

Free space path loss depends only on distance and wavelength, 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

References

[Saunders,`99] Simon R. Saunders, Antennas and Propagation for Wireless Communication Systems, John Wiley and Sons, LTD, 1999.

[Rapp, '96] T.S. Rappaport, Wireless Communications, Prentice Hall, 1996

[Lee, '98] W.C.Y. Lee, Mobile Communications Engineering, McGraw-Hill, 1998

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