Friis Transmission Equation

[Pages:8]Friis Transmission Equation

Group Meeting 10/10/13

Friis Equation Origins

Derived in 1945 by Bell Labs worker Harald T. Friss

Gives the amount of power an antenna received under ideal conditions from another antenna

? Antennas must be in far field ? Antennas are in unobstructed free space ? Bandwidth is narrow enough that a single wavelength

can be assumed ? Antennas are correctly aligned and polarized

Simple Form of Friis Equation

P P

r t

=

Gt

G

r

(

4

R

2

)

Pr : Power at the receiving antenna

Pt : output power of transmitting antenna

Gt, Gr: gain of the transmitting and receiving antenna, respectively

: wavelength

R: distance between the antenna

Derivation of equation

Power from isotropic antenna falls off as r2

Power density (p) would be:

p=

4

P

t

R2

Derivation of equation

Multiplying by gain of the transmitting antenna gives a real antenna pattern

p=

4

P

t

R2

G

t

 If receiving antenna has an effective aperture

of

A eff

the

power

received

by

this

antenna

(Pr)

is

Pr= p Aeff

thus:

P

r

=

4

Pt R

2

G

t

Aeff

 The effective aperture of an antenna can be

written as

Ae

=

2 4

G

plugging in:

P

r

=

P

t

Gt

G

r

(

4

R

2

)

Modifications to Friis equation (Complicated Form)

P P

r t

=

Gt

(t

,

t

)G

r

(r

,

r

)(

4

R

2

)(

1-

t2

)(1-

r2)a tar

* 2e-

R

Gt , Gr : modifications to gain of antennas in which the antennas "see" each other.

t and t are the reflection coefficients of the antennas

at and ar are the polarization vectors of the antennas

is the absorption coefficient of the medium

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