This document discusses Friis transmission formula for free space path loss. It defines key terms like power density, effective aperture, and antenna gain. The Friis formula calculates received power as a function of transmitted power, transmitter and receiver gains, wavelength, and distance. It states that path loss increases with distance and is inversely proportional to the square of the distance. The document also notes some drawbacks of the Friis model and conditions for applying it in the far field region.

1. WIRELESS COMMUNICATION
SERIES
Free Space Path Loss Model –
Frii’s equation
[part – 2]

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3. The Power Density of the Transmitted Signal is given by
PD = Pt / 4π D2
Power density is the measure of
amount of power per unit volume.
PD = Power Received / Surface area
The above Eqn. is valid for the ISOTROPIC Antenna, But in practical situations most of the antennas will be DIRECTIONAL
Antenna. Which do not have the Unit Gain in all directions.( Gain will be Higher in a particular Direction)
Observing from the Transmitter Side:
In this case, We have to consider the Gain of the Transmitting antenna into account, Thus the Eqn.
Becomes
PD = (Pt / 4π D2) . Gt
Observing from the Receiver Side:
In electromagnetics and antenna theory,
antenna aperture, is a measure of how
effective an antenna is at receiving the
radiated power.
Ae = Power Received / Power Density
The amount of power effectively received by the receiving antenna is
decided by the Effective Aperture (Ae) of an Antenna.
Ae= Pr / PD Pr = PD . Ae Pr =
𝑷 𝒕 .𝑮 𝒕
𝟒𝝅𝑫 𝟐 . Ae
The Relation between the G and Ae is
given by
Ae =
λ 𝟐
𝟒π
. GPr =
𝑷 𝒕 .𝑮 𝒕
𝟒𝝅𝑫 𝟐 .
λ 𝟐
𝟒π
Gr Pr =
𝑷 𝒕 .𝑮 𝒕 .𝑮 𝒓.𝝀 𝟐
(𝟒𝝅𝑫) 𝟐.𝑳
Frii’s Free Space Equation

4. Pr (D) =
𝑷 𝒕 .𝑮 𝒕 .𝑮 𝒓.𝝀 𝟐
(𝟒𝝅𝑫) 𝟐.𝑳
Frii’s Free Space Equation:
Path Loss Model for Free Space Propagation:
Path Loss in general is defined by :
FSPL = Transmitted Power / Received Power
FSPL = Pt / Pr
𝑃𝑟
𝑃𝑡
=
𝐺𝑡 .𝐺 𝑟.𝜆2
(4𝜋𝐷)2
𝑃𝑡
𝑃𝑟
=
(4𝜋𝐷)2
𝐺𝑡 .𝐺 𝑟.𝜆2
Gt and Gr are represented in dBi or dBd, But the Path Loss is always measured in dB scale
𝑃𝐿 𝑑𝐵 = 10 log
𝑃𝑡
𝑃𝑟
= 10log
4𝜋𝐷 2
𝐺𝑡 . 𝐺𝑟. 𝜆2 𝑃𝐿 𝑑𝐵 = 10 log
𝑃𝑡
𝑃𝑟
= −10log
𝐺𝑡 . 𝐺𝑟. 𝜆2
4𝜋𝐷 2
Assuming the Gains are Unity then , Gt and Gr = 1
𝑷𝑳 𝒅𝑩 = 𝟏𝟎 𝐥𝐨𝐠
𝑷 𝒕
𝑷 𝒓
= −𝟏𝟎𝐥𝐨𝐠
𝝀
𝟒𝝅𝑫
𝟐

5. Drawbacks of Frii’s Free Space Equation:
1. Frii’s Free Space Model is a valid Predictor for D ≠ 0 .
2. This Model Assumes only a LOS Signal
𝑷𝑳 𝒅𝑩 = 𝟏𝟎 𝐥𝐨𝐠
𝑷 𝒕
𝑷 𝒓
= −𝟏𝟎𝐥𝐨𝐠
𝝀
𝟒𝝅𝑫
𝟐
Fields of Antenna:
L
2L2
2L2
Additionally to be in the far field distance, there are 2 conditions Df >>L Df >>λ
Pr(D) = Pr (do) (do / D)2 ; D≥do≥Df
Pr(D) = 10 log(Pr (do)) + 20 log (do / D) ; D≥do≥Df

6. S U B S C R I B E
Defined the FSPL
Defined antenna
regions
FSPL in far field