Table of Contents

# Link Equation and Link Budget

## FRIIS Transmission Equation

Consider the simplified wireless communication system shown in the Figure. A transmitter with an output power Pt is fed into a transmitting antenna with a gain Gt . The signal is picked up by a receiving antenna with a gain Gr. The received power is Pr and the distance is R. The received power can be calculated in the following if we assume that there is no atmospheric loss, polarization mismatch, impedance mismatch at the antenna feeds, misalignment, and obstructions. The antennas are operating in the far-field regions. The power density at the receiving antenna for an isotropic transmitting antenna is given as:

Simplified wireless communication system.

Since a directive antenna is used, the power density is modified and given by

The received power is equal to the power density multiplied by the effective area of the receiving antenna

The effective area is related to the antenna gain by the following expression:

This equation is known as the Friis power transmission equation.

The received power is proportional to the gain of either antenna and inversely proportional to R^{2}.If Pr=Si,min, the minimum signal required for the system, we have the maximum range given by

This equation is known as the Friis power transmission equation. The received power is proportional to the gain of either antenna and inversely proportional to R^{2}. If Pr=Si,min, the minimum signal required for the system, we have the maximum range given by

Where Si,min can be related to the receiver parameters.

Where k is the Boltzmann constant, T is the absolute temperature, and B is the receiver bandwidth. Substituting gives

The output SNR for a distance of R is given as

# Space Loss

Space loss accounts for the loss due to the spreading of RF energy as it propagates through free space. As can be seen, the power density (Pt/4πR2) from an isotropic antenna is reduced by 1/R2 as the distance is increased. Consider an isotropic transmitting antenna and an isotropic receiving antenna, as shown in the figure.

since Gr ¼ Gt ¼ 1 for an isotropic antenna. The term space loss (SL) is defined by

# Link Equation and Link Budget

For a communication link, the Friis power transmission equation can be used to calculate the received power. The Equation is rewritten here as

This is also called the link equation. System loss Lsys includes various losses due to, for example, antenna feed mismatch, pointing error, atmospheric loss, and polarization loss.

Converting the Equation in decibels, we have

EIRP- effective isotropic radiated power and G/T Parameters

The effective isotropic radiated power (EIRP) is the transmitted power that would be required if the signal were being radiated equally into all directions instead of being focused.

Consider an isotropic antenna transmitting a power Pt and a directional antenna transmitting Pt as shown in the figure below, with a receiver located at a distance R from the antennas. The received power from the isotropic antenna is

The received power from a directive antenna is

Definition of EIRP

Thus EIRP is the amount of power that would be transmitted by an isotropic radiator given the measured receiver power.

In a communication system, the larger the EIRP, the better the system. Therefore, we have

The G/T parameter is a figure of merit commonly used for the earth station to indicate its ability to receive weak signals in noise, where G is the receiver antenna gain (Gr) and T is the system noise temperature (Ts). The output SNR for a communication is given in Eq. (8.11) and rewritten here as

Substituting EIRP, space loss, and the G=T parameter into the above equation, we have

It can be seen from the above equation that the output SNR ratio is proportional to EIRP and Gr=Ts but inversely proportional to the space loss, bandwidth, receiver noise factor, and system loss.