# Friis transmission formula

Explore the Friis Transmission Formula, its components, assumptions, applications, and an example calculation in wireless communication systems.

## Friis Transmission Formula: A Comprehensive Overview

The Friis Transmission Formula is a fundamental equation in the field of wireless communication, specifically in the analysis of radio frequency (RF) signal propagation. This formula provides a method for determining the power received at the receiving antenna from a transmitting antenna, considering factors such as distance, frequency, and antenna gains. In this article, we delve into the components and significance of this equation.

## Understanding the Components of the Formula

The Friis Transmission Formula is expressed as:

Pr = Pt * Gt * Gr * (λ / (4 * π * d))^2

where:

• Pr represents the received power at the receiving antenna;
• Pt is the power transmitted by the transmitting antenna;
• Gt and Gr are the gains of the transmitting and receiving antennas, respectively;
• λ denotes the wavelength of the signal;
• d is the distance between the two antennas;
• π is the mathematical constant Pi (approximately 3.14159).

Note that the gains and wavelength must be expressed in the same units for the equation to be valid.

## Assumptions and Applications of the Formula

The Friis Transmission Formula is based on several key assumptions:

1. The antennas are in the far-field region, meaning they are at a sufficient distance from each other to ensure that the electromagnetic fields they produce have a consistent, predictable pattern;
2. The antennas are both isotropic, meaning they radiate power equally in all directions;
3. The environment between the antennas is free space, devoid of obstructions that might cause signal attenuation or reflection.

These assumptions allow for the simplification of the equation and make it suitable for analyzing the behavior of RF signals in a variety of wireless communication systems, such as satellite communication, microwave links, and cellular networks.

While the Friis Transmission Formula offers valuable insights into the behavior of RF signals in free space, it may not accurately predict signal propagation in real-world scenarios where factors like multipath fading, atmospheric absorption, and other environmental influences come into play. As a result, various adaptations of the formula have been developed to account for these factors, including the Two-Ray Ground Reflection Model, the Hata Model, and the Okumura Model.

In summary, the Friis Transmission Formula serves as a fundamental tool in understanding and analyzing RF signal propagation in wireless communication systems. While it may not provide a perfect representation of real-world scenarios, it remains an essential starting point for further research and development in the field.

## Example of a Friis Transmission Formula Calculation

Let’s consider a hypothetical situation to demonstrate the application of the Friis Transmission Formula. In this example, we will compute the received power at a receiving antenna given the following parameters:

• Transmitted power (Pt) = 10 W;
• Transmitting antenna gain (Gt) = 15 dBi;
• Receiving antenna gain (Gr) = 12 dBi;
• Signal frequency (f) = 2.4 GHz;
• Distance between antennas (d) = 5 km.

First, we need to convert the antenna gains from dBi to absolute values. This can be done using the following formula:

G (linear) = 10^(G (dBi) / 10)

Applying this formula, we can convert the antenna gains:

Gt (linear) = 10^(15 / 10) = 31.62

Gr (linear) = 10^(12 / 10) = 15.85

Next, we calculate the signal wavelength (λ) using the speed of light (c) and the frequency (f):

λ = c / f

Given that c ≈ 3 x 10^8 m/s and f = 2.4 x 10^9 Hz, we obtain:

λ ≈ (3 x 10^8) / (2.4 x 10^9) = 0.125 m

Now, we can apply the Friis Transmission Formula:

Pr = Pt * Gt * Gr * (λ / (4 * π * d))^2

Substituting the given values, we get:

Pr = 10 * 31.62 * 15.85 * (0.125 / (4 * π * 5000))^2

Upon calculating, we find that the received power (Pr) at the receiving antenna is approximately 1.32 x 10-6 W or 1.32 μW.

In this example, we have demonstrated how to use the Friis Transmission Formula to calculate the received power at a receiving antenna, given the transmitted power, antenna gains, signal frequency, and distance between the antennas.

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