Friis transmission formula

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

Introduction to Friis Transmission Formula

The Friis Transmission Formula is a fundamental equation in the field of radio frequency (RF) and wireless communication. Named after Danish engineer Harald T. Friis, it provides a useful way to estimate the received power at the receiving antenna when the transmitting antenna’s power, distance between the antennas, and antenna gains are known. In this article, we will discuss the importance of the Friis Transmission Formula, its components, and applications.

Understanding the Friis Transmission Formula

The formula is typically expressed as:

1. Pr = Pt * Gt * Gr * (λ / (4 * π * R))^2

Where:

• ^Pr is the received power at the receiving antenna
• ^Pt is the transmitted power from the transmitting antenna
• ^Gt is the gain of the transmitting antenna
• ^Gr is the gain of the receiving antenna
• ^λ is the wavelength of the signal
• ^R is the distance between the transmitting and receiving antennas

This equation holds true for antennas operating in the far-field region, where the electromagnetic field is well-established, and the antennas are separated by a considerable distance. It is essential to note that the Friis Transmission Formula assumes a lossless environment and free-space propagation, implying no obstructions or reflections between the antennas.

Antenna Gains and Wavelength

The gains of the transmitting and receiving antennas, Gt and Gr, respectively, are dimensionless parameters that represent the antennas’ ability to focus the radiated power in a specific direction. These gains are often expressed in dBi, a unit that measures an antenna’s gain relative to an isotropic radiator.

The wavelength (λ) of the signal is inversely proportional to the frequency (f) and can be calculated using the speed of light (c) as follows:

1. λ = c / f

This relationship highlights the impact of frequency on the overall received power, where higher frequencies have smaller wavelengths and vice versa.

Applications of the Friis Transmission Formula

Some practical applications of the Friis Transmission Formula include:

• Estimating the required transmitter power to achieve a specific received power level
• Calculating the maximum achievable communication distance between two antennas
• Evaluating the performance of different antenna designs
• Assisting in the design of wireless communication systems, such as cellular networks and satellite communications

In conclusion, the Friis Transmission Formula is a valuable tool for engineers and professionals working in wireless communication and radio frequency engineering. It serves as a foundation for understanding the relationship between transmitted power, antenna gains, distance, and signal wavelength in free-space propagation.

Example of Friis Transmission Formula Calculation

Let’s consider a scenario where we have a transmitting antenna and a receiving antenna separated by a distance of 5 kilometers. We know the following parameters:

• Transmitting power, Pt = 10 W (10 watts)
• Transmitting antenna gain, Gt = 12 dBi
• Receiving antenna gain, Gr = 10 dBi
• Signal frequency, f = 2.4 GHz (2.4 x 10⁹ Hz)

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

1. λ = c / f = (3 x 10⁸ m/s) / (2.4 x 10⁹ Hz) ≈ 0.125 m

Next, we need to convert the antenna gains from dBi to a linear scale:

• Gt_linear = 10^{(Gt / 10)} = 10^{(12 / 10)} ≈ 15.85
• Gr_linear = 10^{(Gr / 10)} = 10^{(10 / 10)} ≈ 10

Now we can plug all the values into the Friis Transmission Formula:

1. Pr = Pt * Gt_linear * Gr_linear * (λ / (4 * π * R))^2
2. Pr = 10 * 15.85 * 10 * ((0.125) / (4 * π * 5000))^2
3. Pr ≈ 1.58 x 10^-7 W

Thus, the received power at the receiving antenna is approximately 1.58 x 10^-7 watts or -78.02 dBm (decibel-milliwatts).

This example demonstrates how to use the Friis Transmission Formula to calculate the received power in a wireless communication scenario, taking into account the transmitting power, antenna gains, distance between the antennas, and signal frequency.