Friis Equation Calculator With Solution

Friis Equation:

\[ P_r = P_t \times G_t \times G_r \times \left( \frac{\lambda}{4 \pi d} \right)^2 \]

Transmitted Power (P_t):

Transmit Gain (G_t):

dimensionless

Receive Gain (G_r):

dimensionless

Wavelength (λ):

Distance (d):

Received Power (P_r):

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1. What is the Friis Equation?

The Friis transmission equation is used in telecommunications engineering to calculate the power received by one antenna from another antenna in free space. It provides a fundamental relationship between transmitted power, antenna gains, wavelength, and distance.

2. How Does the Calculator Work?

The calculator uses the Friis equation:

\[ P_r = P_t \times G_t \times G_r \times \left( \frac{\lambda}{4 \pi d} \right)^2 \]

Where:

\( P_r \) — Received power (W)
\( P_t \) — Transmitted power (W)
\( G_t \) — Transmit antenna gain (dimensionless)
\( G_r \) — Receive antenna gain (dimensionless)
\( \lambda \) — Wavelength (m)
\( d \) — Distance between antennas (m)

Explanation: The equation calculates the power received by an antenna based on transmitted power, antenna gains, wavelength, and distance between antennas.

3. Importance of Friis Equation

Details: The Friis equation is fundamental in wireless communication system design, link budget analysis, and predicting signal strength in free space propagation scenarios.

4. Using the Calculator

Tips: Enter transmitted power in watts, antenna gains as dimensionless values, wavelength in meters, and distance in meters. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What are typical values for antenna gains?
A: Antenna gains typically range from 0 dBi (isotropic antenna) to 20+ dBi for directional antennas. Higher gains indicate more focused radiation patterns.

Q2: How does wavelength relate to frequency?
A: Wavelength (λ) = speed of light (c) / frequency (f), where c ≈ 3×10⁸ m/s. For example, at 2.4 GHz, λ ≈ 0.125 m.

Q3: What are the limitations of the Friis equation?
A: The equation assumes free space propagation, perfect antenna alignment, polarization matching, and no obstructions or reflections.

Q4: How does distance affect received power?
A: Received power decreases with the square of distance (inverse square law), meaning doubling distance reduces power by a factor of 4.

Q5: Can this be used for real-world applications?
A: While the basic equation describes ideal conditions, real-world applications require additional factors like path loss, fading, and environmental effects.