Friis Equation Calculator

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 under ideal conditions. 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 shows how received power decreases with the square of distance and depends on antenna gains and wavelength.

3. Importance of Friis Equation

Details: The Friis equation is fundamental in wireless communication system design, helping engineers predict signal strength, design appropriate antenna systems, and calculate link budgets for reliable communication.

4. Using the Calculator

Tips: Enter all values in the specified units. Ensure transmitted power, gains, wavelength, and distance are positive values. The calculator provides the received power in watts.

5. Frequently Asked Questions (FAQ)

Q1: What are the assumptions of the Friis equation?
A: The equation assumes free space propagation, no obstructions, perfect antenna alignment, impedance matching, and no atmospheric absorption.

Q2: How does wavelength affect received power?
A: Received power is proportional to the square of wavelength, meaning longer wavelengths generally result in higher received power for the same distance and antenna gains.

Q3: What are typical values for antenna gains?
A: Isotropic antennas have gain of 1 (0 dBi), while directional antennas can have gains from 2-1000 (3-30 dBi) or more depending on design and frequency.

Q4: When is the Friis equation not applicable?
A: The equation doesn't account for multipath propagation, atmospheric absorption, rain fade, obstacles, or other real-world effects that can significantly affect signal strength.

Q5: How is wavelength related 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.