Friis Equation Calculator Python

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 calculates the power received under free-space conditions, accounting for the inverse square law of electromagnetic wave propagation.

3. Importance of Received Power Calculation

Details: Accurate received power calculation is crucial for wireless communication system design, link budget analysis, and determining signal strength at the receiver.

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 ideal conditions for the Friis equation?
A: The equation assumes free-space propagation, no obstructions, impedance matching, and polarization alignment between antennas.

Q2: How is wavelength related to frequency?
A: Wavelength (λ) = speed of light (c) / frequency (f), where c ≈ 3×10⁸ m/s.

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

Q4: What are the limitations of the Friis equation?
A: It doesn't account for atmospheric absorption, multipath propagation, obstacles, or other real-world effects that cause signal loss.

Q5: How accurate is this calculation for real systems?
A: It provides a theoretical maximum. Real-world systems typically experience additional losses of 3-20 dB or more due to various factors.