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Example Presets:
Received Power (\(P_r\)):
-25.0
dBmFriis Transmission Link Diagram
The Friis Transmission Formula
The Friis Transmission Equation is a fundamental principle in radio engineering that relates the power at a receiving antenna to the power delivered to a transmitting antenna. It assumes line-of-sight propagation in free space.
Linear Form
Logarithmic (dB) Form
This is the most common form used by engineers as it simplifies calculations by converting multiplication and division into simple addition and subtraction.
Variable Definitions
| Variable | Description | Common Units |
|---|---|---|
| \(P_r\) | Received Power | W, dBm, dBW |
| \(P_t\) | Transmit Power | W, dBm, dBW |
| \(G_t\) | Transmit Antenna Gain | dBi, dBd (unitless) |
| \(G_r\) | Receive Antenna Gain | dBi, dBd (unitless) |
| \(\lambda\) | Wavelength | m, cm |
| \(d\) | Distance between Antennas | m, km, miles |
Assumptions and Limitations
While the Friis equation is a powerful tool, it is an idealized model. For accurate real-world predictions, it is crucial to understand its core assumptions and limitations.
- Free Space: The formula assumes propagation in a vacuum, without any objects, reflections, or obstructions.
- Line-of-Sight (LOS): The antennas must be in a clear, unobstructed line of sight with no obstacles in the Fresnel zone.
- Far-Field: The formula is only valid when the antennas are far enough apart to be in each other's "far-field" region.
- No Losses: The basic formula does not account for real-world factors like cable losses, polarization mismatch, atmospheric absorption, or rain fade.
Practical Example: Wi-Fi Link
Let's calculate the expected received power for a typical home Wi-Fi link.
Scenario: A Wi-Fi router transmitting at 100 mW, with a 3 dBi antenna, to a laptop 20 meters away. The laptop has a 2 dBi antenna. The frequency is 2.4 GHz.
The calculator above can be used by setting \(P_t\) to 20 dBm (100 mW), \(G_t\) to 3 dBi, \(G_r\) to 2 dBi, distance to 20 meters, and frequency to 2.4 GHz.
Frequently Asked Questions
What is the Friis Transmission Equation?
It's a mathematical formula used in telecommunications to calculate the power received by an antenna from another antenna in a free-space, line-of-sight environment.
How do I calculate received power using the Friis formula?
You use the formula \(P_r = P_t + G_t + G_r - 20 \log_{10}(f) - 20 \log_{10}(d) - C\) (in dBm/dBi units) or the linear equation \(P_r = P_t \times G_t \times G_r \times \left(\frac{c}{4 \pi d f}\right)^2\). The calculator on this page automates this for you.
Can the calculator handle different frequency units?
Yes, the calculator automatically converts inputs for Hertz (Hz), kilohertz (kHz), megahertz (MHz), and gigahertz (GHz) to the standard unit of Hertz for calculation.
