Friis Transmission Equation
The Friis equation is the fundamental relation giving the received power between two antennas in free space: received power depends on the transmitted power, the gain of both antennas and the factor (λ/4πd)². The free space path loss formula derives directly from it. The equation shows that received power falls inversely with the square of distance and the square of frequency.
Once put in dB form, the products become sums and the familiar line of the link budget appears: received power = transmitter power + transmit antenna gain + receive antenna gain − path loss.
- Distance term: because it is d², doubling the distance drops the received power to a quarter, that is 6 dB down.
- Wavelength term: because it is λ², lower frequency is advantageous; with antennas of the same gain, 433 MHz is about 15 dB ahead of 2.45 GHz.
- Critical detail: the advantage holds under the assumption of fixed antenna gain. At high frequency it is possible to build a higher gain antenna in the same physical size.
Friis is valid only for free space and assumes there is no reflection, diffraction or obstacle. Values measured on a real crane site come out below this calculation; the function of the equation is not to know the absolute range, but to see in advance how many dB a change will gain you.
Context where this term is used: Wireless remote control installation: pairing, relay, safety