Received Power

\[P_r=P_tG_tG_r\left(\frac{\lambda}{4\pi d}\right)^2\]

Variables

Prreceived power (W)

Pttransmitted power (W)

Gttransmitting antenna gain

Grreceiving antenna gain

lambda[λ]signal wavelength (m)

ddistance between antennas (m)

Description

What is this formula?

The Received Power equation, commonly known as the Friis Transmission Equation, estimates the power received by an antenna under ideal free-space propagation conditions. It relates transmitted power, antenna gains, wavelength, and separation distance.

When to use it

Use this formula when designing wireless communication links, satellite systems, microwave links, telemetry systems, radar systems, or performing link budget calculations.

Example

A transmitter radiates 10 W using an antenna gain of 10. A receiving antenna also has a gain of 10. The antennas are separated by 1000 m and operate at a wavelength of 0.125 m.

Formula:

Pr = Pt*Gt*Gr*(λ/(4πd))²

Substitution:

Pr = 10*10*10*(0.125/(4π*1000))²

Result:

Pr = 9.89×10^-6 W

Pr = 9.89 μW

Applications

Wireless communications, satellite links, microwave systems, radio network planning, radar engineering, telemetry systems, and RF link budget analysis.

Note

The Friis equation assumes ideal free-space propagation, perfect antenna alignment, matching polarization, and no atmospheric, terrain, cable, connector, or multipath losses. Real communication systems typically experience additional attenuation that must be included separately in a complete link budget.