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propagationintermediateFriis, H.T., "A Note on a Simple Transmission Formula", 1946

Friis Transmission Equation

#friis#link budget#received power#antenna gain#path loss

Friis Transmission Equation

The Friis transmission equation is the cornerstone of RF link budget analysis. It relates the power received by one antenna to the power transmitted by another, accounting for antenna gains and path loss.

Pr=Pt+Gt+Gr−FSPLP_r = P_t + G_t + G_r - FSPL

Alternative Forms

Linear Form
Pr=PtGtGr(λ4πd)2P_r = P_t G_t G_r \left(\frac{\lambda}{4\pi d}\right)^2
Power in watts, gains as ratios
Full dB Form
Pr=Pt+Gt+Gr−32.45−20log⁡10(fMHz)−20log⁡10(dkm)P_r = P_t + G_t + G_r - 32.45 - 20\log_{10}(f_{MHz}) - 20\log_{10}(d_{km})
All terms in dB/dBm/dBi

Input Variables

dBm

Power delivered to the transmitting antenna(Range: -30 – 60 dBm)

dBi

Gain of the transmitting antenna(Range: -10 – 50 dBi)

dBi

Gain of the receiving antenna(Range: -10 – 50 dBi)

MHz

Operating frequency(Range: 1 – 300000 MHz)

km

Distance between antennas(Range: 0.001 – 100000 km)

Results

Received Power (P_r)
—
Free Space Path Loss (FSPL)
—

📖 Example: Point-to-Point Wireless Link

Calculate received power for a 1 km wireless link at 5.8 GHz

Reference: Friis, H.T., "A Note on a Simple Transmission Formula", 1946

Related Formulas

propagation

Free Space Path Loss (FSPL)

Signal attenuation in free space due to geometric spreading

propagation

Wavelength-Frequency Relationship

Convert between wavelength and frequency using speed of light

system design

Link Budget Equation

Complete power budget for a wireless communication link