Friis Transmission
Understanding the Friis Equation
The Friis transmission equation is one of the most important equations in RF engineering. It provides the foundation for all link budget calculations, determining whether a wireless link can close (deliver sufficient power for reliable communication).
Friis Equation
P_r = P_t + G_t + G_r - FSPL (dB)
Where:
P_r = received power (dBm)
P_t = transmit power (dBm)
G_t = transmit antenna gain (dBi)
G_r = receive antenna gain (dBi)
FSPL = 20log(4 pi d/lambda) dB
Example: 1W TX, 10 dBi antennas, 10 km at 10 GHz:
P_t = 30 dBm
FSPL = 20log(4pi*10000/0.03) = 132.4 dB
P_r = 30 + 10 + 10 - 132.4 = -82.4 dBm
Link Budget Extension
Real links add losses: cable loss, atmospheric absorption, rain attenuation, pointing loss, and polarization mismatch. Gains include processing gain and coding gain. Link margin = P_r - sensitivity.
Frequently Asked Questions
What is the Friis equation?
The Friis equation calculates received power in a free-space link: P_r = P_t + G_t + G_r - FSPL. It is the fundamental equation for link budget analysis, determining whether a radio link delivers sufficient signal for reliable communications.
Does the Friis equation work for all environments?
No. Friis assumes free-space conditions. Real environments have multipath, atmospheric absorption, rain attenuation, and obstructions. Additional loss terms must be added to the basic Friis equation for practical link budgets.
What is FSPL?
Free Space Path Loss is the spreading loss as a wave propagates: FSPL = 20log(4 pi d/lambda) dB. At 10 GHz over 10 km: 132.4 dB. FSPL increases 6 dB per doubling of distance and 6 dB per doubling of frequency.