Friis Equation
Understanding the Friis Noise Equation
The Friis noise equation is one of the most important equations in RF receiver design. It quantifies how each stage in a receiver chain contributes to the overall noise figure, guiding the placement and specification of every component.
Friis Equation Application
All values in LINEAR (not dB)!
Example receiver chain:
LNA: NF = 1 dB (1.26), Gain = 20 dB (100)
Filter: IL = 3 dB (NF = 2.0), Gain = -3 dB (0.5)
Mixer: NF = 8 dB (6.31), Gain = -7 dB (0.2)
NF_total = 1.26 + (2.0-1)/100 + (6.31-1)/(100*0.5)
= 1.26 + 0.01 + 0.106 = 1.376 = 1.39 dB
The LNA dominates! Without LNA gain, mixer NF would dominate.
Frequently Asked Questions
What is the Friis noise equation?
NF_total = NF1 + (NF2-1)/G1 + (NF3-1)/(G1*G2). Shows that the first stage noise figure dominates if its gain is high enough. This is why LNAs (low NF, high gain) are placed first in receiver chains.
How much LNA gain is enough?
Rule of thumb: LNA gain should be 15-20 dB to bury the noise contribution of following stages. With 20 dB gain, the second stage NF contributes only 1% of its value to the system NF.
What happens if a lossy element is first?
A cable or switch before the LNA adds its loss directly to the system NF. A 2 dB cable loss before a 1 dB NF LNA: NF_total = 2 + (1.26-1)/0.63 + ... = 2.41 = 3.8 dB. The cable loss ruins the system sensitivity. Always put the LNA first!