What is the difference between noise factor and noise figure?

Noise factor F is a linear ratio (unitless, always greater than or equal to 1). Noise figure NF is the same quantity expressed in decibels: NF = 10 log10(F). A noise factor of 2 equals a noise figure of 3 dB, meaning the component doubles the noise power while amplifying the signal. A perfect noiseless component has F = 1 (NF = 0 dB). Equivalent noise temperature provides a third representation: T_e = T_0 times (F minus 1), where T_0 = 290 K (standard reference temperature). A 1 dB noise figure corresponds to T_e = 75 K. For low-noise systems (radio astronomy, deep-space), noise temperature is preferred because it avoids the compression of small differences near 0 dB.

How does the Friis cascade equation work?

The Friis cascade equation calculates the total noise factor of a chain of components: F_total = F1 plus (F2 minus 1)/G1 plus (F3 minus 1)/(G1 times G2) plus further terms. Each subsequent stage's noise contribution is reduced by the cumulative gain of all preceding stages. This is why the first stage (LNA) dominates: if G1 = 20 dB (100x) and F1 = 1 dB (1.26), even a second stage with F2 = 10 dB (10) contributes only (10 minus 1)/100 = 0.09 to the total noise factor, which is negligible compared to F1. A cable or filter before the LNA adds its full loss as noise figure, severely degrading sensitivity. This is why the LNA should be placed as close to the antenna as possible with minimum cable loss between them.

How does noise figure affect receiver sensitivity?

Receiver sensitivity is the minimum detectable signal level: S_min = kTB times F times SNR_min, or in dB: S_min(dBm) = minus 174 plus NF plus 10 log(BW) plus SNR_min. The minus 174 dBm/Hz is the thermal noise floor at 290 K. Every 1 dB of noise figure directly reduces sensitivity by 1 dB. For an LTE receiver with 10 MHz bandwidth, 7 dB NF, and 3 dB required SNR for QPSK: S_min = minus 174 plus 7 plus 70 plus 3 = minus 94 dBm. Improving NF from 7 to 5 dB improves sensitivity to minus 96 dBm, which translates to approximately 25 percent greater range in free-space conditions.

System Parameter

Noise Factor

/noyz fak-ter/ — F

F = SNR_in/SNR_out (linear, ≥1). NF = 10log(F) dB. T_e = 290×(F−1) K. Friis cascade: F_total = F₁+(F₂−1)/G₁+(F₃−1)/(G₁G₂). First stage dominates: 20 dB LNA gain makes 2nd-stage NF negligible. Sensitivity: S_min = −174 + NF + 10log(BW) + SNR_min dBm. Every 1 dB NF = 1 dB sensitivity loss.

LNA: 0.3-2 dB

Mixer: 5-8 dB

Loss L: NF = L

Understanding Noise Factor

Noise factor is the fundamental metric for receiver sensitivity. Every component in the receive chain adds noise, degrading the signal-to-noise ratio. The noise factor quantifies this degradation: a noise factor of 2 (3 dB noise figure) means the component doubles the noise power while passing the signal. Understanding noise factor and the Friis cascade equation is essential for designing receivers that can detect the weakest possible signals.

The relationship between noise factor and receiver sensitivity is direct: every 1 dB improvement in system noise figure extends the receiver's ability to detect weaker signals by 1 dB. In cellular systems, this translates to approximately 12% greater range per dB of NF improvement. This is why LNA selection is one of the most critical decisions in receiver design, and why cable losses before the LNA must be minimized.

Noise Factor Equations

Definitions:
F = SNR_in/SNR_out (linear, ≥1)
NF = 10 log₁₀(F) (dB, ≥0)
T_e = T₀(F−1) = 290(F−1) K

Friis cascade:
F_tot = F₁+(F₂−1)/G₁+(F₃−1)/(G₁G₂)
LNA: F=1.26 (1dB), G=100 (20dB)
Mixer: F=10 (10dB)
F_tot = 1.26+(10−1)/100 = 1.35 (1.3dB)

Sensitivity:
S_min = −174 + NF + 10log(BW) + SNR_req
NF=5, BW=10MHz, SNR=3dB:
S = −174+5+70+3 = −96 dBm

Component Noise Figure Comparison

Component	NF (dB)	T_e (K)	Technology	Frequency
LNA (GaAs)	0.3-0.8	21-62	pHEMT	1-40 GHz
LNA (SiGe)	0.8-2.0	62-170	HBT	1-20 GHz
Active mixer	5-8	627-1540	Gilbert cell	1-10 GHz
Passive mixer	6-8	865-1540	Diode ring	1-40 GHz
Cable (1 dB loss)	1.0	75	Passive	All

Common Questions

Frequently Asked Questions

Factor vs. figure?

F = linear ratio (≥1). NF = 10log(F) dB (≥0). F=2 = NF=3 dB (doubles noise). T_e = 290×(F−1) K. 1 dB NF = 75 K. For low-noise (astronomy, deep space): noise temperature preferred (avoids compression near 0 dB). F=1 = perfect noiseless component.

Friis cascade?

F_tot = F1+(F2−1)/G1+(F3−1)/(G1G2). Each stage divided by preceding cumulative gain. First stage dominates: 20 dB LNA gain makes 10 dB mixer NF contribute only 0.09 to total F. Cable/filter before LNA adds full loss as NF. LNA must be as close to antenna as possible.

Impact on sensitivity?

S_min = −174+NF+10log(BW)+SNR_req. Every 1 dB NF = 1 dB sensitivity loss. LTE 10 MHz, NF=7, SNR=3: S=−94 dBm. NF=5: S=−96 dBm (+2 dB = ~25% more range). In cellular: ~12% range per dB NF improvement. Critical for IoT, satellite, GPS receivers.

Related Terms

← Noise Figure NPR →

Receiver Design

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