Why does the first stage dominate the system noise figure?

The Friis cascade equation divides each subsequent stage's noise contribution by the cumulative gain of all preceding stages. If the first stage has 20 dB gain, the second stage's noise contribution is divided by 100 (linear). A second-stage mixer with 10 dB NF contributes only 10/100 = 0.1 to the system noise factor, which is negligible compared to the first stage's contribution. This is why receiver front-ends always start with a low-noise amplifier: a 0.5 dB NF LNA with 20 dB gain makes the entire receiver's noise figure approximately 0.6 to 0.8 dB regardless of what follows.

What is the relationship between noise figure and noise temperature?

Noise temperature Te is the physical temperature a matched resistor would need to produce the same noise power as the device under test. The conversion is Te = T0 times (F minus 1), where T0 = 290 K (standard reference temperature) and F is the noise factor (linear, not dB). A 1 dB noise figure corresponds to Te = 290 times (1.259 minus 1) = 75 K. A 3 dB NF corresponds to 290 K. Noise temperature is preferred for very low-noise systems (cryogenic LNAs, radio astronomy) because it provides better resolution: the difference between 10 K and 20 K is significant, but both correspond to approximately 0.15 dB NF.

How is noise figure measured with the Y-factor method?

Connect a calibrated noise source (with known excess noise ratio, ENR) to the device input. Measure the output power with the noise source on (hot, Th) and off (cold, Tc = 290 K). The Y-factor is Y = P_hot / P_cold. The noise factor is F = (ENR) / (Y minus 1), where ENR = (Th minus Tc) / Tc. A typical measurement uses a noise source with 15 dB ENR (Th = 9,461 K). If Y = 12 dB (15.85 linear), then F = 31.62 / 14.85 = 2.13 = 3.3 dB NF. The accuracy depends on ENR calibration, connector repeatability, and the impedance match between the noise source and the DUT.

Signal Processing

Noise Figure

NF (dB) | Noise Factor F (linear)

Every component in an RF signal chain adds noise. An amplifier adds noise from its transistor's channel resistance. A mixer adds noise from its switching transients and conversion loss. Even a passive cable adds noise equal to its attenuation (a 3 dB loss cable has a 3 dB noise figure). Noise figure quantifies this degradation: it is the ratio of the input SNR to the output SNR, expressed in dB. A 2 dB noise figure means the component degrades the SNR by 2 dB. The genius of the Friis cascade equation is showing that only the first stage's noise figure matters significantly, provided it has enough gain to suppress everything behind it.

Category: Signal Processing

Definition: NF = 10·log(SNR_in/SNR_out)

Ideal: 0 dB (no noise added)

Why the First Stage Wins the Noise Budget

Friis cascade equation (noise factor, linear):
F_sys = F₁ + (F₂ − 1)/G₁ + (F₃ − 1)/(G₁·G₂) + ...

Noise temperature conversion:
T_e = T₀ × (F − 1) where T₀ = 290 K

Receiver sensitivity:
MDS = −174 dBm/Hz + 10·log(BW) + NF_sys + SNR_min

Worked example (cellular base station at 1.9 GHz, 10 MHz BW):
LNA: NF = 0.8 dB, Gain = 22 dB | Filter: IL = 1.5 dB | Mixer: NF = 8 dB, Gain = −6 dB
F₁ = 1.202 | F₂ = 1.413 | F₃ = 6.310 | G₁ = 158.5 | G₂ = 0.708
F_sys = 1.202 + 0.413/158.5 + 5.310/112.2 = 1.202 + 0.003 + 0.047 = 1.252
NF_sys = 10·log(1.252) = 0.98 dB
MDS = −174 + 70 + 0.98 + 10 = −93 dBm

Noise Figure by Component Type

Component	Typical NF	Noise Temp	Notes
Cryogenic LNA (20 K)	0.07 dB	5 K	Radio astronomy, deep space
GaAs pHEMT LNA	0.3 to 0.8 dB	20 to 60 K	Cellular, satellite, radar
SiGe BiCMOS LNA	0.8 to 1.5 dB	60 to 120 K	WLAN, consumer
Passive mixer	6 to 8 dB (= conv. loss)	870 to 1,540 K	NF equals conversion loss
Active mixer (Gilbert)	8 to 15 dB	1,540 to 8,880 K	Higher NF but has gain
Coax cable (3 dB loss)	3 dB	290 K	NF = attenuation for passives

Common Questions

Frequently Asked Questions

Why does the first stage dominate?

Friis divides each stage's noise by the cumulative gain before it. With 20 dB LNA gain, a 10 dB NF mixer contributes only 0.1 to the noise factor (negligible). A 0.5 dB NF LNA with 20 dB gain makes the system NF approximately 0.6 to 0.8 dB regardless of what follows.

NF vs. noise temperature?

T_e = 290 × (F − 1). Noise temperature is preferred for very low-noise systems: 10 K vs. 20 K is significant, but both are approximately 0.15 dB NF. At 3 dB NF, T_e = 290 K (equal to room temperature).

How is NF measured (Y-factor)?

Connect a calibrated noise source (known ENR) to the DUT. Measure output power with source on (hot) and off (cold). Y = P_hot/P_cold. F = ENR/(Y − 1). Accuracy depends on ENR calibration, connector match, and cable loss between source and DUT.

Related Terms

← Noise Factor Noise Floor →

System Design

Cascaded Noise Figure Calculator

Enter up to 10 stages with their gain and noise figure to compute the system NF, noise temperature, and receiver sensitivity for any bandwidth.

Calculate NF