Calculate noise figure, noise factor, and noise temperature for single stages and cascaded receiver chains using the Friis formula. Includes sensitivity analysis and stage contribution breakdown.
Noise figure (NF) quantifies how much noise a receiver component or system adds to the signal beyond the fundamental thermal noise floor. Expressed in decibels, a perfect noiseless amplifier would have NF = 0 dB, while real devices always add some noise. A low-noise amplifier (LNA) with NF = 0.5 dB is state-of-the-art for satellite communications, while a basic mixer might have NF = 6–10 dB. Understanding and minimizing system noise figure is critical for achieving good sensitivity in radio receivers, radar systems, and scientific instruments.
The noise factor F (linear, not in dB) relates to noise temperature via T_e = (F − 1)·T₀, where T₀ = 290 K is the standard reference temperature. This equivalent noise temperature represents the thermal noise power that would produce the same output noise as the device. Converting between noise figure (dB), noise factor (ratio), and noise temperature (Kelvin) is a routine but error-prone task in RF engineering.
For multi-stage receiver chains, the Friis cascade formula shows that the first stage dominates the overall noise performance: F_total = F₁ + (F₂ − 1)/G₁ + (F₃ − 1)/(G₁·G₂) + …. This is why placing a high-gain, low-noise LNA as the first stage is the golden rule of receiver design. This calculator handles both single-stage and cascade calculations, displaying each stage's noise contribution and computing system sensitivity.
RF and microwave engineers routinely convert between noise figure, noise factor, and noise temperature, and compute cascade noise performance for receiver chains. This calculator eliminates conversion errors, instantly shows each stage's contribution via the Friis formula, and computes system sensitivity — all essential for link budget analysis and receiver design.
Noise Factor: F = 1 + T_e/T₀. Noise Figure: NF = 10·log₁₀(F). Noise Temperature: T_e = (F − 1)·T₀. Friis Cascade: F_total = F₁ + (F₂−1)/G₁ + (F₃−1)/(G₁G₂) + …. Sensitivity (MDS): P_min = kT₀B·F (or in dBm: −174 + NF + 10·log₁₀(BW_Hz)).
Result: NF = 1.500 dB, F = 1.4125, T_e = 119.6 K
F = 10^(1.5/10) = 1.4125. T_e = (1.4125 − 1) × 290 = 119.6 K. This means the LNA adds noise equivalent to a 119.6 K thermal source.
Harald Friis published his cascade noise formula in 1944 while working at Bell Labs. The key insight is that each stage's noise contribution is divided by the total gain preceding it. Consider a 3-stage chain: LNA (NF 1 dB, Gain 20 dB) → Mixer (NF 8 dB, Gain 5 dB) → IF Amp (NF 4 dB, Gain 30 dB). The system NF is dominated by the LNA: F_sys = 1.259 + (6.31 − 1)/100 + (2.51 − 1)/31623 ≈ 1.312 → NF = 1.18 dB.
| Method | Equipment | Accuracy | |---|---|---| | Y-Factor | Hot/cold noise source + power meter | ±0.1–0.3 dB | | Gain Method | Signal generator + power meters | ±0.5 dB | | Cold Attenuator | Precision attenuator + noise source | ±0.05 dB | | Noise Figure Analyzer | Dedicated NFA instrument | ±0.05 dB |
For very low-noise systems, noise temperature is preferred because small dB differences correspond to large temperature differences. For example: NF = 0.5 dB → T_e = 35.4 K; NF = 0.3 dB → T_e = 20.8 K; NF = 0.1 dB → T_e = 6.7 K. Radio telescopes routinely specify receivers in Kelvin rather than dB.
Noise factor (F) is the linear power ratio of input SNR to output SNR. Noise figure (NF) is simply the noise factor expressed in decibels: NF = 10·log₁₀(F). An ideal noiseless device has F = 1 (NF = 0 dB).
The Friis formula divides each subsequent stage's noise contribution by the cumulative gain of all preceding stages. If the first stage has high gain, it makes later stages' noise contributions negligible. That's why LNAs (low-noise amplifiers) are placed at the antenna.
State-of-the-art cryogenic LNAs achieve NF < 0.2 dB. Room-temperature GaAs or InGaP LNAs typically range from 0.3–1.5 dB. For most amateur and commercial receivers, NF < 2 dB is considered excellent.
This is the thermal noise power spectral density at 290 K (room temperature): P = kT₀ = 1.38×10⁻²³ × 290 = 4×10⁻²¹ W/Hz = −174 dBm/Hz. It is the fundamental noise floor for any receiver at room temperature.
Sensitivity degrades by 3 dB for every doubling of bandwidth: MDS (dBm) = −174 + NF + 10·log₁₀(BW). Narrowing the bandwidth improves sensitivity linearly — this is why narrow-band filters are used before the detector.
Yes. A passive lossy component (cable, filter, attenuator) has NF equal to its insertion loss in dB. A 3 dB cable loss means NF = 3 dB. This is why cable runs between the antenna and LNA must be minimized.