Definition
Noise Figure (NF) quantifies how much an RF device degrades the signal-to-noise ratio (SNR) as a signal passes through it. It is measured in dB and defined as:
NF = SNR_in (dB) − SNR_out (dB) [always ≥ 0 dB] NF = 10 · log₁₀(F) Noise Factor F = SNR_in / SNR_out [linear, ≥ 1]
A perfect, noiseless device has NF = 0 dB (F = 1). Every real device adds some thermal noise and produces NF > 0. For passive devices (filters, cables, pads) with insertion loss L (dB), NF = L in dB (a 2 dB loss cable adds 2 dB of noise figure).
Friis Cascaded Noise Formula
For a cascade of N stages (linear): F_total = F₁ + (F₂−1)/G₁ + (F₃−1)/(G₁·G₂) + (F₄−1)/(G₁·G₂·G₃) + ... In dB (approximate for high-gain stages): NF_system ≈ NF₁ + (NF₂ − G₁) + ... [each term in dB] Key insight: The FIRST stage dominates. High G₁ suppresses all later stages.
Practical Cascade Example
| Stage | Component | NF (dB) | Gain (dB) | Contribution to NF_sys |
|---|---|---|---|---|
| 1 | Bandpass filter | 2.0 | −2.0 | 2.00 dB |
| 2 | LNA | 1.5 | +18 | 1.40 dB (at input = 1.5+2 dB) |
| 3 | Cable/loss | 3.0 | −3.0 | 0.02 dB |
| 4 | Mixer | 8.0 | −5.0 | 0.05 dB |
| System NF | ≈ 3.5 dB total | |||
Note: The front-end filter adds 2 dB before the LNA — this directly adds 2 dB to system NF. Placing the LNA before the filter would reduce system NF to ≈1.6 dB (but risks blocking).
Typical Noise Figures
| Device | Typical NF |
|---|---|
| LNA (SiGe, 1–4 GHz) | 0.5–2 dB |
| LNA (GaAs, 1–18 GHz) | 0.3–1.5 dB |
| LNA (CMOS, 1–6 GHz) | 1–3 dB |
| Passive mixer | 6–8 dB (= conversion loss) |
| Active mixer | 8–14 dB |
| Passive filter (1 dB IL) | 1 dB (NF = IL for passive) |
| Coaxial cable (2 dB loss) | 2 dB |
| Attenuator pad (10 dB) | 10 dB |
Receiver Sensitivity
Sensitivity = −174 dBm/Hz + NF_sys + 10·log₁₀(BW) + SNR_min Example: LTE 10 MHz channel, NF_sys = 5 dB, SNR_min = −1 dB: Sen = −174 + 5 + 70 + (−1) = −100 dBm
RF View: RF View's circuit simulator lets you cascade S2P blocks (measured devices) with ideal elements and compute the combined frequency response. While NF computation requires noise data (not just S-parameters), RF View's gain analysis (S21) helps identify where gain compression or loss hurts receiver performance.