Noise Figure
Understanding Noise Figure
Noise figure is one of the most critical parameters in receiver design. It directly determines the system sensitivity, which is the weakest signal a receiver can detect. Every component in the signal chain contributes noise, but the first component has the greatest impact on overall system noise performance.
Noise Factor vs. Noise Figure
Noise factor (F) is the linear ratio of input SNR to output SNR. Noise figure (NF) is simply the noise factor expressed in dB: NF = 10 log10(F). A noise factor of 1 (NF = 0 dB) means the device adds no noise. A noise factor of 2 (NF = 3 dB) means the device doubles the noise power.
Friis Cascade Formula
For a cascade of stages, the overall noise factor is dominated by the first stage, provided it has sufficient gain. The Friis formula shows that the noise contribution of each subsequent stage is reduced by the gain of all preceding stages. This is why a high-gain, low-noise amplifier (LNA) is always placed first in the receiver chain.
Noise Figure Measurement
- Y-factor method: Uses a calibrated noise source with known ENR (excess noise ratio) switched between hot and cold states. The most common measurement technique.
- Cold-source method: Uses a VNA with noise receiver capability. More accurate for on-wafer and high-frequency measurements.
- Signal generator method: Compares output noise with and without a known input signal. Less accurate but requires minimal equipment.
Practical Considerations
- Cable loss before the LNA: Every dB of loss before the LNA adds directly to system noise figure. A 2 dB cable loss before a 1.5 dB NF LNA results in 3.5 dB system NF.
- Temperature dependence: Noise figure is referenced to a standard temperature of 290K (17C). Cryogenic cooling reduces thermal noise dramatically.
- Frequency dependence: NF typically increases with frequency due to reduced transistor gain and increased parasitic effects.
NF (dB) = 10 × log10(F)
where F = SNR_in / SNR_out
Friis Cascade Formula:
F_total = F1 + (F2-1)/G1 + (F3-1)/(G1×G2) + ...
Noise temperature:
T_e = T0 × (F - 1)
where T0 = 290K
Example: LNA with NF=1.2 dB, Gain=25 dB, followed by mixer NF=8 dB:
F_total = 1.318 + (6.31-1)/316.2 = 1.335
NF_total = 1.26 dB (LNA dominates!)
Typical Noise Figures by Device
| Device | Noise Figure | Technology |
|---|---|---|
| Cryogenic LNA (4K) | 0.02 - 0.1 dB | InP HEMT, cryocooled |
| Room-temp LNA (L-band) | 0.3 - 0.8 dB | GaAs pHEMT |
| Room-temp LNA (Ka-band) | 1.5 - 3.0 dB | GaAs/InP MMIC |
| Passive mixer | 6 - 10 dB | Schottky diode |
| Active mixer | 10 - 15 dB | Gilbert cell |
| Coaxial cable (loss = L dB) | L dB | Any (NF = loss) |
Frequently Asked Questions
What is a good noise figure for an RF system?
It depends on the application. For satellite earth stations, system NF below 1.5 dB is typical. For cellular base stations, 2-3 dB is common. For radar receivers, 3-5 dB is acceptable. The lower the noise figure, the weaker the signals the system can detect.
Why does the first amplifier noise figure matter most?
The Friis cascade formula shows that each stage noise contribution is divided by the cumulative gain of all preceding stages. So the first stage noise adds directly to system noise, while the second stage noise is divided by the first stage gain. A high-gain, low-NF first stage suppresses the noise contribution of everything that follows.
What is the relationship between noise figure and noise temperature?
Noise temperature Te = 290 x (F-1) Kelvin, where F is the noise factor (linear). A noise figure of 1 dB corresponds to a noise temperature of about 75K. Noise temperature is preferred in radio astronomy and satellite applications because it handles very low noise levels more intuitively.