For estimating and education only. Results come from the simplified models described below, are provided as is with no warranty, and are not a substitute for engineering analysis, simulation or measurement. Check them before relying on them in a design, purchase or safety decision. See the terms of use.
Equations
F = 10^{\mathrm{NF}/10}F_\mathrm{total} = F_1 + \frac{F_2 - 1}{G_1} + \frac{F_3 - 1}{G_1 G_2} + \cdotsFriisT_e = T_0\,(F - 1), \qquad T_0 = 290\ \mathrm{K}N_\mathrm{floor} = -174\ \mathrm{dBm/Hz} + 10\log_{10} B + \mathrm{NF}dBm; B in Hz\mathrm{MDS} = N_\mathrm{floor} + \mathrm{SNR}_\mathrm{required}dBmPassive stage
\mathrm{NF} = Lloss in dB, at 290 KVariables
| Symbol | Meaning | Unit |
|---|---|---|
F,\ \mathrm{NF} | Noise factor, noise figure | —, dB |
G | Stage gain (linear) | — |
B | Noise bandwidth | Hz |
T_0 | Reference temperature | K |
\mathrm{MDS} | Minimum detectable signal | dBm |
Worked example
| Input | Value |
|---|---|
| Stage 1 | LNA: 20 dB gain, 1.0 dB NF |
| Stage 2 | Filter: 1.5 dB loss |
| Stage 3 | Mixer: 7 dB conversion loss |
| Stage 4 | IF amp: 25 dB gain, 3 dB NF |
| Bandwidth, SNR | 10 MHz, 10 dB |
| Result | Value |
|---|---|
| Cascaded noise figure | 1.431 dB |
| Total gain | 36.5 dB |
| Equivalent noise temperature | 113.2 K |
| Input noise floor | −102.6 dBm |
| Minimum detectable signal | −92.57 dBm |
The LNA sets the system noise figure. Put the 1.5 dB filter ahead of it and the noise figure rises by almost the full 1.5 dB.
Load this example in the calculatorValidity
- Matched, linear stages. Gain compression and image noise are not modeled.
- Use noise figures specified at the same reference temperature and for the same source impedance.
- A mixer’s noise figure also depends on its LO drive and on whether the image band is filtered.
Sources
- H. T. Friis, “Noise Figures of Radio Receivers,” Proc. IRE, vol. 32, no. 7, pp. 419–422, 1944.
- D. M. Pozar, Microwave Engineering, 4th ed., Wiley, 2012. Chapter 10 (noise and nonlinear distortion).