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Communications
Thermal noise power
Unavoidable noise power in a receiver.
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- Result
- N [dBm]
T is the system noise temperature in kelvin and B the receiver bandwidth in MHz. The noise power is kTB in watts (k is Boltzmann’s constant), shown here in dBm. At the standard reference temperature of 290 K the noise density is −174 dBm/Hz. A real receiver adds its noise figure on top.
Unavoidable noise power in a receiver. It grows with temperature and bandwidth, and sets the floor for the weakest detectable signal.
Calculator
- Noise power in watts, kTB4.004 fW
- Noise density kT−174 dBm/Hz
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- The floor for a 1 MHz receiver at 290 K is −114 dBm, which is 4 femtowatts. A signal weaker than that is buried in thermal noise unless it is processed for a long time.
- Narrower bandwidth is the cheapest way to cut noise: reducing the bandwidth from 1 MHz to 10 kHz lowers the floor by 20 dB.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (dBm) | Local step | Change in result |
|---|---|---|---|---|---|---|
| B Bandwidth | 0.001 to 1,000 MHz | −144 | −83.98 | 60 | +10% | +0.414 dBm |
| T System temperature | 50 to 2,000 K | −121.6 | −105.6 | 16.02 | +10% | +0.414 dBm |
Sweep of Bandwidth
| Bandwidth (MHz) | Noise power (dBm) |
|---|---|
| 0.001 | −144 |
| 0.005623 | −136.5 |
| 0.03162 | −129 |
| 0.1778 | −121.5 |
| 1 | −114 |
| 5.623 | −106.5 |
| 31.62 | −98.98 |
| 177.8 | −91.48 |
| 1,000 | −83.98 |
Sweep one variable
Variables and how each one contributes
Noise power
What the equation gives you. Everything else feeds it.
System temperature
The effective noise temperature of the system, in kelvin. Logarithmic: a 10 % rise in T adds only 0.41 dB. Cooling the front end of a receiver lowers the floor, but only by 3 dB for each halving.
Bandwidth
The bandwidth of the receiver, in MHz. Logarithmic, the same as T: every doubling of bandwidth adds 3 dB of noise. A 10 % rise in B adds 0.41 dB.
Worked example with the values above
- Noise power: kTB = 1.381×10−23 × 290 × 1,000,000 = 4.004×10−15 W.
- Convert to milliwatts: 4.004×10−12 mW.
- N = 10 log₁₀(4.004×10−12) = −114 dBm.
Assumptions and limits
- Thermal noise only: no interference, no sky, atmospheric or man-made noise.
- A matched receiver with noise temperature T over the whole bandwidth B.
Common mistakes
- Ignoring the receiver noise figure, which raises the real floor by several dB.
- Mixing dBm and dBW, which differ by 30 dB.
Statistics and uncertainty
Because the result is in dB, errors in T and B are compressed: ±10 % in each gives about ±0.4 dB. The noise figure of the receiver, typically 2 to 10 dB, is a far larger contribution than any uncertainty in these inputs.
Where it is used
- Receiver sensitivity and the minimum detectable signal.
- The noise term in a link budget or radar range equation.
Maths you need
- Decibels: 10 log₁₀ of a power ratio
- Boltzmann’s constant: k = 1.38 × 10⁻²³ J/K