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Tool 15 · Available

Thermal Noise & Sensitivity

Integrate kTB, receiver noise figure, required SNR, and margin at one input plane.

Typical inputs
Temperature, equivalent noise bandwidth, receiver NF, required SNR, and implementation margin.
Calculated output
kTB noise in W/dBm, noise density, effective input noise, and conditional sensitivity.
Model status
Release D · documented and numerically tested
Engineering question

What conditional input sensitivity follows from this temperature, ENBW, and SNR criterion?

Input-referred noise and sensitivity

Use equivalent noise bandwidth at one input plane. Noise figure uses T₀ = 290 K; equivalent receiver noise temperature is converted with the same reference.

Receiver noise entry
Conditional input sensitivity-158.975187 dBmAt 290.000 K and 1 Hz ENBW
Noise density
-173.975187 dBm/Hz
4.00388210e-21 W/Hz
Source kTB
-173.975187 dBm · -203.975187 dBW
0.00000400388 fW
Receiver input noise
-168.975187 dBm · -198.975187 dBW
Noise figure
5.000000 dB
Equivalent receiver temperature
627.0605 K
T₀ = 290 K
Required SNR
10.0000 dB
Implementation margin
0.0000 dB
Each dB term advances the threshold at the same receiver input plane.
TermChangeLevel
Source kTBstart-173.975187 dBm
Receiver NF+5.000000 dB-168.975187 dBm
Required SNR+10.000000 dB-158.975187 dBm
Implementation margin+0.000000 dB-158.975187 dBm

Calculation path

  1. kTB=4.00388210×10−21 WkTB=4.00388210\times10^{-21}\,\mathrm W
  2. F=1+Te290NF=10log⁡10FF = 1 + \frac{T_{\mathrm{e}}}{290}\qquad \mathrm{NF} = 10\log _{10}F
  3. Psens[dBm]=10log⁡10(kTB1 mW)+NF+SNRrequired+MimplP_{\mathrm{sens}}[\mathrm{dBm}]=10\log_{10}\left(\frac{kTB}{1\,\mathrm{mW}}\right)+\mathrm{NF}+\mathrm{SNR}_{\mathrm{required}}+M_{\mathrm{impl}}
  4. −174 dBm/Hz is a rounded near-room-temperature reference, not a temperature-independent constant.
Model

What this calculator is doing

Exact Boltzmann constant k, temperature T, and ENBW B set available thermal noise. NF, required SNR, and margin add in dB at one input plane.

Decision

How to read the result

Sensitivity is conditional on the detector or modulation criterion. It is not comparable unless bandwidth, NF, losses, coding, and conditions match.

Equations & conventions

  • N=kTBN=kTB
  • Sensitivity=N[dBm]+NF+SNRrequired\text{Sensitivity}=N[\mathrm{dBm}]+\mathrm{NF}+\mathrm{SNR}_{\mathrm{required}}
  • k = 1.380649×10⁻²³ J/K exactly; T is kelvin.
  • B is equivalent noise bandwidth in hertz.
  • NF and required SNR are positive dB quantities.

Independently checked example

Checked example: 290 K and 1 Hz gives about −173.975 dBm/Hz; adding 5 dB NF and 10 dB required SNR gives about −158.975 dBm sensitivity.

Common mistakes

  • Using −174 dBm/Hz without adjusting temperature.
  • Using channel width when filter ENBW differs.

Assumptions, validity & omissions

  • Classical matched available-noise model.
  • Bandwidth is equivalent noise bandwidth.
  • Sensitivity is conditional on the entered SNR criterion.

Sources & model provenance

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