Engineering Reference
RF Noise Figure, Noise Temperature and Noise Floor Reference
Reference RF noise factor and figure, equivalent noise temperature, kTB thermal noise, noise density, bandwidth scaling, receiver noise floor, and Friis cascade terminology.
Noise-factor and equivalent-temperature conversions on this page use the conventional reference temperature T0 = 290 K unless stated otherwise. Available kTB noise assumes a matched source and load and an equivalent noise bandwidth in hertz.
Receiver Noise Terms
| Term | Engineering meaning | Unit or boundary |
|---|---|---|
| Noise factor, F | Linear input-to-output SNR degradation ratio | Dimensionless and F >= 1 for a passive, physical receiver model |
| Noise figure, NF | Noise factor expressed logarithmically: NF = 10 log10(F) | dB; convert to linear F before cascade calculations |
| Equivalent noise temperature, Te | Input-referred temperature that represents added device noise | K; Te = T0(F - 1) for the stated reference temperature T0 |
| Available thermal-noise power | Noise deliverable by a matched source over noise bandwidth B | W; Pn = kTB |
| Noise-power density | Available thermal noise normalized to 1 Hz | W/Hz or dBm/Hz; about -173.98 dBm/Hz at 290 K |
| Receiver noise floor | Integrated input-referred noise estimate over bandwidth | dBm; commonly kTB in dBm plus receiver NF under compatible assumptions |
| Receiver sensitivity | Minimum specified input level for a required performance criterion | dBm; also depends on required SNR or Eb/N0, waveform, coding, error rate, bandwidth, and implementation |
| Signal-to-noise ratio, SNR | Signal power divided by noise power at the same reference plane and bandwidth | Linear ratio or dB; not interchangeable with NF |
Core Relationships
| Relationship | Formula | Required convention |
|---|---|---|
| Noise figure to factor | F = 10^(NF/10) | NF in dB; F is linear |
| Factor to noise figure | NF = 10 log10(F) | F must remain linear |
| Equivalent noise temperature | Te = T0(F - 1) | State T0; this Reference uses 290 K unless noted |
| Available thermal noise | Pn = kTB | T in K and equivalent noise bandwidth B in Hz |
| Noise floor estimate | Nfloor(dBm) = Pn(dBm) + NF(dB) | Input-referred estimate with compatible source/reference assumptions |
| Friis cascade | Ftotal = F1 + (F2 - 1)/G1 + (F3 - 1)/(G1G2) + ... | Every F and G inside the equation is linear |
k = 1.380649e-23 J/K
T0 = 290 K
F and G are linear inside Friis cascade equations.
Bandwidth and Temperature Scaling
| Change | Noise-power change | Condition |
|---|---|---|
| Bandwidth x2 | +3.0103 dB | 10 log10(2) |
| Bandwidth x10 | +10 dB | 10 log10(10) |
| Bandwidth /2 | -3.0103 dB | Same temperature and NF |
| Temperature x2 | +3.0103 dB | Ideal kTB comparison with unchanged bandwidth |
Receiver Metric Boundaries
| Metric | What it represents | Do not confuse it with |
|---|---|---|
| Available noise power | Source thermal noise available to a matched load | Do not call it receiver sensitivity |
| Receiver noise floor | Integrated receiver-input noise estimate | Specify bandwidth, temperature, NF, and reference plane |
| Sensitivity | Threshold for a defined receiver performance | Requires an SNR/Eb/N0 or other detection criterion beyond kTB + NF |
| SNR | Signal level relative to noise at one reference plane | NF describes SNR degradation, not the SNR itself |
| Phase noise | Spectral spreading around an oscillator or carrier | Outside this thermal-noise and receiver-cascade lookup |
| ADC noise and ENOB | Converter quantization and circuit-noise performance | Outside this RF receiver-noise lookup |
Cascade Review
| Item | Engineering effect | Review action |
|---|---|---|
| Stage order | Early-stage noise matters most | Later contributions are divided by preceding linear gain |
| Loss before the LNA | Usually worsens system NF directly | Model passive loss at its physical temperature and reference plane |
| Gain units | Convert dB to linear power gain | Never substitute dB gain directly into Friis cascade |
| Noise bandwidth | May differ from nominal 3 dB bandwidth | Use equivalent noise bandwidth when accuracy matters |
| Device conditions | NF and gain vary with frequency, bias, temperature, and matching | Use datasheet conditions or measured data for final design |
Canonical Calculation Anchors
| Case | Calculated result | Interpretation |
|---|---|---|
| 3 dB noise figure | F = 1.995262; Te = 288.626 K | Uses T0 = 290 K |
| 290 K noise density | -173.975 dBm/Hz | Available matched-source noise in 1 Hz |
| 290 K over 1 MHz | -113.975 dBm | kTB before receiver-added noise |
| 1 MHz and 3 dB NF | -110.975 dBm | Input-referred receiver noise-floor estimate |
| 1 dB NF, 20 dB gain LNA; 6 dB NF mixer | 1.102 dB cascade NF | Friis calculation with linear factors and gains |
Engineering Review Checklist
- Define input and output reference planes.
- State the noise reference temperature used.
- Use equivalent noise bandwidth, not an unlabeled nominal bandwidth.
- Convert NF and gain from dB to linear values before Friis cascade.
- Include loss ahead of the first LNA in the cascade.
- Use device gain and NF at the actual frequency, bias, temperature, and match.
- Keep available noise power distinct from receiver sensitivity.
- State the required SNR, Eb/N0, error rate, or detection criterion.
- Check gain compression and dynamic range separately.
- Validate critical receiver chains with measurement or a trusted RF simulation.
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FAQ
What is the difference between noise factor and noise figure?
Noise factor F is a linear SNR degradation ratio. Noise figure NF expresses the same ratio in decibels using NF = 10 log10(F).
What reference temperature is used for noise temperature conversion?
This Reference uses the conventional standard noise temperature T0 = 290 K unless another value is explicitly stated.
What does kTB calculate?
kTB calculates available thermal-noise power from a matched source at absolute temperature T over equivalent noise bandwidth B.
Why is thermal noise about -174 dBm per hertz?
At 290 K, kT converted to dBm for a 1 Hz bandwidth is approximately -173.98 dBm/Hz, commonly rounded to -174 dBm/Hz.
How does bandwidth affect receiver noise floor?
Integrated noise changes by 10 log10 of the bandwidth ratio. Doubling bandwidth adds about 3.01 dB; increasing it tenfold adds 10 dB.
Is receiver noise floor the same as sensitivity?
No. Sensitivity additionally requires a defined SNR, Eb/N0, error-rate, detection, waveform, or coding criterion and relevant implementation margins.
Is noise figure the same as SNR?
No. Noise figure quantifies how much a device or chain degrades SNR between its input and output; it is not the signal-to-noise ratio itself.
Why must Friis cascade use linear values?
Friis cascade adds linear noise-factor contributions divided by preceding linear power gains. Values in dB must be converted before substitution.
Why is the first receiver stage important?
Sufficient low-noise gain in the first stage suppresses the input-referred contribution of later stages in the Friis equation.
Does a link budget include receiver noise figure?
A power link budget estimates received level. Noise figure and bandwidth may then be used with a performance criterion to assess SNR or sensitivity, but they are distinct calculations.