TOOL 05 / THE NOISE LIMIT

Receiver Performance

Follow the noise budget to a theoretical minimum input signal.

Noise & bandwidth

INPUT REFERRED

Source noise temperature Ts (K)

Absolute kelvin: 1–100000 K. Default 290 K (16.85 °C). This is the source's available noise temperature at the receiver input, not the receiver enclosure temperature.

Effective noise bandwidth B

Bandwidth unit

1e-6–1e12 Hz, greater than zero. Use equivalent noise bandwidth: the rectangular bandwidth passing the same white-noise power. It need not equal a filter's −3 dB width or channel spacing.

Known receiver noise quantity

Noise figure NF (dB)

Reference T₀ is fixed at 290 K.

Required signal-to-noise ratio (dB)

−100 to +100 dB; negative values are allowed. Supply the required signal/noise power ratio for this same effective bandwidth, referred to the receiver input. This tool does not infer it from modulation, BER, SINAD, Eb/N₀ or post-detection audio quality.

Compare another bandwidth

Comparison bandwidth B₂

Comparison unit

Same 1e-6–1e12 Hz limits. Holds Ts, receiver noise and required SNR fixed; assumes white noise across both bandwidths.

Display precision

Use dot decimals or scientific notation, without commas or unit suffixes. Changing a unit reinterprets its number. Changing the known noise quantity loads a labelled example. Display precision is not measurement accuracy.

Theoretical noise budget

T₀ = 290 K

THEORETICAL NOISE-LIMITED SENSITIVITY

—dBm

— W · required input signal power

Calculated estimate. Not a measurement or a guaranteed receiver specification.

Source noise density—dBm/Hz · kTs

Total noise density—dBm/Hz · k(Ts + Te), input referred

Source density in W/Hz—Available power per hertz

Receiver-added density—dBm/Hz · kTe, input referred

Noise figure NF: — dB
Noise factor F: — ×
Equivalent input temperature Te: — K
Total input-referred Ts + Te: — K
Required SNR power ratio: — ×
Effective noise bandwidth: — Hz

Noise powers integrated over B; dBm is referenced to 1 milliwatt
Noise over B	W	dBm
Source · kTsB	—	—
Receiver added · kTeB	—	—
Total · k(Ts + Te)B	—	—

Bandwidth effect · B₂ relative to B

Bandwidth ratio B₂ / B: — ×
Noise / sensitivity change: — dB
Theoretical sensitivity at B₂: — dBm

Powers are available at a matched receiver input, or input referred. No gain or output noise power is calculated. Use a receiver noise figure applicable to the operating frequency, source impedance and configuration. Te describes equivalent added noise; it is not a physical thermometer reading.

Equations & assumptions

SHOW THE WORK

Available thermal noise and receiver noise

k = 1.380649 × 10⁻²³ J/K · exact SI value

N₀,source = kTs [W/Hz] · Nsource = kTsB [W]

F = SNRin / SNRout at Ts = T₀ = 290 K

NF [dB] = 10 log₁₀(F) · F = 10^(NF/10)

Te = T₀(F − 1) · F = 1 + Te/T₀

Nadded = kTeB · Ntotal = k(Ts + Te)B [W]

Ts is the source's available input noise temperature. T₀ = 290 K is the fixed conventional reference for NF/F/Te conversion. Selecting a different Ts leaves T₀ unchanged. At Ts = T₀, Ntotal = kT₀BF. At other Ts, use Ts + Te; do not simply add NF to kTsB in dBm.

NF is an entered receiver property or a conversion of F/Te, not a measurement inferred from thermal noise alone. The model assumes classical white thermal noise, a matched available-power reference plane, frequency-flat applicable receiver noise and effective noise bandwidth. Use where the classical approximation hν ≪ kTs is suitable; this module does not model quantum or coloured noise.

Required SNR and theoretical sensitivity

SNRlinear = 10^(SNRrequired[dB]/10)

Pmin [W] = Ntotal × SNRlinear

P [dBm] = 10 log₁₀(P[W] / 0.001 W)

Pmin [dBm] = Ntotal [dBm] + SNRrequired [dB]

At 290 K: Pmin = −173.975187… + 10 log₁₀(B/1 Hz) + NF + SNRrequired [dBm]

ΔN = ΔPmin = 10 log₁₀(B₂/B) [dB]

Required SNR is a signal/noise power ratio over this same effective noise bandwidth. Negative SNR means a signal below integrated noise; it does not establish that a particular waveform can be decoded. Narrowing B reduces noise only under the stated assumptions; it can also remove wanted signal or change the required SNR.

Measured sensitivity needs an actual test with a defined waveform, frequency, bandwidth, receiver settings and acceptance criterion. This calculation alone cannot establish that result. No measurement import, demodulation/BER model, implementation margin, interference model or receiver chain cascade is included.

Quick reference · source thermal noise at 290 K

Rounded values for orientation. NF and required SNR are zero in this table; the calculator uses the exact k value rather than a rounded −174 dBm/Hz constant.

Effective bandwidth	kT₀B (W)	kT₀B (dBm)
1 Hz	4.0038821e-21	−173.975187
1 kHz	4.0038821e-18	−143.975187
3 kHz	1.20116463e-17	−139.203975
12.5 kHz	5.004852625e-17	−133.006087
25 kHz	1.000970525e-16	−129.995787
1 MHz	4.0038821e-15	−113.975187

Double B: +3.010300 dB. Half B: −3.010300 dB. Ten times B: +10 dB. At T₀ = 290 K, NF = 0 dB gives F = 1 and Te = 0 K; F = 2 gives NF = 3.010300 dB and Te = 290 K; NF = 5 dB gives Te ≈ 627.060521 K. At 300 K, source density is ≈ −173.827955 dBm/Hz.

Input limits, numerical boundaries & verification

All bounds are inclusive: Ts 1–100000 K; B and B₂ 1e-6–1e12 Hz; NF zero or 1e-12–100 dB; F 1–1e10; Te zero or 1e-12–2899999999710 K; required SNR −100 to +100 dB. Limits constrain this calculation, not equipment ratings. NF ≥ 0/F ≥ 1/Te ≥ 0 is the model domain. Absolute-zero source temperature and zero bandwidth are rejected. Te = 0 is a valid ideal receiver boundary.

Blank, malformed, nonfinite and out-of-range inputs clear dependent outputs. Source and receiver densities stay available when bandwidth is invalid; valid receiver noise conversions remain available when source temperature is invalid. A bad comparison does not clear the main sensitivity.

IEEE-754 double precision. expm1 and log1p retain small receiver-added noise near NF = 0/F = 1. Te is kept separately even if the displayed factor rounds to 1. Zero added noise displays 0 W and −∞ dBm. Display choices are 3, 6 or 9 significant figures for every Tool 05 result, including dB values. Displayed rounding never feeds back.

Calculation checks cover fixed reference values, units, invalid inputs and numerical boundaries, with separate high-precision numerical comparisons. Theoretical sensitivity remains subject to the stated model assumptions.

Primary references checked 24 October 2026: NIST SI defining constants · Keysight 5952-8255, noise figure / temperature, pp. 7–8 · Analog Devices MT-006, effective noise bandwidth, p. 3. External references need internet; calculations run in your browser after the page loads.