Engineering Guide

RF Noise Figure, Noise Temperature, Receiver Sensitivity, and Cascaded Noise

Receiver noise design connects source temperature, filter bandwidth, device noise, gain distribution, and the SNR required by a real waveform. This guide develops that chain from the input reference plane to sensitivity without confusing noise floor with received power or link margin.

RFIntermediate18 min readUpdated October 3, 2026

Receiver Noise Design Workflow

Start with reference planes and bandwidth. A mathematically correct noise figure applied at the wrong plane or over the wrong bandwidth still produces a misleading sensitivity estimate.

Step	Task	Engineering Check
1	Define the input reference plane	Include every loss ahead of the first active stage and use gain/NF data at the actual frequency and match.
2	Define noise bandwidth	Use equivalent noise bandwidth, not an unlabeled channel width or sample rate.
3	Set source temperature	Use the physical source temperature for kTB and state the noise-factor reference temperature T0.
4	Build the cascade	Convert every gain and noise figure from dB to linear values before applying Friis.
5	Calculate input-referred floor	Combine source thermal noise and receiver-added noise under compatible assumptions.
6	Derive sensitivity	Add required SNR, Eb/N0-derived requirement, implementation loss, and detection criterion.
7	Close the link	Compare sensitivity with received power and allocate fade, interference, and production margin.
8	Verify	Measure gain, NF, bandwidth, compression, and sensitivity at operating bias, temperature, and match.

Noise Factor, Noise Figure, and Noise Temperature

The Noise Figure & Noise Temperature Calculator converts among linear noise factor, noise figure, and equivalent input noise temperature. Noise factor is the ratio of input SNR to output SNR under defined conditions; noise figure is its decibel form.

Formula reference

Noise conversions

F = SNRin / SNRoutNF(dB) = 10log10(F)F = 10^(NF/10)Te = T0(F - 1)NF = 10log10(1 + Te/T0)

Variable definitions

F: linear noise factor
NF: noise figure in dB
Te: equivalent input noise temperature
T0: stated standard reference temperature; ECParts uses 290 K

Thermal Noise and Equivalent Noise Bandwidth

Formula reference

Available thermal-noise power

Pn = kTBN0 = kT W/HzPn(dBm) = 10log10(kTB / 1 mW)At 290 K: N0 ≈ -173.98 dBm/Hz

Variable definitions

k: 1.380649 × 10^-23 J/K
T: absolute source temperature in kelvin
B: equivalent noise bandwidth in hertz; The model is available noise from a matched source

Increasing bandwidth by a factor of ten raises integrated thermal noise by 10 dB. Equivalent noise bandwidth is the width of an ideal rectangular filter that passes the same noise power as the actual response. It may differ from 3 dB bandwidth, channel spacing, sample rate, or symbol rate.

Friis Cascaded Noise

Formula reference

Cascaded noise factor

Ftotal = F1 + (F2 - 1)/G1 + (F3 - 1)/(G1G2) + ...NFtotal = 10log10(Ftotal)Glinear = 10^(GdB/10)

Variable definitions

All F values are linear noise factors

All G values are linear available power gains

Loss ahead of the first LNA belongs in the cascade

Never substitute dB values directly into Friis. High first-stage gain suppresses later input-referred noise, which is why a low-loss path to a stable, linear LNA is usually more valuable than improving a later stage by the same nominal NF amount.

Stage	Noise Role	Design Action
Passive loss before LNA	Linear loss L has gain 1/L and noise factor approximately L at T0	Directly degrades system NF; minimize feedline, switch, and filter loss
First LNA	F1 and G1 dominate later terms	Use low NF plus enough gain without sacrificing linearity or stability
Mixer / second stage	Contribution is (F2 - 1)/G1	High first-stage gain suppresses its input-referred contribution
Later IF stages	Divided by preceding gain product	Still check compression, dynamic range, and gain distribution
Attenuator after gain	Adds loss but contribution is divided by earlier gain	Placement changes system NF even when total loss is unchanged

From Noise Floor to Receiver Sensitivity

Formula reference

First-pass input sensitivity

Noise floor ≈ 10log10(kTB / 1 mW) + NFSensitivity ≈ Noise floor + SNRrequired + implementation lossFor a 290 K reference: ≈ -173.98 dBm/Hz + 10log10(B) + NF + SNRrequired + losses

Variable definitions

Use equivalent noise bandwidth

Required SNR depends on modulation, coding, data rate, error criterion, and detector

Implementation loss must be explicitly defined

Sensitivity is not a universal receiver number. It must name the waveform, data rate or bandwidth, coding, BER/PER or detection probability, temperature, and test setup. The RF Link Budget Calculator treats sensitivity as an input; it does not derive it from NF.

Worked Examples

3 dB NF conversion

F = 10^(3/10) = 1.9953. With T0 = 290 K, Te = 290(F - 1) = 288.63 K.

Thermal noise in 1 MHz

At 290 K, 10log10(kTB/1 mW) = -113.98 dBm. This is available source noise before receiver NF.

Receiver floor

For 1 MHz bandwidth and 3 dB NF, the input-referred floor is approximately -110.98 dBm.

Two-stage cascade

A 1 dB NF, 20 dB gain LNA followed by a 6 dB NF mixer gives Ftotal = 1.288 and NFtotal ≈ 1.10 dB.

Pre-LNA cable loss

A 2 dB cable ahead of the LNA contributes roughly 2 dB NF at T0 and weakens the signal by 2 dB before amplification.

Sensitivity estimate

With floor -110.98 dBm, required SNR 10 dB, and implementation loss 2 dB, a first-pass sensitivity is -98.98 dBm.

Measurement and Datasheet Checks

Use NF and gain at the actual frequency, bias, temperature, and source/load match. De-embed fixtures and input losses consistently. Confirm the measurement method, calibration plane, analyzer noise floor, uncertainty, and whether quoted NF is typical or guaranteed. Measure sensitivity with the intended modulation and error criterion, then verify blockers and compression separately.

Common Mistakes

Putting dB gains directly into the linear Friis equation.

Ignoring cable, filter, switch, or duplexer loss before the LNA.

Using channel width when equivalent noise bandwidth is required.

Treating -174 dBm/Hz as exact at every temperature.

Confusing equivalent noise temperature with physical device temperature.

Calling noise floor receiver sensitivity without a required SNR or detection criterion.

Comparing receiver sensitivity values measured at different bandwidths or error targets.

Optimizing NF while ignoring stability, linearity, blockers, compression, and power.

Adding noise powers or gains at inconsistent reference planes.

Using a calculated sensitivity as a substitute for measurement.

Related Calculators

Noise Figure & Noise Temperature CalculatorOpen Calculator RF Link Budget CalculatorOpen Calculator Coaxial Cable Loss CalculatorOpen Calculator RF Power ConverterOpen Calculator

Related Engineering Resources

RF Noise Figure, Noise Temperature and Noise Floor ReferenceRead Resource RF Link Budget and Received Power BasicsRead Resource RF Impedance Matching and Transmission Line DesignRead Resource

Support reference

FAQ

What is RF noise figure?

Noise figure is the decibel form of noise factor, which describes how much a device or chain degrades input signal-to-noise ratio under defined reference conditions.

What is the difference between noise factor and noise figure?

Noise factor F is linear and at least one for an ordinary noisy device. Noise figure is NF = 10log10(F) in decibels.

How is equivalent noise temperature calculated?

For a stated reference temperature T0, Te = T0(F - 1). ECParts uses T0 = 290 K unless another value is explicitly stated.

What does kTB calculate?

kTB is the available thermal-noise power from a matched source at absolute temperature T over equivalent noise bandwidth B.

Why is thermal noise approximately -174 dBm/Hz?

At 290 K, kT in a one-hertz bandwidth is about -173.98 dBm, commonly rounded to -174 dBm/Hz.

Why must Friis calculations use linear gain?

The Friis cascade equation adds linear noise factors and divides later contributions by linear gain products. Substituting dB values directly gives an invalid result.

Why is the first LNA so important?

Its own noise enters directly, while its gain divides the input-referred contributions of later stages. Loss before it is especially damaging.

Is noise figure the same as receiver noise floor?

No. Noise figure is receiver-added SNR degradation; noise floor also depends on source temperature and equivalent noise bandwidth.

How is receiver sensitivity estimated?

A first-pass input sensitivity is thermal noise over equivalent bandwidth plus receiver NF plus required SNR and implementation losses, all under compatible conditions.

Is channel bandwidth the same as noise bandwidth?

Not always. Equivalent noise bandwidth integrates the actual filter response and can differ from nominal 3 dB width, symbol rate, or channel spacing.

Does lower noise figure always make a better receiver?

No. Gain, linearity, stability, power, matching, selectivity, dynamic range, cost, and interference performance also matter.

Can a link budget use calculated sensitivity without measurement?

It can support early design, but final sensitivity depends on modulation, coding, error criterion, interference, implementation loss, and hardware verification.

Summary

Define reference planes, physical temperature, and equivalent noise bandwidth first. Convert dB quantities to linear values for Friis cascades, include every pre-LNA loss, and derive sensitivity only after adding a documented SNR or detection requirement. Verify the real gain, NF, bandwidth, linearity, and sensitivity under operating conditions.