Noise Figure Cascade Calculator

Cascade preset:

Start with a familiar signal path; editing a stage changes the selection to Custom without discarding values.

RF chain stages:

Enter stages from antenna input to final output. Early loss raises the total before useful gain can suppress later contributions.

Stage name

Gain

Noise figure

Stage controls

Analysis bandwidth:

Use the channel, IF filter, FFT bin, or measurement noise bandwidth.

Required SNR:

Use 0 dB for noise-floor crossing or the demodulator/detector requirement for a sensitivity estimate.

Noise figure target:

Type the receiver-budget target or tune the comparison slider.

Exact dB

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Reference temperature:

Use the passive-device physical/reference temperature for this matched small-signal estimate.

Display precision:

Choose more decimals only when the source data supports that reporting precision.

Stage	Role	Gain	Effective NF	Friis term	Share	Cumulative gain	Cascade NF	Copy
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Metric	Value	Meaning	Copy
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Check	Status	Action	Copy
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Every receiver stage adds noise or changes how strongly later noise appears at the input. Noise figure (NF) expresses the loss of signal-to-noise ratio caused by a device or complete signal chain. A lower value preserves weak signals better; 0 dB would be an ideal noiseless stage, while a positive value means the output signal-to-noise ratio is worse than the input.

Stage order matters as much as individual specifications. The Friis cascade relation refers each stage’s excess noise back through all gain before it. An amplifier with useful early gain suppresses the input-referred effect of later mixers, filters, and IF amplifiers. The same low-noise amplifier placed after a lossy cable cannot undo the signal-to-noise ratio already lost in that cable.

Terms used in cascaded receiver noise analysis
Term	Meaning	How to read it
Gain	Power increase through a stage; loss is entered as negative gain.	Early positive gain reduces later input-referred noise contributions.
Noise factor	The linear ratio corresponding to noise figure.	Factors, not dB values, are combined in the Friis equation.
Noise figure	10 log₁₀(noise factor), expressed in dB.	Compare the cascade value with the receiver budget at the same conditions.
Input noise floor	Thermal noise over the analysis bandwidth plus cascade NF.	A wider bandwidth raises the integrated noise floor.
Sensitivity	Input noise floor plus the required signal-to-noise ratio.	It is a modeled minimum input level, not a measured detection guarantee.

Passive loss ahead of the first active stage is especially expensive. Under the matched reference-temperature assumption, a 1 dB filter or cable loss has 1 dB noise figure and reduces the level delivered to the following amplifier. Moving that loss after sufficient low-noise gain can sharply reduce its contribution, although real designs must still satisfy selectivity, stability, overload, and linearity requirements.

Bandwidth connects device noise figure to a receiver noise floor. Doubling noise bandwidth adds about 3 dB of integrated thermal noise, even though the stage cascade is unchanged. A sensitivity estimate then adds the detector or demodulator’s required SNR. Results from different designs are comparable only when bandwidth, reference temperature, SNR requirement, frequency, impedance, and the noise-figure basis of every stage are consistent.

Friis analysis is a matched, small-signal model. It does not capture impedance mismatch, correlated noise, compression, intermodulation, phase noise, local-oscillator leakage, quantization, or all mixer image-noise effects. Mixer data must use a basis compatible with the receiver architecture; confusing single-sideband and double-sideband noise figure can make an apparently precise cascade wrong.

How to Use This Tool:

Enter the signal path in physical order from antenna input to final output and keep all specifications on a compatible basis.

Choose the nearest Cascade preset or build a custom lineup. For every included stage, enter its name and role, then supply gain for all stages and noise figure for active devices.
Use negative gain for passive loss. Passive and filter roles derive effective NF from the entered loss, so positive gain is rejected for those roles.
Enter the analysis bandwidth, required SNR, target noise figure, and reference temperature. Use the channel, IF filter, FFT bin, or measurement noise bandwidth that matches the comparison.
Review the total NF and margin, then inspect Noise contributors and Stage guidance to find early loss or a dominant stage. Re-run the chain after any proposed stage-order or gain change.

Interpreting Results:

NF margin equals the entered target minus the calculated cascade NF. A positive value meets the mathematical target; a negative value misses it. Less than 0.5 dB of positive margin is shown as tight because component tolerance, temperature, mismatch, and frequency response can consume the headroom.

Contribution share divides the cascade’s excess noise factor among stages. It is useful for prioritizing changes, but it is not a percentage of output noise power.
Input noise floor includes thermal density, bandwidth, and cascade NF. Minimum input signal adds the required SNR.
Output noise floor and output sensitivity add total cascade gain. They do not test compression or whether the following ADC or detector has enough headroom.
More displayed decimals do not create more certainty. Keep precision consistent with the stage data and verify important budgets with measured or corner-condition values.

Technical Details:

Noise figure values in dB are first converted to linear noise factors, and stage gains in dB are converted to linear power gains. Friis summation then refers each stage’s excess factor through the product of all preceding gains. The first stage is unsuppressed; every later term is divided by earlier gain.

Formula Core

For stage i, let g_i be gain in dB and NF_i noise figure in dB. Passive and filter stages use effective NF equal to −g_i under the matched reference-temperature assumption.

G_{i} = 10^{\frac{g_{i}}{10}} F_{i} = 10^{\frac{{NF}_{i}}{10}}

The matched-stage Friis relation for n ordered stages is:

F_{total} = 1 + \sum_{i = 1}^{n} \frac{F_{i} - 1}{\prod_{j = 1}^{i - 1} G_{j}}

The empty gain product for the first stage is 1. Total gain is the sum of stage gains in dB, and the final factor returns to dB as follows:

{NF}_{total} = 10 \log_{10} (F_{total}) g_{total} = \sum_{i = 1}^{n} g_{i}

Thermal-noise density uses the exact Boltzmann constant k = 1.380649 × 10⁻²³ J/K and the entered reference temperature T. Division by 0.001 converts watts to dBm.

N_{0} = 10 \log_{10} (\frac{k T}{0.001}) N_{in} = N_{0} + 10 \log_{10} (B) + {NF}_{total} Sensitivity = N_{in} + {SNR}_{required}

B is bandwidth in hertz. Output-referred noise floor and sensitivity add total gain. Equivalent input noise temperature is T(F_total − 1), and target margin is target NF − total NF.

Rule Core

Cascade rules and interpretation boundaries
Rule	Exact behavior
Stage order	One to eight stages are evaluated from input to output. Reordering changes the preceding-gain products.
Passive stage	Gain must be 0 dB or negative; effective NF is the magnitude of that loss in dB.
Contribution share	Each Friis excess-factor term ÷ total excess factor × 100%. Shares are zero when every stage is ideal.
Dominant stage	The stage with the largest contribution share. Equal maxima keep the earliest stage.
Front-end loss	The sum of passive losses before the first active stage.
Target margin	Target NF − calculated NF; ≥ 0 meets the entered target, while < 0 misses it.

Accuracy and Assumptions:

Use stage gain and NF at compatible frequency, impedance, bias, temperature, and measurement conditions. Typical values do not establish worst-case margin.
The cascade assumes matched, linear, small-signal stages and uncorrelated added noise. It does not include mismatch or noise-parameter effects.
Passive NF equals insertion loss only under the stated matched reference-temperature assumption. A passive device at another physical temperature needs a temperature-aware model.
Confirm whether mixer NF is single-sideband or double-sideband and whether image-noise folding changes the appropriate cascade relation.
Sensitivity is based only on bandwidth, thermal noise, NF, and required SNR. Verify demodulation, interference, phase noise, dynamic range, and nonlinear limits separately.

Worked Examples:

Receiver with a switch before the LNA

A five-stage path contains a 0.7 dB antenna-switch loss, a 20 dB-gain LNA with 0.9 dB NF, a 1.2 dB image-filter loss, a −6 dB mixer with 7 dB NF, and a 24 dB IF amplifier with 3 dB NF. Friis summation gives about 1.966 dB cascade NF and 36.1 dB total gain. At 290 K over 200 kHz, the input noise floor is about −118.998 dBm. Adding a 10 dB SNR requirement gives about −108.998 dBm sensitivity. Against a 2.5 dB target, the NF margin is about +0.534 dB, and the LNA contributes the largest share of excess noise.

References:

RF Signal Chain Discourse: Properties and Performance Metrics, Analog Devices.
Fundamentals of RF and Microwave Noise Figure Measurements, Keysight Technologies, Application Note 5952-8255.
SI base unit: kelvin, International Bureau of Weights and Measures.