RF and Antennas
Model class: Exact ideal relationship
Cascaded gain and noise figure
Apply the Friis formula to combine two-stage linear gain and noise figures into a total cascaded noise figure.
Interactive engine
Start with the stated conditions.
Values stay in this browser. Choose a representative scenario, then calculate deliberately.
Example ready
Calculate to inspect the result.
The result will identify the direct answer, assumptions, and any warning that changes the next decision.
Assumptions to check
- The entered cascaded-noise-figure values represent the stated operating condition.
- This exact ideal relationship is evaluated in the declared lumped or first-pass model.
- A cascaded-noise-figure calculation is not a component qualification or safety approval.
What this cascaded-noise-figure calculation establishes
Apply the Friis formula to combine two-stage linear gain and noise figures into a total cascaded noise figure. The useful result is the stated electrical quantity and the decision it supports, not an unstated claim about a finished product. This engine keeps the governing relationship visible so an input, unit, condition, or model boundary can be reviewed before a value becomes a component or layout choice.
Total noise factor is the first stage's noise factor plus the second stage's noise factor minus one, divided by the first stage's linear gain, per the Friis cascade formula. Treat the number as a first-pass result for the declared operating point. When a source, load, temperature, frequency, waveform, component tolerance, or measurement condition changes, repeat the calculation at the relevant corner rather than assuming the nominal answer persists.
Worked decision context
Two stages with G1 = 10, NF1 = 2 dB, and NF2 = 5 dB give total noise factor 1.8007 and NF 2.556 dB. That example verifies the equation and illustrates the scale of the result, but it does not select a part by itself. Compare the result with available values, ratings, tolerance bands, and the receiving circuit or physical environment before implementation.
Use the primary output to identify the binding constraint. If it leaves little margin, document which input dominates and use selected-part data, a higher-fidelity model, simulation, or measurement. This is especially important when a small numerical difference changes a thermal, timing, noise, or reliability decision.
Limits and validation handoff
Stage order matters: placing the higher-gain, lower-noise stage first minimizes the contribution of every later stage's noise. The calculation does not silently include omitted parasitics, installation conditions, manufacturing variation, or product policy. Those conditions can be decisive even when the arithmetic is exact for the selected model.
Record inputs, units, model assumptions, and the intended decision with the result. Verify the leading risk against the selected component data sheet and a representative measurement when the circuit has consequential energy, high voltage, safety, compliance, or reliability requirements.
Common mistakes
- Treating the cascaded-noise-figure result as a guaranteed operating limit rather than a first-pass exact ideal relationship estimate.
- Mixing a data-sheet value measured under one condition with this cascaded-noise-figure calculation performed at another.
- Selecting a component before checking the boundary this calculation names: stage order matters: placing the higher-gain, lower-noise stage first minimizes the contribution of every later stage's noise.
Model limit and handoff
Keep the entered cascaded-noise-figure conditions with the calculation, then validate the binding limit using the selected component, physical implementation, and representative operating corner.
FAQs
Is this cascaded-noise-figure result sufficient to approve a design?
No. It applies exact ideal relationship reasoning to the entered cascaded-noise-figure values and names the checks that still need selected-part data, a higher-fidelity model, or measurement. Stage order matters: placing the higher-gain, lower-noise stage first minimizes the contribution of every later stage's noise.
What does this cascaded-noise-figure calculator assume that could make the result wrong?
Total noise factor is the first stage's noise factor plus the second stage's noise factor minus one, divided by the first stage's linear gain, per the Friis cascade formula. If the entered values do not match the real operating condition, the result no longer describes the actual circuit.
Where should this cascaded-noise-figure result go next?
Compare this cascaded-noise-figure result with RF levels, impedance, and mismatch, then use the stated next decision below the calculator to move from this first-pass number toward an implementation.