Cascaded Noise Figure Calculator based on Friis’ cascade formula: determine system noise figure, total gain, and equivalent noise temperature per stage
Calculate Cascaded Noise Figure for Multi-Stage RF Receiver Chains
This calculator combines the gain and noise figure of each stage in a receiver chain into a single cascaded noise figure, per Friis’ cascade formula. RF and microwave engineers rely on it during receiver front-end design to confirm that an LNA’s gain is high enough to suppress the noise contributed by later stages such as filters, mixers, and IF amplifiers.
How to Use
Enter gain (G) and noise figure (NF) in dB for each stage (Stage 1 LNA, Stage 2 filter/mixer, Stage 3 IF/output). The tool returns cascaded noise figure in dB, total system gain in dB, cascaded noise factor as a linear ratio, equivalent noise temperature in K, and the first stage’s percentage contribution to total system noise.
Formula
The formula is Friis’ cascade equation, from H. T. Friis, “Noise Figures of Radio Receivers,” Proc. IRE 32(7), pp. 419–422 (1944) — cross-verified against the same equation in Pozar’s Microwave Engineering (Ch. 10) and Razavi’s RF Microelectronics (Ch. 2).
Step 1 — convert each stage’s dB values to linear noise factor and gain:
$$F_i = 10^{NF_i/10}, \qquad G_i = 10^{G_i/10}$$
Step 2 — apply Friis’ cascade formula in linear terms:
$$F_{total} = F_1 + \frac{F_2 – 1}{G_1} + \frac{F_3 – 1}{G_1 G_2}$$
Step 3 — convert back to dB:
$$NF_{total} = 10\log_{10}(F_{total})$$
Step 4 — equivalent noise temperature, using the standard reference temperature $T_0 = 290\ \text{K}$ from Friis’ original definition:
$$T_e = T_0\,(F_{total} – 1)$$
Non-obvious nuance: stage order changes the result even with identical component specs, because each stage’s $(F_i – 1)$ term is divided by the cumulative gain of every stage before it.
A passive loss placed ahead of the LNA — a feeder cable, connector, or preselector filter — has $G < 1$ and $F = 1/G$, and algebraically reduces to $NF_{total} = NF_{LNA} + \text{Loss(dB)}$: the loss degrades system noise figure dB-for-dB.
The same loss placed after a high-gain LNA is suppressed almost entirely by division through $G_1$. This is why cable runs and switches are routed after the LNA whenever the chain allows it, not before.
Common input mistake: summing NF values directly in dB instead of converting to linear F and G first. Friis’ formula is only valid in linear terms — adding dB values directly (rather than converting, summing, then converting back) gives a wrong and usually optimistic result.
FAQ
Why does stage order matter in a cascade?
Friis’ formula divides each later stage’s noise contribution by the cumulative gain of every stage before it. Moving a noisy component earlier in the chain removes that suppression and raises system noise figure.
Why must I convert dB to linear before combining stages?
Friis’ equation is additive in linear noise factor and gain, not in dB. Converting, summing, then converting the result back to dB is required for a correct answer.
What does equivalent noise temperature represent?
Te expresses the same noise factor as an added temperature above the standard 290 K reference. It’s the conventional unit in satellite and deep-space receiver specifications.
How much does cable loss before the LNA affect system noise figure?
Almost dB-for-dB. A 3 dB loss ahead of the LNA raises system noise figure by nearly 3 dB, per Friis’ formula, since that loss is not divided down by any preceding gain.
Can this formula be extended beyond three stages?
Yes. Friis’ series extends to any number of stages, with each additional term’s noise factor divided by the product of all prior stage gains.