RF Cascade Analysis: Friis, IIP3 & Monte Carlo

Why Nominal Values Aren't Enough

Open any RF front-end datasheet and you'll see a single noise figure and gain — measured at 25 °C, nominal supply, centre frequency. Production parts arrive as distributions. The 1.5 dB LNA is 1.5 dB on average.

Say the receiver's sensitivity budget allows a cascaded NF of 2.5 dB. Whether the design meets it depends on the nominal cascade and on how the stage tolerances stack up. The RF Cascade Budget Analyzer computes the cascaded NF, gain, IIP3 and P1dB with the standard formulas, then runs a Monte Carlo over the stage tolerances and reports the yield against your specs.

Setting Up a 5-Stage Receive Chain

A 2.4 GHz superheterodyne front-end: LNA → band-select filter → mixer → IF amplifier → IF filter. The stage list is JSON:

[
  {"name": "LNA",          "type": "amp",    "gain_db": 15.0, "nf_db": 1.5, "iip3_dbm": -5.0, "p1db_dbm": -15.0},
  {"name": "BPF",          "type": "filter", "gain_db": -1.5, "nf_db": 1.5},
  {"name": "Mixer",        "type": "mixer",  "gain_db": -6.0, "nf_db": 7.5, "iip3_dbm": 12.0, "p1db_dbm": -2.0},
  {"name": "IF Amplifier", "type": "amp",    "gain_db": 20.0, "nf_db": 5.0, "iip3_dbm": 20.0, "p1db_dbm": 10.0},
  {"name": "IF Filter",    "type": "filter", "gain_db": -2.0, "nf_db": 2.0}
]

For each stage, the values given as iip3_dbm and p1db_dbm are input-referred. Filters, attenuators and switches are treated as linear (IIP3 = +99 dBm) unless you give them an IIP3 of at least 50 dBm, and their noise figure should equal their insertion loss.

The specs for this example: NF ≤ 2.5 dB, gain ≥ 24 dB, input IIP3 ≥ −12 dBm, in a 1 MHz noise bandwidth.

Nominal Cascade Results

The chain misses its NF spec by 0.55 dB before any tolerance is applied.

Where the Noise Comes From

The per-stage table shows the cascade building up:

The IF amplifier adds almost a full decibel. The mixer's 6 dB conversion loss leaves only 7.5 dB of gain ahead of the IF amplifier, so its 5 dB noise figure is barely suppressed. The tool's contribution breakdown agrees: the LNA accounts for 70 % of the cascaded noise factor, the IF amplifier 19 % and the mixer 10 %.

Linearity is the opposite story. The mixer, behind 13.5 dB of gain, is the limiting stage: the input IIP3 barely moves from the LNA's −5 dBm until the mixer, then settles at −6.66 dBm.

P1dB From the Stages, Not From IIP3

A common shortcut takes P1dB as IIP3 − 10 dB. For this chain that gives −16.7 dBm. The tool cascades each stage's own P1dB with the same reciprocal rule as IIP3 and gets −18.3 dBm: the mixer's P1dB sits 14 dB below its IIP3, not 10. Output P1dB is the input P1dB plus the chain gain, less the 1 dB of compression that defines it: −18.3 + 25.5 − 1 = +6.2 dBm.

Monte Carlo: From Nominal to Production Yield

The Monte Carlo perturbs every stage at once — gain (σ = 0.5 dB), noise figure of active stages (σ = 0.3 dB) and IIP3 (σ = 2 dB) — and reruns the full cascade for each trial: 200,000 trials on a paid account, 50,000 on the free tier.

Overall yield — all three specs at once — is 3.5 %. Nearly every board fails noise figure.

Improving Yield

Three changes, each run in the tool:

A quieter IF amplifier alone lands exactly on the spec — so half the boards fail. More LNA gain fixes the noise figure but costs 3.7 dB of IIP3: the IIP3 yield drops to 82 % and the overall yield stops at 77 %. That's the fundamental cascade trade-off in one row. The balanced fix improves both noisy stages and leaves the linearity alone: 84 % overall, with the remaining losses coming from the gain spec.

SFDR and the Dynamic Range Constraint

Cascaded IIP3 and the noise floor set the spurious-free dynamic range:

with $P_{floor} = -174 + 10\log_{10}(B) + NF$ = −110.95 dBm for 1 MHz and 3.05 dB. Two interferers at −45 dBm each produce third-order products at

input-referred — below the noise floor, so they don't desensitize the receiver. At −30 dBm each they would reach −76.7 dBm, 34 dB above it.

Updated 2026-09-19. The analyzer now cascades P1dB from each stage's own P1dB instead of assuming IIP3 − 10 dB, and the stage list above uses its real input format. The earlier example's cascaded figures and yields did not match the tool; these do. RF Cascade Budget Analyzer