Documentation sections

Cascaded Noise Figure Calculator

POSThttps://rftools.io/api/py/v1/calculate

Slug noise-figure-cascade. Calculate cascaded noise figure and IP3 for multi-stage RF receiver chains using the Friis formula. Optimize LNA and filter ordering. Free, instant results.

Inputs

Send every one of these in inputs, in the units shown. Most are required: a call without one is refused (400) and costs nothing; one the calculator can do without takes the default shown. An input outside its range is still computed and flagged in the provenance.

Inputs of noise-figure-cascade
Name	Unit	Range	Default	Description
numStagesnumber	none	1 … 10	3	Number of cascaded RF stages (1–10)
stage1NFnumber	dB	0 … 30	1.5	Noise figure of stage 1 (typically the LNA)
stage1Gainnumber	dB	−20 … 40	15	Gain of stage 1
stage1IIP3number	dBm	−40 … 50	-5	Input third-order intercept point of stage 1 (LNA). Typical LNA: −5 to +10 dBm.
stage2NFnumber	dB	0 … 30	8	Noise figure of stage 2 (e.g. mixer)
stage2Gainnumber	dB	−20 … 40	-6	Gain of stage 2 (may be negative for a mixer)
stage2IIP3number	dBm	−40 … 50	10	Input third-order intercept point of stage 2 (e.g. mixer). Typical passive mixer: +10 to +20 dBm.
stage3NFnumber	dB	0 … 30	6	Noise figure of stage 3 (e.g. IF amplifier)
stage3Gainnumber	dB	−20 … 40	20	Gain of stage 3
stage3IIP3number	dBm	−40 … 50	20	Input third-order intercept point of stage 3 (IF amplifier). Typical: +15 to +25 dBm.
stage4NFnumber	dB	0 … 30	3	Noise figure of stage 4
stage4Gainnumber	dB	−20 … 40	10	Gain of stage 4
stage4IIP3number	dBm	−40 … 50	25	Input third-order intercept point of stage 4.
stage5NFnumber	dB	0 … 30	3	Noise figure of stage 5
stage5Gainnumber	dB	−20 … 40	10	Gain of stage 5
stage5IIP3number	dBm	−40 … 50	25	Input third-order intercept point of stage 5.
stage6NFnumber	dB	0 … 30	3	Noise figure of stage 6
stage6Gainnumber	dB	−20 … 40	10	Gain of stage 6
stage6IIP3number	dBm	−40 … 50	25	Input third-order intercept point of stage 6.
stage7NFnumber	dB	0 … 30	3	Noise figure of stage 7
stage7Gainnumber	dB	−20 … 40	10	Gain of stage 7
stage7IIP3number	dBm	−40 … 50	25	Input third-order intercept point of stage 7.
stage8NFnumber	dB	0 … 30	3	Noise figure of stage 8
stage8Gainnumber	dB	−20 … 40	10	Gain of stage 8
stage8IIP3number	dBm	−40 … 50	25	Input third-order intercept point of stage 8.
stage9NFnumber	dB	0 … 30	3	Noise figure of stage 9
stage9Gainnumber	dB	−20 … 40	10	Gain of stage 9
stage9IIP3number	dBm	−40 … 50	25	Input third-order intercept point of stage 9.
stage10NFnumber	dB	0 … 30	3	Noise figure of stage 10
stage10Gainnumber	dB	−20 … 40	10	Gain of stage 10
stage10IIP3number	dBm	−40 … 50	25	Input third-order intercept point of stage 10.
bandwidthnumber	MHz	0.000001 … 100000	1	The bandwidth the noise floor is given in: kT₀B at 290 K plus the cascaded noise figure. Changes no other result.

Outputs

Returned in values, by key. A value that is unbounded or undefined is null.

Outputs of noise-figure-cascade
Field	Unit	Description
cascadedNFheadline	dB	Total cascaded noise figure of the signal chain
cascadedF	none	Total cascaded noise factor (linear)
stage1Contribution	dB	Noise figure contribution from stage 1
stage2Contribution	dB	Noise figure contribution of stage 2 (referred to input)
stage3Contribution	dB	Noise figure contribution of stage 3 (referred to input)
cascadedIIP3	dBm	Input-referred third-order intercept point of the cascade. Higher is better (less intermodulation distortion).
cascadedOIP3	dBm	Output-referred third-order intercept point. OIP3 = IIP3 + cascaded gain.
cascadedGain	dB	Sum of the stage gains in dB
noiseTemperature	K	T_e = 290 K × (F − 1), the input-referred noise temperature of the chain
noiseFloor	dBm	Input-referred noise power in the noise bandwidth: 10·log₁₀(k·290 K·B) + NF

Calling it

Calculate: one call, the request and response in full, and its errors.
Batch: this calculator with others, or a sweep, in one request.
Solve for a target: the value of one input that brings an output to a target.

curl -X POST https://rftools.io/api/py/v1/calculate \
  -H "X-API-Key: $RFTOOLS_API_KEY" \
  -H "Content-Type: application/json" \
  -d '{
    "slug": "noise-figure-cascade",
    "inputs": {
      "numStages": 3,
      "stage1NF": 1.5,
      "stage1Gain": 15,
      "stage1IIP3": -5,
      "stage2NF": 8,
      "stage2Gain": -6,
      "stage2IIP3": 10,
      "stage3NF": 6,
      "stage3Gain": 20,
      "stage3IIP3": 20,
      "stage4NF": 3,
      "stage4Gain": 10,
      "stage4IIP3": 25,
      "stage5NF": 3,
      "stage5Gain": 10,
      "stage5IIP3": 25,
      "stage6NF": 3,
      "stage6Gain": 10,
      "stage6IIP3": 25,
      "stage7NF": 3,
      "stage7Gain": 10,
      "stage7IIP3": 25,
      "stage8NF": 3,
      "stage8Gain": 10,
      "stage8IIP3": 25,
      "stage9NF": 3,
      "stage9Gain": 10,
      "stage9IIP3": 25,
      "stage10NF": 3,
      "stage10Gain": 10,
      "stage10IIP3": 25,
      "bandwidth": 1
    }
  }'

import rftools

client = rftools.Client()  # reads RFTOOLS_API_KEY, or the key `rftools login` saved

result = client.calculate("noise-figure-cascade", {
    "numStages": 3,
    "stage1NF": 1.5,
    "stage1Gain": 15,
    "stage1IIP3": -5,
    "stage2NF": 8,
    "stage2Gain": -6,
    "stage2IIP3": 10,
    "stage3NF": 6,
    "stage3Gain": 20,
    "stage3IIP3": 20,
    "stage4NF": 3,
    "stage4Gain": 10,
    "stage4IIP3": 25,
    "stage5NF": 3,
    "stage5Gain": 10,
    "stage5IIP3": 25,
    "stage6NF": 3,
    "stage6Gain": 10,
    "stage6IIP3": 25,
    "stage7NF": 3,
    "stage7Gain": 10,
    "stage7IIP3": 25,
    "stage8NF": 3,
    "stage8Gain": 10,
    "stage8IIP3": 25,
    "stage9NF": 3,
    "stage9Gain": 10,
    "stage9IIP3": 25,
    "stage10NF": 3,
    "stage10Gain": 10,
    "stage10IIP3": 25,
    "bandwidth": 1,
})
print(result.values)
print(result.warnings, result.provenance.formula_ref)

const response = await fetch("https://rftools.io/api/py/v1/calculate", {
  method: "POST",
  headers: {
    "X-API-Key": process.env.RFTOOLS_API_KEY,
    "Content-Type": "application/json",
  },
  body: JSON.stringify({
    "slug": "noise-figure-cascade",
    "inputs": {
      "numStages": 3,
      "stage1NF": 1.5,
      "stage1Gain": 15,
      "stage1IIP3": -5,
      "stage2NF": 8,
      "stage2Gain": -6,
      "stage2IIP3": 10,
      "stage3NF": 6,
      "stage3Gain": 20,
      "stage3IIP3": 20,
      "stage4NF": 3,
      "stage4Gain": 10,
      "stage4IIP3": 25,
      "stage5NF": 3,
      "stage5Gain": 10,
      "stage5IIP3": 25,
      "stage6NF": 3,
      "stage6Gain": 10,
      "stage6IIP3": 25,
      "stage7NF": 3,
      "stage7Gain": 10,
      "stage7IIP3": 25,
      "stage8NF": 3,
      "stage8Gain": 10,
      "stage8IIP3": 25,
      "stage9NF": 3,
      "stage9Gain": 10,
      "stage9IIP3": 25,
      "stage10NF": 3,
      "stage10Gain": 10,
      "stage10IIP3": 25,
      "bandwidth": 1
    }
  }),
});
console.log(response.status, await response.json());

package main

import (
	"bytes"
	"fmt"
	"io"
	"net/http"
	"os"
)

func main() {
	body := []byte(`{
	  "slug": "noise-figure-cascade",
	  "inputs": {
	    "numStages": 3,
	    "stage1NF": 1.5,
	    "stage1Gain": 15,
	    "stage1IIP3": -5,
	    "stage2NF": 8,
	    "stage2Gain": -6,
	    "stage2IIP3": 10,
	    "stage3NF": 6,
	    "stage3Gain": 20,
	    "stage3IIP3": 20,
	    "stage4NF": 3,
	    "stage4Gain": 10,
	    "stage4IIP3": 25,
	    "stage5NF": 3,
	    "stage5Gain": 10,
	    "stage5IIP3": 25,
	    "stage6NF": 3,
	    "stage6Gain": 10,
	    "stage6IIP3": 25,
	    "stage7NF": 3,
	    "stage7Gain": 10,
	    "stage7IIP3": 25,
	    "stage8NF": 3,
	    "stage8Gain": 10,
	    "stage8IIP3": 25,
	    "stage9NF": 3,
	    "stage9Gain": 10,
	    "stage9IIP3": 25,
	    "stage10NF": 3,
	    "stage10Gain": 10,
	    "stage10IIP3": 25,
	    "bandwidth": 1
	  }
	}`)
	req, err := http.NewRequest("POST", "https://rftools.io/api/py/v1/calculate", bytes.NewReader(body))
	if err != nil {
		panic(err)
	}
	req.Header.Set("X-API-Key", os.Getenv("RFTOOLS_API_KEY"))
	req.Header.Set("Content-Type", "application/json")
	res, err := http.DefaultClient.Do(req)
	if err != nil {
		panic(err)
	}
	defer res.Body.Close()
	out, _ := io.ReadAll(res.Body)
	fmt.Println(res.Status, string(out))
}

application/json

{
  "slug": "noise-figure-cascade",
  "values": {
    "cascadedNF": 2.9131016165970944,
    "cascadedF": 1.955735691965814,
    "stage1Contribution": 1.5000000000000002,
    "stage2Contribution": 0.6740694317085234,
    "stage3Contribution": 1.383957669598209,
    "cascadedIIP3": -8.064505192055673,
    "cascadedOIP3": 20.935494807944327,
    "cascadedGain": 29,
    "noiseTemperature": 277.16335067008606,
    "noiseFloor": -111.06208557763102
  },
  "warnings": [],
  "errors": [],
  "provenance": {
    "method": "calculator:noise-figure-cascade",
    "version": "api@3f2c1a9b04de",
    "formulaRef": "Friis, \"Noise Figures of Radio Receivers\" (1944); Pozar Chapter 10; Razavi \"RF Microelectronics\"",
    "assumptions": [],
    "validRange": {
      "status": "inside",
      "bounds": {
        "numStages": {
          "min": 1,
          "max": 10,
          "unit": ""
        },
        "stage1NF": {
          "min": 0,
          "max": 30,
          "unit": "dB"
        },
        "stage1Gain": {
          "min": -20,
          "max": 40,
          "unit": "dB"
        },
        "stage1IIP3": {
          "min": -40,
          "max": 50,
          "unit": "dBm"
        },
        "stage2NF": {
          "min": 0,
          "max": 30,
          "unit": "dB"
        },
        "stage2Gain": {
          "min": -20,
          "max": 40,
          "unit": "dB"
        },
        "stage2IIP3": {
          "min": -40,
          "max": 50,
          "unit": "dBm"
        },
        "stage3NF": {
          "min": 0,
          "max": 30,
          "unit": "dB"
        },
        "stage3Gain": {
          "min": -20,
          "max": 40,
          "unit": "dB"
        },
        "stage3IIP3": {
          "min": -40,
          "max": 50,
          "unit": "dBm"
        },
        "stage4NF": {
          "min": 0,
          "max": 30,
          "unit": "dB"
        },
        "stage4Gain": {
          "min": -20,
          "max": 40,
          "unit": "dB"
        },
        "stage4IIP3": {
          "min": -40,
          "max": 50,
          "unit": "dBm"
        },
        "stage5NF": {
          "min": 0,
          "max": 30,
          "unit": "dB"
        },
        "stage5Gain": {
          "min": -20,
          "max": 40,
          "unit": "dB"
        },
        "stage5IIP3": {
          "min": -40,
          "max": 50,
          "unit": "dBm"
        },
        "stage6NF": {
          "min": 0,
          "max": 30,
          "unit": "dB"
        },
        "stage6Gain": {
          "min": -20,
          "max": 40,
          "unit": "dB"
        },
        "stage6IIP3": {
          "min": -40,
          "max": 50,
          "unit": "dBm"
        },
        "stage7NF": {
          "min": 0,
          "max": 30,
          "unit": "dB"
        },
        "stage7Gain": {
          "min": -20,
          "max": 40,
          "unit": "dB"
        },
        "stage7IIP3": {
          "min": -40,
          "max": 50,
          "unit": "dBm"
        },
        "stage8NF": {
          "min": 0,
          "max": 30,
          "unit": "dB"
        },
        "stage8Gain": {
          "min": -20,
          "max": 40,
          "unit": "dB"
        },
        "stage8IIP3": {
          "min": -40,
          "max": 50,
          "unit": "dBm"
        },
        "stage9NF": {
          "min": 0,
          "max": 30,
          "unit": "dB"
        },
        "stage9Gain": {
          "min": -20,
          "max": 40,
          "unit": "dB"
        },
        "stage9IIP3": {
          "min": -40,
          "max": 50,
          "unit": "dBm"
        },
        "stage10NF": {
          "min": 0,
          "max": 30,
          "unit": "dB"
        },
        "stage10Gain": {
          "min": -20,
          "max": 40,
          "unit": "dB"
        },
        "stage10IIP3": {
          "min": -40,
          "max": 50,
          "unit": "dBm"
        },
        "bandwidth": {
          "min": 0.000001,
          "max": 100000,
          "unit": "MHz"
        }
      },
      "outside": [],
      "model": null
    },
    "computedAt": "2026-09-24T14:05:11.003Z",
    "inputs": {
      "numStages": 3,
      "stage1NF": 1.5,
      "stage1Gain": 15,
      "stage1IIP3": -5,
      "stage2NF": 8,
      "stage2Gain": -6,
      "stage2IIP3": 10,
      "stage3NF": 6,
      "stage3Gain": 20,
      "stage3IIP3": 20,
      "stage4NF": 3,
      "stage4Gain": 10,
      "stage4IIP3": 25,
      "stage5NF": 3,
      "stage5Gain": 10,
      "stage5IIP3": 25,
      "stage6NF": 3,
      "stage6Gain": 10,
      "stage6IIP3": 25,
      "stage7NF": 3,
      "stage7Gain": 10,
      "stage7IIP3": 25,
      "stage8NF": 3,
      "stage8Gain": 10,
      "stage8IIP3": 25,
      "stage9NF": 3,
      "stage9Gain": 10,
      "stage9IIP3": 25,
      "stage10NF": 3,
      "stage10Gain": 10,
      "stage10IIP3": 25,
      "bandwidth": 1
    },
    "seed": null,
    "elapsedSeconds": 0.003
  }
}

{
  "detail": [
    {
      "type": "float_parsing",
      "loc": [
        "body",
        "inputs",
        "numStages"
      ],
      "msg": "Input should be a valid number, unable to parse string as a number",
      "input": "abc"
    }
  ]
}

An input sent as text. Nothing was counted.

{
  "detail": "More than 120 requests in 60 seconds from this address.",
  "errorKind": "rate_limited",
  "limit": 120,
  "windowSeconds": 60,
  "upgradeUrl": "https://rftools.io/pricing/"
}

Too many requests in a minute, with Retry-After.

Same inputs on the calculator pageCascaded Noise Figure Calculator, at these values