Documentation sections

Phase Noise Under Vibrations Calculator

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

Slug vibration-phase-noise. Calculate vibration-induced phase noise for oscillators using acceleration sensitivity (Gamma). Analyze sinusoidal and random vibration profiles. 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 vibration-phase-noise
Name	Unit	Range	Default	Description
carrierFreqnumber	GHz	at least 0.001	10	Oscillator carrier frequency in GHz
vibSensitivitynumber	ppb/g	0.001 … 100	1	Oscillator acceleration sensitivity (Gamma) in parts per billion per g
vibAccelnumber	g rms	0.001 … 50	1	RMS vibration acceleration level in g
vibFreqnumber	Hz	1 … 10000	100	Vibration frequency or offset frequency at which to evaluate phase noise
offsetBandLownumber	Hz	at least 0.001	1000	Where the offsets from the carrier that matter start: a radar's Doppler band (1 to 10 kHz is 15 to 150 m/s at 10 GHz), or a receiver's close-in band
offsetBandHighnumber	Hz	at least 0.001	10000	Where the offset band ends

Outputs

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

Outputs of vibration-phase-noise
Field	Unit	Description
lvibheadline	dBc	Sinusoidal Vibration Sideband at ±f_vib
lRandom	dBc/Hz	Phase noise from a flat random-vibration PSD G = a²/(f_vib − 10 Hz), evaluated at the offset f = f_vib
freqDev	Hz	Γ·a_pk·f₀, with the peak acceleration a_pk = √2 × the rms input
degradation	dB	Degradation vs Quiescent
sidebandsInBand	none	Sidebands at ±f_vib, ±2·f_vib and ±3·f_vib inside the offset band, where they read as false targets or close-in noise

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": "vibration-phase-noise",
    "inputs": {
      "carrierFreq": 10,
      "vibSensitivity": 1,
      "vibAccel": 1,
      "vibFreq": 100,
      "offsetBandLow": 1000,
      "offsetBandHigh": 10000
    }
  }'

import rftools

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

result = client.calculate("vibration-phase-noise", {
    "carrierFreq": 10,
    "vibSensitivity": 1,
    "vibAccel": 1,
    "vibFreq": 100,
    "offsetBandLow": 1000,
    "offsetBandHigh": 10000,
})
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": "vibration-phase-noise",
    "inputs": {
      "carrierFreq": 10,
      "vibSensitivity": 1,
      "vibAccel": 1,
      "vibFreq": 100,
      "offsetBandLow": 1000,
      "offsetBandHigh": 10000
    }
  }),
});
console.log(response.status, await response.json());

package main

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

func main() {
	body := []byte(`{
	  "slug": "vibration-phase-noise",
	  "inputs": {
	    "carrierFreq": 10,
	    "vibSensitivity": 1,
	    "vibAccel": 1,
	    "vibFreq": 100,
	    "offsetBandLow": 1000,
	    "offsetBandHigh": 10000
	  }
	}`)
	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": "vibration-phase-noise",
  "values": {
    "lvib": -23.010299956639813,
    "lRandom": -42.552725051033065,
    "freqDev": 14.142135623730953,
    "degradation": 96.98970004336019,
    "sidebandsInBand": 0
  },
  "warnings": [],
  "errors": [],
  "provenance": {
    "method": "calculator:vibration-phase-noise",
    "version": "api@3f2c1a9b04de",
    "formulaRef": "Filler, \"The acceleration sensitivity of quartz crystal oscillators: a review\", IEEE Trans. UFFC 35(3), 1988; Vig, \"Quartz Crystal Resonators and Oscillators\"; IEEE 1139",
    "assumptions": [],
    "validRange": {
      "status": "inside",
      "bounds": {
        "carrierFreq": {
          "min": 0.001,
          "max": null,
          "unit": "GHz"
        },
        "vibSensitivity": {
          "min": 0.001,
          "max": 100,
          "unit": "ppb/g"
        },
        "vibAccel": {
          "min": 0.001,
          "max": 50,
          "unit": "g rms"
        },
        "vibFreq": {
          "min": 1,
          "max": 10000,
          "unit": "Hz"
        },
        "offsetBandLow": {
          "min": 0.001,
          "max": null,
          "unit": "Hz"
        },
        "offsetBandHigh": {
          "min": 0.001,
          "max": null,
          "unit": "Hz"
        }
      },
      "outside": [],
      "model": null
    },
    "computedAt": "2026-09-24T14:05:11.003Z",
    "inputs": {
      "carrierFreq": 10,
      "vibSensitivity": 1,
      "vibAccel": 1,
      "vibFreq": 100,
      "offsetBandLow": 1000,
      "offsetBandHigh": 10000
    },
    "seed": null,
    "elapsedSeconds": 0.003
  }
}

{
  "detail": [
    {
      "type": "float_parsing",
      "loc": [
        "body",
        "inputs",
        "carrierFreq"
      ],
      "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 pagePhase Noise Under Vibrations Calculator, at these values