Documentation sections

Digital Filter Order Calculator

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

Slug digital-filter-order. Calculate minimum filter order for Butterworth, Chebyshev, and elliptic designs. Determine order from passband ripple and stopband attenuation specs. 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 digital-filter-order
Name	Unit	Range	Default	Description
passbandFreqnumber	Hz	at least 1	1000	Frequency where passband ripple specification is met
stopbandFreqnumber	Hz	at least 1	2000	Frequency where stopband attenuation must be achieved
passbandRipplenumber	dB	at least 0.01	3	Maximum allowed ripple in the passband (typically 0.1–3 dB)
stopbandAttenuationnumber	dB	at least 1	40	Minimum attenuation required in the stopband
toneFreqnumber	Hz	at least 0.001	1000	A tone the filter must pass while it rejects the tone's harmonics: a transmitter's carrier, the mains fundamental, a test tone
maxHarmonicnumber	none	1 … 50	5	The highest harmonic of the tone the frequency plan follows

Outputs

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

Outputs of digital-filter-order
Field	Unit	Description
butterworthOrderheadline	none	Butterworth Order
chebyshevOrder	none	Chebyshev Order
ellipticOrder	none	Elliptic Order
transitionRatio	none	Transition Ratio
harmonicsInPassband	none	Harmonics of the tone, up to the highest, at or below the passband edge: the filter passes them with the tone
harmonicsInTransition	none	Harmonics between the passband and stopband edges: attenuated, but by less than the stopband attenuation is guaranteed
nearestHarmonic	Hz	The lowest harmonic of the tone above the passband edge, up to the highest harmonic; none if every one is in the passband
butterworthAttenuation	dB	What the Butterworth of the order above does to that harmonic: 10·log10(1 + ε_p²·(f/f_p)^2n)
chebyshevAttenuation	dB	What the Chebyshev of the order above does to that harmonic: 10·log10(1 + ε_p²·cosh²(n·acosh(f/f_p)))

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": "digital-filter-order",
    "inputs": {
      "passbandFreq": 1000,
      "stopbandFreq": 2000,
      "passbandRipple": 3,
      "stopbandAttenuation": 40,
      "toneFreq": 1000,
      "maxHarmonic": 5
    }
  }'

import rftools

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

result = client.calculate("digital-filter-order", {
    "passbandFreq": 1000,
    "stopbandFreq": 2000,
    "passbandRipple": 3,
    "stopbandAttenuation": 40,
    "toneFreq": 1000,
    "maxHarmonic": 5,
})
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": "digital-filter-order",
    "inputs": {
      "passbandFreq": 1000,
      "stopbandFreq": 2000,
      "passbandRipple": 3,
      "stopbandAttenuation": 40,
      "toneFreq": 1000,
      "maxHarmonic": 5
    }
  }),
});
console.log(response.status, await response.json());

package main

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

func main() {
	body := []byte(`{
	  "slug": "digital-filter-order",
	  "inputs": {
	    "passbandFreq": 1000,
	    "stopbandFreq": 2000,
	    "passbandRipple": 3,
	    "stopbandAttenuation": 40,
	    "toneFreq": 1000,
	    "maxHarmonic": 5
	  }
	}`)
	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": "digital-filter-order",
  "values": {
    "butterworthOrder": 7,
    "chebyshevOrder": 5,
    "ellipticOrder": 3,
    "transitionRatio": 2,
    "harmonicsInPassband": 0,
    "harmonicsInTransition": 0,
    "nearestHarmonic": 2000,
    "butterworthAttenuation": 42.12384131963093,
    "chebyshevAttenuation": 51.1535803101314
  },
  "warnings": [],
  "errors": [],
  "provenance": {
    "method": "calculator:digital-filter-order",
    "version": "api@3f2c1a9b04de",
    "formulaRef": null,
    "assumptions": [],
    "validRange": {
      "status": "inside",
      "bounds": {
        "passbandFreq": {
          "min": 1,
          "max": null,
          "unit": "Hz"
        },
        "stopbandFreq": {
          "min": 1,
          "max": null,
          "unit": "Hz"
        },
        "passbandRipple": {
          "min": 0.01,
          "max": null,
          "unit": "dB"
        },
        "stopbandAttenuation": {
          "min": 1,
          "max": null,
          "unit": "dB"
        },
        "toneFreq": {
          "min": 0.001,
          "max": null,
          "unit": "Hz"
        },
        "maxHarmonic": {
          "min": 1,
          "max": 50,
          "unit": ""
        }
      },
      "outside": [],
      "model": null
    },
    "computedAt": "2026-09-24T14:05:11.003Z",
    "inputs": {
      "passbandFreq": 1000,
      "stopbandFreq": 2000,
      "passbandRipple": 3,
      "stopbandAttenuation": 40,
      "toneFreq": 1000,
      "maxHarmonic": 5
    },
    "seed": null,
    "elapsedSeconds": 0.003
  }
}

{
  "detail": [
    {
      "type": "float_parsing",
      "loc": [
        "body",
        "inputs",
        "passbandFreq"
      ],
      "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 pageDigital Filter Order Calculator, at these values