Documentation sections

PLL Loop Filter Designer

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

Slug pll-loop-filter. Design a type-2 second-order PLL passive loop filter. Calculates time constants, capacitor and resistor values for target loop bandwidth and phase margin.

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 pll-loop-filter
Name	Unit	Range	Default	Description
fRefnumber	kHz	at least 0.001	100	Reference (comparison) frequency at phase detector input
loopBWnumber	kHz	at least 0.001	5	Desired closed-loop bandwidth (crossover frequency). Typically 1/10 to 1/100 of reference frequency.
phaseMarginnumber	deg	10 … 89	45	Desired phase margin for loop stability. 45° provides good transient response.
kvconumber	MHz/V	at least 0.001	20	VCO frequency tuning gain (sensitivity). From VCO datasheet.
nnumber	none	at least 1	100	Feedback divider ratio N. f_out = N × f_ref.
icpnumber	μA	1 … 10000	500	Charge pump output current. From PLL IC datasheet.
eSeriesnumber	none	0 … 96	0	Rounds every part to the nearest value in the series; the response and the export are the rounded design's.One of: 0 Ideal values · 12 E12 (10%) · 24 E24 (5%) · 48 E48 (2%) · 96 E96 (1%)

Outputs

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

Outputs of pll-loop-filter
Field	Unit	Description
c1headline	nF	Primary integrating capacitor. Determines loop gain.
r1	kΩ	Resistor in series with C1. Sets the stabilizing zero.
c2	pF	Secondary capacitor, γ·C1, where γ = T3/T1 is at most 0.1 and smaller for high phase margins. Provides high-frequency spur filtering.
pmActual	°	Computed phase margin at the crossover frequency; with a part series, the rounded parts' margin at the frequency where their loop crosses 0 dB.
bwRatio	none	Loop bandwidth to reference frequency ratio. Should be < 0.1 for low spurs.
crossoverBuilt	kHz	Where the open-loop gain of the loop these parts build crosses 0 dB, in the model the filter is designed with; the loop bandwidth entered with ideal values

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": "pll-loop-filter",
    "inputs": {
      "fRef": 100,
      "loopBW": 5,
      "phaseMargin": 45,
      "kvco": 20,
      "n": 100,
      "icp": 500,
      "eSeries": 0
    }
  }'

import rftools

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

result = client.calculate("pll-loop-filter", {
    "fRef": 100,
    "loopBW": 5,
    "phaseMargin": 45,
    "kvco": 20,
    "n": 100,
    "icp": 500,
    "eSeries": 0,
})
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": "pll-loop-filter",
    "inputs": {
      "fRef": 100,
      "loopBW": 5,
      "phaseMargin": 45,
      "kvco": 20,
      "n": 100,
      "icp": 500,
      "eSeries": 0
    }
  }),
});
console.log(response.status, await response.json());

package main

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

func main() {
	body := []byte(`{
	  "slug": "pll-loop-filter",
	  "inputs": {
	    "fRef": 100,
	    "loopBW": 5,
	    "phaseMargin": 45,
	    "kvco": 20,
	    "n": 100,
	    "icp": 500,
	    "eSeries": 0
	  }
	}`)
	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": "pll-loop-filter",
  "values": {
    "c1": 623.4225133057242,
    "c2": 62342.25133057242,
    "r1": 0.3932298415799784,
    "pmActual": 45,
    "bwRatio": 0.05,
    "crossoverBuilt": 5
  },
  "warnings": [],
  "errors": [],
  "provenance": {
    "method": "calculator:pll-loop-filter",
    "version": "api@3f2c1a9b04de",
    "formulaRef": null,
    "assumptions": [],
    "validRange": {
      "status": "inside",
      "bounds": {
        "fRef": {
          "min": 0.001,
          "max": null,
          "unit": "kHz"
        },
        "loopBW": {
          "min": 0.001,
          "max": null,
          "unit": "kHz"
        },
        "phaseMargin": {
          "min": 10,
          "max": 89,
          "unit": "deg"
        },
        "kvco": {
          "min": 0.001,
          "max": null,
          "unit": "MHz/V"
        },
        "n": {
          "min": 1,
          "max": null,
          "unit": ""
        },
        "icp": {
          "min": 1,
          "max": 10000,
          "unit": "μA"
        },
        "eSeries": {
          "min": 0,
          "max": 96,
          "unit": ""
        }
      },
      "outside": [],
      "model": null
    },
    "computedAt": "2026-09-24T14:05:11.003Z",
    "inputs": {
      "fRef": 100,
      "loopBW": 5,
      "phaseMargin": 45,
      "kvco": 20,
      "n": 100,
      "icp": 500,
      "eSeries": 0
    },
    "seed": null,
    "elapsedSeconds": 0.003
  }
}

{
  "detail": [
    {
      "type": "float_parsing",
      "loc": [
        "body",
        "inputs",
        "fRef"
      ],
      "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 pagePLL Loop Filter Designer, at these values