Documentation sections

PCB Via Stub Resonance Calculator

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

Slug via-stub-resonance. Calculate via stub resonant frequency, signal notch depth, and backdrill benefit for high-speed PCB design. Optimize stub length. 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 via-stub-resonance
Name	Unit	Range	Default	Description
pcbThicknessnumber	mm	0.1 … 10	1.6	Total PCB board thickness
layernumber	none	1 … 32	4	Layer number where the signal exits the via (counting from top, layer 1)
totalLayersnumber	none	2 … 40	8	Total number of PCB copper layers
ernumber	none	1 … 20	4.3	PCB dielectric constant (FR4 = 4.3–4.8)
dataRatenumber	Gbps	at least 0.1	10	The signal's NRZ bit rate; for PAM4 enter the symbol rate, half the bit rate. Its band runs from DC to the Nyquist frequency, half the rate, and its main lobe to the rate itself

Outputs

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

Outputs of via-stub-resonance
Field	Unit	Description
stubLength	mm	Length of the unused via stub below the signal exit layer
resonantFreqheadline	GHz	Quarter-wave resonant frequency of the via stub — causes signal notch
notchDepth	dB	Approximate signal attenuation notch depth at resonance (~−20 dB)
backdrillBenefit	GHz	Approximate resonance frequency improvement after back-drilling the stub
nyquistFreq	GHz	Half the data rate: the top of the band an NRZ signal needs
resonancesInBand	none	Resonances n·f₀ (n odd) from DC to the Nyquist frequency: each cuts a notch the signal needs
resonancesNearBand	none	Resonances between the Nyquist frequency and the bit rate, where NRZ's spectrum still carries energy up to its first null

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": "via-stub-resonance",
    "inputs": {
      "pcbThickness": 1.6,
      "layer": 4,
      "totalLayers": 8,
      "er": 4.3,
      "dataRate": 10
    }
  }'

import rftools

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

result = client.calculate("via-stub-resonance", {
    "pcbThickness": 1.6,
    "layer": 4,
    "totalLayers": 8,
    "er": 4.3,
    "dataRate": 10,
})
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": "via-stub-resonance",
    "inputs": {
      "pcbThickness": 1.6,
      "layer": 4,
      "totalLayers": 8,
      "er": 4.3,
      "dataRate": 10
    }
  }),
});
console.log(response.status, await response.json());

package main

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

func main() {
	body := []byte(`{
	  "slug": "via-stub-resonance",
	  "inputs": {
	    "pcbThickness": 1.6,
	    "layer": 4,
	    "totalLayers": 8,
	    "er": 4.3,
	    "dataRate": 10
	  }
	}`)
	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": "via-stub-resonance",
  "values": {
    "stubLength": 0.8,
    "resonantFreq": 45.17898781603898,
    "notchDepth": -20,
    "backdrillBenefit": 135.53696344811695,
    "nyquistFreq": 5,
    "resonancesInBand": 0,
    "resonancesNearBand": 0
  },
  "warnings": [],
  "errors": [],
  "provenance": {
    "method": "calculator:via-stub-resonance",
    "version": "api@3f2c1a9b04de",
    "formulaRef": "Eric Bogatin, \"Signal and Power Integrity Simplified\" 3rd ed.",
    "assumptions": [],
    "validRange": {
      "status": "inside",
      "bounds": {
        "pcbThickness": {
          "min": 0.1,
          "max": 10,
          "unit": "mm"
        },
        "layer": {
          "min": 1,
          "max": 32,
          "unit": ""
        },
        "totalLayers": {
          "min": 2,
          "max": 40,
          "unit": ""
        },
        "er": {
          "min": 1,
          "max": 20,
          "unit": ""
        },
        "dataRate": {
          "min": 0.1,
          "max": null,
          "unit": "Gbps"
        }
      },
      "outside": [],
      "model": null
    },
    "computedAt": "2026-09-24T14:05:11.003Z",
    "inputs": {
      "pcbThickness": 1.6,
      "layer": 4,
      "totalLayers": 8,
      "er": 4.3,
      "dataRate": 10
    },
    "seed": null,
    "elapsedSeconds": 0.003
  }
}

{
  "detail": [
    {
      "type": "float_parsing",
      "loc": [
        "body",
        "inputs",
        "pcbThickness"
      ],
      "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 pagePCB Via Stub Resonance Calculator, at these values