Documentation sections

Broadside-Coupled Differential Pair Calculator

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

Slug broadside-coupled-pair. Calculate differential and common-mode impedance for a broadside-coupled pair — two traces stacked on adjacent layers — for both shielded (between planes) and unshielded geometries.

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 broadside-coupled-pair
Name	Unit	Range	Default	Description
shieldednumber	none	0 … 1	1	GeometryOne of: 1 Shielded (between planes) · 0 Unshielded (no planes)
traceWidthnumber	mm	0.02 … 10	0.15	Trace Width
traceSeparationnumber	mm	0.01 … 5	0.2	Dielectric thickness between the two stacked traces
planeSpacingnumber	mm	at least 0.05	1	Shielded geometry only — ignored when no planes are present
copperThicknessnumber	μm	at least 5	35	Copper Thickness
dielectricConstnumber	none	at least 1	4.2	Dielectric Constant
frequencynumber	GHz	0.001 … 300	2.4	Used only for the guided wavelength; the impedances do not depend on it in this model

Outputs

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

Outputs of broadside-coupled-pair
Field	Unit	Description
diffImpedanceheadline	Ω	Differential Impedance
oddImpedance	Ω	Odd-Mode (Single-Ended) Impedance
commonImpedance	Ω	Undefined (reported as 0) for the unshielded geometry
uncoupledImpedance	Ω	Reference value — the same trace with the other layer removed
heightToPlane	mm	Each Trace to Its Nearer Plane
propagationDelay	ps/mm	Propagation Delay
guidedWavelength	mm	Guided Wavelength
quarterWavelength	mm	Quarter Wavelength

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": "broadside-coupled-pair",
    "inputs": {
      "shielded": 1,
      "traceWidth": 0.15,
      "traceSeparation": 0.2,
      "planeSpacing": 1,
      "copperThickness": 35,
      "dielectricConst": 4.2,
      "frequency": 2.4
    }
  }'

import rftools

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

result = client.calculate("broadside-coupled-pair", {
    "shielded": 1,
    "traceWidth": 0.15,
    "traceSeparation": 0.2,
    "planeSpacing": 1,
    "copperThickness": 35,
    "dielectricConst": 4.2,
    "frequency": 2.4,
})
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": "broadside-coupled-pair",
    "inputs": {
      "shielded": 1,
      "traceWidth": 0.15,
      "traceSeparation": 0.2,
      "planeSpacing": 1,
      "copperThickness": 35,
      "dielectricConst": 4.2,
      "frequency": 2.4
    }
  }),
});
console.log(response.status, await response.json());

package main

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

func main() {
	body := []byte(`{
	  "slug": "broadside-coupled-pair",
	  "inputs": {
	    "shielded": 1,
	    "traceWidth": 0.15,
	    "traceSeparation": 0.2,
	    "planeSpacing": 1,
	    "copperThickness": 35,
	    "dielectricConst": 4.2,
	    "frequency": 2.4
	  }
	}`)
	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": "broadside-coupled-pair",
  "values": {
    "diffImpedance": 83.9945342291409,
    "oddImpedance": 41.99726711457045,
    "commonImpedance": 49.35860909148314,
    "uncoupledImpedance": 68.79029737334884,
    "heightToPlane": 0.365,
    "propagationDelay": 6.83602972157465,
    "guidedWavelength": 60.95155867325418,
    "quarterWavelength": 15.237889668313546
  },
  "warnings": [],
  "errors": [],
  "provenance": {
    "method": "calculator:broadside-coupled-pair",
    "version": "api@3f2c1a9b04de",
    "formulaRef": "B. C. Wadell, \"Transmission Line Design Handbook\", Artech House 1991, §4.5 (broadside-coupled lines)",
    "assumptions": [],
    "validRange": {
      "status": "inside",
      "bounds": {
        "shielded": {
          "min": 0,
          "max": 1,
          "unit": ""
        },
        "traceWidth": {
          "min": 0.02,
          "max": 10,
          "unit": "mm"
        },
        "traceSeparation": {
          "min": 0.01,
          "max": 5,
          "unit": "mm"
        },
        "planeSpacing": {
          "min": 0.05,
          "max": null,
          "unit": "mm"
        },
        "copperThickness": {
          "min": 5,
          "max": null,
          "unit": "μm"
        },
        "dielectricConst": {
          "min": 1,
          "max": null,
          "unit": ""
        },
        "frequency": {
          "min": 0.001,
          "max": 300,
          "unit": "GHz"
        }
      },
      "outside": [],
      "model": null
    },
    "computedAt": "2026-09-24T14:05:11.003Z",
    "inputs": {
      "shielded": 1,
      "traceWidth": 0.15,
      "traceSeparation": 0.2,
      "planeSpacing": 1,
      "copperThickness": 35,
      "dielectricConst": 4.2,
      "frequency": 2.4
    },
    "seed": null,
    "elapsedSeconds": 0.003
  }
}

{
  "detail": [
    {
      "type": "float_parsing",
      "loc": [
        "body",
        "inputs",
        "shielded"
      ],
      "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 pageBroadside-Coupled Differential Pair Calculator, at these values