Documentation sections

Edge-Coupled Embedded Microstrip Calculator

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

Slug edge-coupled-embedded. Calculate differential and common-mode impedance for an edge-coupled pair under soldermask, coating or prepreg — with a separate effective permittivity per mode, so the skew the cover introduces is visible.

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 edge-coupled-embedded
Name	Unit	Range	Default	Description
traceWidthnumber	mm	0.02 … 10	0.2	Trace Width
traceSpacingnumber	mm	0.02 … 10	0.2	Trace Spacing (edge to edge)
substrateHeightnumber	mm	at least 0.02	0.2	Dielectric between the traces and the reference plane below
coverThicknessnumber	mm	at least 0	0.025	Soldermask, coating or prepreg over the traces. Zero gives a bare surface pair.
coverDielectricnumber	none	at least 1	3.5	Cover Dielectric Constant
copperThicknessnumber	μm	at least 5	35	Copper Thickness
dielectricConstnumber	none	at least 1	4.2	Substrate Dielectric Constant
frequencynumber	GHz	0.001 … 300	2.4	Used only for the guided wavelength of the differential (odd) mode; 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 edge-coupled-embedded
Field	Unit	Description
diffImpedanceheadline	Ω	Differential Impedance
commonImpedance	Ω	Common-Mode Impedance
oddImpedance	Ω	Odd-Mode Impedance
evenImpedance	Ω	Even-Mode Impedance
uncoupledImpedance	Ω	Single Trace Without Its Partner
erEffOdd	none	Odd-Mode Effective Er
erEffEven	none	Differs from the odd mode because the two modes put different amounts of field in the air above the cover
propagationDelay	ps/mm	Propagation Delay (odd mode)
propagationDelayEven	ps/mm	The gap between the two is the mode skew that converts differential signal into common mode
inValidatedRange	none	1 when the geometry lies inside the range the model was checked against a field solver
guidedWavelength	mm	Wavelength of the differential (odd) mode on the pair at the frequency, c/(f·√εeff,odd)
quarterWavelength	mm	Quarter Wavelength (odd mode)

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": "edge-coupled-embedded",
    "inputs": {
      "traceWidth": 0.2,
      "traceSpacing": 0.2,
      "substrateHeight": 0.2,
      "coverThickness": 0.025,
      "coverDielectric": 3.5,
      "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("edge-coupled-embedded", {
    "traceWidth": 0.2,
    "traceSpacing": 0.2,
    "substrateHeight": 0.2,
    "coverThickness": 0.025,
    "coverDielectric": 3.5,
    "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": "edge-coupled-embedded",
    "inputs": {
      "traceWidth": 0.2,
      "traceSpacing": 0.2,
      "substrateHeight": 0.2,
      "coverThickness": 0.025,
      "coverDielectric": 3.5,
      "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": "edge-coupled-embedded",
	  "inputs": {
	    "traceWidth": 0.2,
	    "traceSpacing": 0.2,
	    "substrateHeight": 0.2,
	    "coverThickness": 0.025,
	    "coverDielectric": 3.5,
	    "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": "edge-coupled-embedded",
  "values": {
    "diffImpedance": 107.4493991345428,
    "commonImpedance": 36.883126735598346,
    "oddImpedance": 53.7246995672714,
    "evenImpedance": 73.76625347119669,
    "uncoupledImpedance": 64.08472525189151,
    "erEffOdd": 3.1222600711428257,
    "erEffEven": 3.4717326408569606,
    "propagationDelay": 5.89405025697189,
    "propagationDelayEven": 6.215161717487868,
    "inValidatedRange": 1,
    "guidedWavelength": 70.69275769642525,
    "quarterWavelength": 17.67318942410631
  },
  "warnings": [
    "The two modes travel at different speeds (0.321 ps/mm apart), so this pair converts differential energy into common mode over length — a stripline pair does not"
  ],
  "errors": [],
  "provenance": {
    "method": "calculator:edge-coupled-embedded",
    "version": "api@3f2c1a9b04de",
    "formulaRef": "Filling factors fitted to the layered method-of-moments solver committed in src/lib/pcb/__tests__/solver, which reproduces Hammerstad–Jensen to 0.1% and the fully-embedded limit to 0.005%.",
    "assumptions": [],
    "validRange": {
      "status": "inside",
      "bounds": {
        "traceWidth": {
          "min": 0.02,
          "max": 10,
          "unit": "mm"
        },
        "traceSpacing": {
          "min": 0.02,
          "max": 10,
          "unit": "mm"
        },
        "substrateHeight": {
          "min": 0.02,
          "max": null,
          "unit": "mm"
        },
        "coverThickness": {
          "min": 0,
          "max": null,
          "unit": "mm"
        },
        "coverDielectric": {
          "min": 1,
          "max": null,
          "unit": ""
        },
        "copperThickness": {
          "min": 5,
          "max": null,
          "unit": "μm"
        },
        "dielectricConst": {
          "min": 1,
          "max": null,
          "unit": ""
        },
        "frequency": {
          "min": 0.001,
          "max": 300,
          "unit": "GHz"
        }
      },
      "outside": [],
      "model": {
        "description": "trace width 0.2–4× and spacing 0.1–3× the substrate height",
        "worstCaseError": 0.02,
        "inside": true
      }
    },
    "computedAt": "2026-09-24T14:05:11.003Z",
    "inputs": {
      "traceWidth": 0.2,
      "traceSpacing": 0.2,
      "substrateHeight": 0.2,
      "coverThickness": 0.025,
      "coverDielectric": 3.5,
      "copperThickness": 35,
      "dielectricConst": 4.2,
      "frequency": 2.4
    },
    "seed": null,
    "elapsedSeconds": 0.003
  }
}

{
  "detail": [
    {
      "type": "float_parsing",
      "loc": [
        "body",
        "inputs",
        "traceWidth"
      ],
      "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 pageEdge-Coupled Embedded Microstrip Calculator, at these values