Documentation sections

Edge-Coupled Internal Symmetric Stripline Calculator

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

Slug edge-coupled-internal-symmetric. Calculate differential, common-mode, odd- and even-mode impedance for an edge-coupled differential pair centred between two reference planes. Exact conformal-mapping solution, not an empirical fit.

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-internal-symmetric
Name	Unit	Range	Default	Description
traceWidthnumber	mm	0.02 … 10	0.15	Trace Width
traceSpacingnumber	mm	0.02 … 10	0.2	Gap between the facing edges of the two traces
planeSpacingnumber	mm	at least 0.05	0.6	Total dielectric height between the two reference planes
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 edge-coupled-internal-symmetric
Field	Unit	Description
diffImpedanceheadline	Ω	Differential Impedance
commonImpedance	Ω	Common-Mode Impedance
oddImpedance	Ω	Odd-Mode Impedance
evenImpedance	Ω	Even-Mode Impedance
uncoupledImpedance	Ω	Reference value — the same trace with the other one removed
couplingCoefficient	none	(Z_even − Z_odd)/(Z_even + Z_odd); zero when the traces are uncoupled
propagationDelay	ps/mm	Both modes travel at the same speed in a stripline — the dielectric is homogeneous
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": "edge-coupled-internal-symmetric",
    "inputs": {
      "traceWidth": 0.15,
      "traceSpacing": 0.2,
      "planeSpacing": 0.6,
      "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-internal-symmetric", {
    "traceWidth": 0.15,
    "traceSpacing": 0.2,
    "planeSpacing": 0.6,
    "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-internal-symmetric",
    "inputs": {
      "traceWidth": 0.15,
      "traceSpacing": 0.2,
      "planeSpacing": 0.6,
      "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-internal-symmetric",
	  "inputs": {
	    "traceWidth": 0.15,
	    "traceSpacing": 0.2,
	    "planeSpacing": 0.6,
	    "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-internal-symmetric",
  "values": {
    "diffImpedance": 98.36281821659115,
    "commonImpedance": 31.153436728310847,
    "oddImpedance": 49.181409108295576,
    "evenImpedance": 62.306873456621695,
    "uncoupledImpedance": 56.07425158039217,
    "couplingCoefficient": 0.11772954113526181,
    "propagationDelay": 6.83602972157465,
    "guidedWavelength": 60.95155867325418,
    "quarterWavelength": 15.237889668313546
  },
  "warnings": [],
  "errors": [],
  "provenance": {
    "method": "calculator:edge-coupled-internal-symmetric",
    "version": "api@3f2c1a9b04de",
    "formulaRef": "S. B. Cohn, \"Shielded Coupled-Strip Transmission Line\", IRE Trans. MTT-3 (1955), pp. 29–38. Verified against a 2-D method-of-moments solve to 0.008%.",
    "assumptions": [],
    "validRange": {
      "status": "inside",
      "bounds": {
        "traceWidth": {
          "min": 0.02,
          "max": 10,
          "unit": "mm"
        },
        "traceSpacing": {
          "min": 0.02,
          "max": 10,
          "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": {
      "traceWidth": 0.15,
      "traceSpacing": 0.2,
      "planeSpacing": 0.6,
      "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 Internal Symmetric Stripline Calculator, at these values