Documentation sections

Directional Coupler Calculator — Coupled-Line Even & Odd Mode Impedance

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

Slug directional-coupler. Design a single-section quarter-wave coupled-line directional coupler: the even- and odd-mode impedances for the coupling you need, the coupled length, the through-path loss and the isolation, with a warning when the coupling is too tight for a single edge-coupled section.

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 directional-coupler
Name	Unit	Range	Default	Description
couplingnumber	dB	at least 0.1	20	Ratio of input power to coupled-port power, in dB (10 dB couples a tenth of the power)
z0number	Ω	at least 1	50	Impedance every port is matched to
frequencynumber	GHz	at least 0.001	3	Frequency at which the coupled section is a quarter wavelength long and the coupling peaks
effPermittivitynumber	none	at least 1	2.2	Effective permittivity of the coupled section; equal to εr in stripline
directivitynumber	dB	at least 0	30	Coupled-port power over isolated-port power, in dB; set by layout and mode-velocity balance, not by this design
couplingLimitnumber	dB	at least 0	8	Couplings tighter than this are flagged: a single edge-coupled section then needs an impractically narrow gap

Outputs

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

Outputs of directional-coupler
Field	Unit	Description
evenModeImpedanceheadline	Ω	Even-Mode Impedance
oddModeImpedance	Ω	Odd-Mode Impedance
couplingFactor	none	Voltage Coupling Factor
throughLoss	dB	Through-Path Loss (Power Coupled Out)
isolation	dB	Isolation (I = C + D)
coupledLength	mm	Coupled Length (λ/4)

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": "directional-coupler",
    "inputs": {
      "coupling": 20,
      "z0": 50,
      "frequency": 3,
      "effPermittivity": 2.2,
      "directivity": 30,
      "couplingLimit": 8
    }
  }'

import rftools

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

result = client.calculate("directional-coupler", {
    "coupling": 20,
    "z0": 50,
    "frequency": 3,
    "effPermittivity": 2.2,
    "directivity": 30,
    "couplingLimit": 8,
})
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": "directional-coupler",
    "inputs": {
      "coupling": 20,
      "z0": 50,
      "frequency": 3,
      "effPermittivity": 2.2,
      "directivity": 30,
      "couplingLimit": 8
    }
  }),
});
console.log(response.status, await response.json());

package main

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

func main() {
	body := []byte(`{
	  "slug": "directional-coupler",
	  "inputs": {
	    "coupling": 20,
	    "z0": 50,
	    "frequency": 3,
	    "effPermittivity": 2.2,
	    "directivity": 30,
	    "couplingLimit": 8
	  }
	}`)
	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": "directional-coupler",
  "values": {
    "evenModeImpedance": 55.27707983925667,
    "oddModeImpedance": 45.22670168666455,
    "couplingFactor": 0.1,
    "throughLoss": 0.04364805402450088,
    "isolation": 50,
    "coupledLength": 16.843336162593108
  },
  "warnings": [],
  "errors": [],
  "provenance": {
    "method": "calculator:directional-coupler",
    "version": "api@3f2c1a9b04de",
    "formulaRef": "Pozar, Microwave Engineering, 4th ed. (2012), §7.1, Eqs. (7.20)–(7.21), and §7.6, Eqs. (7.85)–(7.87)",
    "assumptions": [
      {
        "code": "equal-mode-velocities",
        "text": "The even and odd modes travel at the same phase velocity (TEM, as in stripline); in microstrip they do not, and the directivity is degraded."
      },
      {
        "code": "single-section",
        "text": "One quarter-wave coupled section, so the coupling is exact only at the centre frequency; losses are not modelled."
      }
    ],
    "validRange": {
      "status": "inside",
      "bounds": {
        "coupling": {
          "min": 0.1,
          "max": null,
          "unit": "dB"
        },
        "z0": {
          "min": 1,
          "max": null,
          "unit": "Ω"
        },
        "frequency": {
          "min": 0.001,
          "max": null,
          "unit": "GHz"
        },
        "effPermittivity": {
          "min": 1,
          "max": null,
          "unit": ""
        },
        "directivity": {
          "min": 0,
          "max": null,
          "unit": "dB"
        },
        "couplingLimit": {
          "min": 0,
          "max": null,
          "unit": "dB"
        }
      },
      "outside": [],
      "model": null
    },
    "computedAt": "2026-09-24T14:05:11.003Z",
    "inputs": {
      "coupling": 20,
      "z0": 50,
      "frequency": 3,
      "effPermittivity": 2.2,
      "directivity": 30,
      "couplingLimit": 8
    },
    "seed": null,
    "elapsedSeconds": 0.003
  }
}

{
  "detail": [
    {
      "type": "float_parsing",
      "loc": [
        "body",
        "inputs",
        "coupling"
      ],
      "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 pageDirectional Coupler Calculator — Coupled-Line Even & Odd Mode Impedance, at these values