Documentation sections

Wilkinson Power Divider Calculator — Equal & Unequal Split

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

Slug wilkinson-power-divider. Design a two-way Wilkinson power divider for any power ratio: the quarter-wave arm impedances, the isolation resistor, the output terminations and their matching transformers, and the physical quarter-wave length, with every line checked against the impedance range your process can make.

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 wilkinson-power-divider
Name	Unit	Range	Default	Description
z0number	Ω	at least 1	50	Impedance of the input port and of the system the outputs are matched back to
powerRationumber	none	at least 0.01	1	Power delivered to port 3 divided by the power delivered to port 2; 1 is an equal split
frequencynumber	GHz	at least 0.001	2.4	Frequency at which every line is a quarter wavelength long
effPermittivitynumber	none	at least 1	3.3	Effective permittivity of the lines; 1 for air, εr for stripline, about 3.3 for 50 Ω microstrip on FR-4. One value is used for every line
zMinnumber	Ω	at least 1	20	Lowest characteristic impedance your board process can make (widest practical line)
zMaxnumber	Ω	at least 2	150	Highest characteristic impedance your board process can make (narrowest practical line)
eSeriesnumber	none	0 … 96	0	Rounds every part to the nearest value in the series; the response and the export are the rounded design's.One of: 0 Ideal values · 12 E12 (10%) · 24 E24 (5%) · 48 E48 (2%) · 96 E96 (1%)

Outputs

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

Outputs of wilkinson-power-divider
Field	Unit	Description
arm2Impedanceheadline	Ω	Arm Line to Port 2 (Z₀₂)
arm3Impedance	Ω	Arm Line to Port 3 (Z₀₃)
isolationResistor	Ω	Z₀(K + 1/K), rounded to the part series when one is chosen
port2Load	Ω	Port 2 Termination (R₂ = Z₀K)
port3Load	Ω	Port 3 Termination (R₃ = Z₀/K)
port2Transformer	Ω	Port 2 Quarter-Wave Transformer to Z₀
port3Transformer	Ω	Port 3 Quarter-Wave Transformer to Z₀
port2Share	dB	Power to Port 2
port3Share	dB	Power to Port 3
quarterWaveLength	mm	Quarter-Wave Line Length
isolationBuilt	dB	Isolation between the two output arms at the centre frequency with the isolation resistor as rounded, from the nodal solution of Pozar Fig. 7.11 with the arms in R₂ and R₃; infinite (perfect) with the exact resistor

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": "wilkinson-power-divider",
    "inputs": {
      "z0": 50,
      "powerRatio": 1,
      "frequency": 2.4,
      "effPermittivity": 3.3,
      "zMin": 20,
      "zMax": 150,
      "eSeries": 0
    }
  }'

import rftools

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

result = client.calculate("wilkinson-power-divider", {
    "z0": 50,
    "powerRatio": 1,
    "frequency": 2.4,
    "effPermittivity": 3.3,
    "zMin": 20,
    "zMax": 150,
    "eSeries": 0,
})
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": "wilkinson-power-divider",
    "inputs": {
      "z0": 50,
      "powerRatio": 1,
      "frequency": 2.4,
      "effPermittivity": 3.3,
      "zMin": 20,
      "zMax": 150,
      "eSeries": 0
    }
  }),
});
console.log(response.status, await response.json());

package main

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

func main() {
	body := []byte(`{
	  "slug": "wilkinson-power-divider",
	  "inputs": {
	    "z0": 50,
	    "powerRatio": 1,
	    "frequency": 2.4,
	    "effPermittivity": 3.3,
	    "zMin": 20,
	    "zMax": 150,
	    "eSeries": 0
	  }
	}`)
	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": "wilkinson-power-divider",
  "values": {
    "arm2Impedance": 70.71067811865476,
    "arm3Impedance": 70.71067811865476,
    "isolationResistor": 100,
    "port2Load": 50,
    "port3Load": 50,
    "port2Transformer": 50,
    "port3Transformer": 50,
    "port2Share": -3.010299956639812,
    "port3Share": -3.010299956639812,
    "quarterWaveLength": 17.190657985216998,
    "isolationBuilt": null
  },
  "warnings": [],
  "errors": [],
  "provenance": {
    "method": "calculator:wilkinson-power-divider",
    "version": "api@3f2c1a9b04de",
    "formulaRef": "Pozar, Microwave Engineering, 4th ed. (2012), §7.3, Eqs. (7.37a)–(7.37c)",
    "assumptions": [
      {
        "code": "ideal-tem-lines",
        "text": "The lines are lossless TEM lines, each exactly a quarter wavelength at the centre frequency in the one effective permittivity entered."
      },
      {
        "code": "single-section",
        "text": "One section, matched and isolated only at the centre frequency; junction and resistor parasitics are not modelled."
      }
    ],
    "validRange": {
      "status": "inside",
      "bounds": {
        "z0": {
          "min": 1,
          "max": null,
          "unit": "Ω"
        },
        "powerRatio": {
          "min": 0.01,
          "max": null,
          "unit": ""
        },
        "frequency": {
          "min": 0.001,
          "max": null,
          "unit": "GHz"
        },
        "effPermittivity": {
          "min": 1,
          "max": null,
          "unit": ""
        },
        "zMin": {
          "min": 1,
          "max": null,
          "unit": "Ω"
        },
        "zMax": {
          "min": 2,
          "max": null,
          "unit": "Ω"
        },
        "eSeries": {
          "min": 0,
          "max": 96,
          "unit": ""
        }
      },
      "outside": [],
      "model": null
    },
    "computedAt": "2026-09-24T14:05:11.003Z",
    "inputs": {
      "z0": 50,
      "powerRatio": 1,
      "frequency": 2.4,
      "effPermittivity": 3.3,
      "zMin": 20,
      "zMax": 150,
      "eSeries": 0
    },
    "seed": null,
    "elapsedSeconds": 0.003
  }
}

{
  "detail": [
    {
      "type": "float_parsing",
      "loc": [
        "body",
        "inputs",
        "z0"
      ],
      "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 pageWilkinson Power Divider Calculator — Equal & Unequal Split, at these values