Documentation sections

Circular Waveguide Calculator — Cutoff Frequency, TE11 & TM01 Modes

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

Slug circular-waveguide. Cutoff frequency of any TE or TM mode of a circular waveguide, the single-mode band between TE₁₁ and TM₀₁, and above cutoff the guide wavelength, phase constant, phase and group velocities, wave impedance and the conductor and dielectric losses; below cutoff, the evanescent attenuation.

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 circular-waveguide
Name	Unit	Range	Default	Description
radiusnumber	mm	0.01 … 1000	5	Inside radius of the guide (half the inside diameter)
permittivitynumber	none	at least 1	2.08	Relative permittivity of the material filling the guide; 1 for air
frequencynumber	GHz	0.001 … 1000	14	Operating Frequency
modeTypenumber	none	0 … 1	0	A transverse-electric (TE) or transverse-magnetic (TM) modeOne of: 0 TE · 1 TM
modeNnumber	none	0 … 5	1	Number of circumferential field variations, 0 to 5
modeMnumber	none	1 … 5	1	Number of radial field variations, 1 to 5
conductivitynumber	MS/m	at least 0.01	41	Conductivity of the inner wall or its plating
lossTangentnumber	none	at least 0	0.0004	Loss tangent of the filling; 0 for air
lengthnumber	m	at least 0	0.3	Length of guide, for the total loss

Outputs

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

Outputs of circular-waveguide
Field	Unit	Description
cutoffFreqheadline	GHz	Cutoff Frequency of the Selected Mode
te11Cutoff	GHz	TE₁₁ Cutoff (Single-Mode Band Starts)
tm01Cutoff	GHz	TM₀₁ Cutoff (Single-Mode Band Ends)
propagates	none	Selected Mode Propagates (1 = yes, 0 = no)
beta	rad/m	Phase Constant
guideWavelength	mm	Guide Wavelength
phaseVelocity	×c	Phase Velocity (× c)
groupVelocity	×c	Group Velocity (× c)
waveImpedance	Ω	Wave Impedance
conductorAttenuation	dB/m	Conductor Attenuation
dielectricAttenuation	dB/m	Dielectric Attenuation
totalLoss	dB	Total Loss over the Guide Length
evanescentAttenuation	dB/m	Evanescent Attenuation (Below Cutoff)

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": "circular-waveguide",
    "inputs": {
      "radius": 5,
      "permittivity": 2.08,
      "frequency": 14,
      "modeType": 0,
      "modeN": 1,
      "modeM": 1,
      "conductivity": 41,
      "lossTangent": 0.0004,
      "length": 0.3
    }
  }'

import rftools

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

result = client.calculate("circular-waveguide", {
    "radius": 5,
    "permittivity": 2.08,
    "frequency": 14,
    "modeType": 0,
    "modeN": 1,
    "modeM": 1,
    "conductivity": 41,
    "lossTangent": 0.0004,
    "length": 0.3,
})
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": "circular-waveguide",
    "inputs": {
      "radius": 5,
      "permittivity": 2.08,
      "frequency": 14,
      "modeType": 0,
      "modeN": 1,
      "modeM": 1,
      "conductivity": 41,
      "lossTangent": 0.0004,
      "length": 0.3
    }
  }),
});
console.log(response.status, await response.json());

package main

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

func main() {
	body := []byte(`{
	  "slug": "circular-waveguide",
	  "inputs": {
	    "radius": 5,
	    "permittivity": 2.08,
	    "frequency": 14,
	    "modeType": 0,
	    "modeN": 1,
	    "modeM": 1,
	    "conductivity": 41,
	    "lossTangent": 0.0004,
	    "length": 0.3
	  }
	}`)
	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": "circular-waveguide",
  "values": {
    "cutoffFreq": 12.18249672658006,
    "te11Cutoff": 12.18249672658006,
    "tm01Cutoff": 15.911925676420427,
    "propagates": 1,
    "beta": 208.5133965531654,
    "guideWavelength": 30.13324520651382,
    "phaseVelocity": 1.4071916141772767,
    "groupVelocity": 0.34165157461538415,
    "waveImpedance": 530.1317381983713,
    "conductorAttenuation": 0.5825753543015417,
    "dielectricAttenuation": 1.4919287295260026,
    "totalLoss": 0.6223512251482632,
    "evanescentAttenuation": null
  },
  "warnings": [],
  "errors": [],
  "provenance": {
    "method": "calculator:circular-waveguide",
    "version": "api@3f2c1a9b04de",
    "formulaRef": "Pozar, Microwave Engineering, 4th ed. (2012), §3.4, Tables 3.3–3.5, Eqs. (3.127)–(3.140); NIST DLMF §10.21",
    "assumptions": [
      {
        "code": "homogeneous-fill",
        "text": "The guide is a perfect circular cylinder uniformly filled with one lossy dielectric."
      },
      {
        "code": "perturbation-loss",
        "text": "Conductor and dielectric losses are computed by perturbation from the lossless fields, which holds for good conductors and small loss tangents away from cutoff."
      }
    ],
    "validRange": {
      "status": "inside",
      "bounds": {
        "radius": {
          "min": 0.01,
          "max": 1000,
          "unit": "mm"
        },
        "permittivity": {
          "min": 1,
          "max": null,
          "unit": ""
        },
        "frequency": {
          "min": 0.001,
          "max": 1000,
          "unit": "GHz"
        },
        "modeType": {
          "min": 0,
          "max": 1,
          "unit": ""
        },
        "modeN": {
          "min": 0,
          "max": 5,
          "unit": ""
        },
        "modeM": {
          "min": 1,
          "max": 5,
          "unit": ""
        },
        "conductivity": {
          "min": 0.01,
          "max": null,
          "unit": "MS/m"
        },
        "lossTangent": {
          "min": 0,
          "max": null,
          "unit": ""
        },
        "length": {
          "min": 0,
          "max": null,
          "unit": "m"
        }
      },
      "outside": [],
      "model": null
    },
    "computedAt": "2026-09-24T14:05:11.003Z",
    "inputs": {
      "radius": 5,
      "permittivity": 2.08,
      "frequency": 14,
      "modeType": 0,
      "modeN": 1,
      "modeM": 1,
      "conductivity": 41,
      "lossTangent": 0.0004,
      "length": 0.3
    },
    "seed": null,
    "elapsedSeconds": 0.003
  }
}

{
  "detail": [
    {
      "type": "float_parsing",
      "loc": [
        "body",
        "inputs",
        "radius"
      ],
      "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 pageCircular Waveguide Calculator — Cutoff Frequency, TE11 & TM01 Modes, at these values