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Rectangular & Circular Waveguide: Equations, Fields, & fco Calculator

The following equations and images describe electromagnetic waves inside both rectangular waveguide and circular (round) waveguides. Oval waveguide equations are not included due to the mathematical complexity.

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Rectangular Waveguide Cutoff Frequency

The lower cutoff frequency (or wavelength) for a particular mode in rectangular waveguide is determined by the following equations (note that the length, x, has no bearing on the cutoff frequency):

Rectangular Waveguide - RF Cafe

Rectangular Waveguide Cutoff Frequency equation - RF Cafe

Rectangular Waveguide TEm,n Mode
Cutoff Frequency Calculator

This example is for TE1,0 (the mode with the lowest cutoff frequency) in WR284 waveguide (commonly used for S-band radar systems). It has a width of 2.840" (7.214 cm) and a height of 1.340"(3.404 cm).

where a =
b =
m =
n =
ε =
µ =
Inside width (m), longest dimension
Inside height (m), shortest dimension
Number of ½-wavelength variations of fields in the "a" direction
Number of ½-wavelength variations of fields in the "b" direction
Permittivity (8.854187817E-12 for free space)
Permeability (4πE-7 for free space)

TE (Transverse Electric) Mode

The TE10 mode is the dominant mode of a rectangular waveguide with a>b, since it has the lowest attenuation of all modes. Either m or n can be zero, but not both.


Waveguide equation formula drawing fields End View TE - RF Cafe
End View (TE10)

 

Waveguide equation formula drawing fields Side View TE - RF Cafe

Side View (TE10)

 

Waveguide equation formula drawing fields Top View TE - RF Cafe

Top View (TE10)

____ Electric field lines
p    _ _ _ Magnetic field lines

TM (Transverse Magnetic) Mode

For TM modes, m=0 and n=0 are not possible, thus, TM11 is the lowest possible TM mode.

Waveguide equation formula drawing fields End View TM - RF Cafe
End View (TM11)

 

Waveguide equation formula drawing fields Side View TM - RF Cafe
Side View (TM11)

____ Electric field lines
   _ _ _ Magnetic field lines

TE (Transverse Electric) Mode Circular Waveguide - RF Cafe

The lower cutoff frequency (or wavelength) for a particular TE mode in circular waveguide is determined by the following equation: Circular Waveguide Cutoff Wavelength equation - RF Cafe, where p'mn is

m p'm1 p'm2 p'm3
0 3.832 7.016 10.174
1 1.841 5.331 8.536
2 3.054 6.706 9.970

TM (Transverse Magnetic) Mode

The lower cutoff frequency (or wavelength) for a particular TM mode in circular waveguide is determined by the following equation: Waveguide equation formula drawing fields (m), where pmn is

m pm1 pm2 pm3
0 2.405 5.520 8.654
1 3.832 7.016 10.174
2 5.135 8.417 11.620

Related Pages on RF Cafe

- Properties of Modes in a Rectangular Waveguide
- Properties of Modes in a Circular Waveguide
- Waveguide & Flange Selection Guide
- Rectangular & Circular Waveguide: Equations & Fields
- Rectangular waveguide TE1,0 cutoff frequency calculator.
- Waveguide Component Vendors
- Waveguide Design Resources
- NEETS - Waveguide Theory and Application
- EWHBK, Microwave Waveguide and Coaxial Cable