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1996 
2016
Webmaster:
Kirt
Blattenberger,
BSEE  KB3UON
RF Cafe began life in 1996 as "RF Tools" in an AOL screen name web space totaling 2 MB. Its primary purpose was to provide me with ready access to commonly needed formulas and reference material while performing my work as an RF system and circuit design engineer. The Internet was still largely an unknown entity at the time and not much was available in the form of WYSIWYG ...
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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.
Click here for a transmission lines & waveguide presentation.
A Cavity Resonance Calculator is included in RF Cafe Calculator Workbook for FREE.
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 TE_{m,n} Mode This example is for TE_{1,0} (the mode with the lowest cutoff frequency) in WR284 waveguide (commonly used for Sband radar systems). It has a width of 2.840" (7.214 cm) and a height of 1.340"(3.404 cm).




TE (Transverse Electric) Mode The TE_{10} 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.
____ Electric field lines 
TM (Transverse Magnetic) Mode For TM modes, m=0 and n=0 are not possible, thus, TM_{11} is the lowest possible TM mode.
____ Electric field lines 
TE (Transverse Electric) Mode  
The lower cutoff frequency (or wavelength) for a particular TE mode in circular waveguide is determined by the following equation: , where p'_{mn} is


TM (Transverse Magnetic) Mode  
The lower cutoff frequency (or wavelength) for a particular TM mode in circular waveguide is determined by the following equation: (m), where p_{mn} is

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 TE_{1,0} cutoff frequency calculator.
 Waveguide Component
Vendors
 Waveguide Design Resources

NEETS  Waveguide Theory and Application
 EWHBK, Microwave Waveguide
and Coaxial Cable