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Rectangular & Circular Waveguide: Equations & Fields

PLease click to visit the Anatech Microwave websitePlease click to visit the Vector Telecom websiteWenteq Microwave


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.

See the online cavity resonance calculator here.

Here is a waveguide selection chart.

Here is a circular waveguide mode equation chart.

Click here for a transmission lines & waveguide presentation.




Rectangular Waveguide
Click here for a table of TE and TM mode field equations for rectangular waveguides.
Cutoff Frequency
Rectangular Waveguide - RF CafeThe lower cutoff frequency (or wavelength) for a particular mode in rectangular waveguide is determined by the following equations: Waveguide equation formula drawing - RF Cafe (Hz) Waveguide equation formula drawing - RF Cafe (m)
wherea =
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
    _ _ _ Magnetic field lines
 

Rectangular Waveguide TE Mode
Cutoff Frequency Calculator


This example is for WR284, which is 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).

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
 
Circular Waveguide
Click here for a table of TE and TM mode field equations for circular waveguides.
TE (Transverse Electric) ModeCircular Waveguide - RF Cafe
The lower cutoff frequency (or wavelength) for a particular TE mode in circular waveguide is determined by the following equation: Waveguide equation formula drawing fields (m), where p'mn is
 
mp'm1p'm2p'm3
03.8327.01610.174
11.8415.3318.536
23.0546.7069.970

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
 
mpm1pm2pm3
02.4055.5208.654
13.8327.01610.174
25.1358.41711.620

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
- Waveguide Component Vendors
- Waveguide Design Resources
- Waveguide Design Books
- NEETS - Waveguide Theory and Application
- EWHBK, Microwave Waveguide and Coaxial Cable

RF Cafe Software

RF Cascade Workbook
 RF Cascade Workbook is a very extensive system cascaded component Excel workbook that includes the standard Gain, NF, IP2, IP3, Psat calculations, input & output VSWR, noise BW, min/max tolerance, DC power cauculations, graphing of all RF parameters, and has a graphical block diagram tool. An extensive User's Guide is also included. - Only $35.
RF system analysis including
frequency conversion & filters

Smith Chart™ for Excel
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RF & EE Symbols Word
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