Search RFCafe.com                           
      More Than 17,000 Unique Pages
Please support me by ADVERTISING!
Serving a Pleasant Blend of Yesterday, Today, and Tomorrow™ Please Support My Advertisers!
   Formulas & Data
Electronics | RF
Mathematics
Mechanics | Physics
     AI-Generated
     Technical Data
Pioneers | Society
Companies | Parts
Principles | Assns


 About | Sitemap
Homepage Archive
        Resources
Articles, Forums Calculators, Radar
Magazines, Museum
Radio Service Data
Software, Videos
     Entertainment
Crosswords, Humor Cogitations, Podcast
Quotes, Quizzes
   Parts & Services
1000s of Listings
 Vintage Magazines
Electronics World
Popular Electronics
Radio & TV News
QST | Pop Science
Popular Mechanics
Radio-Craft
Radio-Electronics
Short Wave Craft
Electronics | OFA
Saturday Eve Post

Software: RF Cascade Workbook
RF Stencils Visio | RF Symbols Visio
RF Symbols Office | Cafe Press
Espresso Engineering Workbook

Aegis Power  |  Alliance Test
Centric RF  |  Empower RF
ISOTEC  |  Reactel  |  RFCT
San Fran Circuits

everythingRF RF & Microwave Parts Database (h1)



Anritsu Test Equipment - RF Cafe

Please Support RF Cafe by purchasing my  ridiculously low-priced products, all of which I created.

RF Cascade Workbook for Excel

RF & Electronics Symbols for Visio

RF & Electronics Symbols for Office

RF & Electronics Stencils for Visio

RF Workbench

T-Shirts, Mugs, Cups, Ball Caps, Mouse Pads

These Are Available for Free

Espresso Engineering Workbook™

Smith Chart™ for Excel

Innovative Power Products (IPP) RF Combiners / Dividers

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.

Click here for a transmission lines & waveguide presentation.

A Cavity Resonance Calculator is included in Espresso Engineering Workbook™ for FREE.

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 Cutoff Wavelength 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).

Espresso Engineering Workbook™

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

Innovative Power Products (IPP) RF Combiners / Dividers
Cafe Press

ConductRF Phased Matched RF Cables - RF Cafe

Rigol DHO1000 Oscilloscope - RF Cafe