
Properties of Modes in a Rectangular Waveguide


Rectangular waveguides, as opposed to circular and elliptical waveguides, are by far the dominant configuration
for the installed base of waveguides for compact systems like radar and inside equipment shelters. That is
probably due to the generally greater rigidity of rectangular structures because the wall thickness can be easily
made thicker than with circular. It is also easier to route and mount in close quarters, and attaching penetrating
objects like probes and switches is much simpler.
Most
rectangular waveguide calculations can be performed on any calculator that has trig function keys. Calculations
for circular waveguide, on the other hand, requires the application of Bessel functions, so working equations with
a cheap calculator is not going to happen. However, even spreadsheets have Bessel function capability nowadays, so
determining
cutoff frequencies, field strengths, and any of the other standard
values associated with circular waveguide can be done relatively easily. The formulas below represent those
quantities most commonly needed for rectangular waveguides. Please see the figure at the right for variable
references.
Note: I received the following note from Brian Sequeira,
of the Johns Hopkins University Applied Physics Laboratory. "I reviewed tables on rectangular and circular
waveguides, and based on my experience of what confuses firsttime readers and what does not, I made adjustments
to notation & symbols, corrected a couple of sign errors, and put expressions in a form that make their units more
apparent." The table for rectangular waveguide can be viewed fullsize by clicking on the thumbnail to the right.
Brian also provided a table for circular waveguide.
Quantity 
TE Modes 
TM Modes 
H_{z} 

0 
E_{z} 
0 

E_{x} 


E_{y} 


H_{x} 


H_{y} 


Z_{h,nm} 


Z_{e,nm} 


k_{c,nm} 


βnm 


λc,nm 


α^{†} 


†

The expression for α
is not valid for degenerate modes. Equations derived from "Foundations for Microwave Engineering, R.E. Collin,
McGrawHill



