Properties of Modes in a Circular WaveguideCalculations for circular waveguide requires the application of Bessel functions, so working equations with a cheap calculator is not going to happen. However, even spreadsheets have Bessel function (J_{n}) 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 circular 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 first-time 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 circular waveguide can be viewed full-size by clicking on the thumbnail to the right. Brian also provided a table for rectangular waveguide.
Values of p_{nm} for TM Modes
Values of p'_{nm} for TE Modes
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