 Circular waveguides offer implementation advantages over rectangular waveguide in that installation is much simpler when forming runs for turns and offsets - particularly when large radii are involved - and the wind loading is less on a round cross-section, meaning towers do not need to be as robust. Manufacturing is generally simpler, too, since only one dimension - the radius - needs to be maintained. Applications where differential rotation is required, like a rotary joint for a radar antenna, absolutely require a circular cross-section, so even if rectangular waveguide is used for the primary routing, a transition to circular - and then possibly back to rectangular - is needed.Calculations 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 (Jn) 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. |
Values of pnm for TM Modes | n | pn1 | pn2 | pn3 | | 0 | 2.405 | 5.520 | 8.654 | | 1 | 3.832 | 7.016 | 10.174 | | 2 | 5.135 | 8.417 | 11/620 |
Values of p'nm for TE Modes | n | p'n1 | p'n2 | p'n3 | | 0 | 3.832 | 7.016 | 10.174 | | 1 | 1.841 | 5.331 | 8.536 | | 2 | 3.054 | 6.706 | 9.970 |
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