The effects of random geometric imperfections on the transmission of the TE01 wave in circular waveguide are studied; the necessary theory of guides with known arbitrary imperfections is first developed. The TE01 transmission statistics are determined in terms of the statistics of the various types of geometric imperfections. Both discrete mode converters — i.e., localized imperfections such as tilts, offsets, or diameter changes at joints between pipes that are perfect right‐circular cylinders — and continuous geometric imperfections — such as straightness deviation, diameter variation, ellipticity, etc., that vary smoothly with distance along the guide — are considered. The average, variance, power spectrum, and probability distribution of the TE01 loss‐frequency curve are discussed.
Continuous straightness deviation (of the individual pipes of the guide) appears to be the most serious tolerance in present copper waveguide, and a significant factor in helix guide as well. The power spectrum of the straightness deviation is all‐important in determining the TE01 loss due to mode conversion. Fourier components of straightness deviation having wavelengths between roughly 1.4 and 4‐4 feet are the significant ones for the present 2‐inch I.D. guide operated in a frequency band from 35 to 90 kmc.
Departures from perfect geometry in a multi‐mode circular waveguide used for circular electric wave transmission will cause coupling between the TE01 signal mode and the other propagating modes. Such coupling causes serious degradation of signal fidelity after long travel distances. These effects have been studied in a long 5‐inch‐diameter guide in the 9000‐mc band, for effective pulse travel distances up to 12 miles. Mode filters have been developed which suppress all spuriously generated modes in this guide. It is found that the insertion of these mode filters at reasonable intervals along the waveguide reduces pulse distortion to a negligible level and smooths the variations in the loss versus frequency characteristic.
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