Transmission in Multimode Waveguide with Random Imperfections

Abstract

The effects of random geometric imperfections on the transmission of the TE <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">01</inf> wave in circular waveguide are studied; the necessary theory of guides with known arbitrary imperfections is first developed. The TE <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">01</inf> 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 TE <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">01</inf> 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 TE <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">01</inf> 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.