Helix Waveguide

Helix waveguide, composed of closely wound turns of insulated copper wire covered with a lossy jacket, shows great promise for use as a communication medium. The properties of this type of waveguide have been investigated using the sheath helix model. Modes whose wall currents follow the highly conducting helix have attenuation constants which are essentially the same as for copper pipe. The other modes have very large attenuation constants which depend upon the helix pitch angle and the electrical properties of the jacket. Approximate formulas are given for the propagation constants of the lossy modes. The circular electric mode important for longdistance communication has low loss for zero-pitch helices. The propagation constants of some of the lossy modes in helix waveguide of zero pitch have been calculated numerically, as f unctions of the jacket parameters and the guide size, in regions where the approximate formulas are no longer valid. Under certain conditions the attenuation constant of a particular mode may pass through a maximum as the jacket conductivity is varied. GLOSSARY OF SYMBOLS a Inner radius of waveguide h = /3 -- ia Complex phase constant n Angular mode index p Denotes pnm or pnm' according to context pnm w t h zero of Jn(x) pnm' mth zero of Jn'(x) r, 9, z Right-handed cylindrical coordinates a Attenuation constant /3 Phase constant (3o = 2t/ = co(/nno)1/2 Free-space phase constant e0 Permittivity of interior medium e Permittivity of exterior medium e/eo e (r/coc o 1347 1348 T H E BELL SYSTEM TECHNICAL J O U R N A L , NOVEMBER 1 9 5 6 r 2 ,211/2 [w noeo -- h J [coVo60(6' - »Y') - A2]1'2 Free-space wavelength Cutoff wavelength Permeability of interior and exterior media p/2ira Cutoff ratio ft · 2 .