6 BELL SYSTEM TECHNICAL JOURNAL 



wave guide radius for each signal wave length and by an optimum signal 

 wave length for each wave guide radius. 



Numerical examples are given for sinusoidal bends. 



Summary of Results 



1. The energy loss of TEoi waves in curved wave guides by conversion 

 into the TMu rnode is interpreted as a case of coupling between 

 resonant transmission lines. 



2. In a pair of coupled lines the energy cannot be confined entirely to a 

 single Une but travels through both in one or both of two possible 

 combination modes. 



3. All important properties of coupled circuits, including wave guide 

 modes, are functions of a single discriminant. 



4. When the discriminant is much smaller than one, most of the energy 

 can be carried in one line or component mode. 



5. When the discriminant is much larger than one, the energy flow is 

 nearly equally divided between the two lines or component modes. 



6. In wave guides of typical dimensions the coupling discriminant 

 becomes one for a "critical" bending radius greater than a mile. 

 For all sharper bends, that is for most practical installations, the 

 discriminant is greater than one. 



7. In a long wave guide section with more than critical curvature the 

 average attenuation constant is the arithmetic mean between those 

 of the TEoi and the TMu modes. 



8. If a wave guide region carrying pure TEoi is followed by a curved 

 region, the energy in the curved region fluctuates back and forth 

 between pure TEoi and predominant TMu . The location of TEoi 

 minima and maxima is a function of the signal frequency, the wave 

 guide diameter and the total bending angle. 



9. For highly supercritical curvatures the bending angles at which 

 minima and maxima occur are nearly independent of the curvature 

 and approach the limiting values previously computed by Jouguet 

 and Rice. The minima approach zero. When the bending radius 

 approaches or exceeds the critical value, the maxima and minima 

 become shallower and their spacing is increased by a function of the 

 coupling discriminant. 



10. For regular serpentine bends or random angular deviations from an 

 average straight course which are much smaller than the first extinc- 

 tion angle, the percentage increase in average attenuation is propor- 

 tional to the square of the maximum deviation and to the fourth 

 power of wave guide diameter and signal frequency. 



11. Wave guide installations of practical dimensions for frequencies now 



