1290 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1957 



_l 

 LJJ 



o 



UJ 



Q 



UJ 



> 



a 

 O 



(/) 



D 

 O 



<r 



D 

 Q- 

 10 



-100 

 -80 



-60 

 -40 



-20 



-to 



-6 

 - 6 



- 1 



10 20 40 60 80 100 200 400 600 1000 



SPACING OF MODE FILTERS IN FEET 



2000 4000 



10000 



Fig. 3 — Spurious mode level of TE01-TE12 coupling in serpentine bends with 

 mode filters; 2-inch I.D. 2f-inch O.D., X = 5.4 mm. Serpentine bends are 

 caused by equally spaced supports and the elasticity of the copper pipe. The sup- 

 porting distance is a multiple of the beat -wavelength between TEoi and TE12 . 



The loss to the TEoi wave caused by the mode conversion is eqiii\'alent 

 to an increase in TEoi attenuation 



Aa, = 



1 



w 



Co 



_EI (2A/3)2J 



L. 



(35) 



L is the spacing between two successive mode-fihers. In (34) and (35) 

 the attenuation constants of Ei and E2 are assumed to be equal. Further- 

 more (34) and (35) hold only as long as the E2 power level is small com- 

 pared to the El power level. 



Ideal mode filters is a rather optimistic assumption. Practical mode 

 filters present only a limited attenuation to the unwanted modes. There- 

 fore a more realistic procedure is to represent the effect of the mode 

 filters by a uniform increase of unwanted mode attenuation. 



B. The mode filters with a loss A are considered to cause a uniform 

 increase in E2 attenuation Aa = A/L. Equations (32) and (33) modified 

 to include this attenuation increase are: 



Aa, 

 aoi 



w 



Co 



EI (2A(3y-m,_\ 



aoi 



2Aa I -1- 



A 



(36) 



