1288 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1957 



power abstraction is seen from this expression to be 



2 ,2 



Atts 



9 



Cod 



1 



m%4 2Aa|2 

 The condition (27) may now be written 



2Aa, « I Aa I , 



(29) 



(30) 



or, the rate of conversion loss has to be small compared to the difference 

 between E2 attenuation and Ei attenuation. 



When the wave is travelling through a large number of serpentine 

 bends, power is built up gradually in the E2 mode to a constant value. 



E2 

 E, 



= 3 



Cod 



7n~Tr^ 



1 



2Aa/ 



(31) 



Both the attenuation increase and the power level in spurious modes can 

 seriously affect the Ei transmission. 



To evaluate (29) and (31) we rewrite them with jnr = AjSl and 

 d = wf /12E I tm follows; 



(32) 



Aa, 



aoi 



Eo 

 E[ 



w 



Co 



w 



EI (2A^)2aoi 



Co 



aoi 



2A 



a 



aoi 



(33) 

 EI (2A/3)2aoi 2A • ^ ^ 



We note from (32) and (33) that the coupling effects cannot be controlled 

 by changing the supporting distance. Only the nvmiber of critical fre- 

 quencies in a given range decreases with decreasing supporting distance. 

 The previously cited numerical example of the 2 inch copper pipe 

 yields the following values at the critical frequencies of the two lowest 

 TEi„ waves near X = 5.4 mm: 



TEii 



Aa, 



aoi 



ia 



= 0.114 



TE12 ^^ = 0.855 

 aoi 



20 log 



20 log 



E2 

 El 



E2 

 El 



23 A db. 



= -6.85 dh. 



The mode conversion, especially to the TE12 wave, causes a seriously 

 high additional attenuation and spurious mode level. 



v. MODE FILTERS IN SERPENTINE BENDS 



Periodically spaced supports are a condition for the critical case de- 

 scribed by (32) and (33). Accordingly, the coupling effects can be con- 

 trolled by removing the periodicity of the supports. 



