336 



BELL SYSTEM TECHNICAL JOURNAL 



The main conducting tube is represented by an L network containing 

 the total distributed capacity of the tube in the shunt arm, and the 

 total distributed inductance of the tube in the series arm. The side 

 branch impedance shunts the two L networks at their center. 



The propagation constant and characteristic impedance of this 

 structure are given by the expressions 



cosh 



P = 1 



2ix)'-L'- jicpL I (jo'-L'~ 



/^2^ 1 



1 + 



joopL 

 2Zo.S', 



J PC-' 1 



1 - 



•) f •' \ -1 



wLSi{2Z2) 



L- 



1 - 



CO 



'-IJ 



{^) 



where S\ is the area of the main branch. 



If these equations are compared with those given in the former 

 paper,- it is seen that they are approximately those obtained by taking 

 the first two terms of the expansions of the trigonometrical functions. 

 The characteristics of the filter are not very readily seen from equation 

 (5), but can be readily found by transforming the network shown on 

 Fig. 6, into the much more general lattice network shown in Fig. 7. 





