694 



BELL SYSTEM TECHNICAL JOURNAL 



Sometimes in practice a quarter wavelength may not be sufficient spacing 

 to avoid mutual impedances arising between adjacent elements, in which 

 event the connecting line may be increased to a higher odd multiple of quar- 

 ter wavelength. This accentuates the frequency sensitivity of the connect- 



L 



o — nsw^ 



h*i 



Yo E 



Zo 



•Zo 



Z'=Zo2Yo(l+j2rL) 



Fig. 6 — Illustrating the impedance inverting property of a quarter wavelength of trans- 

 mission line. 



LUMPED CONSTANT FILTER USING SERIES & SHUNT ELEMENTS 





■Pon.^n 



LUMPED CONSTANT FILTER USING ONLY SHUNT ELEMENTS 



Fig. 7 — Simulation of ladder network by shunt branches at quarter wave intervals. 



ing line, but this efifect can be taken into account by decreasing the selectiv- 

 ities of the branches themselves by appropriate amounts. In narrow-band 

 filters this may be negligible, but in broad-band filters it may be consider- 

 able, as shown in the following analysis. 



Selectivity of Connecting Lines 

 Consider a length of transmission line having a surge impedance Zo = 



— and terminated in a parallel resonant circuit containing an inductance, a 



