14 



BELL SYSTEM TECHNICAL JOURNAL 



the following twelve conditions: four at the critical frequencies f ,f u 

 / 2 and/ 3 , where - — = — 1; four at frequencies f al and f a2 where both z n 



4Z21 



and z 2 i are anti-resonant; one at a variable frequency in the internal 

 transmitting band where z n is resonant and z lx anti-resonant; one at 



HU, HH 



Transmitting Band 







f f' 



f f 



MOD 'l 



f, f, 



f f 



Fig. 3 — General Mid-Series Equivalent Low-Band-and-High Pass Wave-Filter 



one other frequency where the absolute value of the characteristic 

 impedance is fixed; and two added conditions at the adjustable fre- 

 quencies of infinite attenuation / 100 and / 2 », bringing the total up 

 to twelve. 



In brief, the procedure for designing the general mid-series equiva- 

 lent wave-filter is: 



(1) Write down from the known " constant k " wave-filter having 

 n preassigned attenuating bands the form of the series impedance 

 with undetermined coefficients mi ... m n as in (14). 



