822 BELL SYSTEM TECHNICAL JOURNAL 



furnished by these more comph'cated structures exactly. Close 

 approximations however can be obtained by modifying the "tuned 

 circuit" characteristic slightly through the introduction of extra 

 elements. Suitable configurations for 2 and 3 branch networks have 

 already been given in Fig, 5. They should furnish susceptance 

 characteristics at least as good as the corresponding conductance 

 characteristics. An example of the susceptance correction of a three 

 branch network, using the configuration of Fig. 5-c, is shown in Fig. 11. 

 Curve I represents the ideal susceptance characteristic, Curve II that 

 actually obtained. 



Impedance Correction of Paralleled Filters 



An interesting modification of the process of susceptance correction 

 occurs when a number of filters are to be connected in parallel. Since 

 the impedance of an attenuating filter is almost a pure reactance the 

 conductance component of a system of parallel filters at a given fre- 

 quency is furnished almost entirely by the filter in whose transmission 

 band that frequency lies. If the system as a whole is to have the 

 correct conductance throughout each transmission band, therefore, 

 every filter must be given the conductance controlling network which 

 would be appropriate if it were operating alone. While the process of 

 conductance correction is thus exactly the same for multipled and 

 individual filters, the process of susceptance correction of paralleled 

 filters must be modified somewhat to take account of the susceptance 

 component furnished by the attenuating filters. A single susceptance 

 network will serve for the whole system. We have merely to compute 

 the susceptance characteristics furnished by the various filters termin- 

 ated in their conductance controlling networks and annul them through- 

 out every transmission band by a two terminal network in parallel with 

 the system as a whole. An example of the application of the method 

 to a pair of parallel complementary filters having 2 branch conductance 

 controlling networks is given by Fig. 12. Curve I in this diagram 

 represents the susceptance of the transmitting filter, Curves II the 

 susceptance of the attenuating filter for several different choices of its 

 cutoff frequency. Curves III the susceptances of the corresponding 

 auxiliary networks, and Curves IV the net result. A series combina- 

 tion of the series and shunt impedances of either filter ^ resonating 

 at the geometric mean of the cutoff frequencies was chosen for the 



^ Since the filters are complementary the series impedance of one is similar to 

 the shunt impedance of the other, and vice versa. By choosing the resonance 

 frequency of the auxiliary network symmetrically with respect to the two filters, 

 as we have done, all of the susceptance relations become symmetrical, and the 

 network functions as well for one filter as it does for the other. 



