190 BELL SYSTEM TECHNICAL JOURNAL 



the transfer constant of the second. The impedance from the load 

 of the second filter depends in the same way upon the transfer constant 

 of the first. The proof of these relations is based upon both networks 

 being purely reactive. 



Applications 



The use of the constant resistance pairs of filters is indicated 

 wherever the impedance at the junction of two filters is of major 

 importance. Another application which is of some importance is that 

 of separating the energy in a band of frequencies into two or more 

 channels, delivering all of the energy into one or the other of the loads. 



The method may be extended to more than two networks in parallel 

 or series to give a constant resistance. For example, the combination 



Gi 



G.= 



1 



[l + f.(X)][l+^]' 



1 



6^3== 



1 



1 + FM ' 



will give a constant resistance for the three networks. Designs have 

 been carried through on this basis where the networks are low-pass, 

 high-pass and band-pass, respectively. This is one method of avoiding 

 the Hmit of three db in the loss of the low-pass and the high-pass 

 filters at their cross-over point, since in this case the band-pass filter 

 will take up the power. A second method is to use a pair of low and 

 high-pass filters, each terminated in another pair with different cross- 

 over points. This method requires the use of both a low-pass and a 

 high-pass filter as power absorbing networks but they would be 

 simple structures and together would require no more elements than 

 the single band-pass filter in a three-filter combination. 



The two methods are illustrated in Fig. 7 and Fig. 8, respectively. 

 The structures for the second type are given by Fig. 9. Note that 

 the filters designated L.P. II, L.P. Ill, H.P. II and H.P. Ill have 

 one series arm missing and are apparently terminated at a shunt point 

 at the load end of the filter. This is a consequence of selecting the 

 two P's in such a way that the coefficient ai becomes zero, a matter 

 of no particular difficulty in the case of a two-section filter. 



