834 BELL SYSTEM TECHNICAL JOURNAL 



Difficulties appearing in a direct application of the impedance cor- 

 recting process may also be avoided if we adopt the reverse method of 

 impedance correction suggested by the theorem on reciprocal im- 

 pedance relationships. The method has already been applied to the 

 construction of alternative filter impedance correcting sections. 

 Similar alternative configurations can be built up in any impedance 

 correcting problem if we consider that the structure is terminated by 

 the conjugate of the desired impedance and adjust its parameters to 

 produce the conjugate of the given impedance. Since the desired 

 impedance will in general be a relatively simple function of frequency, 

 this alternative procedure at least avoids analytical complexities. In 

 spite of these possibilities however it seems probable that the method 

 will fail in many situations. It seems best adapted to such problems 

 as that of filter impedance correction, where a transformation must be 

 made from one fairly simple characteristic to another simple character- 

 istic. An attempt to apply it to more difficult problems should result, 

 at best, in very complicated networks. 



Transmission Properties of Impedance Correcting Networks 



The close relationship between the impedance correcting properties 

 of our networks and their transmission characteristics has been mani- 

 fest from time to time in the previous discussion. The networks used 

 at filter terminations, for example, transmitted freely within the range 

 in which they functioned satisfactorily as impedance correctors but 

 attenuated other frequencies. That this will be true in general is 

 easily seen by inspection. Within the range in which a desired im- 

 pedance characteristic is obtained, of course, our previous argument 

 from the principle of conservation of energy is alone sufficient to show 

 that the networks transmit with the maximum efficiency compatible 

 with the impedance requirements imposed upon the circuit. On the 

 other hand, it is evident from the filter-like configuration of the net- 

 works that at frequencies remote from the operating range of the 

 networks, where the parameter "x" becomes large, the structures will 

 ordinarily introduce attenuation. From the impedance standpoint 

 this means merely that for sufficiently large values of x the polynomial 

 approximations upon which the analysis is based no longer hold, and 

 the resulting mismatch between the generator and network im- 

 pedances diminishes the amount of power which can enter the struc- 

 ture. 



When the impedance correcting analysis is stated in a slightly 

 modified form, whose possibilities have not as yet been completely 

 investigated, the impedance and transmission characteristics of the 



