832 BELL SYSTEM TECHNICAL JOURNAL 



of the structure actually have the same dissipation constant. It is 

 usually sufficient, however, to assume that "(/" in the above formulae 

 is the average of the dissipation constants for coils and condensers. 

 When well designed impedance correcting networks are used the react- 

 ance and resistance characteristics of the structure will be approxi- 

 mately constant over the operating range. The derivatives occurring 

 in the above formulae will consequently reflect only the presence of 

 slight ripples in these characteristics about their mean values. The 

 slopes of these ripples will usually be quite small. We can therefore 

 conclude that moderate amounts of dissipation will have no appreciable 

 effect upon the impedance of a properly terminated filter. The chief 

 exceptions to this rule occur in low pass filters, where, at low frequencies 

 the assumption that the dissipation constant is small is no longer 

 satisfied. 



In attempting to extend this principle to broader problems in 

 impedance correction it is, of course, necessary to bear in mind that 

 the analysis holds only for networks of resistances, inductances and 

 capacities. We cannot expect the same results when the load im- 

 pedance of the circuit has some arbitrary variation with frequency. 

 For example, if we take the load impedance as the image impedance of 

 a dissipationless "constant-^" filter and assume that parasitic re- 

 sistances occur only in the termination, we will find that dissipation 

 does change the impedance of the circuit. The circuit impedance 

 will be insensitive to dissipation only when we include the complete 

 structure, and not merely the terminations, in our analysis. 



More General Problems of Impedance Correction 



This general method of impedance correction having worked with 

 reasonable success in its application to "constant-^" wave filter 

 impedances, it is natural to inquire whether it can be applied to other 

 problems with equal ease. Further possibilities for example might 

 include the correction of other types of filter impedances, or the cor- 

 rection over extremely wide frequency bands for the efi^ects of leakage 

 inductance and finite mutual inductance in transformers, or the reduc- 

 tion of actual transmission line impedances to constant resistances. 

 All of these possible applications assume that the impedance correcting 

 device is a 4-terminal network, transmitting useful signal energy to its 

 load impedance. When terminated by such an element as a simple 

 resistance, however, it might also be used as a 2-terminal network, 

 forming one branch of a complete system. By appropriate adjustment 

 of the impedance controlling parameters the network could, theore- 

 tically at least, be given a wide range of impedance characteristics. 



