342 



THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1954 



II. ELIMINATION OF INDUCTANCE 



In the practical realization of frequency selective networks it is some- 

 times awkward, difficult, or even impossible to make effective use of coils 

 as inductive elements. This is true, because of severe limitations on space, 

 exacting tolerances on undesired modulation, or necessity for operation 

 at extremely low frecjuencies. 



It has been well known for some time that inductive elements can be 

 eliminated without restricting the repertoire of the network designer 

 provided he is willing to purchase this freedom by introducing active 

 elements to supply gain. ' 



It can be easily shown that the transmission through a high gain feed- 

 back amplifier is proportional to the product of the short circuit transfer 

 admittance of the input network and the short circuit transfer impedance 

 of the feedback network : 



e"" = YiZi 



In addition it is also known from energy relations that passive net- 

 works containing only one kind of reactance cannot produce complex 

 poles in the short circuit transfer admittance. It is instructive to con- 

 sider the application of these principles to some familiar kinds of trans- 

 mission networks. These networks can be logically divided into two 

 classes: those which are primarily concerned with amplitude such as 

 filters, and those mainly concerned with phase such as delay equalizers. 



(a) (b) 



Fig. 11, — Use of series negative resistance, (a) M-derived low pass filter, (b) 

 Band elimination filter. 



