DESIGN OF REACTIVE EQUALIZEKS 



719 



quiremenl is fulfilled by providing both coupling circuits with a balancing 

 network, connected as shown in Fig. ^. By accepting a small constant trans- 

 mission loss,' the relationship ZiZo = R- is satisfied if the im[)edance Zo 

 of the balancing network is made the inverse of the transmission circuit 

 inii)edance Zi. Because of the relative ease of designing an inverse impedance 

 /■:, once Zi is known in the final stages of a particular design, it is appropriate 

 to omit from further discussion the presence of the balancing networks. 



The fundamental theoretical limitation in the maximum transmission 

 performance of these coupling networks is due directly to the presence of 

 the parasitic tube capacitances Co and d . If the parasitic capacitances were 

 not present, the turns ratios of the transformers in the coupling circuits 

 could quite evidently be made extremely high in order to produce over any 

 specified frequency band as large a transmission response as desired. How- 

 ever, even though these capacitances are usually small, they always tend to 

 short circuit the coupling networks whenever the impedance ratios of the 



Fig. 3 — Balancing network arrangement. 



transformers are made too high. The determination of the maximum re- 

 sponse of these networks over a prescribed frequency range is thus a basic 

 problem in the design of reactive equalizers. 



The fundamental limitation on the response of these networks is expressed 

 in terms of the total area available under the transfer characteristic.^ When 

 this characteristic is a desired function over a finite frequency band, the 

 maximum utilization of the area available is obviously attained when all 

 the area is included in the useful band. This condition is described as a 

 resistance efficiency of 100 per cent. A smaller resistance eflficiency, 75 per 

 cent for example, means that three-fourths of the total area under the 

 characteristic is available in the useful frequency region, while the remainder 

 of the area may be utilized to decrease the rate at which the characteristic 

 is cul-ojf. Hence, the realization of a prescribed resistance efiiciency in the 



* The effective impedance of the hne as viewed from the coupling circuit is equal to 



twice the actual line impedance. Thus, a penalty of 10 log -^ = 3db is imposed by the 



K 



presence of the balancing network. 



^ See eq. (4) and discussion in the following section. 



