DESIGN OF REACTIVE EQUALIZERS 



725 



In the figure, Lm represents the magnetizing inductance, L^ represents the 

 leakage reactance, and Ci and Cs represent, respectively, the low-side and 

 high-side parasitic winding capacitances. The magnetizing inductance Lm , 

 suice it is usually large so that its impedance is substantially infinite com- 

 pared with the other impedances of the circuit at high frequencies, affects 

 the response of the transformer at low frequencies only. Since the useful 

 band ordinarily specified does not include the range of frequencies where 

 the effects of Lm are noticeable, its presence may be omitted from further 

 consideration. In addition, it is never practical to retain Cz as the final 

 element of the reactive coupling network N. In this case, the parallel combi- 

 nation of Cz and C„ would, of course, seriously limit the final response of the 

 network. Thus, the least number of shaping elements is a series inductance 

 Li which splits the high-side winding capacitance C3 from the prescribed 

 terminating capacitance C„ . Hence, in general, the reactive coupling net- 

 work N is an (n — 1) element unbalanced ladder structure of alternating 

 series inductances and shunt capacitances beginning with a shunt capacitance 





= <Rc 





IDEAL 



Fig. 8 — High-side equivalent circuit of either coupling transformer of Figs. 4 and 5. 



and ending with a series inductance. Figure 9, then, indicates the general 

 form of the coupling network to be realized by the function chosen to 

 approximate e "* in this problem. 



Without loss of generality, it is convenient at this point to modify Figs. 6 

 and 7 in the manner indicated in Figs. 10 and 11. By including C„ as part 

 of A^' the problem has not been altered. However, it is necessary to recognize 

 that the final adjustment of the impedance level, i.e., the choice of Rq , must 

 be made in such a manner that the total area requirement, as specified in 

 eq. (4), is still met. In each figure Zn , Z22 , and 012 are the open-circuit driving- 

 point and transfer impedances of the network N'. 



With the element configuration specified and the reactive couplmg net- 

 work N defined, it is now appropriate to carry out the modification in the 



7 ( ' ") ^ R 



-^-^ — indicated previously. Thus, the fact that ~ = 1 at co = 0, 

 Ro Ro 



and that an )i element unbalanced ladder structure of alternating series 

 inductances and shunt capacitances terminated in a resistance has only an 



Zi2(X) 



form of 



nth order zero of the transfer impedance. 



Ro 



at infinity, allows the 



