DESIGN OF REACTIVE EQUALIZERS 



743 



coefficients a^ ■ ■ ■ a,, after they have been obtained from eq. (2Uj in order 



n 



to compensate for this decreased tolerance of 2J a/ cos j^p at hi^'h frequencies 



J=0 



in the useful band. The exact method of accomplishing this modification 

 depends on the particular design and the ingenuity of the designer. Never- 

 theless, no more than a few trials are necessary, in general, to produce'the 

 desired precision at all frequencies in the useful band. 



In practice, then, it is not appropriate that the Fourier cosine coefficients 

 finally chosen represent the optimum coefficients in the mean-square sense. 

 However, the important result established is that a systematic method 

 which realizes a satisfactory'^ set of coefficients Ao ■ ■ ■ A „ of f(x-) has been 

 developed. 



L2 L4 



;C3 C5: 



Z=R+JX 



N N' 



Fig. 22 — Input coupling network configuration. 



5. Illustrative Design 



The numerical example which will be considered is the design of an input 

 coupling network to equalize partially the loss characteristic of a coaxial 

 line. On the basis of the previous discussion of the design method it is ad- 

 vantageous to break down the procedure into four general operations: 



(1) Network Specifications 



(2) Transfer Specifications 



(3) Solution of Approximation Problem 



(4) Realization of Non-dissipative Network 



The first two of these operations are the choice of the appropriate form of 

 the design requirements while the last two represent the major divisions in 

 the procedure for designing the network to meet these requirements. 



In this design, a set of network requirements which are consistent with 

 the requirements indicated in Section 2 may be chosen as indicated in Fig. 22. 

 Thus, in order that the network N' correspond to the high-side equivalent 

 circuit of the coupling transformer and, at the same time, have a final 

 capacitance C„ , the least number of elements which may be chosen in a 

 practical design is n = 5. The specified elements of Fig. 22 are the parasitic 

 terminating capacitance C^ and the eflfective impedance of the line, Rl .-* 



^ See footnote 4. 



