POTENTIAL ANALOGUE METHOD OF NETWORK SYNTHESIS 



351 



the polynomials are not of the Tchebycheff type, and as a rule they are not 

 orthogonal. 



By its definition in (63) T(w) can always be expanded in a series of the 

 form 



r(w) = TI,W + ^0 + JlgnW ", 



(97) 



valid on and outside Ci . It follows that ^", which transforms into [r(w)]", 

 can always be expanded as an n degree polynomial in w plus a power series 

 in 1/w, and these correspond to Faiw) and Fbiw) respectively. The charge 



FREQUENCY, UJ 



Fig. 18— Illustrating the effect of contour shape on the accuracy of the approximate 

 transmission function for a flat filter. 



on C] corresponding to ^" is determined by Faiw) and is therefore a finite 

 Fourier sine series, similar to (88) except for more general coefl&cients. Con- 

 versely, we can always construct a polynomial in p of degree n, by choosing 

 appropriate coefficients for the various powers of p, in such a way that the 

 charge on Ci is merely sin nj^. In other words if 



then 



g'ii9) = sin ni^ 



F^(p) = Pvnip) 



