Passive, active, and digital filters (3ed., CRC, 2009) - tiera.ru

IIR Filters 19-17110.90.90.80.80.70.7Magnitude response0.60.50.4N = 4, λ s = 1.2λ p , δ 2 = 0.2Magnitude response0.60.50.4N=5, λ s = 1.2λ p , δ 2 = 0.20.30.30.20.20.10.100 1 2 3 4 5λ/λ p00 1 2 3 4 5λ/λ pFIGURE 19.11Magnitude responses of inverse Chebyshev filters.Note that the zeros are on the imaginary axis on the s plane. The filter order N required tosatisfy the specification in Equation 19.27 is the same as the order for the Chebyshev filter, given byEquation 19.38.Another form for the inverse Chebyshev filter has magnitude response square given byjH a (l)j 2 ¼11 þ e 2 T2 N (ls=lp)T 2 N (l s=l)(19:44)which passes through 1=(1 þ e 2 )atl ¼ l p . For further details of this form see Ref. [1].19.2.2.4 Elliptic Filters (Cauer Filters)Elliptic filters have equiripples in both the passband and the stopband. We summarize themagnitude response and the transfer function of an elliptic filter as follows. Detail of derivation can befound in Refs. [2,3].The magnitude response square is given byjH a (l)j 2 ¼11 þ e 2 R 2 N (l) (19:45)