0.8 50° Two-pole filte -200° Y Three-pole filter FIGURE 10.7 Frequency curves of two- and three-pole Chebyshev filters with o.= 2.5 rad/s: (a)magnitude curves;(b phase curves. Using Eq(10.10), the two-pole type 1 Chebyshev filter has the following frequency function +∈2(o/o1)2-1 For the case of a 3-dB ripple(e= 1), the transfer functions of the two-pole and three-pole type 1 Chebyshev 0.50 H=2+064505+07080 0.2510 H(s)= s3+0.5970s2+0.92802s+0.25l0 where (.=3-dB bandwidth. The frequency curves for these two filters are plotted in Fig. 10. 7 for the case o The magnitude response functions of the three-pole Butterworth filter and the three-pole type 1 Chebyshev filter are compared in Fig. 10.8 with the 3-dB bandwidth of both filters equal to 2 rad. Note that the transition om passband to stopband is sharper in the Chebyshev filter; however, the Chebyshev filter does e 2000 by CRC Press LLC© 2000 by CRC Press LLC Using Eq. (10.10), the two-pole type 1 Chebyshev filter has the following frequency function For the case of a 3-dB ripple (e = 1), the transfer functions of the two-pole and three-pole type 1 Chebyshev filters are where wc = 3-dB bandwidth. The frequency curves for these two filters are plotted in Fig. 10.7 for the case wc = 2.5 rad. The magnitude response functions of the three-pole Butterworth filter and the three-pole type 1 Chebyshev filter are compared in Fig. 10.8 with the 3-dB bandwidth of both filters equal to 2 rad. Note that the transition from passband to stopband is sharper in the Chebyshev filter; however, the Chebyshev filter does have the 3- dB ripple over the passband. FIGURE 10.7 Frequency curves of two- and three-pole Chebyshev filters with wc = 2.5 rad/s: (a) magnitude curves; (b) phase curves. w Three-pole filter Two-pole filter 0 1 2 3 4 5 6 7 8 9 10 0.707 1 0.8 0.6 0.4 0.2 0 Passband |H(w)| (a) w Three-pole filter Two-pole filter 0 1 2 3 4 5 6 7 8 9 10 –50° –100° –150° –200° –250° –300° 0 |H(w)| (b) *H( )* [ ( / ) ] w w w = + - 1 1 2 1 2 1 2 2 e H s s s H s s s s c c c c c c c ( ) . . . ( ) . . . . = + + = + + + 0 50 0 645 0 708 0 251 0 597 0 928 0 251 2 2 2 3 3 2 2 3 w w w w w w w