Design a Butterworth bandstop filter with the following specifications:

Question

Lower passband cutoff frequency = f1 = 1125 Hz Lower stopband cutoff frequency = f2 = 2455 Hz Upper stopband cutoff frequency = f3 = 3055 Hz Upper passband cutoff frequency = f4 = 4255 Hz Maximum attenuation in the passband (dB) = Ap = 0.87 dB Minimum attenuation in the stopband (dB) = As = 4.37 dB excess='pass' km = 1000

(a) Find ?1, ?2, ?3, ?4, ?s, and order n.
(b) Find the recalculated values of Ap1, As1, ?, ?c.
(c) Find the poles S and zeros SZ of the normalized lowpass filter before multiplication by ?c.
(d) Find the transfer function of the frequency transformed bandstop filter and find Q values and ?0 values of the second-order sections.
(e) Find the normalized component values for Sallen-Key circuit for each second-order section.
(f) Find the scaled component values for Sallen-Key circuit for each second-order section.

Answer 1

(a) ?1 = 7068.5835 rad/s, ?2 = 15425.22 rad/s, ?3 = 19195.1311 rad/s, ?4 = 26734.9535 rad/s, ?s = 2.10335, n = ceil (1.38) = 2

(b) Ap1 = 0.3689 dB, As1 = 4.37 dB, ? = 0.2978, ?c = 1.8326 rad/s (c) Poles: S = -0.7071 ± j0. 7071 Zeros: SZ = ?, SZ = ?







(e)-(f) First second-order section (kf = ?p = 18234.2389), case 1 Normalized: C1 = 1.3264 F, C2 = 1.3264 F, C3 = 2.6528 F, R1 = 1 ?, R2 = 0.5 ?, R3 = 1 ?, R4 = 2.6337 ?, RB = 1 ? , RA = 1.02775 ?

Scaled: C1 = 72.7435 nF, C2 = 72.7435 nF, C3 = 0.1455 ?F, R1 = 1 k?, R2 = 1 k?, R3 = 500 ?, R4 = 1 ?, RB = 1 k? , RA = 1.02775 k?

Second second-order section (kf = ?p = 10363.9232), case 2 Normalized: C1 = 0.7539 F, C2 = 0.7539 F, C3 = 1.5078 F, C4 = 0.2863 F, R1 = 1 ?, R2 = 1 ?, R3 = 0.5 ?, RB = 1 ? , RA = 1.02775 ?

Scaled: C1 = 72.7435 nF, C2 = 72.7435 nF, C3 = 0.1455 ?F, C4 = 27.6205 nF, R1 = 1 k?, R2 = 1 k?, R3 = 500 ?, RB = 1 k? , RA = 1.02775 k?