Design a Butterworth bandpass filter with the following specifications:
Lower stopband cutoff frequency = f1 = 1225 Hz Lower passband cutoff frequency = f2 = 2425 Hz Upper passband cutoff frequency = f3 = 3025 Hz Upper stopband cutoff frequency = f4 = 4175 Hz Maximum attenuation in the passband (dB) = Ap = 1.07 dB Minimum attenuation in the stopband (dB) = As = 22.25 dB excess='stop' 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 bandpass filter and find Q values and ?0 values of the second-order sections.
(e) Find the normalized component values for Deliyannis-Friend circuit.
(f) Find the scaled component values for Deliyannis-Friend circuit.
(a) ?1 = 7696.9020 rad/s, ?2 = 15236.7244 rad/s, ?3 = 19006.6356 rad/s, ?4 = 26232.2987 rad/s, ?s = 4.03, n = ceil (2.29) = 3
(b) Ap1 = 1.07 dB, As1 = 30.7835 dB, ? = 0.5286, ?c = 1.2368 rad/s
(c) Poles: S = -1, S = -0.5 ± j0. 866 Zeros: SZ = ?, SZ = ?, SZ = ?
(e)-(f) First second-order section (kf = ?o = 17017.6046) Normalized: C1 = 0.137 F, C2 = 0.137 F, R2 = 53.2836 ?, Ra = 26.6418 ?, Rb = 1.039 ?
Scaled: C1 = 8.0502 nF, C2 = 8.0502 nF, R2 = 1 k?, Ra = 26.6418 k?, Rb = 1.039 k?
Second second-order section (kf = ?o = 19161.1730) Normalized: C1 = 0.068 F, C2 = 0.068 F, R2 = 216.1484 ?, Ra = 108.0742 ?, Rb = 1.00934 ?
Scaled: C1 =3.55 nF, C2 = 3.55 nF, R2 = 216.1484 k?, Ra = 108.0742 k?, Rb = 1.00934 k?
Third second-order section (kf = ?o = 15113.8381) Normalized: C1 = 0.068 F, C2 = 0.068 F, R2 = 216.1484 ?, Ra = 108.0742 ?, Rb = 1.00934 ?
Scaled: C1 = 4.5 nF, C2 = 4.5 nF, R2 = 216.1484 k?, Ra = 108.0742 k?, Rb = 1.00934 k?
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