Design a Butterworth bandpass filter with the following specifications:
Lower stopband cutoff frequency = f1 = 1120 Hz Lower passband cutoff frequency = f2 = 2225 Hz Upper passband cutoff frequency = f3 = 3125 Hz Upper stopband cutoff frequency = f4 = 4275 Hz Maximum attenuation in the passband (dB) = Ap = 1.17 dB Minimum attenuation in the stopband (dB) = As = 8.33 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 bandpass 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.
(a) ?1 = 7037.1675 rad/s, ?2 = 13980.0873 rad/s, ?3 = 19634.9541 rad/s, ?4 = 26860.6172 rad/s, ?s = 2.9428, n = ceil (1.36) = 2
(b) Ap1 = 0.3239 dB, As1 = 8.33 dB, ? = 0.2783, ?c = 1.8957 rad/s (c) Poles: S = -0.7071 ± j0. 7071 Zeros: SZ = ?, SZ = ?
(e)-(f) First second-order section (kf = ?o = 20905.6387) Normalized: C1 = 1.4142 F, C2 = 1.4142 F, R2 = 1 ?, R3 = 1 ?, RB = 1 ? , RA = 2 – 1/Q = 2.37 ?, Ra = 5.35 ?, Rb = 1.23 ?
Scaled: C1 = 67.6475 nF, C2 = 67.6475 nF, R2 = 1 k?, R3 = 1 k?, RB = 1 k? , RA = 2.37 k?, Ra = 5.35 k?, Rb = 1.23 k?
Second second-order section (kf = ?o = 13130.3509)
Normalized: C1 = 1.4142 F, C2 = 1.4142 F, R1 = 1 ?, R2 = 1 ?, R3 = 1 ?, RB = 1 ? , RA = 2 – 1/Q = 2.37 ?, Ra = 5.35 ?, Rb = 1.23 ?
Scaled: C1 = 0.1077 ?F, C2 = 0.1077 ?F, R2 = 1 k?, R3 = 1 k?, RB = 1 k? , RA = 2.37 k?, Ra = 5.35 k?, Rb = 1.23 k?
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