Design a Butterworth highpass filter with the following specifications:

Question

Passband cutoff frequency = fp = 2725 Hz Stopband cutoff frequency = fs = 1125 Hz Maximum attenuation in the passband (dB) = Ap = 0.97 dB Minimum attenuation in the stopband (dB) = As = 29.15 dB excess='pass'

(a) Find ?p, ?s, ?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 (do not multiply by ?c)
(d) Find the transfer function of the normalized lowpass filter and find Q values of the second- order sections.
(e) Find the normalized component values for unity gain Sallen-Key circuit.
(f) Find the scaled (km = 1000, kf = ?p/?c) component values for unity gain Sallen-Key circuit.

Answer 1

(a) ?p = 17121.68 rad/s, ?s = 7068.5835 rad/s, ?s = 2.4222, n = ceil (4.57) = 5

(b) Ap1 = 0.4849 dB, As1 = 29.15 dB, ? = 0.3437, ?c = 1.2381 rad/s

(c) Poles: S = -1, S = -0.3090 ± j0.9511, S = -0.8090 ± j0.5878 Zeros: SZ = ?, SZ = ?, SZ = ?, SZ = ?, SZ = ?







(e)-(f) kf = ?o =?p /?c = 13828.6422 rad/s First second-order section (Q = 0.618) Normalized: C1 = 1 F, C2 = 1 F, R1 = 0.8090 ?, R2 = 1.2361 ?

Scaled: C1 = 72.3137 nF, C2 = 72.3137 nF, R1 = 809.017 ?, R2 = 1.2361 k?

Second second-order section (Q = 1.618) Normalized: C1 = 1 F, C2 = 1 F, R1 = 0.309 ?, R2 = 3.2361 ?

Scaled: C1 = 72.3137 nF, C2 = 72.3137 nF, R1 = 309.017 ?, R2 = 3.2361 k?

First-order section: Normalized: R = 1 ?, C = 1 F Scaled: R = 1 k?, C = 72.3137 nF