Design a Butterworth highpass filter with the following specifications:

Question

Passband cutoff frequency = fp = 2525 Hz
Stopband cutoff frequency = fs = 1025 Hz
Maximum attenuation in the passband (dB) = Ap = 1.12 dB Minimum attenuation in the stopband (dB) = As = 19.05 dB excess='stop'
(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 Equal R, Equal C Sallen-Key circuit.
(f) Find the scaled (km = 1000, kf = ?p/?c) component values for Equal R, Equal C Sallen-Key circuit.

Answer 1

(a) ?p = 15865.0429 rad/s, ?s = 6440.2649 rad/s, ?s = 2.4634, n = ceil (3.10) = 4

(b) Ap1 = 1.12 dB, As1 = 26.0202 dB, ? = 0.5424, ?c = 1.1652 rad/s

(c) Poles: S = -0.3827 ± j0.9239, S = -0.9239 ± j0.3827 Zeros: SZ = ?, SZ = ?, SZ = ?, SZ = ?







(e)-(f) kf = ?o =?p /?c = 13615.0994 rad/s First second-order section (Q = 0.5412) Normalized: C1 = 1 F, C2 = 1 F, R1 = 1 ?, R2 = 1 ?, RB = 1 ? , RA = 2 – 1/Q = 0.152241 ?

Scaled: C1 = 73.4479 nF, C2 = 73.4479 nF, R1 = 1 k?, R2 = 1 k?, RB = 1 k? , RA = 152.241 ?

Second second-order section (Q = 1.3066) Normalized: C1 = 1 F, C2 = 1 F, R1 = 1 ?, R2 = 1 ?, RB = 1 ? , RA = 2 – 1/Q = 1.2346 ?

Scaled: C1 = 73.4479 nF, C2 = 73.4479 nF, R1 = 1 k?, R2 = 1 k?, RB = 1 k? , RA = 1.2346 k?