3. Design a Butterworth low pass filter based on the following specifications: t

Question

3. Design a Butterworth low pass filter based on the following specifications: the magnitude response H(j@)| must be down 1 dB at a frequency of 4 KHz and must be down 50 dB at a 35 KHz frequency Determine the order of the filter that achieves these design constraints and specify the transfer function H(s) that implements the filter. The denominator polynomials D(s) of H(s) for filter orders 1-1, 2, 3, 4, 5, 6, 7, 8 normalized to 1 rps cutoff frequency are given. D(s)-s+ 1 , D(s)-s2 + +1 , D,(s) = s3 +2s2 +2s +1 , D.(s) = s4 +2.613r + 3.4 14S +2.613s+1, D,(s) s+3.236s4 +5.236s+5.236s2+3.236s +1 D,(s) = s6 + 3.864S + 7.464s4 +9.1 41s. 7.464s2 +3.864s + 1 D, (s)-s'+4.494s +10.103s+ 14.606s +14.606s + 10.103s+4.494s+1 D, (s)s+5.126s' +13.138s +21.848s +25.691s'+21.848s +13.138s2 +5.126s+1

Explanation / Answer

fc=1/2*pi*RC Hz

for desgining we nee

H(jw)=1/1+e2(w/wp)2n

H1=H0/1+e2

H(jw)=(vout(jw)/vin(jw))

H(s)=vout/vin

the oreder of the filter is n=log28.475/log4=2.42

Related Questions

Navigate

• Browse (All)
• Browse 3
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.