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Design an analog Butterworth filter that has 2 passband attenuation at frequency of 20....

Design an analog Butterworth filter that has 2 passband attenuation at frequency of 20rad/sec& at least 10dB stop band attenuation at 30rad/sec.

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Solution:

Given:

Ap=2dBAs=10dBfΩp=20rad/sec.Ωs=30rad/sec.

Ap=20logδq2=20logδ7δ7=0.7943

As=20logδ210=20logδ2

Ωc=Ωp(1/δ211)1/2N=

((301/0.794321)1/8)

Ωc=32.079rad/sec

sik=Ωcejπ/2ej(2k+1)π/2N=32.079ejπ/2ej(2k+1)π/8

S0=32.079ejπ/2ejπ/8=32.079ej5π/8=32.079[cos(5π/8)+jsin(5π/8)]=12.276+j29.637

S1=32.079ejπ/2ej3π/8=32.079ej7π/8=32.079[cos(7π/8)+jsin(7π/8)]=29.637+j12.276

S3=32.079ejπ/2ej>π/8=32.079ejππ/8=32.079[cos(11π/8)+jsin(11π/8)]=12.276j29.637

H(S)=S0S1S2S3(SS0)(SS1)(SS2)(SS3)=(12.276+j29.637)(12.276j29.637)[S(12.276+j29.637)][S(12.276j29.637)][S(29.637j12.276)][S(29.637+j12.276)]

=[(2.276)2+(29.637)2][(29.637)2+(12.276)2][(s+12.276)2+(29.637)2][(s+29.637)2+(12.276)2]=1.0589×106[(5+12.276)2+(29.637)2][(s+29.637)2+(2.276)2]

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