Question

6 2. Design an active filter to achieve the following transfer function: V. (0 Vi 3 + 2x10²s + 106

Answer 1

Griven Vo = 106 s²+2x1035 + 100 Now compairing in with standard and order trans for function given by Wa? 5²+2Ewns twn2 Wn = 103 rad/sec 2 Ewn = 2x103 &= 1 E is damping factor on is natural frequency For W=0 106 - Vo 0 +0+ 106 for 0 So this is and order low pass filter low pass filter gain is high at low frequency at higher frequency and zero

Now and order Actuie filter wing Opamp is given as: GH Vinom R3 Av R4 (2 R2 RI Open loop 12 here Av is a voltage gain It R2 =k R, #k= 1+R2 R, Transfer function is given by Vo Rg Rq C, (2 5²+5lt + ka Rah R3C, Ral Ralz R3 R4 C G Vin ㅗ T L-k. 7. Now take Rz=Rq=R C,= (2 = 0 and here k=1 (Re)? 2JS > - Vin

by compairing with standard equation we get RC= I wo RC = 1 RCE 103 #RC= 10-3 Let us take R= loka i.e lotr 3 こ 10 10-7E 104 * c = 0.1 uF as k=1 11 1 + R2 = .1 R, R2=0 Let us take R = lokz The active filter will be as- 10kr Oluf lokn Vire UF R = 10kh