For the second-order bandpass filter assume the op amp is ideal (40 points) (a) Find the...

 

 
 

Transcribed Image Text:

For the second-order bandpass filter assume the op amp is ideal (40 points) (a) Find the transfer function, Vourt (joo)/ Vin(jo) Vin R1 C1 (b) How many poles and how many zeros are in the transfer function? (5 points) C2 (c) Rewrite the denominator of the transfer function obtained in (a) in the normalized form (i.e., products of jo/o, and/or (1+joo/op)). Use 0₁ and ₁ to represent the low and high frequency poles and relate them to parameters such as R₁, C₁, R₂, C₂ (you don't have to solve these equations for , and on's explicit expressions, 10 points) V₂ Problem 4 (continued): (d) Choose R₁, R₂, C₁, and C₂ (note the parameter choices won't be unique) such that you have a bandpass filter working for frequencies between 18 Hz and 18 kHz (i.e., frequencies less than 18 Hz or larger than 18 kHz are filtered out). The passband gain should be at least 1 (i.e., 0 dB). For practical reasons you should use capacitors no larger than 100 nF (Hint: Use the relations in (c) to help you narrow down the parameter choices, 10 points) Problem 4 (continued): (e) Use MATLAB/Python to generate a Bode plot of the magnitude of the transfer function Vout(jo)/Vin(jo). Check whether all the design goals (in terms of frequency range and passband gain) are satisfied; otherwise modify the parameters to improve your design. Attach the MATLAB/Python code and the Bode plot as a separate page (10 points) For the second-order bandpass filter assume the op amp is ideal (40 points) (a) Find the transfer function, Vourt (joo)/ Vin(jo) Vin R1 C1 (b) How many poles and how many zeros are in the transfer function? (5 points) C2 (c) Rewrite the denominator of the transfer function obtained in (a) in the normalized form (i.e., products of jo/o, and/or (1+joo/op)). Use 0₁ and ₁ to represent the low and high frequency poles and relate them to parameters such as R₁, C₁, R₂, C₂ (you don't have to solve these equations for , and on's explicit expressions, 10 points) V₂ Problem 4 (continued): (d) Choose R₁, R₂, C₁, and C₂ (note the parameter choices won't be unique) such that you have a bandpass filter working for frequencies between 18 Hz and 18 kHz (i.e., frequencies less than 18 Hz or larger than 18 kHz are filtered out). The passband gain should be at least 1 (i.e., 0 dB). For practical reasons you should use capacitors no larger than 100 nF (Hint: Use the relations in (c) to help you narrow down the parameter choices, 10 points) Problem 4 (continued): (e) Use MATLAB/Python to generate a Bode plot of the magnitude of the transfer function Vout(jo)/Vin(jo). Check whether all the design goals (in terms of frequency range and passband gain) are satisfied; otherwise modify the parameters to improve your design. Attach the MATLAB/Python code and the Bode plot as a separate page (10 points)