1. Second-order Butterworth Low-pass Filter Minh N Nguyen

2. Characteristics of Butterworth Filter Maximally flat magnitude response Maximally flat magnitude response A pulse input shows moderate overshoot and ringing A pulse input shows moderate overshoot and ringing The attenuation is -3dB at the cutoff frequency The attenuation is -3dB at the cutoff frequency

3. Multiple-feedback low- pass filter

4. The form of 2 nd low-pass filter T(S) = A0*ω0 ------------------------------------------------ s² + s(ω0/Q) + (ω0)^2

5. Transfer Function T(S) = - (G1G3/C2C5) ------------------------------------------------s²+s[(G1+G3+G4)/C2]+(G3G4/C2C5)

6. Low-pass filter parameters Open Loop DC Gain (A o ) of a low-pass filter. Open Loop DC Gain (A o ) of a low-pass filter. Determining the values of Pole Frequency (f o ) Determining the values of Pole Frequency (f o ) Magnitude of the peaking relative to the DC Gain (Q) Magnitude of the peaking relative to the DC Gain (Q)

7. Equations to calculate the parameters Ao = - (G1/G4) fo = (1/2pi) * [(G3/G4)/(C2C5)]^(1/2) Q = (1/(G1 + G3 + G4)) * [(G3G4C2)/C5]^(1/2)

8. Components Selection R1 = 81.98 kΩ R2 = 82.39 kΩ R3 = 38.77 kΩ C2 = 698 pF C5 = 136 pF 741 Op-Amp

9. Theoretical Calculations G1 = 1/R1 = 1.21E-5 G1 = 1/R1 = 1.21E-5 C2 = 698E-12 C2 = 698E-12 G3 = 1/R3 = 2.57E-5 G3 = 1/R3 = 2.57E-5 G4 = 1/R4 = 1.21E-5 G4 = 1/R4 = 1.21E-5 C5 = 136E-12 C5 = 136E-12

10. Theoretical Calculations (continue) Ao = - (G1/G4) = -1 fo = (1/2pi) * [(G3/G4)/(C2C5)]^(1/2) = 9.109 kHz Q = (1/(G1 + G3 + G4)) * [(G3G4C2)/C5]^(1/2) = 0.801 = 0.801

11. Schematic 2 nd low-pass filter

12. Graph of DC Analysis

13. Graph of AC Analysis