5. Determine the transfer function of a second order Butterworth Lowpass filter

Question

5. Determine the transfer function of a second order Butterworth Lowpass filter with a 3dB cutoff of 5 Kilo Hertz. Design a circuit which realizes this filter using Sallen-Key configuration. Show the circuit below. Find all the values of the circuit elements and determine the DC gain. For sake of easy availability of parts to build the circuit, chose the capacitors needed to be 0.01 microFarads (0.01 x 10-6 F) Then simulate the circuit on Multisim and prove that it does indeed realize the lowpass filter. Attach the results to the home work.

Explanation / Answer

Out = In / (1 + 2 s csi / omega + ( s / omega )2) where s is Laplace variable [s/rad] csi is the damping factor omega is the resonating frequency If you want to calculate the Vout/Vin ratio: ----L---- | C | ---------- csi = 0 (damping comes from resistive component) omega = 1/sqrt(LC)

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