A unitygain Butterworth lowpass filter has specifications om

A unity-gain Butterworth low-pass filter has specifications omega_c = 1000 rad/s and A_1 = 60 dB at 5000 rad/s. What order n is required?___An n^th order Butterworth LPF is formed of cascaded 1st and 2nd order Sallen-Key stages. For this problem, just consider one of the 2nd order stages. The 2nd order Sallen-Key circuit (with R_1 = R_2 = R) and its transfer function are shown here. H(s) = 1/R^2C_1C_2/5^2+2/RC_1 s+1/R^2C_1C_2 The transfer function of prototype 2nd order states is 1/s^2+bs+1; for this stage, b = 1.247. Starting with the prototype circuit (with R = 1 ohm and omega_c = 1 rad/s.) design the state for a final circuit with R\' = 1 k ohm and omega_c = 1000 rad/s Find the prototype capacitors C_1 and C_2 C_1 = C_2 = Find the scaling factors k_m and k_r k_m= k_r = Find the actual capacitors C_1\' and C_2\' C_1\' = C_2\'= What is the main advantages of Butterworth low-pass filters? Simple and versatile circuit design always critically-damped, which gives maximum flat response (sharpest cutoff with no peak) Q = 1/ squareroot 2, which gives maximum flat response (sharpest cutoff with no peak) can look up the transfer function in tables for any order

Solution

c)...(iii)