Active Filter Design

A filter allows for useful frequencies of electronic signals to pass through while blocking or suppressing noise and unwanted frequencies. Using resistors, capacitors, and inductors filters can be designed. For low frequency filters op-amps instead of inductors are used, in order to avoid bulkiness and difficult production requirements. The later is called the active filter, and prior passive filter. Active filter design process is summarized in the block diagram.

Example

Specifications:

• Low pass filter
• Ap = pass band allowance = 3 dB
• As = stop band attenuation >= 40 dB
• Fp = pass band frequency = 159.15 Hz
• Fs = stop band frequency = 318.30 H

Butterworth filter type was selected and the order was calculated to be n >= 7. Then, the filter was simulated in MATLAB, and the design was found to be stable and suitable. The denominators of Butterworth low-pass filters for normalized cutoff frequency of wc=1 rad/s were noted as below:
(s+1)(s2+0.445s+1)(s2+1.247s+1)(s2+s1.802+1)

A Sallen-Key implementation was selected and the values were calculated using relevant equations.