The Frequency Response of the Butterworth Filter Approximation

This study creates the design of a 10th order Butterworth bandpass filter based on an operational amplifier. It also provides the analysis of the results obtained in this context. Higher order filters are constructed using a combination of second and third order filters. Four parameters need to be specified in order to design a Butterworth bandpass filter, namely Ap (passband attenuation in dB), As (stopband attenuation in dB), fp (frequency at which Ap occurs), and fs (frequency at which As occurs). The design procedure involves two steps: one is to find the required filter order, and the other is to find the scaling factor which is to be applied to the formatted parameter values. The Butterworth bandpass filter is a combination of a low-pass filter and a high-pass filter. For a Butterworth low-pass filter, the resistance is approximately of 100 kΩ and the capacitor value is found by inverse scaling with the frequency and the chosen resistance value. For a Butterworth high pass filter, the used capacitor value is approximately of 0.05 µF and the resistor value is found by inverse scaling with the frequency and the chosen resistance value.