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Sallen-Key BandPass Analog Filter Frequency Response & Transfer Function

Engineering Prof. 2,538 1 year ago
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How to design and Band-pass Sallen-Key filter and choose value of resistors and capacitors are discussed in this Filter Design Tutorial and Example. This filter is implemented in the form of cascade of high-pass and low-pass filters realized with two op amps. For more amplifier example see https://www.youtube.com/playlist?list=PLrwXF7N522y4c7c-8KBjrwd7IyaZfWxyt . The overall bandpass filter (BPF) frequency response and transfer function is the product of computed frequency response and transfer functions of the cascades two sub filters each implemented with one operational amplifier and a pair of resistors and capacitors as discussed. The natural frequency and damping factor (zeta) for the highpass filter (HPF) and for the lowpass filter (LPF) are computed applying a combination of Kirchhoff circuit laws including KVL and KCL, virtual short of the properly biased op amp with negative feedback. Setting damping factor to 1/sqrt(2) results in a Butterworth Sallen-Key implementation for both sub-filters and hence flattest magnitude frequency response with minimal ringing in time-domain response for the overall filter. The time constant of the transient response of the sub-filters is defined by 1/(dampingfactor*cutoff frequency). The frequency response and overall functionality of the design are also intuitively discussed in this bandpass filter circuit design tutorial. A low noise low voltage offset Field Effect Transistor FET-input Op Amp from for example Analog Devices or Texas instruments with proper gain-bandwidth product is practically suitable for this design. It is shown that R1=2*R2 and C2=2*C1 in order to set damping factor to slightly underdamped value of 1/sqrt(2) needed to the Butterworth implementation of sub-filters as discussed in this video.

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