Q.What is an active filter?

An active filter uses an op-amp together with resistors and capacitors to select or reject bands of frequencies. Unlike a passive filter, it needs no bulky, lossy inductors, and because the op-amp can provide gain, the signal is not attenuated in the passband. Filters are classified by which frequencies they pass: low-pass (passes frequencies below a cut-off), high-pass (passes frequencies above a cut-off), band-pass and band-reject.

A first-order low-pass active filter is a passive RC low-pass section (resistor in series, capacitor to ground) feeding an op-amp connected as a non-inverting amplifier. It gives flat gain up to a cut-off ($-3\ \text{dB}$) frequency, after which the gain falls off at $20\ \text{dB/decade}$. The cut-off frequency and passband gain are

A first-order high-pass filter simply interchanges the R and C of the input network, so it blocks low frequencies and passes high frequencies above the same $f_c$. …