Electronics & discrete devices

Active filter

A filter passes the frequencies you want and blocks the ones you don't — like a bouncer letting only certain tones through. A passive filter does this with just resistors, capacitors and inductors; an active filter adds an op-amp, which lets it sharpen the response, provide gain, and avoid the bulky, lossy inductors that passive designs need at audio frequencies.

The four basic flavours are low-pass (keep the bass, cut the hiss), high-pass (keep the treble, cut the rumble), band-pass (keep a chosen band, like a radio tuner), and notch (kill one annoying frequency, like 60 Hz mains hum). Cascading op-amp stages — the famous Sallen-Key topology is the textbook example — builds steep, precise roll-offs from cheap resistors and capacitors alone.

First-order low-pass cutoff: f_c = 1 / (2π·R·C)

Each first-order stage rolls off at 20 dB/decade (≈6 dB/octave); to get a sharper 'brick wall' you cascade stages, and the chosen response shape (Butterworth = flattest passband, Chebyshev = sharpest knee with ripple, Bessel = cleanest phase) is a deliberate trade-off.

Also called
op-amp filter低通/高通/帶通濾波器