Frequency-selective circuits that shape signals — essential for audio, RF, and signal processing.
Filter Fundamentals
Filters pass desired frequencies and attenuate others. Key specs: cutoff frequency fc (-3dB point, power halved), roll-off rate (dB/decade or dB/octave, depends on filter order), passband ripple (Chebyshev vs Butterworth), stopband attenuation, and phase response (linear phase = constant group delay, important for digital signals).
Filter Types & Orders
1st order (1 RC stage): -20dB/decade roll-off. Gentle, no resonance. 2nd order: -40dB/decade, can have resonance (Q factor). Butterworth: maximally flat passband. Chebyshev: steeper roll-off but passband ripple. Bessel: maximally flat group delay (best for square waves). Elliptic: steepest roll-off, ripple in both passband and stopband. For audio crossovers, Linkwitz-Riley is standard.
Cutoff for RC filters | Q factor = center freq / bandwidth (for bandpass)
🎮 Interactive: Filter Designer
🎮 Interactive: Filter Designer
Choose low-pass/high-pass, adjust R and C — see the frequency response curve.
For fc=1000Hz with R=1k\u03A9: C = 1/(2\u03C0\u00D7159\u03A9\u00D71000Hz) = 159nF
Active vs Passive
Passive: just R, L, C — no external power needed, but no gain, and inductors are bulky/expensive at low frequencies. Active: uses op-amps, can provide gain, high input impedance, low output impedance. Sallen-Key topology is most common. No inductors needed — simulate inductance with capacitors and op-amps (gyrator). For precision filters: switched-capacitor (LTC1060) or digital (FIR/IIR in DSP).