2026-05-11
A notch filter (band-stop filter) rejects a narrow band of frequencies while passing everything above and below. The classic application: killing 60 Hz mains hum contaminating an ECG, audio preamp, or strain-gauge signal. Unlike a low-pass that throws away everything above the cutoff, a notch keeps your wideband signal intact and only deletes the offending frequency.
The workhorse topology is the twin-T notch. It uses two RC T-networks in parallel: one acting as a low-pass T (two Rs with a 2C shunt to ground) and one as a high-pass T (two Cs with an R/2 shunt to ground). At the notch frequency, their outputs are exactly 180° out of phase and cancel.
The center frequency is:
For 60 Hz, pick C = 0.1 μF, then R = 1/(2π · 60 · 0.1×10⁻⁶) ≈ 26.5 kΩ. Use 26.7 kΩ (1% standard). The shunt elements must be exactly 2C (0.2 μF) and R/2 (13.3 kΩ) — matching tolerance directly sets the notch depth. With 1% parts you'll get roughly 40 dB of rejection at f₀; with 5% parts, maybe 20 dB.
The passive twin-T has two annoying problems: low Q (broad notch, ~0.25) and loading sensitivity. The fix is to bootstrap it with an op-amp buffer that drives the junction of the shunt elements with a fraction k of the output. This forms an active twin-T:
Set k = 0.9 and Q jumps to 2.5 — a much narrower notch that won't gut nearby audio content. Push k too close to 1 and the circuit oscillates; stay below 0.95 in practice.
Real-world example: A biopotential front-end measuring 0.5–100 Hz ECG signals will pick up massive 60 Hz hum from fluorescent lights and power wiring through capacitive coupling to the patient's body. A bootstrapped twin-T at 60 Hz with Q ≈ 3 drops the hum 30+ dB while leaving the QRS complex (5–40 Hz) essentially untouched. Pair it with an instrumentation amp front-end and a right-leg drive circuit for clean traces.
Practical tips: Use C0G/NP0 ceramics or film caps — X7R drifts with temperature and voltage, smearing your notch. Hand-match resistors and capacitors with a DMM/LCR meter; a 1% mismatch on the shunt 2C is the single biggest depth-killer. For variable mains frequency (50/60 Hz regions), use a switched-capacitor universal filter IC like the LTC1059 instead.