A band reject filter circuit (often called a notch filter) attenuates a specific, narrow frequency band while passing all others unaltered. If you are building an audio preamp, an ECG sensor front-end, or a high-gain analog stage, 50 Hz or 60 Hz mains hum will ruin your signal-to-noise ratio. The most practical, bench-proven solution is the active Twin-T notch filter. By combining a passive Twin-T network with an op-amp buffer, you achieve a deep, high-Q notch without the loading effects that plague purely passive designs.
The Active Twin-T Topology: Nodes and Configuration
The Twin-T network consists of two parallel T-shaped voltage dividers: a low-pass T (resistors and a shunt capacitor) and a high-pass T (capacitors and a shunt resistor). At the target notch frequency, the phase-shifted signals from both T-networks cancel each other out perfectly.
Here is the node mapping for the active configuration:
- Vin: Signal input, feeding both the LP and HP T-networks.
- Node X (LP Junction): Junction of series resistors R1, R2, and shunt capacitor C3.
- Node Y (HP Junction): Junction of series capacitors C1, C2, and shunt resistor R3.
- V_sum: The tied outputs of Node X and Node Y, feeding the non-inverting input of the op-amp.
- Vout: Op-amp output. A portion of this is often fed back to the shunt leg (C3/R3 ground reference) via a voltage divider to tune the Q-factor (sharpness) of the notch.
You could use an LC (inductor-capacitor) series notch, but inductors are physically bulky, expensive, and ironically act as antennas that pick up the very magnetic mains hum you are trying to reject. Alternatively, a State-Variable (Biquad) filter offers excellent tuning, but it requires three separate op-amps and complex matching. The active Twin-T requires only one op-amp (like the low-noise NE5532 or TL072, costing ~$1.50) and standard passive components, making it the undisputed choice for fixed-frequency hum rejection.
Design Walkthrough: Sizing Components for a 60 Hz Notch
Let’s design a filter to kill 60 Hz hum. The center frequency formula for a symmetrical Twin-T is:
f_c = 1 / (2 * π * R * C)
We need to pick real, purchasable components. Capacitors dictate the noise floor and stability; always use C0G/NP0 ceramic or polypropylene film for the T-network. X7R ceramics introduce microphonic and voltage-coefficient distortion that will warp your notch.
- Select C: Choose C = 100 nF (0.1 µF). This is a standard value, readily available in C0G dielectric (approx. $0.15 each).
- Calculate R: R = 1 / (2 * π * 60 * 100e-9) ≈ 26,525 Ω.
- Select R: The closest standard 1% metal film resistor is 26.1 kΩ. This shifts the notch slightly to 61.3 Hz, which is perfectly acceptable for 60 Hz broadband hum.
- Scale the Shunt Legs: The Twin-T requires specific ratios. The LP shunt cap (C3) must be 2C. The HP shunt resistor (R3) must be R/2.
Final Bill of Materials (BOM)
| Component | Designator | Value | Implementation Note |
|---|---|---|---|
| Series Resistors | R1, R2 | 26.1 kΩ | 1% Metal Film |
| Shunt Resistor | R3 | 13.0 kΩ | 1% Metal Film (or two 26.1k in parallel) |
| Series Capacitors | C1, C2 | 100 nF | C0G/NP0 Ceramic, 50V |
| Shunt Capacitor | C3 | 200 nF | C0G/NP0 (two 100nF in parallel) |
| Op-Amp | U1 | NE5532 | Dual low-noise audio op-amp |
Breadboard Testing and Failure Mode Analysis
A Twin-T filter is highly sensitive to component mismatch. If your resistors are off by 2%, your notch depth will degrade from -60 dB to -20 dB. Here is how to validate it on the bench.
Step-by-Step Breadboard Verification
- Power the Op-Amp: Apply ±12V or ±15V to the NE5532 VCC/VEE pins. Place 100 nF bypass capacitors physically adjacent to the power pins. Tie the ground reference of your Twin-T shunt legs to the op-amp's virtual ground (mid-supply) if running single-supply, or true ground for dual-supply.
- Inject the Sweep: Connect a function generator to Vin. Set it to a 1 Vpp sine wave. Connect your oscilloscope Channel 1 to Vin and Channel 2 to Vout.
- Find the Null: Slowly sweep the frequency from 40 Hz to 80 Hz. Watch Vout. You should see the amplitude collapse dramatically between 58 Hz and 63 Hz.
- Measure the Depth: Switch the scope to RMS measurement or use a true-RMS multimeter. At the exact null, Vout should be at least 40 dB lower than Vin (a 1V input yields < 10mV output).
Behavior Table: Component Drift and Extremes
What happens when things go wrong? Understanding failure modes saves hours of debugging when a breadboard circuit refuses to notch.
| Failure / Change | Circuit Behavior | Scope Observation |
|---|---|---|
| R1 drifts high (+5%) | LP and HP paths unbalance; phase cancellation fails. | Notch depth degrades to -15 dB; asymmetrical skirts. |
| C3 (200nF) Opens | Low-pass T-network is broken; no LP signal reaches V_sum. | Circuit acts as a high-pass filter with a 60 Hz cutoff. |
| R3 (13k) Shorts | High-pass T-network shunts directly to ground. | Severe signal attenuation across all high frequencies. |
| C1 (100nF) Shorts | DC and low frequencies bypass the HP network. | Notch disappears; circuit passes all frequencies (unity gain). |
| Op-amp feedback open | Passive Twin-T is loaded by the scope probe (1 MΩ). | Notch depth limited to roughly -20 dB due to loading. |
Frequently Asked Questions
How do I tune a band reject filter circuit for 50 Hz instead of 60 Hz?
To shift the notch to 50 Hz (standard in the UK, EU, and Australia), you must increase the RC time constant. Keeping the same 100 nF C0G capacitors, recalculate R: R = 1 / (2 * π * 50 * 100e-9) ≈ 31,830 Ω. The closest 1% standard resistor is 31.6 kΩ. Swap R1 and R2 for 31.6 kΩ, and use two 31.6 kΩ resistors in parallel (yielding 15.8 kΩ) for the R3 shunt leg. Do not attempt to change the frequency by swapping just one capacitor; the 2:1 ratio between the series and shunt legs must be strictly maintained to preserve the null depth.
Why is my band reject filter circuit ringing or oscillating on the breadboard?
Oscillation in an active Twin-T usually stems from two issues: parasitic capacitance on the breadboard, or inadequate power decoupling. The NE5532 has a high gain-bandwidth product (10 MHz). If the V_sum node (the high-impedance input to the op-amp) picks up stray capacitance from adjacent breadboard rows, it introduces a phase shift that turns your negative feedback into positive feedback at high frequencies. Fix this by moving the op-amp physically closer to the V_sum junction, keeping lead lengths under 5 mm, and ensuring you have 100 nF ceramic bypass caps on the op-amp supply pins. If you are using a potentiometer in the feedback loop to tune the Q-factor, ensure it is wired as a variable resistor (rheostat) with the wiper tied to the unused terminal to prevent open-circuit oscillation if the wiper bounces.
Can I use a band reject filter circuit to remove PWM switching noise?
Yes, but the Twin-T is rarely the right tool for PWM noise. PWM switching frequencies (typically 20 kHz to 500 kHz for motor drivers and buck converters) usually present as broadband hash rather than a single, stable fundamental tone. A Twin-T notch will only kill the exact fundamental frequency, leaving the 3rd, 5th, and 7th harmonics intact. For PWM noise, a multi-pole active low-pass filter (like a 4th-order Butterworth Sallen-Key) with a cutoff set a decade below the PWM frequency is vastly more effective. If you are dealing with a specific, fixed-frequency resonant ringing spike (e.g., a 150 kHz LC tank ring), a Twin-T tuned to that exact spike can work, provided you use high-frequency suitable op-amps like the OPA1612 and keep parasitic breadboard capacitance to an absolute minimum.
