A stopband filter is a circuit that heavily attenuates a specific, targeted range of frequencies while allowing both lower and higher frequencies to pass through unaffected. In a real circuit or installation, it changes the signal-to-noise ratio by surgically removing a known interference source—like 60 Hz mains hum or a specific RF carrier—without rolling off your desired high-frequency data or low-frequency baseline. Beginners commonly confuse it with a band-pass filter (which does the exact opposite, passing only the target band) or a low-pass filter (which blocks everything above a single cutoff point). When you need to kill a specific noise frequency but preserve the spectrum on both sides of it, the stopband is your only option.
The Anatomy of a Stopband (and Why "Notch" Matters)
While "stopband" is the umbrella term for any filter that blocks a middle range of frequencies, practical engineering divides them into two distinct categories based on their Quality Factor (Q-factor):
- Band-Reject Filter (Wide): Has a low Q-factor (typically Q < 2). It blocks a broad swath of the spectrum. You use this when an entire band of frequencies is useless or harmful, such as blocking the entire 88–108 MHz FM broadcast band from a wideband software-defined radio (SDR) antenna.
- Notch Filter (Narrow): Has a high Q-factor (typically Q > 10, often > 50). It creates a deep, incredibly narrow "notch" or spike of attenuation at one exact frequency. You use this when the interference is a single, precise tone, like a 50 Hz or 60 Hz AC mains ground loop in an audio amplifier.
Worked Numeric Example: Designing a 60 Hz Twin-T Notch
Let’s design a passive Twin-T notch filter to strip 60 Hz hum from an ECG biopotential sensor front-end. The Twin-T topology uses two parallel RC branches (one low-pass, one high-pass) that sum together to create a deep null at the target frequency.
The center null frequency is defined by the standard RC time constant formula:
$$f_c = \frac{1}{2 \pi R C}$$
Step 1: Pick a standard capacitor value.
Let’s choose C = 100 nF (0.1 µF). This is a readily available film capacitor value.
Step 2: Calculate the required resistance.
Rearranging the formula to solve for R at exactly 60 Hz:
$$R = \frac{1}{2 \pi \times 60 \times 100 \times 10^{-9}}$$
$$R = \frac{1}{0.000037699} \approx 26,525 \Omega$$
Step 3: Select standard 1% E96 resistors.
The closest standard 1% metal film resistor value is 26.7 kΩ. Let’s verify our actual null frequency with this real-world part:
$$f_c = \frac{1}{2 \pi \times 26700 \times 100 \times 10^{-9}} = 59.6 \text{ Hz}$$
Step 4: Build the Twin-T network.
To complete the circuit, you don't just use one R and one C. The classic Twin-T requires:
- Branch 1 (Low-pass): Two 26.7 kΩ resistors in series, with a 200 nF capacitor (two 100 nF in parallel) tied to ground from their midpoint.
- Branch 2 (High-pass): Two 100 nF capacitors in series, with a 13.35 kΩ resistor (half of R) tied to ground from their midpoint.
This passive network will yield a deep null at 59.6 Hz. However, to achieve a Q-factor high enough to prevent attenuation of neighboring ECG signal harmonics, you must buffer this network with an op-amp in a positive feedback loop to boost the Q from a native ~0.3 up to 20 or higher.
Where You Meet This in Practice
If you are building or debugging hardware, you will run into stopband requirements in three primary domains:
- Biopotential Sensors (ECG/EEG): The human body acts as a massive antenna for 50/60 Hz mains fields. While modern ADCs like the TI ADS1298 use a Right-Leg Drive (RLD) circuit to cancel common-mode noise, residual differential 60 Hz hum still requires a high-Q analog or digital notch filter before the signal is digitized.
- Software Defined Radio (SDR): If you live near a high-power FM broadcast tower, that single 100 kW transmitter will overload the 8-bit ADC in an RTL-SDR dongle, causing aliasing that blinds you to the rest of the spectrum. A wide band-reject filter blocking 88–108 MHz is mandatory to preserve the ADC's dynamic range.
- Switch-Mode Power Supplies (SMPS): A buck converter switching at 500 kHz might generate a stubborn harmonic at 1.5 GHz that fails FCC radiated emissions testing. A surface-mount LC stopband trap tuned precisely to 1.5 GHz is placed in series with the output trace to kill the harmonic without affecting the DC output.
Decision Path: Choosing Your Stopband Topology
Do not default to a passive RC network just because it is easy to simulate. Use this decision matrix to select the right architecture for your specific frequency and bandwidth constraints.
| Application Domain | Frequency Range | Bandwidth (Q) | Recommended Topology | Concrete Part Pick |
|---|---|---|---|---|
| Audio / Bio Hum | < 1 kHz | Narrow (Q > 10) | Active State-Variable IC | Texas Instruments UAF42 |
| SDR / RF Front-End | > 1 MHz | Wide (Q < 2) | Passive LC Cavity / Ceramic | Mini-Circuits BFCN-100+ |
| SMPS Harmonic Trap | 10 MHz - 3 GHz | Narrow (Q > 50) | Passive Surface Mount SAW / LC | Custom LC parallel resonant trap |
| Data Acquisition | Any (Post-ADC) | Any | Digital IIR/FIR Notch | ARM CMSIS-DSP arm_biquad_cascade_df2T |
The Tolerance Trap: Common Bench Mistakes
The most frequent reason a homebrew passive notch filter "doesn't work" on the bench is component tolerance. A Twin-T or bridged-T notch relies on the exact mathematical cancellation of two signal paths.
If you build the 60 Hz filter calculated above using standard 5% carbon film resistors and 10% ceramic capacitors, the two branches will not cancel perfectly. Instead of a -60 dB deep null, your oscilloscope will show a shallow, wide -15 dB dip. The 60 Hz hum will still be clearly audible in your audio amp or visible in your ECG trace.
The Fix: For any passive analog notch filter below 100 kHz, you must use 1% (or better) metal film resistors and 2% (or better) C0G/NP0 dielectric film capacitors. Furthermore, at frequencies above 1 MHz, parasitic trace capacitance and component lead inductance will shift your null frequency. For RF work, abandon discrete LC networks and use integrated ceramic or cavity filters like the Analog Devices MT-222 tutorial recommends for high-frequency precision.
FAQ: Stopband Filter Troubleshooting
Why is my notch frequency shifted from the calculation?
Beyond component tolerance, stray capacitance is the usual culprit. A standard breadboard introduces 2 pF to 5 pF of parasitic capacitance between adjacent rows. In a high-impedance 100 kHz notch filter, 5 pF is enough to shift the null by several kilohertz. Move the circuit to a soldered perfboard or PCB with a ground plane to lock in the parasitics.
Can I cascade two notch filters to make the stopband wider?
Yes, but with a severe warning regarding insertion loss. Cascading two passive Twin-T filters tuned to 58 Hz and 62 Hz will widen your stopband, but the overlapping "skirts" of the filters will heavily attenuate your passband signals (the frequencies you actually want to keep). If you need a wide, flat-bottomed stopband, switch to an active Sallen-Key band-reject topology or a digital FIR filter.
Should I use an analog notch or a digital notch in my microcontroller?
If your ADC has sufficient bit-depth (16-bit or higher) and the interference isn't so massive that it clips the ADC's input voltage range, always use a digital IIR notch filter in firmware. Digital filters suffer from zero component drift, zero temperature coefficients, and can be tuned via software registers. Only use an analog stopband if the noise is so large it destroys your ADC's dynamic range before digitization.
