A band‑stop filter, also known as a band‑reject or notch filter, is a signal‑processing circuit or algorithm that attenuates frequencies within a specific range while allowing frequencies outside that range to pass with minimal alteration. The filtered frequency band is referred to as the stopband; frequencies below the lower cutoff and above the upper cutoff constitute the passbands.
Principle of operation
The filter’s frequency response exhibits a dip (or notch) centered at the stopband frequency. The depth of attenuation and the width of the stopband are controlled by circuit parameters (e.g., component values in passive LC or active op‑amp configurations) or by digital filter coefficients in discrete‑time implementations.
Types
- Passive band‑stop filter – realized with resistors, inductors, and capacitors; typically limited to low‑frequency applications because inductors become bulky at higher frequencies.
- Active band‑stop filter – uses amplifiers (operational amplifiers) together with reactive components, providing gain and better control of the stopband without large inductors.
- Digital band‑stop filter – implemented with finite‑impulse‑response (FIR) or infinite‑impulse‑response (IIR) algorithms; offers precise shaping of the stopband and can be reconfigured via software.
Design parameters
- Center frequency (f₀): the midpoint of the stopband.
- Bandwidth (Δf): the width of the frequency range that is attenuated.
- Quality factor (Q): defined as f₀ / Δf; higher Q yields a narrower stopband.
- Insertion loss: attenuation level within the stopband.
- Ripple: variations in magnitude response in the passbands (especially for filters designed with equiripple criteria).
Standard analog design equations for a second‑order band‑stop LC filter are:
$$ H(s) = \frac{s^{2} + \omega_{0}^{2}}{s^{2} + \frac{\omega_{0}}{Q}s + \omega_{0}^{2}} $$
where $ \omega_{0}=2\pi f_{0} $ and $ Q $ determines the sharpness of the notch.
Common applications
- Audio engineering: removal of unwanted hum (e.g., 50 Hz/60 Hz power‑line noise) or specific resonances.
- Communication systems: suppressing interfering carriers or spurious emissions without affecting adjacent channels.
- Instrumentation: eliminating narrow‑band disturbances in measurement signals.
- Medical devices: filtering out power‑line artifacts in electro‑cardiogram (ECG) or electro‑encephalogram (EEG) recordings.
Advantages and limitations
Band‑stop filters provide targeted attenuation without the need to redesign separate high‑pass and low‑pass stages. However, achieving a very narrow stopband with steep roll‑off may require higher‑order designs, increasing circuit complexity and potential phase distortion.
Related concepts
- Band‑pass filter: passes frequencies within a band and rejects those outside it.
- Notch filter: a special case of a band‑stop filter with a very narrow stopband (high Q).
- Low‑pass and high‑pass filters: the basic building blocks that can be cascaded to form a band‑stop response.
References
Standard signal‑processing textbooks and IEEE standards on filter design provide detailed methodologies for both analog and digital band‑stop filters.
