Notch Filter Calculator

A notch filter, also known as a band-stop or band-reject filter, is an electronic filter that passes most frequencies unaltered but attenuates a very specific, narrow frequency range to very low levels. It is the opposite of a band-pass filter. The "notch" in the frequency response graph gives it its name.

This type of filter is highly selective, meaning it affects only a small band of frequencies. This makes it ideal for removing a single, unwanted interfering frequency from a signal, such as the 50Hz or 60Hz "hum" from AC power lines that can contaminate audio or sensor readings.

Center Frequency ($f_c$): This is the frequency at which the filter provides the maximum attenuation. It is the center of the "notch".

Q Factor (Quality Factor): The Q factor is a dimensionless parameter that describes how narrow the notch is. A higher Q factor corresponds to a narrower and deeper notch, making the filter more selective. A lower Q means a wider notch.

Bandwidth (BW): The range of frequencies that are attenuated. It's related to the center frequency and Q factor by the formula: $BW = f_c / Q$.

Passive Twin-T Notch Formula: For a standard Twin-T circuit, the center frequency is determined by the resistors (R) and capacitors (C):

$$f_c = \frac{1}{2 \cdot \pi \cdot R \cdot C}$$

• Audio Engineering: Removing power-line hum (50/60 Hz) from audio signals, eliminating feedback frequencies in live sound systems, and for creative sound shaping.
• Instrumentation & Control: Filtering out known interference frequencies in sensitive measurement equipment (like ECG/EEG machines).
• Radio Communications: Rejecting strong, interfering signals from nearby transmitters to improve reception of a desired signal.
• Speaker Crossovers: Used to flatten the impedance curve of a speaker driver at its resonant frequency, allowing for a more effective crossover design.

Passive Twin-T scope: the calculator uses R1 = R2 = R, R3 = R/2, C1 = C2 = C, and C3 = 2C. Its ideal passive Q is fixed at 0.25; a higher-Q notch needs an active feedback implementation and precision component matching.

Worked example: for 60 Hz and C = 100 nF, R = 1/(2πfC) = 26.526 kΩ, R3 = 13.263 kΩ, and C3 = 200 nF. Recalculate the achieved frequency after choosing real standard values.

RLC scope: L = 1/((2πf)²C) and R = 2πfL/Q describe an ideal series RLC branch. Actual notch depth depends on source/load impedance, component ESR, parasitics, and tolerance; the plotted response is an idealized aid, not a measured guarantee.

Verification: measure the assembled filter with a swept source and oscilloscope or network analyzer, then compare the measured center frequency and attenuation with the calculated values.

Primary references: Analog Devices MT-225 Twin-T Notch Filter and TI LPV521 60-Hz Twin-T application.