Filters and resonance: keeping only the frequencies you want
The RC low-pass cut-off 1/(2πRC), the high-pass filter, and LC resonance. The basics of removing sensor noise and filtering power.
RC low-pass filter
Put a capacitor to ground after a resistor and low frequencies pass while high frequencies drain away through the capacitor.
fc = 1 / (2πRC)
- 1 kΩ, 100 nF → fc ≈ 1.6 kHz
- At the cut-off the output is -3 dB (about 70%), and above it the output falls to 1/10 for every tenfold increase in frequency (-20 dB/dec).
High-pass filter
Swap the capacitor and resistor and DC is blocked while changes pass. Used to remove the DC component of an audio signal.
RoadmapSee where this note sits in Circuit Theory→Choosing the filter in front of an ADC
Noise above half the sampling frequency (Nyquist) cannot be filtered out after sampling. So an analog low-pass filter (anti-aliasing filter) goes in front of the ADC. Sampling at 1 kHz, put the cut-off at a few hundred Hz.
LC resonance
With an inductor and a capacitor together, the two reactances become equal at f0 = 1 / (2π√(LC)) and the circuit resonates.
- Crystal oscillators and radio circuits make use of resonance.
- An LC filter on a power input that resonates unintentionally makes the voltage overshoot, so a damping resistor is added.
Chain two or three filters to raise the order and the cut-off becomes sharper. When a still sharper filter is needed, use an active filter built with an op-amp.