Explainer · Intermediate · about 30 minutes
Filters and frequency
A resistor and a capacitor together can let slow signals through and block fast ones, or the other way round. That simple idea removes noise from sensors, turns PWM into a steady voltage, and shapes the sound in every speaker. Change the parts and the input frequency, and watch what comes out.
The idea
A capacitor needs time to charge. Feed a resistor and capacitor a slowly changing voltage and the capacitor keeps up; change it quickly and the capacitor cannot follow.
- Low-pass: take the output across the capacitor. Slow signals pass; fast ones are reduced.
- High-pass: swap the parts and take the output across the resistor. Fast signals pass; slow ones, and steady DC, are blocked.
The dividing line is the cutoff frequency:
fc = 1 ÷ (2π × R × C)
At fc the output is 70.7% of the input (−3 dB, half the power), shifted by 45°. Far beyond fc, each tenfold change in frequency changes the output tenfold (20 dB per decade).
Try it
Frequency response
gain (dB) your frequency −3 dB
What goes in and what comes out
input output
Model: ideal resistors and capacitors driven by an ideal source, with nothing connected to the output. The two-stage and band-pass circuits assume a buffer (an op-amp follower) between stages, so one stage does not load the next. Without buffers, real stages interact and the results differ.
Where you meet filters
- PWM to a steady voltage: a low-pass filter with fc well below the PWM frequency leaves just the average. This is a cheap digital-to-analogue converter.
- Quieter sensor readings: a low-pass filter before an ADC removes fast noise from a slow signal such as temperature.
- Blocking DC: a capacitor in series (a high-pass filter) passes an audio signal but not the steady voltage it rides on.
- Speakers and tone controls: crossovers send low frequencies to the woofer and high ones to the tweeter.
- Button debouncing: a small low-pass filter smooths out the rapid bouncing of a switch's contacts.
- On the oscilloscope: the sandbox low-pass example drives a real RC circuit at its cutoff frequency; probe 2 shows 70.7% of probe 1, an eighth of a cycle (45°) behind. There is a high-pass example too.