RC Filter, Low & High Pass

A capacitor's opposition to current depends on frequency. Its reactance is X_C = 1/(2πfC), which is large at low frequency and small at high frequency. An RC filter is just a potential divider between the fixed resistor and that changing reactance, so the split between them, and therefore the output, changes with frequency. That is the whole mechanism.

Which way it filters depends on where you take the output. Take it across the capacitor and you have a low-pass filter: at low frequency the capacitor's reactance is high so it keeps most of the voltage, while at high frequency its reactance collapses and the output falls. Take the output across the resistor instead and you have a high-pass filter, the reverse. The component values are identical; only the output tap changes.

The cut-off is the reference point. At f_c = 1/(2πRC) the reactance equals the resistance, the output has dropped to 1/√2, which is 70.7% or −3 dB, and the phase has shifted 45°. Beyond the cut-off a simple RC filter rolls off at 6 dB per octave, or 20 dB per decade. Note that only R and C set the cut-off: to move it you change the components, not the signal.

• Try this: Set a low-pass filter, then sweep the input frequency from low to high. Where does the output visibly start to shrink, and how does that line up with the cut-off marker?
• Try this: Park the frequency exactly on the cut-off. What percentage does the output read, and what is that in decibels?
• Try this: Halve R, then halve C. Each moves the cut-off. Which way, and why does the product RC being what matters mean two very different component pairs can give the same filter?