How this is calculated. The corner is where the capacitor's reactance equals the
resistance, giving
fc = 1 / (2πRC). At that point the output is
1/√2 of the input —
−3 dB, not zero, which is the most common
misunderstanding about filters. A first-order RC rolls off gently at 20 dB per decade, so a
signal one decade past the corner is still only attenuated tenfold; if you need a sharper edge
you need more poles. Phase shifts too, reaching 45° at the corner and approaching 90° far from
it, which matters in any control loop. In the time domain the same circuit is a step response
with
τ = RC and a 10–90 % rise time of
2.2τ — the filter that cleans
up your signal also slows your edges.