RC Low-Pass Filter
Cutoff frequency and time constant for the single-pole RC.
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The engineering
One pole: −3 dB at fc, −20 dB per decade after, and 45° of phase lag right at cutoff. The settle row matters for multiplexed DAQ — switch channels faster than ~5τ and you're reading the filter, not the signal.
1 kΩ and 1 µF is the classic 159 Hz anti-alias pole in front of a slow ADC.
Where this math comes from
The exponential charge curve is telegraph mathematics: William Thomson's 1855 analysis of the transatlantic cable showed signals smearing by exactly this RC law, which set the speed limit of Victorian communication.
Oliver Heaviside turned the differential equations into usable operator arithmetic in the 1880s, and Stephen Butterworth's 1930 paper on 'maximally flat' filters opened the systematic filter-design era this single pole begins.
- 1855Lord KelvinRC law of the telegraph cable — the time constant's debut.
- 1885Oliver HeavisideOperational calculus makes filter math tractable.
- 1930Stephen ButterworthMaximally flat filter paper starts modern filter design.
See the full timeline of the math behind every calculator →
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