RC & RL Filter and Time Constant Calculator

Covers the two first-order circuits every electronics course starts with. Enter a resistor and a capacitor (RC) or an inductor (RL) and choose whether the output is taken as a low-pass or a high-pass filter; the tool gives the time constant τ (RC, or L/R), the cutoff frequency fc = 1/(2πτ) where the output is 3.01 dB down, and the 5τ time after which a step has settled to within 0.7 %. For a step of the voltage you give it returns the output at any moment — rising as V(1 − e^−t/τ) for a low-pass, decaying as V·e^−t/τ for a high-pass — and how long the output takes to reach a target voltage, or says that it never will. For a sine wave at a frequency you choose it gives the gain in decibels and as a ratio, the phase shift, the output amplitude, the reactance of the capacitor or inductor and the total series impedance. Which element the output is taken across is stated each time: the capacitor for an RC low-pass, the resistor for an RC high-pass and an RL low-pass, the inductor for an RL high-pass. Values accept SI prefixes (10k, 4k7, 100n, 10m for 10 mH, 1m for 1 ms). The results match a numerical integration of the circuit and scipy's frequency response. The model is ideal: it assumes a source with no internal resistance and no load on the output, so anything connected to the output becomes part of the circuit and moves the cutoff; real inductors have winding resistance and real capacitors leak and have ESR, which matter most at the extremes of frequency.