RC Time Constant and LC Resonance Calculator
Time constant, corner frequency, rise time and the charge curve for an RC pair, plus resonant frequency, Q and bandwidth for an LC tank.
At resonance the inductive and capacitive reactances are equal and opposite, so they cancel and only the resistance in the loop is left. That is why a high-Q tuned circuit can carry a very large circulating current from a very small drive.
The corner frequency is not an edge
This is the misreading worth fixing. At the frequency a filter is named for, the signal is already down 3 dB — 70.7% of the input, not 100%. Past it the slope is a gentle 6 dB per octave, or 20 dB per decade. A single RC stage does not remove a frequency, it leans on it. If you need something actually gone, you need several stages or an active filter, and you should place the corner well away from the band you care about.
- Only the product matters. 10 kΩ with 100 nF and 1 kΩ with 1 µF are the same filter. Choose the split by what else the circuit needs — a lower resistance loads the source more, a higher one is noisier and more easily disturbed.
- Five time constants is "settled". One τ gets to 63.2%, three to 95%, five to 99.3%. Nothing ever fully arrives, which is why the convention is a percentage rather than a time.
- Rise time is 2.2 τ. The 10% to 90% figure quoted on scopes and datasheets, and the fastest edge an RC will pass.
- The time and frequency views are one circuit. τ = RC is the same product that sets f = 1/(2πRC). A filter that passes a frequency also passes an edge of the matching sharpness — you cannot have a slow filter and fast edges.
How to use
- Enter a resistance and capacitance in any notation — 10k and 100n works.
- Read the time constant, the corner frequency and the 10 to 90 percent rise time.
- Enter a frequency to see how far a single stage attenuates it, in decibels.
- Switch to the LC tab for resonant frequency, reactance, Q and bandwidth.
Frequently asked questions
What does the time constant actually mean?
It is the time for a capacitor to charge to 63.2 percent of the way to its final value, and it is the same figure for discharging down to 36.8 percent. The curve is exponential, so it never truly arrives: three time constants reach 95 percent, five reach 99.3 percent, and the usual engineering convention is to call five time constants settled.
Is the corner frequency where the filter stops?
No, and this is the single most common misreading. At the frequency a filter is named for, the output is already down 3 decibels, which is 70.7 percent of the input. Beyond it the slope is a gentle 6 decibels per octave. A single RC stage does not remove a frequency, it leans on it — put the corner well clear of the band you care about, or use several stages.
Does it matter which resistor and capacitor I choose?
Only the product sets the timing, so 10 kilohms with 100 nF behaves identically to 1 kilohm with 1 microfarad. The split matters for everything else: a lower resistance loads whatever drives it more heavily, and a higher one is noisier and more easily disturbed by stray currents. Above a megohm or so, board leakage and op-amp bias current start to compete with the resistor you chose.
Why is rise time 2.2 times the time constant?
Because rise time is conventionally measured from 10 percent to 90 percent rather than from zero to everything, and the natural logarithm of nine is about 2.197. It is the figure scopes and datasheets quote, and it tells you the fastest edge the network will pass — which is why a slow filter and fast edges are not something you can have at once.
What happens at LC resonance?
The inductive and capacitive reactances become equal and opposite, so they cancel and only the resistance in the loop is left. In a series circuit that means the impedance collapses to almost nothing at one frequency; in a parallel tank it means the impedance peaks. Either way a very small drive can sustain a very large circulating current, which is what makes tuned circuits useful for selecting one station out of a band.
What is Q telling me?
How sharp the resonance is — reactance at resonance divided by the resistance in the loop, and equivalently the resonant frequency divided by the 3 decibel bandwidth. A Q of 100 on a 1.6 megahertz tank gives a 16 kilohertz window, which is about right for separating AM stations. Losses in the inductor usually dominate, so real Q is set by the coil far more than by anything else in the circuit.
Do these formulas hold for real parts?
Closely enough at low frequencies, and less so as you climb. Real capacitors have series resistance and inductance, real inductors have winding resistance and self-capacitance, and both drift with temperature. Electrolytics in particular can be 20 percent off their marking when new. Treat the answer as the design target and expect to trim it on the bench.
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