Calculators / 01
LC and RLC Resonance Calculator
An inductor and a capacitor trade energy back and forth at one frequency, where their reactances cancel. What the resistance decides is how sharply: a small series resistance gives a deep, narrow dip; a large one flattens it. Choose Capacitor to treat a decoupling part as what it really is — a series RLC whose inductance is its ESL.
Reading the numbers
- Series circuits dip to their lowest impedance, R, at f0; parallel circuits peak at R there. The shaded band spans the two half-power points.
- Q is how many times narrower than f0 that band is. Above about 10 the dip or peak is sharp enough that a small shift in L or C moves the answer a long way.
- √(L/C) is the impedance at which the inductive and capacitive branches are equal. A decoupling capacitor whose ESR is far below it resonates sharply — the root of anti-resonance peaks between capacitors.
Every value is in the address bar as you change it, so a link reproduces the calculation exactly.
Type values with SI prefixes — 100n, 2.2p, 16G — or
drag the sliders; a bare number keeps the prefix already shown.
The formulas
Go deeper — assumptions, how it is checked, and sources
Assumptions. Ideal, frequency-independent R, L and C. In capacitor mode the ESR is held constant; a real part's ESR falls and then rises with frequency, and its capacitance drops with DC bias — Real Capacitors models both. The plot runs two decades either side of f0.
How it is checked. check-models.js asserts that the series circuit
is purely resistive at f0 (|Z| = R, zero phase), that f1·f2 =
f0², that the band is exactly f0/Q wide, that |Z| falls as 1/f far below
resonance and rises as f far above it, and that scaling L up and C down by the same factor leaves
f0 unchanged.
Source. D. M. Pozar, Microwave Engineering, 4th ed., Wiley, 2012, §6.1 (series and parallel resonant circuits).