LC Resonance Calculator
Find the resonant frequency of an LC circuit, plus characteristic impedance, Q, and -3 dB bandwidth. Solve for f, L, or C, in series or parallel.
Solve for
Inductance L
Capacitance C
Resistance R (optional, for Q)
Frequency
1.59 MHz
f0 = 1 / (2π√(LC))
Resonator
How LC resonance works
An inductor and a capacitor store energy in opposite ways: the inductor in a magnetic field, the capacitor in an electric field. Connect them and energy sloshes between the two. The rate it sloshes is the resonant frequency:
f0 = 1 / (2π·√(LC))
At f₀ the inductive reactance and capacitive reactance are equal, so they cancel. What's left depends on how the parts are wired. In a series LC the two reactances cancel and the impedance collapses to just the resistance R, so current peaks. In a parallel LC, a tank, the impedance shoots up instead, so the current the source has to supply drops to a minimum. Same frequency, opposite behavior.
Q, bandwidth, and impedance
Resistance is what makes a resonance lossy, and the quality factor Q captures how lossy. A high-Q circuit rings cleanly with a tall, narrow peak; a low-Q one is broad and damped. The two wiring styles flip the formula:
Series: Q = (1/R)·√(L/C) Parallel: Q = R·√(C/L)
The term √(L/C) is the characteristic impedance Z₀, the reactance of each element at resonance. So Q is just Z₀/R for a series circuit and R/Z₀ for a parallel one. Once you have Q, the -3 dB bandwidth is fixed:
BW = f0 / Q
That's why Z₀ matters when you pick parts. Two L/C pairs can land on the same f₀ but a higher L/C ratio gives a higher Z₀, which means a higher Q for the same resistance, hence a sharper filter.
Practical Examples
- RF tank circuit: 100 µH with 100 pF resonates at f₀ ≈ 1.59 MHz, with Z₀ = 1 kΩ. Add 10 Ω of coil resistance in series and Q = 100, so the -3 dB bandwidth is about 15.9 kHz, narrow enough to pick one station out of the band.
- AM tuning: to tune 1 MHz with a 220 µH loopstick antenna, you need about 115 pF. A standard 10–140 pF variable capacitor covers the whole medium-wave band against a fixed coil.
- Buck converter output filter: 22 µH with 47 µF gives f₀ ≈ 4.95 kHz. The LC corner sits well below the switching frequency, so the filter smooths the ripple while passing the DC.
Design rules of thumb
- Set the frequency with L·C, the selectivity with L/C: the product fixes f₀, the ratio fixes Z₀ and therefore Q. Tune them independently.
- Buy the inductor, solve for the cap: good inductors come in coarse standard values, capacitors are finer and cheaper. Fix L, then set Solve for to C.
- The coil usually sets the loss: an inductor's winding resistance dominates Q in most LC circuits. A higher-Q coil buys a narrower bandwidth more than a better capacitor does.
- Leave room to trim: ceramic caps drift ±10–20%, so a circuit that needs a precise f₀ wants a small variable cap or a trimmer in parallel.
- Watch self-resonance: every inductor self-resonates with its own parasitic capacitance. Stay well below that frequency or the part stops behaving like an inductor.
FAQ
What is the resonant frequency of an LC circuit?
It's the frequency where the inductor's reactance and the capacitor's reactance are equal and cancel: f0 = 1 / (2π·√(LC)). At that point the circuit stores energy by swapping it back and forth between the inductor's magnetic field and the capacitor's electric field. The frequency depends only on the product L·C, so many L/C pairs give the same f0.
What's the difference between series and parallel resonance?
Both resonate at the same f0, but the impedance behaves oppositely. A series LC drops to its minimum impedance at resonance (just the series resistance R), so current peaks. A parallel LC, a tank circuit, rises to its maximum impedance at resonance, so the current drawn from the source dips. Series resonance is used to pass or trap a frequency; parallel resonance is used to select one in oscillators and filters.
What is the Q factor and how does R change it?
Q (quality factor) measures how sharp the resonance is: high Q means a narrow, tall peak; low Q means a broad, lossy one. For a series RLC, Q = (1/R)·√(L/C); for a parallel RLC, Q = R·√(C/L). The -3 dB bandwidth follows directly: BW = f0 / Q. Resistance is the loss term, so in a series circuit more R lowers Q, while in a parallel tank more R (a lighter load) raises it.
What is characteristic impedance Z0?
Z0 = √(L/C) is the reactance of the inductor (and of the capacitor, since they're equal) at resonance. It sets the energy stored per cycle and ties R to Q: series Q = Z0/R, parallel Q = R/Z0. Two LC pairs can share a resonant frequency but have very different Z0; raising the L/C ratio raises Z0, which raises Q for the same resistance.
How do I choose L and C for a target frequency?
Pick the frequency first, then split it between L and C using Z0 = √(L/C). For RF, a Z0 of a few hundred ohms to a couple kΩ is typical, which keeps both values practical. Fix one component to a value you can actually buy (a standard inductor or a variable cap), then solve for the other. This calculator does that directly: set Solve for to L or C.
Why doesn't my real circuit resonate exactly where the math says?
Parasitics. Real inductors have winding resistance and self-capacitance; real capacitors have lead inductance and ESR. The biggest offender for timing is usually the inductor's self-resonant frequency and the capacitor tolerance, which can be ±10-20% on ceramics. The formula gives the ideal f0; expect a few percent of drift on a real board, and trim with a variable cap if it matters.
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