LC Resonance Frequency Calculator
Enter L and C (or L and a target frequency) with the loss resistance to get f0, Q, bandwidth and impedance.
Step-by-step
- Enter valid values to begin.
Ideal lumped L and C with constant loss resistances. Series mode uses Rs only. Parallel mode combines the coil loss, shown as the equivalent parallel resistance L/(C·Rs), with any extra Rp you enter (0 means none). Half-power frequencies use the exact second-order relations and the BW = f0/Q rule is accurate for Q of about 5 and above. Self-resonance, parasitic capacitance, and component tolerance shift real circuits; lumped modelling gets poor once the wavelength approaches component size.
LC Resonance: Where Inductor and Capacitor Cancel
Core Engineering Principles
An inductor’s reactance rises with frequency and a capacitor’s falls. At one frequency they are equal in size and opposite in sign, and that is f0 = 1 / (2π√(LC)). At resonance a series circuit looks like just its loss resistance, so the current peaks. A parallel circuit does the opposite: the reactive currents circulate between L and C and the line sees a very high impedance. The reactance at that point is the characteristic impedance, Z0 = √(L/C), and it tells you how hard the tank has to be driven.
Q measures how sharp the resonance is, the ratio of that reactance to the loss. Series: Q = X/Rs. Parallel: Q = Rp/X. The 3 dB bandwidth is BW = f0 / Q, so a Q of 300 at 5 MHz is a 16 kHz-wide filter. Higher Q is not always better; a very narrow tank is hard to tune and drifts. In real circuits the capacitor is rarely the limit, because C0G ceramics have a Q in the hundreds or thousands; the inductor’s winding resistance and core loss usually set it. And remember the formulas assume lumped parts. Above a few hundred MHz, stray capacitance and lead inductance move the resonance more than your component tolerances do.
Q = X / Rs (series) • Q = Rp / X (parallel) • BW = f0 / Q
Zdyn = L / (C × Rs) • λ = c / f0
NEC & Standard References
IEEE Std 100 defines resonance, quality factor and bandwidth. IEC 60050 (the International Electrotechnical Vocabulary) gives the same terms in an international form. IEC 60384-8 covers class 1 ceramic capacitors such as C0G, which are the right choice for stable resonant circuits. Radio use must also respect the ITU Radio Regulations and your national spectrum rules, since a tuned circuit is often what sets the operating frequency. The Q figures here are a lumped-model estimate, not a guarantee.1. f0 = 1 / (2π√(10 × 10−6 × 100 × 10−12)) = 5.033 MHz.
2. Z0 = √(10 × 10−6 / 100 × 10−12) = 316.2 Ω, so XL = XC = 316.2 Ω.
3. Series Q = 316.2 / 1 = 316.2; BW = 5.033 MHz / 316.2 = 15.92 kHz.
4. Half-power points: 5.0250 MHz and 5.0409 MHz.
5. Parallel dynamic impedance = L / (C Rs) = 100 kΩ.
6. Wavelength = 299,792,458 / 5.033 × 106 = 59.6 m.
7. Solving instead for exactly 5 MHz with the same L gives C = 101.3 pF; the nearest E12 value, 100 pF, lands within +0.66%.
- Probe capacitance detunes high-impedance tanks. A 10 pF probe across 100 pF shifts f0 by about 5%; use a low-capacitance probe or loosely couple.
- Voltage magnification is real. At resonance, series L and C each see Q times the source voltage, so a 316 Q circuit driven at 1 V has 316 V across the capacitor.
- Tolerances stack. 5% parts can move f0 by about 5%, which exceeds a narrow bandwidth. Use trimmers for high-Q work.