Formula Used
- Capacitor energy: UC = ½ C V²
- Inductor energy: UL = ½ L I²
- Resonant angular frequency: ω = 1 / √(LC)
- Frequency: f = ω / (2π), and period: T = 1 / f
- Ideal time forms: V(t) = Vmax cos(ωt + φ), I(t) = Imax sin(ωt + φ)
In an ideal LC oscillator, total energy is conserved and alternates between electric and magnetic storage.
How to Use This Calculator
- Select a calculation mode that matches your known values.
- Enter inductance L and capacitance C, and choose correct units.
- Provide peak or instantaneous voltage/current as required.
- For time-based results, enter t and optional phase φ.
- Press Calculate to view results above the form.
- Use CSV or PDF buttons to export the computed table.
Example Data Table
| L (mH) | C (µF) | Vmax (V) | f (Hz) | Utotal (J) |
|---|---|---|---|---|
| 10 | 0.47 | 12 | 232.50 | 0.00003384 |
| 5 | 1.00 | 9 | 71.18 | 0.00004050 |
| 1 | 0.10 | 5 | 503.29 | 0.00000125 |
| 22 | 0.22 | 24 | 72.39 | 0.00006336 |
| 0.47 | 0.01 | 3.3 | 2323.79 | 0.00000005445 |
Examples assume ideal conditions and peak-voltage mode.
LC Oscillator Energy Article
1) Why energy matters in an LC resonator
An ideal LC resonator stores energy without loss, trading it between electric and magnetic fields. This calculator helps quantify that exchange using your inductance, capacitance, and voltage or current inputs. It is useful for checking designs, validating measurements, and estimating safe operating limits.
2) Capacitor energy and voltage sensitivity
Electric energy in the capacitor is UC = ½ C V². The square term means small voltage changes can strongly affect stored energy. For example, doubling V increases UC by four, which is critical when selecting dielectric ratings and insulation clearances.
3) Inductor energy and current stress
Magnetic energy in the inductor is UL = ½ L I². Peak current drives copper loss and core stress in real coils. Higher inductance reduces peak current for a given peak voltage when C is fixed, but it also changes frequency and transient response.
4) Total energy and the exchange cycle
In the ideal case, Utotal = UC + UL stays constant. At voltage peaks, energy is mostly electric; at current peaks, it is mostly magnetic. The time-based mode uses V(t) and I(t) to show both energies at a chosen instant.
5) Frequency from component selection
Resonant frequency depends on f = 1 / (2π√(LC)). Smaller L or C increases frequency. Practical designs often use C from pF to µF and L from nH to H, spanning audio to radio ranges.
6) Peak relations and characteristic impedance
The calculator also reports √(L/C), a useful scale for the circuit’s reactive impedance. It links peaks through Imax = Vmax√(C/L) and Vmax = Imax√(L/C), helping you translate voltage measurements into current stress.
7) Using real measurements responsibly
When you enter instantaneous V and I, the computed total reflects that measurement moment. In real circuits, resistance and radiation reduce total energy over time. Treat results as an ideal baseline, then add safety margins for temperature rise and component tolerances.
8) Engineering checks and common applications
Typical uses include tank circuits, filters, oscillators, wireless power links, and pulse-forming networks. Compare peak energy to capacitor ripple limits and inductor saturation. If computed peak current is high, consider increasing L, reducing Vmax, or improving conductor cross-section and cooling.
For consistent results, use realistic component values and correct units. The output table reports frequency, period, and characteristic impedance along with energies in joules. If values seem extreme, recheck unit prefixes such as mH versus H or µF versus nF. In lab work, measure voltage with a compensated probe and current with a low-inductance shunt or current probe, then compare the instant-energy mode to the expected conserved total. Export CSV for spreadsheets and PDF for documentation.
FAQs
1) What does “total energy” mean here?
Total energy is the sum of capacitor and inductor stored energy at the same instant. In an ideal LC circuit it stays constant and only shifts between electric and magnetic forms.
2) Why can peak capacitor energy equal peak inductor energy?
They peak at different times. At voltage peak, energy is mostly in the capacitor. Half a period later, current peaks and the same total energy appears as magnetic energy in the inductor.
3) Which mode should I use if I only know Vmax?
Use “Peak Energy from Vmax.” Enter L and C with units, then Vmax. The calculator returns total energy, peak current estimate, and the resonance frequency for your component pair.
4) Can I compute energy from a scope snapshot of V and I?
Yes. Use “Instant Energy from V and I.” Enter the measured voltage and current at the same time point. The tool computes Uc, Ul, and their sum for that instant.
5) What does the phase φ input change?
Phase shifts the time reference in the time-based mode. If you do not know it, set φ to 0°. Use a measured waveform reference to estimate phase when needed.
6) Why might my real circuit show decreasing total energy?
Real circuits have resistance, dielectric losses, and radiation. These dissipate energy each cycle, so total energy decays. The calculator assumes ideal storage to provide a clean baseline.
7) How do I reduce peak current in my design?
Reduce Vmax, increase L, or decrease C while respecting the target frequency. Also check that the inductor does not saturate and that wiring resistance and heating remain acceptable.