LC Resonance Calculator
Calculate resonant frequency for LC tank circuits, filters, and oscillators.
LC Resonance Formulas
At resonance, XL = XC and the reactive components cancel. In a parallel tank, impedance peaks at resonance; in series LC, impedance minimizes.
Understanding LC Resonance
An LC circuit consists of an inductor and capacitor that exchange energy. At the resonant frequency, energy oscillates between the magnetic field of the inductor and electric field of the capacitor. This creates a natural frequency determined by L and C values.
Parallel Tank Circuit
Impedance peaks at resonance. Used for bandpass filters, oscillator tanks, and impedance matching. Energy circulates between L and C with minimal loss.
Series LC Circuit
Impedance minimizes at resonance. Used for notch filters, traps, and tuned circuits. At resonance, XL and XC cancel, leaving only resistance.
Common Applications
Radio Tuning
Variable capacitors or inductors tune receivers to specific frequencies. Each station has a unique carrier frequency selected by LC resonance.
Oscillators
LC tanks determine oscillation frequency in Colpitts, Hartley, and Clapp oscillators. Q factor affects frequency stability.
Bandpass Filters
Select a narrow band of frequencies while rejecting others. Cascade multiple LC stages for sharper selectivity.
Antenna Matching
LC networks match antenna impedance to transmission lines for maximum power transfer and minimum standing waves.
EMI Filters
LC filters attenuate specific interference frequencies. Common mode chokes combined with capacitors form LC filters.
RFID Systems
Tag antennas are LC circuits tuned to reader frequency. Resonance maximizes energy transfer for powering passive tags.
Design Considerations
Q Factor (Quality Factor)
Higher Q means sharper resonance, less energy loss, but narrower bandwidth. Q = XL/R at resonance. Use low-loss components for high Q.
Component Tolerance
Inductors typically have ±10-20% tolerance; capacitors vary by type. Use tight tolerances or trimmable components for precision tuning.
Self-Resonant Frequency
Real inductors and capacitors have parasitic elements. Inductors have inter-winding capacitance; capacitors have lead inductance. Stay well below self-resonant frequency.
Temperature Stability
Both L and C drift with temperature. Use NP0/C0G capacitors and air-core inductors for temperature-stable oscillators.