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LC Resonance Calculator

Calculate resonant frequency for LC tank circuits, filters, and oscillators.

LC
Parallel LC Tank Circuit
f = 1 / (2π√LC)
Resonant Frequency
f = 1 / (2π√LC)
Char. Impedance
1000.00 Ω
XL at resonance
1000.00 Ω
XC at resonance
1.00 kΩ
ω (angular)
10.00 Mrad/s
Wavelength: 188.50 m

LC Resonance Formulas

f = 1 / (2π√LC)
L = 1 / (4π²f²C)
C = 1 / (4π²f²L)
Z₀ = √(L/C)
XL = 2πfL
XC = 1/(2πfC)

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.