Calculate resonant frequency for LC tank circuits, filters, and oscillators.
At resonance, XL = XC and the reactive components cancel. In a parallel tank, impedance peaks at resonance; in series LC, impedance minimizes.
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.
Impedance peaks at resonance. Used for bandpass filters, oscillator tanks, and impedance matching. Energy circulates between L and C with minimal loss.
Impedance minimizes at resonance. Used for notch filters, traps, and tuned circuits. At resonance, XL and XC cancel, leaving only resistance.
Variable capacitors or inductors tune receivers to specific frequencies. Each station has a unique carrier frequency selected by LC resonance.
LC tanks determine oscillation frequency in Colpitts, Hartley, and Clapp oscillators. Q factor affects frequency stability.
Select a narrow band of frequencies while rejecting others. Cascade multiple LC stages for sharper selectivity.
LC networks match antenna impedance to transmission lines for maximum power transfer and minimum standing waves.
LC filters attenuate specific interference frequencies. Common mode chokes combined with capacitors form LC filters.
Tag antennas are LC circuits tuned to reader frequency. Resonance maximizes energy transfer for powering passive tags.
Higher Q means sharper resonance, less energy loss, but narrower bandwidth. Q = XL/R at resonance. Use low-loss components for high Q.
Inductors typically have ±10-20% tolerance; capacitors vary by type. Use tight tolerances or trimmable components for precision tuning.
Real inductors and capacitors have parasitic elements. Inductors have inter-winding capacitance; capacitors have lead inductance. Stay well below self-resonant frequency.
Both L and C drift with temperature. Use NP0/C0G capacitors and air-core inductors for temperature-stable oscillators.