The LC (inductor-capacitor) resonant circuit is a fundamental component in electronics used in filters, oscillators, and frequency-selective networks. The resonance frequency occurs when the inductive reactance equals the capacitive reactance, resulting in a purely resistive impedance at that frequency.
At resonance, the energy oscillates between the magnetic field of the inductor and the electric field of the capacitor. The total impedance of the circuit is minimized in a series LC circuit and maximized in a parallel LC circuit. This behavior allows LC circuits to serve as bandpass or band-stop filters.
When resistance is included (RLC circuit), the circuit exhibits damped oscillations. The amount of damping depends on the resistance and is characterized by the quality factor \( Q \). Higher Q indicates lower energy loss and sharper resonance.
Resonant Frequency: \[ f = \frac{1}{2\pi\sqrt{LC}} \]
Quality Factor (Q): \[ Q = \frac{1}{R} \sqrt{\frac{L}{C}} \]
Bandwidth: \[ \text{Bandwidth} = \frac{f_0}{Q} \]