• Tags: bandwidth, half-power, selectivity
• Difficulty: Advanced

The half-power frequencies omega_1 and omega_2 are where the power drops to half its maximum value (equivalently, current drops to I_max/sqrt(2)). Bandwidth = omega_2 - omega_1 = R/L = omega_0/Q. The resonance curve is symmetric on a logarithmic frequency scale: omega_1*omega_2 = omega_0^2. For high Q circuits (Q > 10), the curve is approximately symmetric on a linear scale too: omega_1 ≈ omega_0 - R/(2L), omega_2 ≈ omega_0 + R/(2L). Selectivity = Q = f_0/Delta_f. Radio receivers use LC circuits with high Q to select a narrow band of frequencies. Tuning is achieved by varying C (variable capacitor), which changes omega_0 = 1/sqrt(LC) while keeping bandwidth approximately constant.