• 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 = $omega_2$ - $omega_1$ = $\frac{R}{L}$ = $\frac{omega_0}{Q}$. 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: $omega_1$ ≈ $omega_0$ - $\frac{R}{2L}$, $omega_2$ ≈ $omega_0$ + $\frac{R}{2L}$. Selectivity = Q = $\frac{f_0}{Delta_f}$. 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.