Figure 10.19 shows a series RLC circuit. Calculate the resonant frequency, quality factor, bandwidth and half-power frequencies.

Question

Accepted Answer

The resonant frequency is,

[latex]f_{0}={\frac{1}{2\pi{\sqrt{600 imes10^{-3} imes80 imes10^{-12}}}}}=22.97\,\mathrm{kHz}[/latex] (10.125)

The quality factor is calculated as,

[latex]Q_{s}={\frac{1}{R}}{\sqrt{\frac{L}{C}}}={\frac{1}{540}}{\sqrt{\frac{600 imes10^{-3}}{80 imes10^{-12}}}}=160.38[/latex] (10.126)

The bandwidth is calculated as,

[latex]B W={\frac{f_{0}}{Q_{s}}}={\frac{22.97}{160.38}}=167.8\,{\mathrm{kHz}}/{\mathrm{s}}[/latex] (10.127)

The half-power frequencies are determined as,

[latex]f_{1}=22970-{\frac{540}{4\pi imes600 imes10^{-3}}}=22.90\,\mathrm{kHz}[/latex] (10.128)

[latex]f_{2}=22970+{\frac{540}{4\pi imes600 imes10^{-3}}}=23.04\,\mathrm{kHz}[/latex] (10.129)

Question 10.4: Figure 10.19 shows a series RLC circuit. Calculate the reson......