A tank circuit has a capacitor of 100 pF and an inductor of 100 μH. The resistance of the inductor is 5 Ω. Determine the (a) resonant frequency, (b) impedance at resonance (c) Q-factor, and (d) bandwidth.

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Accepted Answer

Given L = 100 μH, C = 100 pF and R = 5Ω

(a) The resonant frequency, [latex]f_{O} =\frac{1}{2\pi \sqrt{LC} }= \frac{1}{2\pi \sqrt{100 imes 10^{-6} imes 100 imes 10^{-12} } }= 1592 MHz[/latex]

(b) The impedance of resonance, [latex]Z_{o} =\frac{L}{CR}= \frac{100 imes 10^{-6} }{100 imes 10^{-12} imes 5 } = 200 K \Omega [/latex]

(c) The quality factor, [latex]Q =\frac{2\pi f_{O} L}{R}= \frac{2\pi imes 1592 imes 10^{3} imes 100 imes 10^{-6}}{5} = 200[/latex]

(d) The bandwidth, [latex]BW =\frac{f_{O} }{Q}= \frac{1592 imes 10^{3} }{200} = 7.96 KHz[/latex]

Question 13.5: A tank circuit has a capacitor of 100 pF and an inductor of ...

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