Solved: Suppose the inductor and capacitor in the LC oscillator circuit in Fig. 8.21 are
Chapter 8, Problem 8.68(choose chapter or problem)
Suppose the inductor and capacitor in the LC oscillator circuit in Fig. 8.21 are not ideal, but instead have some small resistance that can be lumped together. Assume that \(V=10 \mathrm{~V}, R=25 \Omega, L=5 \mathrm{nH}\), and C = 2 pF, just as in Problem 8.66. Suppose the resistance associated with the inductor and capacitor is \(10 \mathrm{~m} \Omega\).
a) Calculate the values of the neper frequency, \(\alpha\), and the resonant radian frequency, \(\omega_{0}\).
b) Is the response of this circuit over-, under-, or critically damped?
c) What is the actual frequency of oscillation, in GHz?
d) Approximately how long will the circuit oscillate?
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