Suppose the inductor and capacitor in the LC oscillator circuit in Fig. 8.22 are not ideal, but instead have some small resistance that can be lumped together. Assume that V = 10 V, Rs = 25 Ă˘â€žÂ¦, L = 5 nH, and C = 2 pF, just as in Problem 8.66. Suppose the resistance associated with the inductor and capacitor is 10 mĂ˘â€žÂ¦.
Ă‚Â a) Calculate the values of the neper frequency, a, and the resonant radian frequency, v0.
b) Is the response of this circuit overdamped, underdamped, or critically damped?
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Ă‚Â c) What is the actual frequency of oscillation, in GHz?
Ă‚Â d) Approximately how long will the circuit oscillate?
a) Suppose the circuit in Fig. 8.22 has a 5 nH inductor and a 2 pF capacitor. Calculate the frequency, in GHz, of the sinusoidal output for t Ă˘â€°ÂĄ 0.
b) The dc voltage source and series-connected resistor in Fig. 8.22 are used to establish the initial energy in the inductor. If V = 10 V and Rs = 25 Ă˘â€žÂ¦, calculate the initial energy stored in the inductor.
Ă‚Â c) What is the total energy stored in the LC circuit for any time t Ă˘â€°ÂĄ 0?