D 15.3 The characteristic equation of the oscillator circuit of Fig. 15.2(a) is derived in Example 15.2 and given by Eq. (15.6):
Note that while r2 = 0 results in sustained oscillation, making r2 > 0 places the poles in the right half of the s-plane and ensures that oscillation will start and grow until a nonlinear amplitude-control mechanism kicks in. Using an inductance of 0.1 mH, find
(a) the value of C to obtain sinusoidal oscillations with 107 rad/s frequency;
(b) the value of R so that the LCR circuit has a Q factor of 50 (note: a high Q-factor, Q = ω0CR, increases the purity of the generated sine waves); and
(c) the value of (r2/r1) to place the poles at a horizontal distance of 100 rad/s from the jω-axis.
(a) 100 pF; (b) 50 kΩ; (c) 0.001