مرکز منطقه ای اطلاع رساني علوم و فناوري - Parametric Oscillation in a Damped Resonant System

Abstract :

Parametric oscillation can be induced in a simple passive resonant system with losses for certain ranges of values of the pump frequency $\\omega _p$ , provided a threshold value of the reactance variation has been exceeded. Assuming the reactance variation to be of the form $C(t) = C_{0} + C_{1}\\cos \\omega _{p} t$ . and the depth of modulation $C_1/C_0 \\not> 0.2$ , Mathieu\´s equation is taken to apply and iso- $\\mu$ curves have been computed and plotted in the first unstable region on an $a - q$ chart (after McLachlan) for values of $q$ from 0 to 0.3. Using a simple semigraphical method, it was found that to just permit oscillation the threshold variation $C_1/C_0$ varied from 0.024 at $Q = 100$ to 0.2 at $Q = 20$ , while the pump-frequency range over which oscillation could be induced varied from 0 to $0.2 \\omega _0$ for modulation depths from 0.024 to 0.2 at $Q = 100$ and from 0 to $0.17 \\omega _0$ for modulation depths from 0.99 to 0.2 at $Q = 20$ .