Parametric Oscillation in a Damped Resonant System
- 1 December 1963
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Circuit Theory
- Vol. 10 (4) , 512-515
- https://doi.org/10.1109/TCT.1963.1082188
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 formC(t) = C_{0} + C_{1}\cos \omega_{p} t. and the depth of modulationC_1/C_0 \not> 0.2, Mathieu's equation is taken to apply and iso-\mucurves have been computed and plotted in the first unstable region on ana - qchart (after McLachlan) for values ofqfrom 0 to 0.3. Using a simple semigraphical method, it was found that to just permit oscillation the threshold variationC_1/C_0varied from 0.024 atQ = 100to 0.2 atQ = 20, while the pump-frequency range over which oscillation could be induced varied from 0 to0.2 \omega_0for modulation depths from 0.024 to 0.2 atQ = 100and from 0 to0.17 \omega_0for modulation depths from 0.99 to 0.2 atQ = 20.Keywords
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