DocumentCode
1158035
Title
Parametric Oscillation in a Damped Resonant System
Author
PHILLIPS, R.F.
Volume
10
Issue
4
fYear
1963
fDate
12/1/1963 12:00:00 AM
Firstpage
512
Lastpage
515
Abstract
Parametric oscillation can be induced in a simple passive resonant system with losses for certain ranges of values of the pump frequency 
, provided a threshold value of the reactance variation has been exceeded. Assuming the reactance variation to be of the form 
. and the depth of modulation 
, Mathieu\´s equation is taken to apply and iso- 
curves have been computed and plotted in the first unstable region on an 
chart (after McLachlan) for values of 
from 0 to 0.3. Using a simple semigraphical method, it was found that to just permit oscillation the threshold variation 
varied from 0.024 at 
to 0.2 at 
, while the pump-frequency range over which oscillation could be induced varied from 0 to 
for modulation depths from 0.024 to 0.2 at and from 0 to 
for modulation depths from 0.99 to 0.2 at .
, provided a threshold value of the reactance variation has been exceeded. Assuming the reactance variation to be of the form . and the depth of modulation , Mathieu\´s equation is taken to apply and iso- curves have been computed and plotted in the first unstable region on an chart (after McLachlan) for values of from 0 to 0.3. Using a simple semigraphical method, it was found that to just permit oscillation the threshold variation varied from 0.024 at to 0.2 at , while the pump-frequency range over which oscillation could be induced varied from 0 to for modulation depths from 0.024 to 0.2 at and from 0 to for modulation depths from 0.99 to 0.2 at .Keywords
Coupling circuits; Equations; Frequency estimation; Magnetic fields; Magnetic modulators; Magnetic resonance; Magnetoelasticity; Physics; Radio frequency; Seals;
fLanguage
English
Journal_Title
Circuit Theory, IEEE Transactions on
Publisher
ieee
ISSN
0018-9324
Type
jour
DOI
10.1109/TCT.1963.1082188
Filename
1082188
Link To Document