Using modal series to analyze the transient response of oscillators

In this paper, a new form of Modal series is used to obtain the transient time‐domain response of oscillators. It is applicable to n‐dimensional systems and is not dependent on the existence of a small parameter in circuit's model. In addition, it provides an approximate analytical expression f...

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Bibliographic Details
Published in:International journal of circuit theory and applications 2011-02, Vol.39 (2), p.127-134
Main Authors: Khatibi, Mahmood, Shanechi, Hasan Modir
Format: Article
Language:English
Subjects:
Approximation
Circuits
Colpitts oscillator
Exact solutions
Mathematical analysis
Mathematical models
modal series
nonlinear circuits
oscillator
Oscillators
Steady state
transient response
Transient responses
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Summary:In this paper, a new form of Modal series is used to obtain the transient time‐domain response of oscillators. It is applicable to n‐dimensional systems and is not dependent on the existence of a small parameter in circuit's model. In addition, it provides an approximate analytical expression for the transient response instead of numerical solutions. It is valuable since the transient response of oscillators is not frequency stationary and therefore the FFT of numerical methods may not be so useful. The Colpitts oscillator is selected as a case study and a closed‐form expression for its transient response is derived which approximates the real response up to the steady state. Copyright © 2009 John Wiley & Sons, Ltd.
ISSN:0098-9886
1097-007X
1097-007X
DOI:10.1002/cta.621