DocumentCode :
704011
Title :
Initial transient response of oscillators with long settling time
Author :
Brachtendorf, Hans Georg ; Bittner, Kai
Author_Institution :
Univ. of Appl. Sci. of Upper Austria, Hagenberg, Austria
fYear :
2015
fDate :
9-13 March 2015
Firstpage :
1162
Lastpage :
1167
Abstract :
The initial transient response of oscillators with high quality factor Q such as quartz crystal oscillators is orders of magnitudes larger than the period of oscillation. Therefore numerical solution by standard techniques of the underlying system of ordinary differential algebraic equations (DAEs) resulting from Kirchhoff´s current and voltage laws is run time inefficient. In this paper numerical techniques for the calculation of the initial transient response and steady state solution are investigated. The efficiency results from reformulating the underlying system of ordinary DAEs by a suitable system of partial DAEs, known as multirate PDE, and from suitable finite difference time domain (FDTD) methods with small numerical dissipation of energy. Unlike Harmonic Balance the waveforms are free of spurious oscillations, caused by the non-compactness of the trigonometric polynomials.
Keywords :
Q-factor; crystal oscillators; differential algebraic equations; finite difference time-domain analysis; polynomials; transient response; DAE; FDTD methods; Kirchhoff´s current laws; Kirchhoff´s voltage laws; differential algebraic equations; finite difference time domain methods; high quality factor Q; long settling time; multirate PDE; numerical dissipation; numerical techniques; oscillators transient response; quartz crystal oscillators; trigonometric polynomials; Eigenvalues and eigenfunctions; Frequency estimation; Harmonic analysis; Mathematical model; Oscillators; Radio frequency; Steady-state; Hilbert transformation; initial transient response and steady state; multirate PDE method; optimal estimation of instantaneous frequency; oscillator simulation; quartz crystal oscillators; trigonometric BDF methods;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Design, Automation & Test in Europe Conference & Exhibition (DATE), 2015
Conference_Location :
Grenoble
Print_ISBN :
978-3-9815-3704-8
Type :
conf
Filename :
7092563
Link To Document :
بازگشت