TY - GEN
T1 - Initial transient response of oscillators with long settling time
AU - Brachtendorf, Hans Georg
AU - Bittner, Kai
PY - 2015/4/22
Y1 - 2015/4/22
N2 - 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.
AB - 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.
KW - Hilbert transformation
KW - initial transient response and steady state
KW - multirate PDE method
KW - optimal estimation of instantaneous frequency
KW - oscillator simulation
KW - quartz crystal oscillators
KW - trigonometric BDF methods
UR - https://www.scopus.com/pages/publications/84945948513
U2 - 10.7873/date.2015.0008
DO - 10.7873/date.2015.0008
M3 - Conference contribution
AN - SCOPUS:84945948513
T3 - Proceedings -Design, Automation and Test in Europe, DATE
SP - 1162
EP - 1167
BT - Proceedings of the 2015 Design, Automation and Test in Europe Conference and Exhibition, DATE 2015
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2015 Design, Automation and Test in Europe Conference and Exhibition, DATE 2015
Y2 - 9 March 2015 through 13 March 2015
ER -