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- N. Ratier, R. Brendel, P. Guillemot
- 2008

This paper presents the method used to derive the oscillation condition by using symbolic calculus. The program is based on the full nonlinear Barkhausen criterion method. The behaviour of an oscillator is described by a complex polynomial called the characteristic polynomial. This polynomial enables us to calculate the steady state features of the… (More)

The behavior of a quartz crystal oscillator can be described by a nonlinear characteristic polynomial whose coefficients are function of the circuit parameters. Solving the polynomial in the frequency domain leads to the steady state oscillation amplitude and frequency. In the time domain, it gives the oscillator signal transient. Deriving the… (More)

- Robert Brendel
- 2012

- N. Ratter, M. Bruniaux, R. Brendel
- Proceedings of LFNM 2005. 7th International…
- 2005

We present a symbolic-numeric method dedicated to the simulation of ultra stable quartz, oscillators entirely in the frequency domain including the nonlinear parts of the circuit. The main idea is to replace, by symbolic computation, the nonlinear differential system describing the oscillator by a system of nonlinear equations of Fourier coefficients whose… (More)

Increasing performance of quartz crystal oscillators as well as predictability requirements when developing the devices need accurate analysis of noise sources. Our work is devoted to understand how an oscillator reacts to additive noise of an element in the electronic circuit. Up to now, oscillator designers often refer to the well-known Leeson's model to… (More)

The calculation of the oscillation condition is one of the main points of oscillator analysis. Its determination in finite term allows one to calculate the steady state amplitude and frequency of the oscillator. Symbolic solutions provide an additional insight into the behavior of the circuit. As an example the sensitivity of the oscillator to parameter… (More)

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