Slowly varying function method applied to quartz crystal oscillator transient calculation

R Brendel, N Ratier, L Couteleau… - ieee transactions on …, 1998 - ieeexplore.ieee.org
By using an approach based on the full nonlinear Barkhausen criterion, it is possible to
describe oscillator behavior under the form of a nonlinear characteristic polynomial whose …

Analysis of noise in quartz crystal oscillators by using slowly varying functions method

R Brendel, N Ratier, L Couteleau… - IEEE transactions on …, 1999 - ieeexplore.ieee.org
By using formal manipulation capability of commercially available symbolic calculation code,
it is possible to automatically derive the characteristic polynomial describing the conditions …

Automatic formal derivation of the oscillation condition

N Ratier, L Couteleau, R Brendel… - Proceedings of …, 1997 - ieeexplore.ieee.org
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 …

AM and PM noise analysis in quartz crystal oscillators: symbolic calculus approach

N Ratier, L Couteleau, R Brendel… - Proceedings of the …, 1998 - ieeexplore.ieee.org
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 …

Synthetic modeling of quartz crystal oscillator

R Brendel, N Ratier, L Couteleau… - Proceedings of the …, 1999 - ieeexplore.ieee.org
This paper presents a new modeling technique to describe the nonlinear behavior of
complicated oscillator circuits. The simulation program being developed first removes the …

[PDF][PDF] Algebraic Derivation of the Oscillation Condition of High–Q Quartz Crystal Oscillators

N Ratier, R Brendel - WSEAS Transactions on Circuits and …, 2008 - researchgate.net
A symbolic–numeric method to simulate a high–Q quartz crystal oscillator is derived in this
paper. The proposed method can take into account the isochronism defect of the resonator …

High--Q Quartz Crystal Oscillators Analysis by a 5--Terminal Network Method

N Ratier, R Brendel - 9th WSEAS International Conference on …, 2007 - hal.science
A straightforward method to simulate high--Q quartz crystal oscillator is derived in this paper.
The oscillator circuit is expressed under a canonical $5 $--terminal network which can be …