Study of the Oscillation Condition of Quartz Oscillators by Gyrator Transformation
نویسندگان
چکیده
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 change can be expressed in an exact form. Numerical solutions are not as helpful as symbolic solutions in the design stage. We present a technique, based on the gyrator transformation, to set up the nonlinear equation network in a form suitable to be solved with analytical methods. We develop a symbolic program based on this technique. As an example, the symbolic program is applied to compute the exact expression of the steady state frequency and amplitude of the Van der Pol oscillator and the Colpitts oscillator.
منابع مشابه
Analysis of Oscillation Amplitude and Phase Error in Multiphase LC Oscillators
Abstract This work proposes a novel method to find the phase error and oscillation amplitude in multiphase LC oscillators. A mathematical approach is used to find the relationship between every stage's output phase and its coupling factor. To much more general analysis, every stage assumed to have a different coupling factor. The mismatches in LC tanks are considered as the main source of pha...
متن کاملModified homotopy perturbation method for solving non-linear oscillator's equations
In this paper a new form of the homptopy perturbation method is used for solving oscillator differential equation, which yields the Maclaurin series of the exact solution. Nonlinear vibration problems and differential equation oscillations have crucial importance in all areas of science and engineering. These equations equip a significant mathematical model for dynamical systems. The accuracy o...
متن کاملPower Series -Aftertreatment Technique for Nonlinear Cubic Duffing and Double-Well Duffing Oscillators
Modeling of large amplitude of structures such as slender, flexible cantilever beam and fluid-structure resting on nonlinear elastic foundations or subjected to stretching effects often lead to strongly nonlinear models of Duffing equations which are not amendable to exact analytical methods. In this work, explicit analytical solutions to the large amplitude nonlinear oscillation systems of cub...
متن کاملQuartz oscillators: deriving oscillation condition by symbolic calculus
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 oscillation as well as the differential equati...
متن کاملHigh–Q Quartz Crystal Oscillators Analysis by a 5–Terminal Network Method
Abstract: 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 easily handled. The oscillator behavior is then described under the form of a nonlinear characteristic polynomial whose coefficients are functions of the circuit components and of the oscillation amplitude...
متن کامل