Nonlinear model and characteristic analysis of fractional-order high frequency oscillator

Abstract

Recently, fractional calculus theory has been widely used in various fields, including the design of oscillators. However, there are still some issues that need to be studied in depth. Firstly, it is necessary to classify the fractional-order oscillators according to the properties of the frequency selective network components, and analyze the influence of the fractional order of components on the characteristics of different types of fractional-order oscillators. Secondly, for fractional-order oscillators with nonlinear devices such as transistors, the traditional linear models cannot describe them accurately. Thirdly, due to the complexity of fractional differential equation, it is difficult to obtain the general analytical solution of the fractional-order oscillator. For these reasons, this paper takes the fractional-order capacitive feedback LC oscillator as an example, and establishes a nonlinear model of this oscillator based on the transistor characteristic mechanism. With the help of the equivalent small parameter method, the influence of the fractional-order characteristics of the components on the output waveform is analyzed. It is revealed that for the fractional-order capacitive feedback LC oscillator, the order of capacitance C1 has the most significant effect on frequency and amplitude, followed by the order of inductance L2, and the order of the feedback capacitor C2 has very little effect on the oscillator. In addition, although the introduction of fractional order increases the oscillation frequency, it will also lead to an increase in THD in some cases. Simulation and experimental results verify the correctness of the proposed nonlinear model and characteristic analysis of fractional-order high frequency oscillator.