Fundamental study of a non-linear capacitor to use it in non-linear transmission line models

Abstract: The theme of this paper is to analyze a non linear capacitor so that this non linear device can be used in realizing the non linear transmission line to observe the dispersion characteristics. In a linear capacitor, the charge stored on the electrodes and the potential difference between them is a linear function. In this paper, a quadratic relation is considered between charge and the potential difference. The relevance of this analysis can be attributed to the study of non linear transmission lines. This device behavior is observed in both time and frequency domains. The impulse response can be used to find the frequency response for a linear circuit but this is not standard to find the frequency response of a non-linear system. The frequency response for this non linear capacitor is obtained for different inputs by taking the ratio of output Fourier transform to input Fourier transform. After analysis, it is observed that non linearity is giving some odd results indicating that the control on the nonlinearity is of great importance in circuits and systems and if this non linearity can be controlled somehow, these elements are going to give a new class of devices with good applications.

Keywords: non linear circuits, capacitor, admittance, impulse response, Fourier Transform, Frequency response and phase variation.