A Study of Sensitivity of Nonlinear Oscillations of a CLD Parallel Circuit to Parametrization of Tunnel Diode
The Pennsylvania State University, University College, York, PA, 17403.
Abstract: Tunnel diode aka Esaki diode  is a peculiar nonlinear electronic element possessing negative ohmic resistance. We consider a multi-mesh circuit composed of three elements: a charged capacitor, C, a self-inductor, L, and an Esaki diode, D, (CLD) all three in parallel. We parametrize the I-V characteristics of the diode and derive the circuit equation; this is a nonlinear differential equation. Applying a Computer Algebra System (CAS) specifically Mathematica  we solve the circuit equation numerically conducive diode dependent parametric solution; in general the solution has a damped oscillatory character. In this note we investigate the sensitivity of the oscillations as a function of diode’s parameters. We establish the fact that for a set of parameters the tunnel diode behaves almost as an ohmic resistor and that the circuit equation tends toward classic CLR-parallel circuit with linear damped oscillations. Mathematica simulation assists visualizing the transition.
Keywords: Tunnel Diode, Electrical Nonlinear Oscillations, Computer Algebra System, Mathematica.
Pages: 177 – 182 | Full PDF Paper
Rasaki Olawale Olanrewaju1, Johnson Funminiyi Ojo2, Adekola Lanrewaju Olumide3
1. Department of Mathematical Sciences, Pan African University Institute for Basic Sciences, Technology and Innovation. P.O. Box 62000-00200, Nairobi, Kenya.
2. Department of Statistics, University of Ibadan, Ibadan, P.O. Box 200284, Oyo state, Nigeria.
3. Department of Physical Sciences, Bells University of Technology, Ota, Nigeria.
Abstract: We study the assortment of autoregressive random processes via a transmuted Gamma distributed noise. We consider a transmuted re-parameterization of the Gamma parameters in terms of μ and σ2, afterwards ascertained that the transmuted Gamma is a proper probability density function, then proceeded to spelt-out the structural form and traits of the Gamma Mixture Autoregressive generalization in its k-components. The mean and variance of the Gamma Autoregressive model were ascertained coupled with its first and second-order stationarity. The ingrained k-components’ autoregressive coefficients, re-parameterization Gamma coefficients, k-regime transitional weights were estimated via Expectation-Maximization (EM) algorithm. However, some step ahead predictions were derived as well as the model sub-setting estimation via Levinson-Durbin recursive technique.
Keywords: Expectation-Maximization (EM) algorithm, Gamma Autoregressive model, k-components, k-regime transitional weights, Levinson-Durbin recursive, Transmuted.
Pages: 183 – 202 | Full PDF Paper