Marginal Oscillator Conversion Gain: Prediction, Simulation, and Experimental Measurements
Open Access
- Author:
- Tyson, Thomas
- Graduate Program:
- Electrical Engineering
- Degree:
- Master of Science
- Document Type:
- Master Thesis
- Date of Defense:
- July 14, 2011
- Committee Members:
- Jeffrey Louis Schiano, Thesis Advisor/Co-Advisor
Jeffrey Louis Schiano, Thesis Advisor/Co-Advisor
Constantino Manuel Lagoa, Thesis Advisor/Co-Advisor - Keywords:
- Marginal Oscillator
Conversion Gain - Abstract:
- A marginal oscillator (MO) is an instrument for measuring small changes in the losses of a harmonic oscillator. The MO achieves a high conversion gain, which is defined as the sensitivity of the oscillation amplitude to the changes in the losses within the circuit. The high conversion gain results from the use of a memoryless nonlinear element that limits the amplitude of the oscillation. In addition to conversion gain, this thesis is also concerned with three other performance metrics that are the frequency of oscillation, the amplitude of oscillation, and the time constant that describes the transient response of the marginal oscillator due to changes in losses. Viswanathan provides an analytical approach for estimating the conversion gain for a second-order harmonic oscillator with a nonlinear feedback element. This analysis is based on the Krylov and Bogoliubov's result for the behavior of a nonlinear second-order system. As a result this analysis technique is not directly applicable to a practical MO circuit that is described by a higher order model. This thesis shows how to predict the performance metrics using the describing function method, which is applicable to higher-order models. This approach enables bounds to be placed on the performance metrics estimated by the describing function method. Both methods for estimating the performance metrics from theory are verified using numerical simulations and experimental measurements.