# Conversion Gain and Sensitivity in Marginal Oscillators: Continuous and Sampled-Data Negative Resistance Converters

Open Access

- Area of Honors:
- Electrical Engineering
- Degree:
- Bachelor of Science
- Document Type:
- Thesis
- Thesis Supervisors:
- Jeffrey Louis Schiano, Thesis Supervisor
- John Douglas Mitchell, Honors Advisor

- Keywords:
- marginal oscillator
- conversion gain
- sensitivity
- negative resistance converter

- Abstract:
- A marginal oscillator is an instrument used to detect changes in the losses of a tuned circuit. It consists of a parallel RLC circuit driven by a dependent current source that is controlled by the voltage across the RLC circuit. The dependent current source implements a nonlinear negative resistance converter that injects just enough energy to overcome the resistive losses and thereby produce a steady-state oscillation in the voltage across the circuit. The main figure of merit for a marginal oscillator is its conversion gain, which relates the change in the amplitude of oscillation to the change in the losses of the tuned circuit. Viswanathan showed that the conversion gain depends on the shape of the nonlinear negative resistance converter. In general, a higher conversion gain is desired. An earlier study that simulated the marginal oscillator yielded estimates of the conversion gain that were not consistent with theoretical predictions. The objectives of this thesis are threefold. First, we want to reconcile the difference between theory and simulation by choosing an appropriate integration algorithm and its parameters. This thesis shows that by appropriately choosing the integration algorithm and its parameters, the simulation results are in agreement with the theoretical predictions. The second objective is to investigate the feasibility of implementing the dependent current source using a data-sampled system in place of analog circuitry in order to facilitate the implementation of nonlinear characteristics that maximize conversion gain. Specifically, this study uses numerical simulation to determine the effects of quantization in time and amplitude on the the conversion gain. The third objective is to numerically determine the sensitivity of the marginal oscillator, which is the smallest change in losses that can be detected in the presence of thermal noise for a given conversion gain.