Marginal oscillator sensitivity enhancement using full-state nonlinear feedback

A marginal oscillator is a tank circuit with nonlinear output feedback applied to maximize the change in amplitude with respect to the circuit's internal resistance. Although used in many applications, the marginal oscillator is most commonly used in continuous wave magnetic resonance (CW-MR). Continuous-wave is useful under two circumstances. The first is when attempting to find previously undocumented magnetic resonances over a wide range of frequencies. An individual resonance may yield a peak that is only a few kilohertz wide where the search space may span many megahertz. Hence a search may require many hours to complete. Second, CW requires much less power than Fourier or pulsed techniques; this is very useful in field applications, and to avoid quenching superconducting search coils. The currently accepted mathematical model describing a marginal oscillator leads to transcendental analytical expressions that can only be approximated. It also lacks a known path to optimize the nonlinear feedback policy. This dissertation describes a redesign of the marginal oscillator using state-space modeling and feedback of all state variables (i.e. full-state feedback). This achieves several goals, all of which were unachievable using previous analysis. First, the resulting mathematical model, although still nonlinear, can be described in closed form. Second, the circuit model can be revised to better resemble laboratory instrumentation and can be implemented in hardware or software. Third, for this and previous designs, it had been observed that conversion-gain is proportional to the settling time of the circuit. Under very loose constraints, this observation is now proved as a theorem. Alternative measurement methods using the marginal oscillator at smaller conversion gains are briefly discussed. Fourth, the state-space model is mapped to a dimensionless coordinate system inducing data collapse. Therefore, at each data sample the oscillation amplitude is well characterized, where current methods that estimate a signal envelope from the output voltage are susceptible to phase noise. Fifth, the effect of parasitic resistance in the switched capacitor/varactor bank is analyzed. At frequencies near resonance, this is shown as equivalent to changing the resistance of the idealized lumped circuit model.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Electrical and Computer Engineering

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2016

Author dc:creator

• Ginsberg, Mark D

Contributors dc:contributor

• Sauer, Peter W.
• Hovakimyan, Naira
• Pearlstein, Arne J.
• O'Brien, William D.
• Schiano, Jeffrey L

• Nonlinear Feedback
• Marginal Oscillator
• Full-State Feedback
• continuous wave magnetic resonance

Statement dc:rights

• Copyright 2016, Mark D. Ginsberg

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/92795

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/92795