Publication Date


Document Type


First Advisor

Newell, Darrell E.

Degree Name

M.S. (Master of Science)

Legacy Department

Department of Electrical Engineering


Oscillators; Crystal


A critical requirement in the design of circuits using quartz plate resonators is the electrical characterization of the resonator. An equivalent electrical network has long been known that describes the electrical characteristics of quartz plate resonators around the frequency of resonance. A number of techniques have historically been used to measure these equivalent electrical parameters. Reduction of the resulting data eventually leads to values for the circuit elements. The introduction of modem automatic vector network analyzers as a measurement tool has afforded the opportunity to simultaneously measure and visually evaluate the resonator responses to enable a “real-time” analysis of the response. The resulting magnitude and phase information represent the complex reflection coefficient in the case of the single-port measurement. The measured complex reflection coefficients are mathematically transformed through a series of operations into the equivalent network parameters. A technique has been developed that allows the measured complex reflection coefficient information to be transformed into the equivalent network values in a more direct fashion. The parameters are independently derived from the error-corrected information, resulting in potentially more accurate equivalent electrical network elemental values. An approach to the visualization of resonator response through the Smith chart presentation is also presented.


Includes bibliographical references (pages [70]-72)


vii, 72 pages




Northern Illinois University

Rights Statement

In Copyright

Rights Statement 2

NIU theses are protected by copyright. They may be viewed from Huskie Commons for any purpose, but reproduction or distribution in any format is prohibited without the written permission of the authors.

Media Type