LIGO Document G1300724-v1

Measuring the quality factor of a resonator with a lock-in

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G - Presentations (eg Graphics)
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Dual-phase lock-in amplifiers are capable of measuring the in-phase and quadrature components of an AC-signal with respect to a given reference signal. Students already familiar with producing Bode-plots for high-pass, low-pass and resonant circuits via calculations and time-consuming oscilloscope measurements are introduced to the lock-in amplifier through the reproduction of these plots with phase-sensitive detection. Coupled with a dual-channel function generator under computer control, the lock-in amplifier is capable of measuring the quality factor of a resonator, such as a crystal oscillator, in both the frequency and time domains. This tool was initially developed to find and measure resonant modes of both high- and low- quality factor resonators to determine the mechanical loss in mirror coatings for the LIGO collaboration. It has since found use in the advanced undergraduate laboratory as an instructional tool and training exercise for those wishing to pursue LIGO research.
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