White Paper: Test & Measurement

Principles of Lock-In Detection

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Lock-in amplifiers were invented in the 1930s and commercialized in the mid-20th century as electrical instruments capable of extracting signal amplitudes and phases in extremely noisy environments. They employ a homodyne detection scheme and low-pass filtering to measure a signal’s amplitude and phase relative to a periodic reference. The best instruments on the market today are capable of accurately measuring a signal in the presence of noise up to a million times higher in amplitude than the signal of interest.

Over decades of development, researchers have found many ways to use lock-in amplifiers. Most prominently, they are used as precision AC voltage and AC phase meters, noise measurement units, impedance spectroscopes, network analyzers, spectrum analyzers, and phase detectors in phase-locked loops.

The fields of research comprise almost every length scale and temperature such as observing the corona in full sunlight, measuring the fractional quantum Hall effect, or direct imaging of the bond characteristics between atoms in a molecule. Lock-in amplifiers are extremely versatile. As essential as spectrum analyzers and oscilloscopes, they are workhorses in all kinds of laboratory setups, from physics to engineering and life sciences.

As with most powerful tools, only a solid understanding of the working principles and features of a lock-in amplifier enables its user to get the most out of it and to successfully design experiments. This document provides a comprehensive introduction to the principles of lock-in detection and explains the most important measurement settings. The lock-in detection technique is described both in the time and in the frequency domain. Moreover, details are laid out on how signal modulation can be exploited to improve the signal-to-noise ratio (SNR) while keeping acquisition time low. Finally, the document discusses the innovations in digital signal processing that enabled the inclusion of time- and frequency-domain analysis tools such as a spectrum analyzer and an oscilloscope into Zurich Instruments’ lock-in amplifiers. In this way, the functionalities that traditionally required a full rack of instruments are now available in a single box.

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