Switched ratiometric lock-in amplifier enabling sub-ppm measurements in a wide frequency range.

Lock-in amplifiers (LIAs) are extensively used to perform high-resolution measurements. Ideally, when using LIAs, it would be possible to measure a minimum signal variation limited by the instrument input equivalent noise at the operating frequency and the chosen filtering bandwidth. Instead, digital LIAs show an unforeseen 1/f noise at the instrument demodulated output, proportional to the signal amplitude that poses a fundamental limit to the minimum detectable signal variation using the lock-in technique. In particular, the typical resolution limit of fast operating LIAs (>1 MHz) is of tens of ppm, orders of magnitude worse than the expected value. A detailed analysis shows that the additional noise is due to slow fluctuations of the signal gain from the generation stage to the acquisition one, mainly due to the digital-to-analog and analog-to-digital converters. To compensate them, a switched ratiometric technique based on two analog-to-digital converters alternately acquiring the signal coming from the device under test and the stimulus signal has been conceived. A field-programmabale gate array-based LIA working up to 10 MHz and implementing the technique has been realized, and results demonstrate a resolution improvement of more than an order of magnitude (from tens of ppm down to sub-ppm values) compared to standard implementations working up to similar frequencies. The technique is generally applicable without requiring calibration nor ad hoc experimental arrangements.

Note: Differential configurations for the mitigation of slow fluctuations limiting the resolution of digital lock-in amplifiers.

The resolution of digital lock-in amplifiers working with a narrow bandwidth (<100 Hz) is limited by slow fluctuations, which can be two orders of magnitude larger (µV range) than the noise of the input amplifier (tens of nV). In order to tackle this issue, affecting state-of-the-art laboratory instrumentation and here systematically quantified, three differential sensing configurations are presented. They adapt to different setup conditions and are based on manual and automatic tuning of dummy references, allowing a 25-fold resolution improvement for enhanced long-term tracking of impedance sensors.