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.