Hybrid filter for lock-in amplifiers

Lock-in amplifiers are instrumental in the precise measurement of extremely small AC signals within high-noise environments. Traditionally, noise reduction in these instruments relies on infinite impulse response (IIR) filters, which can necessitate prolonged settling times to ensure the acquisition of accurate, statistically independent data. While moving average filters offer faster settling times, their non-monotonic frequency response may not be optimal for noise reduction. Conversely, IIR filters frequently realized as N-pole RC filters exhibit a monotonic frequency response conducive to effective noise reduction. This study presents a hybrid filter architecture that combines a short IIR filter with a longer moving average finite impulse response filter. The objective is to enhance noise reduction as quantified by the filter's equivalent noise bandwidth (ENBW). Theoretical analysis is provided to derive the step response, settling time, frequency response, and ENBW of the hybrid filter configuration. Design methodologies are outlined for hybrid filters that either match the settling time of an N-pole RC filter while achieving a lower ENBW or maintain the ENBW of an N-pole RC filter but with significantly faster settling time. The performance of the hybrid filter is validated through noise measurements of low-value resistors and thermal noise of larger resistors, with results compared to theoretical predictions.