Circular Regression in a Dual-Phase Lock-In Amplifier for Coherent Detection of Weak Signal

Abstract

Lock-in amplification (LIA) is an effective approach for recovery of weak signal buried in noise. Determination of the input signal amplitude in a classical dual-phase LIA is based on incoherent detection which leads to a biased estimation at low signal-to-noise ratio. This article presents, for the first time to our knowledge, a new architecture of LIA involving phase estimation with a linear-circular regression for coherent detection. The proposed phase delay estimate, between the input signal and a reference, is defined as the maximum-likelihood of a set of observations distributed according to a von Mises distribution. In our implementation this maximum is obtained with a Newton Raphson algorithm. We show that the proposed LIA architecture provides an unbiased estimate of the input signal amplitude. Theoretical simulations with synthetic data demonstrate that the classical LIA estimates are biased for SNR of the input signal lower than −20 dB, while the proposed LIA is able to accurately recover the weak signal amplitude. The novel approach is applied to an optical sensor for accurate measurement of NO2 concentrations at the sub-ppbv level in the atmosphere. Side-by-side intercomparison measurements with a commercial LIA (SR830, Stanford Research Inc., Sunnyvale, CA, USA ) demonstrate that the proposed LIA has an identical performance in terms of measurement accuracy and precision but with simplified hardware architecture.

Low-Cost, High-Performance Lock-in Amplifier for Pedagogical and Practical Applications

“…A mathematical derivation and a simulation (Figure S5) showing how the AD630 modulator/demodulator combined with subsequent low pass filtering isolates the desired frequency response are provided in the Supporting Information. Our design extends a prior report of a 1-channel LIA with an in-phase (V x ) output component by constructing a two-channel LIA with an out-of-phase (V y ) output component as well. − The input voltage signal (V in ) to be analyzed by the LIA first goes through a high pass filter, which also removes any time independent (DC) component. The signal then goes to two modulator/demodulators for processing.…”

Design and Analysis of Micro Signal Detection Circuit for Magnetic Field Detection Utilizing Coil Sensors

“…A lock-in amplifier consists of a target signal channel, a reference signal channel, and a correlator channel. From Equation (8) it can be seen that, in a single lock-in amplifier, the final output signal can be controlled by adjusting the phase of the reference signal and thus the value of the phase difference [21]. In studying the principle of lock-in amplification, it is noted that a single lock-in amplifier requires precise adjustment of the phase.…”

“…The filters have different resistance and capacitance values. Based on its sketch, the second-order low-pass filter transfer function T(s) can be calculated as Equation (21).…”

A Wide-Band Digital Lock-In Amplifier and Its Application in Microfluidic Impedance Measurement

“…In the root-mean-square (RMS) module, the RMS amplitude (R) of the input signal can be calculated by Equation (8) and then transferred to the advanced reduced instruction set computer machine (ARM) for further data processing, such as calibration by piecewise polynomial fitting (Supplementary Note S1) and data processing [17]. The phase value (θ) was also calculated in the ARM using Equation (9).…”