Software simulation of a lock-in amplifier with application to the evaluation of uncertainties in real measuring systems

Abstract

Lock-in amplifiers are widely used in metrology to extract a sinusoidal component of a known frequency from a signal that is noisy, returning estimates of the amplitude and phase of the component. A number of questions arise regarding the use by metrologists of the results returned by a lock-in amplifier. For example, what uncertainties should be associated with the estimates returned? How do these uncertainties vary as the signal-to-noise ratio changes? How do instrument errors affect the estimates and the associated uncertainties? In this paper a software simulation tool is described that may be used to process simulated or real (measured) signals, with the user allowed to associate uncertainties with the values of parameters that define the simulated signal and with those that define the operation of the instrument. The results of applying the software simulation tool to both simulated signals and real signals from infrared radiation and nanoindentation experiments are described.

Aparato experimental para medidas de atividade óptica da sacarose usando um amplificador Lock-in

“…O amplificador Lock-iné uma excelente ferramenta para medir sinais com pequenas amplitudes em sistemas imersos em ruído [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21]. Neste caso, um Lock-in de 16 bits de resolução recebe um sinal do Chopper como referência e outro sinal do fotodector através do condicionador de sinais.…”

“…O trabalho de Clarkson et al traz no apêndice o tratamento matemático do Lock-in a partir de funções trigonométricas básicas [22]. A Figura 6 apresenta um diagrama de blocos deste instrumento mostrando sua operação em quatro estágios: ganho, circuito de referência, demodulador e filtro passa-baixa.…”

Sampling, quantization and computational aspects of the quadrature lock-in amplifier

“…We can analyze the operation of this system as follows (we use a notation similar to that of [3], but use radian frequency for simplicity). The source signal is…”

“…Precision aspects of digital lock-in amplifiers were investigated in detail by Clarkson et al [3], who investigated the measurement uncertainty and effects of signal to noise ratio on lock-in estimates. The work described in this paper involves a digital lock-in amplifier [4].…”

“…Recently, the software modelling and measurement aspects of lock-in amplifiers were investigated in detail [3], and this work provides a perspective on the signal processing aspects -in particular, the noise modelling and numerical precision requirements.…”