Education

 

Fourier description of lock-in

 

J. A. Dávila Pintle

 

Benemérita Universidad Autónoma de Puebla, Facultad de Ciencias de la Electrónica, Puebla, 72570 e-mail: jpintle@ece.buap.mx

 

Received 3 May 2012;
Accepted 16 November 2012.

 

Abstract

In this study, a new interpretation about the operation of a traditional lock-in and dual lock-in is presented from the viewpoint of Fourier analysis. Once the mathematical principles under which these devices operate are understood, we could take full advantage of the magnitude and phase of the Fourier coefficients to measure the physical variables, as shown in the final example of this study. Also, a comparison between signal-to-noise ratio (SNR) of a square reference lock-in and a pure sinusoid lock-in is also presented.

Keywords: Lock-in; description; measurement.

PACS: 07.50Qx; 06.20DK; 07,07Hj.

 

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Acknowledgments

The author thanks Dr. Veronica Cerdan Ramirez and Dr. Edmundo Reynoso for their valuable recommendations. This work has been sponsored by CONACyT, grant 51757 and VIEP with grant DAPJ-ING-12.

 

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15. The function of the AC and DC amplifiers is simply to amplify signals, while the function of the Notch filters are to reduce 60 and 120 Hz from the electrical network. Nevertheless we shall see that filters have, in some cases repercussions on the final result.

16. It is common to use a PLL in the cannel of reference to generate cos (mω₀t) from an arbitrary shape signal with frequency mω₀

17. A practical rule is tobs must be greater than 5τ.

18. It can be demonstrated that any n-order LPF under appropriated conditions carries out n times the average of the average.

19. As a dual lock-in generates the quadrature reference [Eq. (19)] from Eq. (18), it is also dephased.

20. This simple circuit may be used to synchronize the lock-in to third harmonic instead of using analog multipliers and signal filters for applications of laser stabilization using third-derivative absorption [11].