HARDWARE IMPLEMENTATION OF LOCK-IN AMPLIFIER FOR NOISY SIGNALS

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1 Integrated Journal of Engineering Research and Technology HARDWARE IMPLEMENTATION OF LOCK-IN AMPLIFIER FOR NOISY SIGNALS Prachee P. Dhapte, Shriyash V. Gadve Department of Electronics and Telecommunication Engineering, Vishwakarma Institute of Article History: Received on- 21 th Mar 2015 Accepted on- 25 th Mar 2015 National Conference for Student in Electrical and Electronics Engineering Information Technology, Pune, India. Keywords: Lock-In Amplifier, Phase Sensitive Detection, IIR Filters. I. INTRODUCTION In many optical measurement situations, detecting low level, slowly varying optical signals is often difficult due to the presence of high level, low frequency optical interference and low frequency (1/f) noise. Use of an intensity modulated optical source and a lock-in detection system is a solution to this problem. The source modulation shifts the measuring signal up the frequency spectrum and away from the low frequency noise. The demodulation is then carried out by a lock-in amplifier (LIA) which recovers the signal while removing the noise and interference. The implementation of lock-in amplifier can be carried out in both analog as well as digital domain. Lock-in amplifiers use complicated analog circuitry to carry out phase sensitive detection and filtering. On the other hand Digital Signal Controllers can be used to remove large amount of analog circuitry by performing the necessary operations in software. Content Available at ABSTRACT Often when the small signal is obscured by noise sources, thousands of times larger, it becomes difficult to get accurate measurements. A lock-in amplifier lets you detect and measure very small AC signals all the way down to a few nanovolts. A lock-in amplifier basically amplifies a small frequency band around the reference frequency by using the phase sensitive detection principle. Noise signals at frequencies other than reference frequency are rejected and do not affect the measurement. This paper encapsulates the theory behind the lock in amplifier, analysis of phase sensitive detector and the implementation of low pass filters. It also includes an analysis for digital as well as analog circuits. The purpose behind developing the LIA is to process and acquire the signals coming from the spectrometer viz. an optical setup arranged to determine the properties (absorption and reflection coefficients) of the material under test. The digital signal processing facilitates high speed, high accuracy measurements on the sensors [1]. II. THEORY A lock-in amplifier provides DC output proportional to the AC signal under measurement. A lock-in amplifier basically consists of five components viz. as follows: AC amplifier, Voltage controlled oscillator (VCO), Phase sensitive detector (PSD), Low pass filter and a DC amplifier. Fig 1: Block diagram of a lock-in amplifier 76

2 An AC amplifier is an amplifier combined with variable filters. A VCO is an oscillator which can synchronize with the reference signal in both phase and frequency. The PSD takes two signals and produces their product at the output. A low pass filter used is the one whose time constant can be selected depending on the sensitivity of the input signal. A DC amplifier is a low- frequency amplifier used to amplify the DC signal at the output of the LPF. III. PHASE SENSITIVE DETECTION A phase sensitive detector is the heart of a lock-in amplifier. Along with the input signal, it is supplied with the periodic reference signal. PSD then carries out multiplication of these two signals. Square wave at frequency wr is used as the reference signal. The sinusoidal signal used to excite the experiment is signal amplitude, where Vsig is the is the signal frequency and sig is the signal s phase. Usually LIAs generate their own internal reference, locked to the external one using a phase locked loop. The internal reference is The following figure shows the external reference, excitation signal and the internal reference. At the PSD output an additive and a subtractive component is obtained. Two AC signals are obtained one at the difference frequency (wr - win) and other at the sum frequency (wr + win). If the PSD output is then passed through a LPF, the AC signals are filtered out and nothing will be left. However, if wr equals win, the difference frequency component will be a DC signal. In this case the filtered PSD output will be: This is a DC signal proportional to the excitation signal amplitude. IV. IMPLEMENTATIONS A. Analog Filters: Filters can be implemented using any of the three approximations viz. Butterworth, Bessel and Chebyshev. Fig 3: Comparison of amplitude responses of Bessel, Butterworth and Chebyshev filters. Fig 2: Signals at PSD The output of PSD is simply the product of two sine signals. Fig 4: Comparison of step and impulse responses of Bessel, Butterworth and Chebyshev filters. From the above comparisons, the Butterworth approximation is selected due its good transient response and flat pass band response. The LIA uses adaptive filtering i.e. the time constants can be selected according to the input signal [3]. Two analog filters with time constants of 30ms and 1s respectively are implemented each having an order of 6. 77

3 a) A Butterworth filter with time constant of 30ms: Specifications: Cut-off frequency = 1.59 Hz Order = 6 Topology = Multiple feedback Butterworth filter. Fig 5: 5.3 Hz filter circuitry. Specifications: Cut-off frequency = 5.30 Hz Order = 6 Topology = Multiple feedback Butterworth filter. Fig 6: Frequency response of 5.3Hz filter. b) A Butterworth filter with time constant of 1s: Fig 8: Frequency response of 0.15Hz filter B. Digital Filters: Though analog filters provide high speed performance, the flatness achievable in the pass band with the analog filters is limited by the accuracy of their resistors and capacitors. Hence, the digital filers are preferred where the flatness is limited by the round-off error, making them hundreds of times flatter than their analog counterparts. a) Determining the sampling rate: In order to decide the digitization rate, an experiment was carried out in Lab VIEW. The LIA was implemented in Lab VIEW and the RMS Mean Square Error was computed at the output of the filter for various sampling rate. Fig 7: Hz filter circuitry. Fig 9: LabVIEW setup. 78

4 Fig 10: Results at sampling rate = 40 KHz. Similarly, the experiment was carried out at various sampling rates and the Mean square error was noted for three cases of signal to noise ratio (Signal amplitude= 1 Vp-p). Table 1: Mean square error at various sampling rates. b) Implementing digital filter in MATLAB: Digital filters are basically classified as: Finite Impulse Response filters (FIR). Infinite Impulse Response filters (IIR). Filters whose impulse response is finite are known as the FIR filters. Such filters do not use any feedback and are hence known as non-recursive. FIR filters are inherently stable filters with a linear phase response. But, implementation of narrow transition band FIR filters is very costly. On the other hand, the IIR filters provide a narrow transition band. These filters use feedback and are hence known as recursive filters. In cases where there is a demand of narrow transition band, IIR filters are used. A second order IIR filter was realized using Direct Form II structure. Fig 11: Sampling frequency v/s RMS mean square error. Inference: From the above experiment two inferences can be made: For a particular sampling rate, the mean square error goes on increasing with the decrease in signal to noise ratio (SNR). For a particular value of SNR, the mean square error decreases with the increase in sampling frequency. From the above inferences, the sampling frequency of 40 KHz can be used for the implementations. Fig 12: 5.3 Hz filter s result when excitation applied is of 5.3 Hz. 79

5 Fig 13: 5.3 Hz filter s result when excitation applied is of 53 Hz. REFERENCES 1. Lyons, R., Understanding Digital Signal Processing, Prentice Hall. 2. Stanford Research Systems, Application note #3. 3. NF Electronic Instruments, 5610B Two phase lockin amplifier manual. The results above show that at the cut-off frequency, the signal is reduced by 3 dbs. APPLICATIONS In spectroscopy for low level light measurement. In communication systems for synchronous detection. Measurement of sinusoidal voltage amplitudes and phase. Measurement of noise around a certain frequency. Power spectral density measurement. CONCLUSION We infer that the results shown imply that the implementation in Lab VIEW show precise lock-in at the desired frequency. We have also implemented the IIR filter and the 6th order analog filter and tested their frequency response. A noise voltage upto 2V can be rejected making the system reasonably efficient. ACKNOWLEDGMENT Behind every achievement lies the contribution of those, Behind every achievement lies the contribution of those, without whom that would have never been achieved. We wish to express our deep sense of gratitude to our guide from TIFR, Dr. S. S. Prabhu and our college guides Prof. C. S. Garde and Mrs. R. G. Purandare. We are absolutely grateful to our seniors and all the nontechnical staff for their suggestions and assistance which was a key factor in our project development. 80

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