A Modern DSP Based Lock-In Amplifier Designed for Code …

1 A Modern DSP Based Lock-In Amplifier Designed for code and hardware experimentation By: Steven C. Hageman / AnalogHome Introduction Lock-In amplifiers have been around since their first development as described by Dicke in the 1940's[1] and they are still used today in many experimental systems. The technique is also called by a variety of names: Phase Sensitive Detection, Synchronous Detection and Narrow Band Detection. Figure 1 A typically challenging optical measurement. High attenuation of the optical Originally the technique was used to enable sample makes measuring the resulting light measurement on very small signals that would intensity difficult because of detector and otherwise be obscured by even the best available Amplifier noise. amplifiers noise.

2 By modulating the signal, AC. amplifying it, then synchronously demodulating it, and applying a very narrow Low Pass Filter, After the light passes through the optical sample it the result is: a very narrow detection bandwidth is attenuated greatly, thus necessitating that totally bypasses the 1/f Amplifier noise amplification to get a measurable signal. The problems and hence produces a very low noise signal plot in figure 2 illustrates the signal and floor. noise problem. Basic Lock-In Technique All electrical systems have increasing noise as the frequency approaches DC [2], this noise is called 1/f noise. Even though Amplifier noise has been reduced nearly 1000x since the 1940's, 1/f noise is still a limiting factor in many high performance measuring systems.

3 The Lock-In Amplifier technique is an effective way to deal with this excess noise problem. A common experiment that is limited by noise is shown in figure 1, this experiment is the Figure 2 A signal and noise diagram for the measurement of optical absorption by measuring system of figure 1. The attenuated illumination of a test sample by a light source. signal (red) is obscured by the Detector +. Amplifier 1/f noise. Interfering signals (Blue) are usually also present. Page 1 of 12 Copyright 2018 Steven C. Hageman As figure 2 demonstrates, this experiment will very small resulting in a greatly improved signal yield poor results as the resulting signal is below to noise ratio. the detector and amplifiers noise. Interfering signals are typically power line (50/60 Hz).

4 Related. The Lock-In Amplifier technique is a solution to this problem (figure 3). First, the light source is modulated or chopped at some frequency high enough to move the signal out of the detectors +. amplifiers 1/f noise region and also away from any interfering signals. In the old days, a rotating mechanical light chopper might have been used, today a LED or Laser illumination source could be electrically switched on and off. The now modulated light is passed through the Figure 4 After modulating (chopping) the signal optical sample and detected by the photo-detector. (Red) is now shifted up in frequency to avoid the The detected AC signal is then amplified by a low Amplifier noise and any interfering signals (Blue). noise Amplifier (figure 4). The signal is then demodulated with a synchronous demodulator operating at the same frequency as the light The Basic Lock-In Amplifier chopper.

5 The basic Lock-In Amplifier consists of some sort of reference source output that is used to modulate the experiments driving signal and a synchronous demodulator that is driven from the same reference (figure 5). As will be shown, the phase relationship between the signal source and the demodulator is important. Figure 3 The Lock-In Amplifier solution to the measurement problem of Figure 1. Here a rotating wheel acts to chop or modulate the light source. After demodulation the original signal is at DC. Figure 5 The basic block diagram of a Lock-In again, and this DC signal can then be filtered with Amplifier . The various function blocks may be: a very narrow Low Pass Filter (LPF). The analog, digital or a combination of both. resulting system noise bandwidth can be made Page 2 of 12 Copyright 2018 Steven C.

6 Hageman Classical Analog Lock-In The circuit of figure 6 is also called a: Phase The first synchronous demodulators were Analog Sensitive Detector. For instance, if the and were built with a switched, +1/-1 gain demodulation signal and the frequency of the Amplifier combination. One possible circuit is switching are in phase the output of the circuit shown in Figure 6. Using the best available will be essentially a full wave rectifier. In this discrete circuits today [3], allows this same case the DC output of the Low Pass Filter will be technique to extend from DC to better than 1 proportional to the amplitude of the signal. MHz modulation frequency. Conversely, if the phase of the demodulating The demodulation function for the circuit shown signal is shifted 90 degrees (or in quadrature) with in Figure 6 is a square wave, so this technique has respect to the input signal, the output of the LPF.

7 A response at the fundamental modulation is now sensitive to the phase of the input signal. frequency, and also at odd harmonics of the modulation frequency. These harmonic responses This phase sensitive demodulation is detailed in are impossible to separate from the desired figures 7 and 8. The input signals in figure 7 and fundamental response and therefore can add to 8 are shown as sine waves as this is the easiest measurement errors if they are large enough [4]. way to visualize the phase relationships of the various signals. The actual input signal can be of any waveform shape. Figure 6 The first Lock-In Amplifiers used a square wave synchronous demodulator similar to what is shown here. The gain is switched from +1. to -1 at the modulation frequency.

8 Figure 7 If the input signal (VG1) and the demodulating signal (VG2) are in phase, then the Other circuit configurations can be used for the circuit of figure 6 acts like a full wave rectifier synchronous demodulator and at higher and the output (VF1) is proportional to the input frequencies the circuit of figure 6 can be replaced signal amplitude. After low pass filtering the with a diode ring mixer. This can extend the output would be a DC signal. useful demodulation frequency range to several hundred MHz. The demodulator of figure 6 has been available in IC form since the 1980's as the Analog Devices AD630 [5]. A more Modern analog / digital crossover IC is also available [6]. Page 3 of 12 Copyright 2018 Steven C. Hageman Figure 8 If the input signal (VG1) and the demodulating signal (VG2) are 90 out of phase Figure 9 DSP Based Lock-In Amplifier , (quadrature), then the circuit of figure 6 acts like everything after the ADC input is implemented a phase detector and the output (VF1) is digitally.

9 Proportional to the phase difference between the signals. As can be seen, the DC Level (VF1) in There are three big advantages with DSP Based this case is zero when the signals are exactly 90 designs, out of phase. 1) All the processing and filtering after the ADC. It is clear from figure 7 and 8 that when using the is done digitally eliminating all the matching, classical synchronous demodulator of figure 6, accuracy, drift and tuning problems of Analog. the phase relationship of the signals is critical when measuring either phase or amplitude. 2) The demodulator implements both an in-phase Wandering amplitude or phase will not give and a quadrature detector section so that the consistent readings with this type of circuit. actual magnitude and phase of the input signal can be determined for any phase relationship Of note: This Analog' Lock-In Amplifier between input signal and the reference.

10 This was a technique was used by Hewlett-Packard starting very important performance improvement. in 1958 in their Microwave Power Meter products and continues to be used today [7]. 3) The Reference signal is implemented as a digital sine wave. When combined with a true, digital multiplying demodulator, this eliminated Classical DSP Based Lock-In the third order response problem of the classic analog demodulator of figure 6. In the mid 1980's analog Lock-In Amplifiers gave way to Digital Signal Processing (DSP) Based These commercial DSP designs have progressed designs. These DSP Based Lock-In Amplifiers in performance over the years and now can were Based on the very common Quadrature or IQ operate from DC to several hundred Megahertz. detection method that is still used in all sorts of digital demodulators today including Software Defined Radios (SDR's) (figure 9).