Enhanced Frequency Resolution Two-Channel Two-Phase Microcontroller Lock-In Amplifier

This article presents a method to obtain a enhanced frequency resolution two-phase lock-in amplifier (LIA) with two channels in a microcontroller using minimum external circuitry. The timer peripheral of the microcontroller was used to generate the square wave signals for both the excitation and the quadrant demodulation, simplifying the waveform synthesis when compared to the use of digital-to-analog converters (DACs). To improve the frequency resolution of the generated signals, the timer signal was dithered to achieve fractional frequency values, while demodulation was executed in real time with signal acquisition. The real and imaginary parts of the signal are then transmitted to the computer by the universal serial bus (USB) interface while the computer sends commands to change the frequency, phase, or control other features. As proof of work, quartz tuning fork (QTF) sensors were measured due to its high $Q$ -factor. The bandwidth of the lock-in was limited by the acquisition and demodulation sample rate of 300 Ks/s, while we showed 1000 times frequency resolution enhancement when compared to the not dithered signal generation. This approach can be applied in embedded design to measure frequency-dependent sensors with high $Q$ , in scientific instrumentation such as scanning probe microscopes (SPMs), or even for educational purposes to teach the working principle of the LIAs.

I. Introduction

Two-phase lock-in amplifiers (LIAs) are instruments that measure the amplitude and phase of amplitude-modulated signals. It is used in a multitude of experiments in science and technology in diverse scenarios. The most common application is in the improvement of the signal-to-noise ratio of an experiment. The lock-in exploits the limited bandwidth of noise and modulates the excitation source of the experiment in a different frequency to finally demodulate a cleaner response signal. In this case, dynamic range and/or dynamic reserve should be enhanced to better recover the signal from the noise. At a different scenario, the LIA can be used to measure the frequency-dependent response of devices and experiments. Different from the application cited before, this application requires an instrument with enhanced frequency resolution and bandwidth of operation allied to the signal recovery capabilities.