Enhanced Frequency Resolution Two-Channel Two-Phase Microcontroller Lock-In Amplifier
Gustavo Marcati A. Alves, Ronaldo Domingues Mansano
Abstract
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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Q$ </tex-math></inline-formula> -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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Q$ </tex-math></inline-formula> , in scientific instrumentation such as scanning probe microscopes (SPMs), or even for educational purposes to teach the working principle of the LIAs.