Analysis on the Performance of a Second-order and a Third-order RLC Circuit of PRBS Generator

Abstract

A pseudo-binary random signal (PRBS) has been widely utilized for system identification in complex signals to develop an experimental approach. PRBS generator is a circuit that generates pseudo-random numbers. This work aims to analyze the best fit value of the PRBS generator with second-order and third-order under-damped black-box RLC circuit of the estimated model. The procedures conducting here can be divided into three parts. First, to design two black boxes using the RLC circuit representing a critically under-damped second-order and third-order system. PRBS generated with maximum-length sequence (MLS) equals 127 bits by using seven shift registers. Second, simulate the PRBS generator using MATLAB software and validate the estimated model from the simulation using the System Identification Tool in MATLAB. Next, connecting hardware RLC circuit and reading input and output signals using an oscilloscope. Finally, 2500 samples of captured data were used for estimation. Then, analyze and compare the best fit of the simulation and experiment with second-order and third-order under-damped black-box RLC circuit. Furthermore, analyze and compare best fit using different sample time. The results showed that the best fit of the second-order model with under-damped black-box RLC circuit was autoregressive with the exogenous term (ARX) 211, where the best fit of the simulation was 99.88%, and the best fit of the experiment was 96.04%. And the results showed that the best fit of the third-order model with an under-damped black-box RLC circuit was ARX 331, where the best fit of the simulation was 99%, and the best fit of the experiment was 94.28%. It was concluded that the best fit value of the second-order was better than the third order. What’s more, the results showed that when the select range is the same, the bigger the sample time, the better the best fit.