An implemented impedance measuring instrument is described in this paper. The device uses a dsPIC (Digital Signal Peripheral Interface Controller) as a processing unit, and a DDS (Direct Digital Synthesizer) to stimulate the measurement circuit composed by the reference impedance and the unknown impedance. The voltages across the impedances are amplified by programmable gain instrumentation amplifiers and then digitized by analog to digital converters. The impedance is measured by applying a seven-parameter sine-fitting algorithm to estimate the sine signal parameters. The dsPIC communicates through RS-232 or USB with a computer, where the measurement results can be analyzed. The device also has an LCD to display the measurement results.
This paper presents a simple DFT-based golden section searching algorithm (DGSSA) for the single tone frequency estimation. Because of truncation and discreteness in signal samples, Fast Fourier Transform (FFT) and Discrete Fourier Transform (DFT) are inevitable to cause the spectrum leakage and fence effect which lead to a low estimation accuracy. This method can improve the estimation accuracy under conditions of a low signal-to-noise ratio (SNR) and a low resolution. This method firstly uses three FFT samples to determine the frequency searching scope, then – besides the frequency – the estimated values of amplitude, phase and dc component are obtained by minimizing the least square (LS) fitting error of three-parameter sine fitting. By setting reasonable stop conditions or the number of iterations, the accurate frequency estimation can be realized. The accuracy of this method, when applied to observed single-tone sinusoid samples corrupted by white Gaussian noise, is investigated by different methods with respect to the unbiased Cramer-Rao Low Bound (CRLB). The simulation results show that the root mean square error (RMSE) of the frequency estimation curve is consistent with the tendency of CRLB as SNR increases, even in the case of a small number of samples. The average RMSE of the frequency estimation is less than 1.5 times the CRLB with SNR = 20 dB and N = 512.