An FPGA-based frequency response analyzer for multisine and stepped sine measurements on stationary and time-varying impedance

Abstract

We report the development of a field programmable gate array (FPGA) based frequency response analyzer (FRA) for impedance frequency response function (FRF) measurements using periodic excitations, i.e. sine waves and multisines. The stepped sine measurement uses two dedicated hardware-built digital embedded multiplier blocks to extract the phase and quadrature components of the output signal. The multisine FRF measurements compute the fast Fourier transform (FFT) of the input/output signals. In this paper, we describe its design, implementation and performance evaluation, performing electrical impedance spectroscopy (EIS) measurements on phantoms. The stepped sine accuracy is 1.21% at 1 kΩ (1%), the precision is 35 mΩ and the total harmonic distortion plus noise (THD+N) is −120 dB. As for the multisine impedance FRF measurements, the magnitude and phase precision are, respectively, 0.23 Ω at 48.828 kHz and 0.021 deg at 8.087 MHz when measuring a resistor 505 Ω (1%). The magnitude accuracy is 0.55% at 8.087 MHz while the phase accuracy is 0.17 deg at 6.54 MHz. In all, the stepped sine signal-to-noise ratio (SNR) is 84 dB and 65 dB at frequencies below and above 1 MHz respectively. The SNR for the multisine FRF measurements is above 65 dB (30 kHz–10 MHz). The FRA bandwidth is 610.4 mHz–12.5 MHz and the maximum FRF measurement rate exciting with multisines starting at 30 kHz is 200 spectra s−1. Based on its technical specifications and versatility, the FRA presented can be used in many applications, e.g. for getting insight quickly into the instantaneous impedance FRF of the time-varying impedance under test.