Phase-increment sampling in chirp signal based impedance measurements

For measuring of the spectra of complex electrical impedance, the chirp excitation signals can be used. The analysis of the response signal of an object, often dynamical, in time, or circuit under test can be performed by short-time Fourier transform in the sliding time-domain window. Computationally more efficient and accurate could be the usage of the simple correlation (multiplication-and accumulation of the discrete samples in the digital processing case) by the excitation waveform (sine chirp) as the first reference signal in the first (“in-phase”) channel and by corresponding cosine-chirp in the other (“quadrature”) channel, both in the same sliding in time window. Still, classical uniform sampling scheme in such solutions is not efficient and not giving accurate result, so the non-uniform sampling scheme of excitation signal and reference waveforms has been proposed and investigated, on some practical examples. For linear chirp - the key is usage of the constant phase increments of the sampling instants of the excitation signal, corresponding to the non-uniform time and frequency increments. Simulations for measurement of the impedance spectra in the frequency range of 10kHz to 1 MHz with 1 ms duration chirp signal has been performed, showing the good performance of the proposed approach at possible simplicity of the implementation.

I. Introduction

Measurement of the electrical impedance spectra (EIS) has several applications and can be used for characterization of materials, structures, tissues, microfluidics, electrochemical processes etc [1]–[3]. Also, EIS has a wide variety of interesting applications with contactless measurements, e.g. based on eddy current phenomena, using inductive sensors [4]. Electrical (and magnetic properties, obtained by eddy current impedance measurements) are often distinctive properties of metallic materials, tissues, electrochemical processes etc, allowing to identify and validate the materials and structures. An example of possible application of the EIS (based on eddy current) is the identification and validation of coins [5]. As coins are often (like 1€ and 2€ multilayer metal structures, the impedance spectroscopy allows to measure the depth profile of properties of such objects, incl the coating layers.