Impedance Spectroscopy for Measurement and Sensor Solutions

The ZARC element is a parallel connection between a constant phase element and an ohmic resistor which describes the charge transfer and the double-layer capacitance at an electrode–electrolyte interface. However, this mathematical object has been determined using measurement data and cannot be derived from physical or chemical processes. In order to understand the dynamics of ZARC and its parameters' influence in frequency and in time domain, we approximate it using fundamental equivalent circuits. Here, we introduce two approaches using RC circuits whose behaviours are well-known. The first method consists of infinitely many serially connected RC circuits which can be uniquely related to ZARC by explicit equations. In contrast, the second uses just three serially connected RC circuits, but adds a minimization problem. Both approaches depend only on three parameters: an ohmic resistance, a capacitance, and a newly defined parameter which is a measure of the modification of the single capacitances. Moreover, we show a decrease of the total capacitance of both impedances for growing deviations from the behavior of an RC circuit. Finally, since the properties of RC circuits are well known in frequency and in time domain, we deduce the behaviours of both methods in the time domain.

A data-driven scheme for modeling electrical impedance in biosensors is presented by a subspace method working with the singular value decomposition of structured voltage and current data. Contrary to the classical electrical impedance spectroscopy (EIS) methods, our scheme uses simple instrumentation, works in time-domain, provides fast results, and does not require semi-empirical assumptions to retrieve structured models from data. We show how data-driven models exhibit a close relationship with lumped-element circuits, encoding dielectric and conductive properties detected by the sensor in the range from 10 kHz up to 10 MHz. Performance results are shown for calibration networks and two case studies: (i) a buffer solution, and (ii) a biological cell suspension. Finally, the viability of the scheme is discussed when compared with the classical EIS method.

Wideband excitation signals are essential in bioimpedance spectroscopy for measurements in a time ensuring a quasi-stable measurement condition. In particular, for wearable biomedical systems, due to limited system resources, several aspects regarding measurement time, crest factor, slew rate requirements, frequency distribution, amplitude spectrum, and energy efficiency need to be thoroughly investigated. In this paper, we present an investigation of excitation signals, which includes not only the theoretical aspects but also aspects of real implementation on microcontroller-based systems. At a fixed number of samples and sampling rate, we investigate the implementability of signal frequencies and the resulting spectral efficiency. We focus on sources of signal distortion due to timer and amplitude deviations. The results show that for 4096 samples and a sampling frequency of 1 MHz, wideband signals are 2.76 times faster than a stepped frequency sweep. The multisine signal provides a better energy efficiency and has a lower slew rate requirement on hardware (around 0.3 V µs⁻¹), but has a relatively high crest factor, even after optimization. An exemplary investigation of the distortion of the time/frequency and amplitudes following implementation on a standard industrial advanced RISC machines microcontroller has shown that a sampling rate compensation is required to overcome timer inaccuracies. Furthermore, non-return-to-zero binary signals are more sensitive to distortion due to hardware-related issues and have a lower signal-to-distortion-and-noise (SINAD) ratio than 24 dB, which is lower than the multisine signal, having a SINAD of 31 dB.

Non-destructive monitoring of metal hardness is important for process monitoring and product quality assessment. In this paper, a partially hardened metal sample is assessed in regards to physical effects using multi-frequency inductance spectroscopy. For this purpose, the influence of change of conductivity, permeability and stress on the inductance spectra are analyzed. To extract the numerical values of permeability, the measured inductance spectra are compared to the analytical inductance model. Statistical analysis with principal component analysis is conducted to fuse the spectral data into a single representative value. The results show the possibility to obtain information from different layers of the partially hardened sample, thus indicating a strong relationship between the measured inductance and restraint hardening.

Electrochemical biosensors employing nano-transduction surfaces are considered highly sensitive to the morphology of nanomaterials. Various interfacial parameters namely charge transfer resistance, double layer capacitance, heterogeneous electron transfer rate and diffusion limited processes, depend strongly on the nanostructure geometry which eventually affects the biosensor performance. The present work deals with a comparative study of electrochemical impedance-based detection of L-tyrosine (or simply tyrosine) by employing carbon nanostructures (graphene quantum dots, single walled carbon nanotubes (CNTs) and graphene) along with tyrosinase as the bio-receptor. Specifically, the role of carbon nanostructures (i.e. 0D, 1D and 2D) on charge transfer resistance is investigated by applying time-varying electric field at the nano-bioelectrode followed by calculating the heterogeneous electron transfer rate, double layer capacitor current and their effects on limits of detection and sensitivities towards tyrosine recognition. A theoretical model based on Randel's equivalent circuit is proposed to account for the redox kinetics at various carbon nanostructure/enzyme hybrid surfaces. It was observed that, the 1D morphology (single walled CNTs) exhibited lowest charge transfer resistance ∼2.62 kΩ (lowest detection limit of 0.61 nM) and highest electron transfer rate ∼0.35 μm s⁻¹ (highest sensitivity 0.37 kΩ nM⁻¹ mm⁻²). Our results suggest that a suitable morphology of carbon nanostructure would be essential for efficient and sensitive detection of tyrosine.