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Electrochemical impedance spectroscopy is finding increasing use in electrochemical sensors and biosensors, both in their characterisation, including during successive phases of sensor construction, and in application as a quantitative determination technique. Much of the published work continues to make little use of all the information that can be furnished by full physical modelling and analysis of the impedance spectra, and thus does not throw more than a superficial light on the processes occurring. Analysis is often restricted to estimating values of charge transfer resistances without interpretation and ignoring other electrical equivalent circuit components. In this article, the important basics of electrochemical impedance for electrochemical sensors and biosensors are presented, focussing on the necessary electrical circuit elements. This is followed by examples of its use in characterisation and in electroanalytical applications, at the same time demonstrating how fuller use can be made of the information obtained from complete modelling and analysis of the data in the spectra, the values of the circuit components and their physical meaning. The future outlook for electrochemical impedance in the sensing field is discussed.

This paper presents two discrete circuit solutions for realizing passive, electronically adjustable constant-phase elements, specifically half-order capacitors with a –45° phase shift. Fractional-order capacitors with electronically adjustable pseudocapacitance are especially useful for designing tunable filters and oscillators. The ability to adjust pseudocapacitance electronically and continuously is a major improvement over traditional passive solutions. Their pseudocapacitance can be controlled by a DC voltage, allowing key parameters like the cut-off or oscillation frequency to be tuned. Two presented design approaches differ in accuracy, tuning range, and signal-handling capability. Both solutions maintain a constant phase over one frequency decade, with a phase ripple within ± 2°. The tuning range spans from hundreds of Hz to several MHz. Presented solutions allow pseudocapacitance tuning in range of hundreds of nano F/sec 0.5 (with varicaps) and tens of micro F/sec 0.5 (with MOSFETs). The MOS-based circuit offers a tuning ratio of 7 but shows a 19% deviation between simulation and measurement. It also suffers from notable nonlinearity, with undistorted operation limited to signal levels up to 20 mV peak-to-peak. The varicap-based solution achieves a tuning ratio of 5, with high accuracy (up to 6% error), and handles input signals in the hundreds of mV with acceptable distortion. PSpice simulations and laboratory measurements confirm the performance of both designs.

One of the main challenges during the integration of a carbon/polymer-based nanocomposite sensor on textile substrates is the fabrication of a homogeneous surface of the nanocomposite-based thin films, which play a major role in the reproducibility of the sensor. Characterizations are therefore required in every fabrication step to control the quality of the material preparation, deposition, and curing. As a result, microcharacterization methods are more suitable for laboratory investigations, and electrical methods can be easily implemented for in situ characterization within the manufacturing process. In this paper, several textile-based pressure sensors are fabricated at an optimized concentration of 0.3 wt.% of multiwalledcarbon nanotubes (MWCNTs) composite material in PDMS. We propose to use impedance spectroscopy for the characterization of both of the resistive behavior and capacitive behavior of the sensor at several frequencies and under different loads from 50 g to 500 g. The impedance spectra are fitted to a model composed of a resistance in series with a parallel combination of resistance and a constant phase element (CPE). The results show that the printing parameters strongly influence the impedance behavior under different loads. The deviation of the model parameter α of the CPE from the value 1 is strongly dependent on the nonhomogeneity of the sensor. Based on an impedance spectrum measurement followed by parameter extraction, the parameter α can be determined to realize a novel method for homogeneity characterization and in-line quality control of textile-integrated wearable sensors during the manufacturing process.

The constant phase element (CPE) is found in most battery and supercapacitor equivalent circuit models proposed to interpret data in the frequency domain. When these models are used in the time domain, the initial conditions in the fractional differential equations must be correctly imposed. The initial state problem remains controversial and has been analyzed by various authors in the last two decades. This article attempts to clarify this problem by proposing a procedure to prepare the initial state and defining a decay function that reveals the effect of the initial state in several illustrative examples. This decay function depends on the previous history, which is reflected in the time needed to prepare the initial state and on the current profile assumed for this purpose. This effect of the initial state is difficult to separate and can lead to the misinterpretation of the CPE parameter values.

System thermal modeling allows heat and temperature simulations for many applications, such as refrigeration design, heat dissipation in power electronics, melting processes and bio-heat transfers. Sufficiently accurate models are especially needed in open-heart surgery where lung thermal modeling will prevent pulmonary cell dying. For simplicity purposes, simple RC circuits are often used, but such models are too simple and lack of precision in dynamical terms. A more complete description of conductive heat transfer can be obtained from the heat equation by means of a two-port network. The analytical expressions obtained from such circuit models are complex and nonlinear in the frequency ω . This complexity in Laplace domain is difficult to handle when it comes to control applications and more specifically during surgery, as heat transfer and temperature control of a tissue may help in reducing necrosis and preserving a greater amount of a given organ. Therefore, a frequency-domain analysis of the series and shunt impedances will be presented and different techniques of approximations will be explored in order to obtain simple but sufficiently precise linear fractional transfer function models. Several approximations are proposed to model heat transfers of a human middle bronchus and will be quantified by the absolute errors.

This paper provides readers with three partial results that are mutually connected. Firstly, the gallery of the so-called constant phase elements (CPE) dedicated for the wideband applications is presented. CPEs are calculated for 9° (decimal orders) and 10° phase steps including ¼, ½, and ¾ orders, which are the most used mathematical orders between zero and one in practice. For each phase shift, all necessary numerical values to design fully passive RC ladder two-terminal circuits are provided. Individual CPEs are easily distinguishable because of a very high accuracy; maximal phase error is less than 1.5° in wide frequency range beginning with 3 Hz and ending with 1 MHz. Secondly, dynamics of ternary memory composed by a series connection of two resonant tunneling diodes is investigated and, consequently, a robust chaotic behavior is discovered and reported. Finally, CPEs are directly used for realization of fractional-order (FO) ternary memory as lumped chaotic oscillator. Existence of structurally stable strange attractors for different orders is proved, both by numerical analyzed and experimental measurement.

A fractor is a simple fractional-order system. Its transfer function is 1 / F s α ; the coefficient, F , is called the fractance, and α is called the exponent of the fractor. This paper presents how a fractor can be realized, using RC ladder circuit, meeting the predefined specifications on both F and α . Besides, commonly reported fractors have α between 0 and 1. So, their constant phase angles (CPA) are always restricted between 0 ∘ and - 90 ∘ . This work has employed GIC topology to realize fractors from any of the four quadrants, which means fractors with α between - 2 and +2. Hence, one can achieve any desired CPA between + 180 ∘ and - 180 ∘ . The paper also exhibits how these GIC parameters can be used to tune the fractance of emulated fractors in real time, thus realizing dynamic fractors. In this work, a number of fractors are developed as per proposed technique, their impedance characteristics are studied, and fractance values are tuned experimentally.

Fractional-order calculus has been used for generalizing many modern and classical control theories including the well establish PID paradigm. The obtained controllers, of non-integer order, must be approximated with high order integer ones, in order to be realized. Successively, analog or digital implementations are used for the real world applications. This approach offers the hip to a classical criticism to fractional calculus. Why design a fractional-order system, which is usually of low order, if you need a high order system to implement it? In order to face this problem, in this paper, a fractional-order capacitor, more specifically a Constant Phase Device, is applied for implementing a first order fractional transfer function. Due to the intrinsic nature of the realized device, just one capacitor is needed for the implementation, avoiding therefore the need of high order RC approximation. Furthermore a fractional-order Wien oscillator and a chaotic Duffing circuit are presented confirming the potentiality of the proposed device in realizing fractional order circuits.

The Cole-Cole model for a dielectric is a generalization of the Debye relaxation model. The most familiar form is in the frequency domain and this manifests itself in a frequency dependent impedance. Dielectrics may also be characterized in the time domain by means of the current and charge responses to a voltage step, called response and relaxation functions respectively. For the Debye model they are both exponentials while in the Cole-Cole model they are expressed by a generalization of the exponential, the Mittag-Leffler function. Its asymptotes are just as interesting and correspond to the Curie-von Schweidler current response which is known from real-life capacitors and the Kohlrausch stretched exponential charge response.

As electrochemical research undergoes rapid technological progression, the acquisition of substantial amounts of electrochemical impedance spectra (EIS) becomes increasingly feasible. Yet, this advancement introduces intricate challenges in data processing, automation, and interpretation. This paper delves into the sufficiency of unsupervised machine learning (ML) and in particular dimensionality reduction methods in decoding EIS complexities, examining its strengths, limitations, and potential pathways for optimization. As we navigated the intricacies of non‐linear dimensionality reduction, spotlighting t‐distributed stochastic neighbor embedding (t‐SNE) and uniform manifold approximation and projection (UMAP) algorithms, a pattern emerged: these techniques excel at categorizing divergent impedance spectra but show limitations when faced with analogous circuit configurations, especially those substituting a capacitor with a constant phase element. This observation not only underscores a limitation but also accentuates that unsupervised ML approaches, alone, may not fully unravel the nuances of EIS spectra. In the concluding section of our manuscript, we discuss the implications of this finding from a practical standpoint, particularly for electrochemists seeking to apply these methods in their work. Unsupervised machine learning cannot distinguish between spectra of similar equivalent circuits with capacitors and constant phase elements interchanged