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The electric characteristics of electric-double layer capacitors (EDLCs) are determined by their capacitance which is usually measured in the time domain from constant-current charging/discharging and cyclic voltammetry tests, and from the frequency domain using nonlinear least-squares fitting of spectral impedance. The time-voltage and current-voltage profiles from the first two techniques are commonly treated by assuming ideal S s C behavior in spite of the nonlinear response of the device, which in turn provides inaccurate values for its characteristic metrics. In this paper we revisit the calculation of capacitance, power and energy of EDLCs from the time domain constant-current step response and linear voltage waveform, under the assumption that the device behaves as an equivalent fractional-order circuit consisting of a resistance R s in series with a constant phase element (CPE( Q, α ), with Q being a pseudocapacitance and α a dispersion coefficient). In particular, we show with the derived ( R s , Q, α )-based expressions, that the corresponding nonlinear effects in voltage-time and current-voltage can be encompassed through nonlinear terms function of the coefficient α , which is not possible with the classical R s C model. We validate our formulae with the experimental measurements of different EDLCs.

The commercial availability of integrated circuits with bioimpedance sensing functionality is advancing the opportunity for practical wearable systems that monitor the electrical impedance properties of tissues to identify physiological features in support of health-focused applications. This technical note characterizes the performance of the MAX3000x (resistance/reactance accuracy, power modes, filtering, gains) and is available for on-board processing (electrode detection) for localized bioimpedance measurements. Measurements of discrete impedances that are representative of localized tissue bioimpedance support that this IC has a relative error of <10% for the resistance component of complex impedance measurements, but can also measure relative alterations in the 250 mΩ range. The application of the MAX3000x for monitoring localized bicep tissues during activity is presented to highlight its functionality, as well as its limitations, for multi-frequency measurements. This device is a very-small-form-factor single-chip solution for measuring multi-frequency bioimpedance with significant on-board processing with potential for wearable applications.

Three fractional-order transfer functions are analyzed for differences in realizing ( 1 + α ) order lowpass filters approximating a traditional Butterworth magnitude response. These transfer functions are realized by replacing traditional capacitors with fractional-order capacitors ( Z = 1 / s α C where 0 ≤ α ≤ 1 ) in biquadratic filter topologies. This analysis examines the differences in least squares error, stability, - 3 dB frequency, higher-order implementations, and parameter sensitivity to determine the most suitable ( 1 + α ) order transfer function for the approximated Butterworth magnitude responses. Each fractional-order transfer function for ( 1 + α ) = 1.5 is realized using a Tow–Thomas biquad a verified using SPICE simulations.

(1) Background: One effect of microgravity on the human body is fluid redistribution due to the removal of the hydrostatic gravitational gradient. These fluid shifts are expected to be the source of severe medical risks and it is critical to advance methods to monitor them in real-time. One technique to monitor fluid shifts captures the electrical impedance of segmental tissues, but limited research is available to evaluate if fluid shifts in response to microgravity are symmetrical due to the bilateral symmetry of the body. This study aims to evaluate this fluid shift symmetry. (2) Methods: Segmental tissue resistance at 10 kHz and 100 kHz was collected at 30 min intervals from the left/right arm, leg, and trunk of 12 healthy adults over 4 h of 6° head-down-tilt body positioning. (3) Results: Statistically significant increases were observed in the segmental leg resistances, first observed at 120 min and 90 min for 10 kHz and 100 kHz measurements, respectively. Median increases were approximately 11% to 12% for the 10 kHz resistance and 9% for the 100 kHz resistance. No statistically significant changes in the segmental arm or trunk resistance. Comparing the left and right segmental leg resistance, there were no statistically significant differences in the resistance changes based on the side of the body. (4) Conclusions: The fluid shifts induced by the 6° body position resulted in similar changes in both left and right body segments (that had statistically significant changes in this work). These findings support that future wearable systems to monitor microgravity-induced fluid shifts may only require monitoring of one side of body segments (reducing the hardware needed for the system).

One method for analyzing bioimpedance measurements collected from a tissue applies equivalent electrical circuits to represent the data. This typically requires curve-fitting or optimization procedures to determine the circuit parameters of the selected equivalent circuit model that best fit the collected data. This work describes the performance (in terms of accuracy and execution time) of a nonlinear least squares optimization implementation using SciPy on a Raspberry Pi (RPi) for the analysis of simulated bioimpedance measurements, compared to MATLAB implementations of the same method. The SciPy/RPi implementation yielded similar accuracy to the MATLAB counterparts though the execution time ranged from 1.4 × to 2.1 × longer than the MATLAB environments and 10× greater than the same Python implementation running on a desktop or laptop environment. The performance of this optimization implementation on the RPi does support its suitability for further bioimpedance applications and its further use for applications requiring postprocessing in addition to data collection from connected sensors.

The article presents a synthesis method to design electrical circuit elements with fractional-order impedance, referred to as a Fractional-Order Element (FOE) or Fractor, that can be implemented by Metal–Oxide–Semiconductor (MOS) transistors. This provides an approach to realize this class of device using current integrated circuit manufacturing technologies. For this synthesis MOS transistors are treated as uniform distributed resistive-capacitive layer structures. The synthesis approach adopts a genetic algorithm to generate the MOS structures interconnections and dimensions to realize an FOE with user-defined constant input admittance phase, allowed ripple deviations, and target frequency range. A graphical user interface for the synthesis process is presented to support its wider adoption. We synthetized and present FOEs with admittance phase from 5 to 85 degrees. The design approach is validated using Cadence post-layout simulations of an FOE design with admittance phase of 74  ± 1 degrees realized using native n-channel MOS devices in TSMC 65 nm technology. Overall, the post-layout simulations demonstrate magnitude and phase errors less than 0.5% and 0.1 degrees, respectively, compared to the synthesis expected values in the frequency band from 1 kHz to 10 MHz. This supports that the design approach is appropriate for the future fabrication and validation of FOEs using this process technology.

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.

In this paper we use a least-squares fitting routine to approximate the stopband ripple characteristics of fractional-order inverse Chebyshev lowpass filters which have fractional-order zeros and poles. MATLAB simulations of ( 1 + α ) -order lowpass filters with fractional steps from α = 0.1 to α = 0.9 are given as examples. SPICE simulations of 1.2-, 1.5-, and 1.8-order lowpass filters and experimental results of a 1.5-order filter using approximated fractional-order capacitors in a Multiple-Input Biquad circuit validate the implementation of these circuits.

We propose the use of nonlinear least squares optimization to approximate the passband ripple characteristics of traditional Chebyshev lowpass filters with fractional order steps in the stopband. MATLAB simulations of (1+α), (2+α), and (3+α) order lowpass filters with fractional steps from α = 0.1 to α = 0.9 are given as examples. SPICE simulations of 1.2, 1.5, and 1.8 order lowpass filters using approximated fractional order capacitors in a Tow-Thomas biquad circuit validate the implementation of these filter circuits.

A novel method for embedded hardware-based parameter estimation of the Cole model of bioimpedance is developed and presented. The model parameters R ∞ , R 1 and C are estimated using the derived set of equations based on measured values of real ( R ) and imaginary part ( X ) of bioimpedance, as well as the numerical approximation of the first derivative of quotient R / X with respect to angular frequency. The optimal value for parameter α is estimated using a brute force method. The estimation accuracy of the proposed method is very similar with the relevant work from the existing literature. Moreover, performance evaluation was performed using the MATLAB software installed on a laptop, as well as on the three embedded-hardware platforms (Arduino Mega2560, Raspberry Pi Pico and XIAO SAMD21). Obtained results showed that the used platforms can perform reliable bioimpedance processing with the same accuracy, while Raspberry Pi Pico is the fastest solution with the smallest energy consumption.