This work compares two design methodologies, emulating both AgCl electrode and skin tissue Cole models for testing and verification of electrical bio-impedance circuits and systems. The models are based on fractional-order elements, are implemented with active components, and capture bio-impedance behaviors up to 10 kHz. Contrary to passive-elements realizations, both architectures using analog filters coupled with adjustable transconductors offer tunability of the fractional capacitors’ parameters. The main objective is to build a tunable active integrated circuitry block that is able to approximate the models’ behavior and can be utilized as a Subject Under Test (SUT) and electrode equivalent in bio-impedance measurement applications. A tetrapolar impedance setup, typical in bio-impedance measurements, is used to demonstrate the performance and accuracy of the presented architectures via Spectre Monte-Carlo simulation. Circuit and post-layout simulations are carried out in 90-nm CMOS process, using the Cadence IC suite.

https://www.mdpi.com/2227-7080/8/4/61/pdf

Analog Realization of Fractional-Order Skin-Electrode Model for Tetrapolar Bio-Impedance Measurements

Reconnection-less reconfigurable low-pass filtering topology suitable for higher-order fractional-order design.

The Cole–Davidson function is an efficient tool for describing the tissue behavior, but the conventional methods of approximation are not applicable due the form of this function. In order to overcome this problem, a novel scheme for approximating the Cole–Davidson function, based on the utilization of a curve fitting procedure offered by the MATLAB software, is introduced in this work. The derived rational transfer function is implemented using the conventional Cauer and Foster RC networks. As an application example, the impedance model of the membrane of mesophyll cells is realized, with simulation results verifying the validity of the introduced procedure.

Realization of Cole–Davidson Function-Based Impedance Models: Application on Plant Tissues

A novel procedure for the circuit implementation of the driving-point impedance of frequency-domain material models, constructed from fractional-order elements of arbitrary type and order, is introduced in this work. Following this newly introduced concept, instead of emulating separately each fractional-order element in the model under consideration, the direct emulation of the complete model can be achieved through the approximation of the total impedance function. The magnitude and phase frequency responses of the impedance function are first extracted and approximated through curve-fitting-based techniques. A rational integer-order driving-point impedance function is then obtained and realized using appropriately configured passive and/or active topologies. Comparison between the conventional method and the proposed method reveals that the achieved benefit is the significant reduction of the passive and/or active components count. Verification of the introduced concept is performed through circuit simulation results using OrCAD PSpice in the case of a root/stem/electrode interface model, as well as through experimental results where the driving-point input impedance of the human respiratory system under different health conditions is synthesized on a Field-Programmable Analog Array device.

Simple implementations of fractional-order driving-point impedances: Application to biological tissue models

An attractive feature of fractional calculus is its application in various interdisciplinary fields, extending from biomedical and biological notions to mechanical properties. For their description, fractional-order models have outperformed the corresponding integer-order models, resulting in a more realistic behavior, due to the additional degrees of freedom offered and the long-term memory effect that reflects the fractional order. These improved features are processed by appropriate circuit implementations, derived through several approximation methods, whose primary objective is to provide electronic tuning of their characteristics for being easily adapted to different conditions. The main circuit blocks, towards this direction, are fractional-order filters and fractional-order impedances, which are properly connected according to well-known models, for the study of specific functions of the corresponding sector. 

A collection of interdisciplinary applications of fractional-order circuits

The fractional-order lung impedance model of the human respiratory tree is implemented in this paper, using Operational Transconductance Amplifiers. The employment of such active element offers electronic adjustment of the impedance characteristics in terms of both elements values and orders. As the MOS transistors in OTAs are biased in the weak inversion region, the power dissipation and the dc bias voltage of operation are also minimized. In addition, the partial fraction expansion tool has been utilized, in order to achieve reduction of the spread of the required time-constants and scaling factors. The performance of the proposed scheme has been evaluated, at post-layout level, using MOS transistors models provided by the 0.35 μ m Austria Mikro Systeme technology CMOS process, and the Cadence IC design suite.

Implementation of a Fractional-Order Electronically Reconfigurable Lung Impedance Emulator of the Human Respiratory Tree

Novel single-input multiple-output and multiple-input single-output fractional-order filter topologies are presented in this paper. They are constructed from two fractional-order integrators with appropriate feedback and feed-forward paths, as well as from summation stages. The employed active cells are Operational Transconductance Amplifiers, providing the capability for electronic tuning of the realized time-constants, while the required fractional-order capacitors are approximated by appropriately configured RC networks. The provided simulation results, obtained using the Analog Design Environment of the Cadence software and the Design Kit from Austrian Mikro Systems1 0.35μ m CMOS process, confirm the correct operation of the proposed topologies.

Elpida Kaskouta

Papers

Implementation of a Fractional-Order Electronically Reconfigurable Lung Impedance Emulator of the Human Respiratory Tree

Single- Input Multiple-Output and Multiple-Input Single-Output Fractional-Order Filter Designs