In this paper a comprehensive procedure for the analog modeling of Fractional-Order Elements (FOEs) is presented. Unlike most already proposed techniques, a standard approach from classical circuit ...theory is applied. It includes the realization of a system function by a mathematical approximation of the desired phase response, and the synthesis procedure for the realization of basic fractional-order (FO) one-port models as passive RC Cauer- and Foster-form canonical circuits. Based on the presented one-ports, simple realizations of two-port differentiator and integrator models are derived. Beside the description of the design procedure, illustrative examples, circuit diagrams, simulation results and practical realizations are presented.
Minimum sensitivity coupled resonators and biquads Jurisic, Drazen; Moschytz, George S.
International journal of circuit theory and applications,
September 2019, 2019-09-00, 20190901, Letnik:
47, Številka:
9
Journal Article
Recenzirano
Summary
The effect of coupling on the overall sensitivity to component tolerances of two second‐order resonators is compared with the sensitivity of a non‐coupled cascade of two second‐order ...resonators. Coupled resonators consist of two second‐order resonators “coupled” within a negative feedback loop. The resulting overall fourth‐order transfer function of the two circuits, coupled and non‐coupled, is identical. The “cascaded” poles, ie, the poles of the two cascaded resonators, are therefore identical to the poles of the coupled circuit, the coupled poles. The poles within the negative‐feedback loop, the “open‐loop” poles, will be different. We assume that the manufacturing technology used to realize the open‐loop poles of the coupled circuit is the same as that of the cascaded, non‐coupled circuit. The open‐loop poles will therefore be subject to the same component tolerances as those of the cascaded non‐coupled circuit. Our analysis leads to the optimum location in the s‐plane with regard to minimum sensitivity, for the open‐loop poles of the coupled circuit. Since resonators are essentially the equivalent of second‐order bandpass filters, the results obtained are applied to coupled second‐order active‐RC filters, or biquads, for which insensitivity to component tolerances is critical. The examples given pertain to the coupling of biquads.
The effect of coupling on the overall sensitivity to component tolerances of two resonators or biquads (CO) is compared with the sensitivity of a noncoupled cascade (CA) realizing the same transfer function. Minimum sensitivity is analytically shown to be obtained when the resonators inside the coupled structure are identical. The effect of parameter variation in an optimized coupled structure of two biquads is shown to be up to 30% lower than in the equivalent cascade.
Summary
In this paper, it is shown that by adding coupling to biquad pairs to obtain a fourth‐order band‐pass filter, the output thermal noise is reduced. It is shown analytically that minimum output ...thermal noise is obtained when the biquads are identical and the negative‐feedback factor used for coupling is the same as for the minimum sensitivity to component tolerances and ambient changes. Furthermore, by optimizing the coupled biquads for maximum dynamic range, the output noise is further decreased.
The effect of coupling on the output thermal noise of two coupled biquads (CO) is compared with that of a non‐coupled cascade (CA) realizing the same filter transfer function. Minimum noise is analytically shown to be obtained when the biquads inside the coupled structure are the same as those optimal for minimum sensitivity, ie, identical. The output thermal noise of an optimized coupled structure of two biquads is shown to be approximately 20% lower than in the equivalent cascade.
The concept of the delta discrete‐time operator‐based doubly terminated two‐pair (ladder) is discussed here for use in sampled‐data and digital filter design. The two‐pair filter utilizes traditional ...backward Euler and forward Euler integrators, is lossless under scaling (LUS), and possesses good magnitude sensitivity which is induced intrinsically due to the filter structure. This paper is an overview and consolidation of results published by the authors over the years in various conferences (Khoo et al., 1998, 1999, 2001, 2008, 2008a, 2008b) in a unifying and tutorial fashion. To achieve the low magnitude sensitivity, the well‐known Feldtkeller equation corresponding to the delta‐operator formulation is derived to establish the theoretical basis for the realization. One significant advantage of the design procedure presented here using the delta operator is that it overcomes the numerical problem at the spectral factorization stage of the conventional z‐domain lossless‐discrete‐time integrator (LDI) synthesis method when the filter poles are clustered around z = 1. Furthermore, the entire operation involves only rational polynomials, as opposed to fractional power polynomials as in the LDI and other methods in z‐domain. The method presented can realize three distinct forms of transfer functions with varied transmission zeros.
The theory of the delta discrete‐time operator‐based doubly terminated two‐pair (ladder) is presented here for use in sampled‐data and digital filter design. The two‐pair filter utilizes traditional forward Euler and backward Euler integrators, is lossless under scaling (LUS), and possesses good magnitude sensitivity which is induced intrinsically due to the filter structure.
This paper presents a method to decompose multichannel long-term intramuscular electromyogram (EMG) signals. In contrast to existing decomposition methods which only support short registration ...periods or single-channel recordings of signals of constant muscle effort, the decomposition software EMG-LODEC (ElectroMyoGram LOng-term DEComposition) is especially designed for multichannel long-term recordings of signals of slight muscle movements. A wavelet-based, hierarchical cluster analysis algorithm estimates the number of classes motor units (MUs), distinguishes single MUAPs from superpositions, and sets up the shape of the template for each class. Using three channels and a weighted averaging method to track action potential (AP) shape changes improve the analysis. In the last step, nonclassified segments, i.e., segments containing superimposed APs, are decomposed into their units using class-mean signals. Based on experiments on simulated and long-term recorded EMG signals, our software is capable of providing reliable decompositions with satisfying accuracy. EMG-LODEC is suitable for the study of MU discharge patterns and recruitment order in healthy subjects and patients during long-term measurements.
Cover Image Jurisic, Drazen; Moschytz, George S.
International journal of circuit theory and applications,
09/2019, Letnik:
47, Številka:
9
Journal Article
This tutorial paper proposes a subclass of cellular neural networks (CNN) having no inputs (i.e., autonomous) as a universal active substrate or medium for modeling and generating many pattern ...formation and nonlinear wave phenomena from numerous disciplines, including biology, chemistry, ecology, engineering, and physics. Each CNN is defined mathematically by its cell dynamics (e.g., state equations) and synaptic law, which specifies each cell's interaction with its neighbors. We focus on reaction-diffusion CNNs having a linear synaptic law that approximates a spatial Laplacian operator. Such a synaptic law can be realized by one or more layers of linear resistor couplings. An autonomous CNN made of third-order universal cells and coupled to each other by only one layer of linear resistors provides a unified active medium for generating trigger (autowave) waves, target (concentric) waves, spiral waves, and scroll waves. When a second layer of linear resistors is added to couple a second capacitor voltage in each cell to its neighboring cells, the resulting CNN can be used to generate various turing patterns.< >
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