Driving-point Impedance Function Research Articles

Sharp Inequalities for Driving Point Impedance Functions

In this paper, positive real functions are considered as driving point impedance functions, Z(s), which are utilized in electrical engineering for characteristic representation of circuits. Accordingly, for the real part of Z(s), sharp inequalities are presented with their extremal functions by using zeros and poles of Z(s). For these extremal functions, corresponding generic circuit schematics are given with their spectral analyses. According to the obtained results, it has been shown that various circuits can be obtained by using the extremal functions of the inequalities presented in this study.

An Analytical Approach to Locate Short Circuit Fault in a Cable Using Sweep Frequency Response Analysis

In this paper, analytical methods are proposed for the location of a short circuit fault in a power cable using sweep frequency response analysis (SFRA). The impedance spectroscopy is estimated using classical transmission line (TL) theory whereas the driving point impedance function (DPIF) of the cable is proposed to be constructed either by using experimental SFRA data or analytically from the knowledge of the frequency-dependent parameters, material properties, and dimensions of the cable. Finally, an analytical formula is proposed for the estimation of the location of a short-circuit fault using the location of poles and zeros of the impedance function before and after the fault. The formulae are validated using FEM software simulations as well as experimentally on a test cable.

Towards Unique Circuit Synthesis of Power Transformer Winding Using Gradient and Population Based Methods

The aim of the paper is to synthesize a nearly unique, physically realizable and mutually coupled ladder circuit representation of a two-winding transformer by identifying the most accurate and reliable optimization technique such that prior knowledge in selecting the initial guess and search space is avoided. To this end, magnitude and phase of the driving-point impedance function are captured by performing sweep frequency response analysis (SFRA). Then, two widely used population-based algorithms namely, particle swarm optimization (PSO) and artificial bee colony (ABC) and one gradient-based sequential quadratic programming (SQP) algorithm are implemented. Two case studies are considered namely, i) 15 MVA, 66/11.55 kV transformer and, ii) 111 kVA, 7.33/1.22 kV transformer. The performance of the aforementioned algorithms is compared using three evaluation parameters namely, repeatability, accuracy and reliability

Applications of the Carathéodory’s Inequality for Driving Point Impedance Functions

In this study, the Carathéodory’s Inequality, which is a highly popular topic of complex analysis theory, has been applied to electrical engineering to obtain novel driving point impedance functions. In electrical engineering, driving point impedance functions correspond to positive real functions and they are used for representation of the spectral characteristics of a particular circuit. Accordingly, boundary version of the Carathéodory’s inequality has been considered here assuming that the driving point empedance function, Z(s) has a fractional function structure with 0 =0 and it is analytic in the right half plane. At the end of the analyses, new driving point impedance functions have been obtained and they have been presented with their spectral characteristics. According to simulation results, it is possible to say that the frequency responses of the obtained generic driving point impedance functions have spiky filter structures where the number of the spikes in the frequency response of these filters depend on a pre-defined parameter, n.

Circuit Applications of Schwarz-Pick Lemma

In this brief, the relation between Schwarz-Pick lemma and driving point impedance function is investigated. Schwarz-Pick lemma is given as the generalized version of Schwarz lemma. Here, a generic driving point impedance function is obtained by applying Schwarz-Pick lemma to positive real functions. At first, a novel inequality is obtained for the modulus of the derivative of the driving point impedance function and in the next step, an extremal function is found by applying sharpness analysis to this inequality. At the end, obtained extremal function is considered as a generic driving point impedance function and corresponding circuit schematics are presented with their spectral analyses. Obtained driving point impedance function is not an arbitrary function but it is the intuitive result of the considered problem in this study. Accordingly, it is guaranteed to obtain a practically realizable driving point impedance function. Also, novel upper bounds are determined for the magnitude of driving point impedance function and for its derivative.

SHARPENED FORMS FOR DRIVING POINT IMPEDANCE FUNCTIONS AT BOUNDARY OF RIGHT HALF PLANE

Driving point impedance functions (DPIFs) are frequently used in electrical engineering, and they represent characteristic properties of various types of circuits such as RL, RC, LC and RLC networks. In this paper, boundary analysis of driving point impedance functions are investigated using Schwarz lemma. Assuming that the driving point impedance function, Z(s), is given as Z(s)=A/2+c_p (s-1)^p+c_(p+1) (s-1)^(p+1)+... and it is analytic in the right half of the s-plane, novel boundaries are obtained for |Z^' (0)|. Accordingly, it is aimed to obtain novel inequalities which presents higher boundaries for |Z'(0)| and derive novel generic driving point impedace functions by performing extremal analysis of these obtained inequalities. It is also aimed to investigate how |Z'(s)| can be interpreted when it is considered at the boundary. According to simulation results, frequency characteristics of obtained driving point impedance functions can be used to design of multi-notch filters which are localized at certain frequency values.

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

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.

Derivative of driving point impedance functions at right half plane

The purpose of this paper is to provide a result which concerns with the boundary behaviour of positive real functions. Z(s) = Z(b)+a1(s - b)+ a2 (s - b)2 +... is an analytic function defined in the right half of the s-plane.We derive inequalities for the modulus of Z(s) function, |Z'(c)|, by assuming the Z(s) function is also analytic at the boundary point s = c on the imaginary axis, where c = iImb and finally, the sharpness of these inequalities is proved.

Design of multiband matching ladders without mutual coupling using parametric representation of Brune functions

In this study, a semianalytical method for the design of mutual coupling free multiband matching networks is introduced. A new parametric representation of Brune functions is used for the construction of multiband ladder network topologies without mutual induction. The method involves the use of Fujisawa's constraints for low pass ladders having finite transmission zeros, in a parametric representation of driving point impedance function resulting in mutual inductance free Brune sections. The developed parametric representation is incorporated with Real Frequency Techniques to design matching networks with a plurality of pass bands. Several illustrative design examples are presented to validate the method.

Uniqueness part of Schwarz lemma for driving point impedance functions

In this paper, a boundary version of the uniqueness part of the Schwarz lemma for driving point impedance functions has been investigated. Also, more general results have been obtained for a different version of the Burns-Krantz uniqueness theorem. In these results, as different from the Burns-Krantz theorem, only the boundary points have been used as the conditions on the function. Also, more general majorants will be taken instead of power majorants in (1.1).

Some Remarks on Positive Real Functions and Their Circuit Applications

In this paper, a boundary version of the Schwarz lemma has been considered for driving point impedance functions at s=0 point of the imaginary axis. Accordingly, under Z(0)=0condition, the modulus of the derivative of the Z(s) function has been considered from below. Here, Z(alfa), c1 and c2 coefficients of the Taylor expansion of the Z(s)=beta+c1(s-alfa)+... function have been used in the obtained inequalities. The sharpness of these inequalities has also been proved.

Schwarz lemma for driving point impedance functions and its circuit applications

SummaryIn this paper, a boundary version of the Schwarz lemma is investigated for driving point impedance functions and its circuit applications. It is known that driving point impedance function, Z(s) = 1 + cp(s − 1)p + cp + 1(s − 1)p + 1 + ..., p > 1, is an analytic function defined on the right half of the s‐plane. Two theorems are presented using the modulus of the derivative of driving point impedance function, |Z′(0)|, by assuming the Z(s) function is also analytic at the boundary point s = 0 on the imaginary axis with . In the obtained inequalities, the value of the function at s = 1 and the derivatives with different orders have been used. Finally, the sharpness of the inequalities obtained in the presented theorems is proved. Simple LC circuits are obtained using the obtained driving point impedance functions.

On boundary analysis for derivative of driving point impedance functions and its circuit applications

In this study, a boundary analysis is carried out for the derivative of driving point impedance (DPI) functions, which is mainly used for the synthesis of networks containing resistor-inductor, resistor–capacitor and resistor–inductor–capacitor circuits. It is known that DPI function, Z ( s ) , is an analytic function defined on the right half of the s-plane. In this study, the authors present four theorems using the modulus of the derivative of DPI function, | Z ′ ( 0 ) | , by assuming the Z ( s ) function is also analytic at the boundary point s = 0 on the imaginary axis and finally, the sharpness of the inequalities obtained in the presented theorems are proved. It is also shown that simple inductor–capacitor tank circuits and higher-order filters are synthesised using the unique DPI functions obtained in each theorem.

Boundary Analysis for the Derivative of Driving Point Impedance Functions

Four theorems are presented in this brief by performing boundary analysis of the derivative of driving point impedance functions evaluated at the origin. Also, the circuits corresponding to these driving point impedance functions, which are obtained as the natural results of presented theorems, are given. Driving point impedance functions are mainly used for synthesis of networks containing RL, RC, and RLC circuits. Considering that the driving point impedance function, ${Z(s)}$ , is an analytic function defined on the right half of the s- plane, we derive inequalities for the modulus of the derivative of driving point impedance function, ${|}{Z}^{\prime } {(0)|}$ , by assuming the ${Z(s)}$ function is also analytic at the boundary point ${s=}{0}$ on the imaginary axis with ${Z(0)=}{0}$ . Finally, the sharpness of these inequalities are proved. Unique driving point impedance functions are obtained as intuitive results of presented theorems in the study and it is also shown that the extremal functions correspond to the driving-point impedances of simple LC circuits.

Bound estimates for the derivative of driving point impedance functions

In this paper, a boundary analysis is carried out for the derivative of driving point impedance functions, which is mainly used for synthesis of networks containing RL, RC and RLC circuits. It is known that driving point impedance function, Z(s), is an analytic function defined on the right half of the s-plane. In this study, we derive inequalities for the modulus of derivative of driving point impedance function, |Z'(0)|, by assuming the Z(s) function is also analytic at the boundary point s = 0 on the imaginary axis and the sharpness of these inequalities is proved. Furthermore, an equation for the driving point impedance function, Z(s), is obtained as a natural result of the proved theorem in this study.

Material performance measurement of a promising circuit element: fractor-part I: driving-point impedance function of the arbitrary-order fractor in its natural implementation

Here and in the companion paper, the physical performance measurement, especially measurement units and physical dimensions of fractance and rules for fractors in series and parallel are discussed. The concept of fractance, as the fractional-order impedance of a fractor, arose following the successful synthesis of a fractional differentiator in an analogue circuit. Until now, however, the measurement units and physical dimensions of fractance have not been proposed. Motivated by this need, in this paper, I studied the electrical properties of fractor. In particular, the driving-point impedance function of the arbitrary-order fractor in its natural implementation is introduced. Through mathematical and physical analysis, the driving-point impedance function of the 1/2-order fractor is studied, following which the driving-point impedance function of the arbitrary-order fractor is proposed. This paper discusses fundamental issues, whereas Part II is devoted to the measurement units and physical dimensions of fractance and the rules for fractors in series and parallel.

Construction of equivalent circuit of a transformer winding from driving-point impedance function – analytical approach

Analytical solution is presented to convert a given driving-point impedance function (in s-domain) into a physically realisable ladder network with inductive coupling between any two sections and losses considered. The number of sections in the ladder network can vary, but its topology is assumed fixed. A study of the coefficients of the numerator and denominator polynomials of the driving-point impedance function of the ladder network, for increasing number of sections, led to the identification of certain coefficients, which exhibit very special properties. Generalised expressions for these specific coefficients have also been derived. Exploiting their properties, it is demonstrated that the synthesis method essentially turns out to be an exercise of solving a set of linear, simultaneous, algebraic equations, whose solution directly yields the ladder network elements. The proposed solution is novel, simple and guarantees a unique network. Presently, the formulation can synthesise a unique ladder network up to six sections.

Construction of Physically Realizable Driving-Point Function From Measured Frequency Response Data on a Model Winding

A simple method is described for constructing physically realizable driving-point impedance function from measured frequency response data (i.e., magnitude and phase) on a model winding and a transformer. A unique feature of the proposed method is that it ensures the constructed rational function is always positive-real, thereby guaranteeing synthesis of a physically realizable network every time. This feature could not always be guaranteed by earlier methods. Hence, it was a limitation. The proposed method is demonstrated on a single-layer model winding and the measured terminal characteristics is converted to a lumped parameter ladder network, since this representation is naturally suited to establish a physical mapping between the actual winding and synthesized circuit. So, the need to guarantee physical realizability is evident. Proceeding further, the terminal characteristics of a 315-kVA, 11/6.9-kV transformer is measured and a rational function representation is obtained. However, its realization as a coupled ladder network requires some more work to be done. In summary, it is believed that this proposal is a step towards providing a solution for localization of deformation in actual transformer windings.

MEASURING THE SIX dof DRIVING POINT IMPEDANCE FUNCTION AND AN APPLICATION TO RB INERTIA PROPERTY ESTIMATION

An accurate driving point measurement is imperative in structural dynamic testing. For example, it is used to derive modal scaling, for experimental correlation of finite element models, impedance modelling and extracting the rigid body (RB) inertia properties of an object. A typical driving point measurement gives the linear force/displacement relationship at a single degree of freedom (dof), but any point on an object actually has rotational dofs as well. For example these rotational dofs must be measured in an impedance model where moments are transmitted at the connection point of two substructures. By ignoring the rotations, an inaccurate model will result. In the past, dynamic sensing technology has been limited to the accurate measurement of translational dofs. While rotational sensors do exist, their accuracy is called into question for certain applications. Rotational dofs have tended to be ignored in the measurement process. Applications, which require their use, such as impedance modelling and RB inertia property estimation, have suffered as a result. A process/sensor is being developed to accurately measure the driving point impedance function in all six dofs. The sensor as well as a calibration procedure will be presented here. In order to verify the validity of the calibration and measurement procedure, a new method for measuring the RB inertia properties of an object will be presented. This new method requires an accurate six dof driving point impedance measurement to provide accurate results. The inertia properties of an automotive brake rotor will be measured and compared with the results of a traditional pendulous swing test.

A transducer modelling technique for the identification of the transfer function and driving-point impedance

A new modelling technique for ultrasonic transducers is proposed in this paper. It consists of a systematic approach that considers the transducer as a two-port black box characterized only by its electrical driving-point impedance and electromechanical transfer function. This transducer modelling technique is therefore suitable for front-end hardware designers because, unlike most widespread models like Mason, KLM and so on, it does not require knowledge of the internal manufacturing characteristics. Driving-point impedance and axial acoustic far-field measurements are experimentally derived from broad-band excitation and stored in a computer memory. With these data sets the transducer model is carried out by identifying two polynomial ratio functions in the s variable domain, which approximates the two experimental data sets. A mean-square-error minimization algorithm has also been developed in order to optimize the identified functions. This algorithm gives good agreement of the identified function with the experimental data. This procedure is applied to different transducers and leads to an effective model since all the actual acousto-electric characteristics are taken into account. The advantages of this technique are exploited when used in conjunction with analog circuit simulation software for the design of front-end electronics. The results presented are relative to the application of this procedure to a transducer operating in the frequency range 3–8 MHz and with characteristic impedance from 10 to 150 ω.