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For the simulation of rectilinearly moving conductors across a magnetic field, the Galerkin finite‐element method (GFEM) is generally employed. The inherent instability of GFEM is very often addressed by employing streamline upwinding/Petrov–Galerkin (SU/PG) scheme. However, the SU/PG solution is known to suffer from distortion at the boundary transverse to the velocity and the remedial measures suggested in fluid dynamics literature are computationally demanding. Therefore, simple alternative schemes are essential. In an earlier effort, instead of conventional finite‐difference‐based approach, the numerical instability was analysed using the Z‐transform. By employing the concept of pole‐zero cancellation, stability of the numerical solution was achieved by a simple restatement of the input magnetic flux in terms of associated vector potential. This approach, however, is restricted for input fields, which vary only along the direction of the velocity. To overcome this, the present work proposes a novel approach in which the input field is restated as a weighted elemental average. The stability of the proposed scheme is proven analytically for both one‐ and two‐dimensional cases. The error bound for the small oscillations remnant at intermittent Peclet numbers is also deduced. Using suitable numerical simulations, all the theoretical deductions are verified. [ABSTRACT FROM AUTHOR]

In this paper, a discrete-time domain synthesizing method was presented to design and implement the active integrator in the microwave frequency range. The frequency-domain GaAs Filed Effect Transistor (FET) scattering parameters are converted into the Z-domain representations. The transfer functions of the networks are formulated in the Z domain and implemented by using cascade serial line and GaAS FET. There are good agreement between the experimental results and the theoretical values. [ABSTRACT FROM AUTHOR]

This paper presents an integrated approach to taking a frequency-domain simulation problem into the discrete time domain, based on z transforms. The ideas are illustrated with free space, the Drude pole, and perfectly matched layer (PML) conversion examples, for both leapfrog time stepping and simultaneous time stepping. Numerical results for various perfectly matched layer methods are given. We then present a two-dimensional scattering example in which the conversion from frequency to discrete time is carried out. Numerical results are presented and compared with results from a Method-of-Moments formulation. [ABSTRACT FROM PUBLISHER]

Abstract: A novel technique for treating electrically thin dispersive layers with the finite-difference time-domain (FDTD) method based on Z transforms is introduced. The proposed model is based on the subcell technique, where the constitutive relations are locally averaged in the FDTD grid. The most significant feature of the proposed model is its ability to model rather complicated dispersive layers having multiple pole pairs. Then, based on the model above, the model for pulse reflection from a coated ideal conductor is proposed. The models are validated with several numerical examples making comparison with the exact results. [Copyright &y& Elsevier]

Abstract: After showing that Daubechies polynomial coefficients can be simply obtained from Pascal''s triangle by some elementary additions, we propose a derivation of the spectral factorization by using the elementary symmetric functions. This derivation leads us to present an analytic expression, able to compute Daubechies wavelet filter coefficients from the roots of the associated Daubechies polynomial. Thus, these coefficients are directly obtained and without recurrence. At last, we measure the quality of the coefficient sets generated by this expression and we compare it with two well-known methods. [Copyright &y& Elsevier]

The finite-difference time-domain (FDTD) technique for simulating electromagnetic wave interaction with a dispersive chiral medium is extended to include the simulation of dispersive bianisotropic media. Due to anisotropy and frequency dispersion of such media, the constitutive parameters are represented by frequency-dependent tensors. The FDTD is formulated using the Z-transform method, a conventional approach for applying FDTD in frequency-dispersive media. Omega medium is considered as an example of bianisotropic media, the frequency-dependent tensors of which are based on analytical models. The extended FDTD method is used to determine the reflection and transmission coefficients of co- and cross-polarized electromagnetic waves from omega slabs, illuminated by normally incident plane waves. Three cases are simulated: 1) a slab of uniaxial omega medium with its optical axis parallel to the propagation vector; 2) a slab of rotated uniaxial omega medium with its optical axis not parallel to the propagation vector; and 3) a slab of biaxial omega medium. The results are validated by means of comparisons with analytical solutions. [ABSTRACT FROM PUBLISHER]

FDTD solutions have their own properties distinct from the discrete samples of corresponding continuous wave solutions. Thus, the discrete equivalent to the Green's function is needed for applications like the one using a hybrid absorbing boundary condition which couples the FDTD algorithm with integral operators for nonconvex scatterers. In this paper we propose a new closed-form expression for the 3-D dyadic FDTD-compatible Green's function in infinite free space via a novel approach with the ordinary z-transform along with the spatial partial difference operators. The final expression involves a summation of standing wave modes with time-varying coefficients. The propagation of waves in the Yee's grid can be interpreted by the selective property of the time-varying coefficients, which is very different from the conventional concept of a traveling wave. The traditional dispersion analysis using plane waves for the FDTD algorithm in a source-free region may not be applicable to explain the wave propagation phenomenon through our analytic expression, because the corresponding z-transform diverges for z on the unit circle. [ABSTRACT FROM AUTHOR]

The impulse-invariance z transform method has been used to discretize frequency-dependent dielectric functions for FDTD simulations. This paper reviews, generalizes, and compares several methods for improving the accuracy of this process. A slightly novel curve-fitting approach is presented for the dielectric function of silver. [ABSTRACT FROM AUTHOR]

Resonant controllers have gained significant importance in recent years in multiple applications. Because of their high selectivity, their performance is very dependent on the accuracy of the resonant frequency. An exhaustive study about different discrete-time implementations is contributed in this paper. Some methods, such as the popular ones based on two integrators, cause that the resonant peaks differ from expected. Such inaccuracies result in significant loss of performance, especially for tracking high-frequency signals, since infinite gain at the expected frequency is not achieved, and therefore, zero steady-state error is not assured. Other discretization techniques are demonstrated to be more reliable. The effect on zeros is also analyzed, establishing the influence of each method on the stability. Finally, the study is extended to the discretization of the schemes with delay compensation, which is also proved to be of great importance in relation with their performance. A single-phase active power filter laboratory prototype has been implemented and tested. Experimental results provide a real-time comparison among discretization strategies, which validate the theoretical analysis. The optimum discrete-time implementation alternatives are assessed and summarized. [ABSTRACT FROM AUTHOR]

This paper presents the hardware-in-the-loop (HIL) simulation of power electronic systems using a unique adaptive discretization technique based on the input of the system, where the coefficient matrices and system equations are changed while the simulation is running. The voltage-sourceconverter (VSC)-based HVDC system is used as a case study. Two z-transform-based discretization techniques, known as the step-invariant transformation (SIT) and the ramp-invariant transformation, and one of their derivative time-shifted SIT are applied for simulating the VSC-HVDC system. Discrete switching synchronization algorithms are used to accommodate the asynchronous events that take place in between two discrete simulation points. The HIL simulation is implemented using an off-the-shelf PC cluster interfaced with a digital controller. The simulator and the controller are connected through I/O ports, which facilitate the exchange of analog and digital signals. A 4-kW VSC-HVDC experimental setup is used to validate the simulation results, using the same digital controller as that in the HIL simulation to supply the necessary gate pulses for the experimental VSCs. A comparative study of the results obtained through offline, HIL simulation, and the experiment is presented. [ABSTRACT FROM AUTHOR]

A well‐known property of the Z transform is the differentiation in z‐domain property, which states that if X(z) ≡ Z{x[n]} is the Z transform of a sequence x[n] then the Z transform of the sequence nx[n] is Z{nx[n]}=−z(dX (z)/dz). It is generally believed that the regions of convergence (ROC) for the two Z transforms are the same. It is shown that this is not true in the general case where X(z) is not rational and an example, in which the ROC is different for X(z) and Z{nx[n]}, is given. [ABSTRACT FROM AUTHOR]

This is an introductory paper on z-transform-based methods for electromagnetic transient simulations of power systems. Since the theory of the z-transform was originally developed for the analysis of time series data defined at equidistant time steps, simulation models developed using z-transforms can readily be used in electromagnetic transient simulations based on the same time step. First, this paper briefly introduces the basics of the z-transform, and then applications to electromagnetic transient simulations of power systems are reviewed. [ABSTRACT FROM AUTHOR]

In this article, we propose a mapping method in which the system function of filter in z-domain is founded by discrete-time domain techniques as well as by chain-scatte ring matrices of various transmission-lines is derived to fulfill a dualbandpass microwave filter based on equal-length nonuniform coupled lines. A dualband filter with the desired bandwidth and low insertion loss is recognized by cascading bandpass and bandstop filters. The five-order Butterworth bandstop filter, which uses a coupled-serial-shunted lines structure, causes the implantation and correct placement of the bandstop filter. The wide-band bandpass filter is implemented by the five-order Chebyshev Type II band-pass filter, which uses serial lines and shunted stubs lines configuration. The design process is finished by using optimization algorithms to tune the values of characteristic impedances of each transmission-line section. Experimental results significantly agree with the theoretical values. Measurement shows that the 3 dB passband widths are about 20% for the frequency of 2.45 GHz and 10% for the frequency of 5.25 GHz. The insertion loss is about 0.831 dB at the frequency of 2.38 GHz and 1.873 dB at the frequency of 5.216 GHz. © 2006 Wiley Periodicals, Inc. Microwave Opt Technol Lett 49: 210–215, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.22075 [ABSTRACT FROM AUTHOR]

The bilinear transformation is employed to represent the trapezoidal-rule integrator in the Z domain. This formulation, in conjunction with the representations of transmission-line elements in the Z domain, leads to the transmission-line configuration that is eligible for a microwave integrator. A microstrip circuit is implemented to verify the feasibility of the technique. Except for the lower-frequency band, the experimental results are in good agreement with the theoretical values of the trapezoidal-rule integrator. © 2006 Wiley Periodicals, Inc. Microwave Opt Technol Lett 48: 822–825, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.21485 [ABSTRACT FROM AUTHOR]

A model describing the time constant of a transmission-line integrator is presented. By representing the formulations of integrators in the discrete-time (or Z) domain, we implement the integrators with equal-length transmission lines. Three integrators with different time constants and frequency bands are built and tested. The experimental results are in good agreement with theoretical values. [ABSTRACT FROM AUTHOR]

Basic units for realization of all-pole and all-zero transfer functions in all-optical systems using ring resonators and electromagnetic-induced transparency (EIT) are introduced. Using the basic blocks for generation of pole and zero proposed Any type and any degree of optical filters and optical processing systems can be implemented. In this paper, z transform is used for design and synthesize of low-pass, bandpass, and high-pass Butterworth optical filters as an example. The stability of optical systems designed by the proposed structures is investigated. In addition, EIT is used for the control of pole and zero position. [ABSTRACT FROM PUBLISHER]

In this paper, an efficient absorbing boundary condition (ABC) constructed in the Z-transform domain [i.e., Z-transform-based absorbing boundary conditions (Z-ABCs)] for the three-dimensional symmetrical condensed-node transmission-line matrix method is presented. Numerical results indicate that the Z-ABCs show better performance than the conventional Higdon's ABC in suppressing instability caused by spurious modes [ABSTRACT FROM PUBLISHER]

In this paper, a new fragile watermarking method for digital image authentication is proposed based on the zero locations of the z-transform. The z-transform domain is a new transform space for fragile watermark embedding. Our watermarking method is designed by exploiting the sensitivity of the positions of the zeroes of the z-transform around the unit circle to any change made on the host image. The watermarking system can localize the portions of a watermarked image that have been tampered with with high accuracy. In addition, the newly proposed scheme is more secure than normal least-significant bits-based fragile watermarking techniques. Experimental results as well as the theoretical analysis demonstrated the fragility and accuracy of the new method. [ABSTRACT FROM PUBLISHER]

In this letter, a state-space integral-equation method in the s-domain has been employed for the accurate analysis of rectangular cavities loaded with cylindrical dielectric resonators. The dielectric obstacles have been treated in terms of their polarization equivalent charge and current densities. The dielectric resonator can be placed at any arbitrary position inside the cavity. The presented technique allows to calculate in a very efficient way a large number of solenoidal modes. The resonant frequencies of dielectric-loaded cavities are calculated and compared with data from literature and a commercial finite element method software, showing a good agreement [ABSTRACT FROM PUBLISHER]

An efficient implementation of the complex frequency-shifted perfectly matched layer (CFS-PML) based on stretched coordinate PML (SC-PML) formulations and the Z-transform method is presented for truncating the finite-difference time domain (FDTD). This method is completely independent of the material properties of the FDTD computational domain and hence can be applied to the modeling of arbitrary media without any modification. A numerical test has been carried out in three dimensions to validate these formulations. It is shown that the proposed formulations with a CFS scheme are efficient in attenuating evanescent waves and reducing late-time reflections [ABSTRACT FROM PUBLISHER]

In this letter, the first implementation of the nearly perfectly matched layer (NPML) for truncating nonlinear dispersive finite-difference time-domain (FDTD) grids is presented. In the proposed method, the Z-transform theory is employed in the FDTD implementations of the NPML formulations. The performance of the NPML was investigated through a numerical example carried out in two-dimensional Kerr-Raman nonlinear and Lorentz-dispersive domain, and it has been observed that the NPML is capable of absorbing nonlinear electromagnetic waves. [ABSTRACT FROM PUBLISHER]

The perfectly matched layer (PML) absorbing boundary condition (ABC) is extended to truncate the boundary of left-handed materials in the Finite-Difference Time-Domain (FDTD) simulation. The uniaxial material parameters are given in the frequency domain, and discretized in the FDTD update procedure by means of the Z-Transform technique. The effectiveness of the PML is demonstrated by numerical results. [ABSTRACT FROM PUBLISHER]

A simple algorithm for implementing the perfectly matched layer (PML) is presented for truncating finite difference time domain (FDTD) computational domains. The algorithm is based on incorporating the Z-transform method into the PML FDTD implementation. The main advantage of the algorithm is its simplicity as it allows direct FDTD implementation of Maxwell's equations in the PML region. In addition, the formulations are independent of the material properties of the FDTD computational domain. Numerical examples are included to demonstrate the effectiveness of these formulations. [ABSTRACT FROM PUBLISHER]

A wideband differentiator is implemented by using nonuniform transmission lines. To utilize the transfer function of a differentiator developed in a study of discrete signal processing (DSP), we formulate the scattering characteristics of equal-length electrical transmission line sections in the Z domain. A uniform line shunted with a two-section stub is obtained to emulate the transfer function of a stable second-order recursive differentiator. A microstrip circuit is implemented to verify this novel method and experimental results are in good agreement with theoretical design parameters. © 2003 Wiley Periodicals, Inc. Microwave Opt Technol Lett 37: 226–228, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.10877 [ABSTRACT FROM AUTHOR]

We develop new formulations of reflection and transmission coefficients of nonuniform transmission lines having unequal reference impedances. By using the ABCD transmission matrix of a transmission line, we express the reflection and transmission coefficients of a nonuniform line as polynominal ratios in Z transforms. These formulations, in conjunction with digital signal processing (DSP) techniques and a reconstruction method, lead to the realization of nonuniform lines which satisfy prescribed scattering characteristics in frequency domain. Some examples are presented to illustrate the validity of this technique [ABSTRACT FROM PUBLISHER]

Until recently it has been impossible to accurately determine the roots of polynomials of high degree, even for polynomials derived from the Z transform of time series where the dynamic range of the coefficients is generally less than 100 dB. In a companion paper, two new programs for solving such polynomials were discussed and applied to signature analysis of one-sided time series [1], We present here another technique, that of root projection (RP), together with a Gram-Schmidt method for implementing it on vectors of large dimension. This technique utilizes the roots of the Z transform of a one-sided time series to construct a weighted least squares modification of the time series whose Z transform has an appropriately modified root distribution. Such a modification can be employed in a manner which is very useful for filtering and deconvolution applications [2]. Examples given here include the use of boundary root projection for front end noise reduction and a generalization of Prony's method.