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The necessary and sufficient conditions for applicability of spatial harmonic expansions (the Rayleigh hypothesis) for plasma wave branches in periodic plasma-loaded waveguides have been obtained for the first time, based on the exact solution for the relevant boundary-value problem. Conditions of oscillation appearance beyond the scope of such expansions and their expected effect on the operation of plasma-filled backward-wave oscillators are discussed. Index Terms - High power backward wave oscillator, microwave tube, periodic structure, plasma-filled waveguide.

Research was conducted to examine the analytical dependence of the free-electron laser saturated power on the cavity detuning as well as the dependence of the higher harmonics generated power on the quantity. It was observed that a suitable modulation of the cavity detuning may provide a pulsed behavior of the laser, superimposed to the natural mode locking. The impact of the modulation on the harmonic generation was also investigated.

A theoretical investigation of the backward second-harmonic generation (SHG) process using subpicosecond and nanosecond laser pulses in periodically poled lithium niobate crystals was conducted. The amounts of pulse broadening and conversion efficiencies were different for the two configurations despite the fact that the temporal behaviors of the second-harmonic radiation were determined by the same functions as those for the forward SHG. The saturation of the conversion efficiencies and the effective third-harmonic generation were also investigated.

In this paper, analytical expressions for calculating the capacitance of an isolated pixel diode as well as a pixel diode in an array are presented. These expressions fit the three-dimensional numerical solution of the Laplace equation better than 10% as previously calculated for these diodes, covering most practical cases. The total pixel capacitance [C.sub.P] is obtained by a simple substitution of parameters in the analytical expressions. In addition, a simple method to obtain the real diode capacitance, the parasitic capacitance, and the substrate concentration is proposed on the basis of the analytical equation for the capacitance for an isolated diode. The coincidence of measured and calculated data for the capacitance is shown. The procedures presented permit a very precise description of the real C-V curve for an isolated diode as well as for diodes in a pixel array, allowing the design of the best coupling between each pixel and its corresponding readout preamplifier with a minimum calculation effort. Index Terms - Detectors, diode capacitance, p-i-n diodes.

A modified form of Laplace's equation, based on coordinate stretching, is proposed, that lends itself to a new convenient numerical grid truncation methodology for the solution of Laplace's equation in open regions. The proposed method eliminates the need for approximate local boundary conditions on the truncation boundary of the numerical grid. Thus, it provides for a simple, robust, computationally efficient and very accurate grid truncation scheme. First, an analytic justification of the proposed grid truncation methodology is presented. Next, its numerical implementation is discussed in conjunction with the numerical solution of Laplace's equation in unbounded two-dimensional regions. Numerical studies are used to illustrate the choice of the parameters used in the numerical implementation of this new truncation scheme, and quantify their impact on solution accuracy.

A novel technique for obtaining superconvergent derivatives of finite element solutions for Laplace and Poisson type equations is presented. This is achieved by analytical integration of Green's function over single triangles. Superconvergent derivatives of FEM potential solutions have an accuracy of higher order than predicted by the finite element theory. Compared to direct evaluation the number of significant digits doubles. The procedure is illustrated by application to several test examples. It is notable that no restrictive regularity assumptions on the mesh topology are made.

Kautz functions constitute a complete orthonormal basis for square-summable functions both on a continuous as well as a discrete semi-infinite axis. A special case of the Kautz functions are the well-known Laguerre functions. The Kautz functions can be used as series expansions for causal impulse responses. Convergence of such series depends on the parameters in the Kautz functions. The conditions for the optimal parameters in a truncated Kautz series are derived.

Recent surveys of 208/120 V three-phase four-wire electric systems, buildings, and industrial plants with computers and nonlinear loads show excessive currents in the neutral. These neutral currents are fundamentally third harmonic, and their presence is tied to wiring failures, elevating of neutral potentials, transformer overheating, etc. In response to these concerns, this paper proposes a new active power filter scheme to cancel neutral current harmonics. The proposed approach employs a star/delta transformer along with a two-switch PWM-controlled active filter. The closed loop control of the active power filter guarantees cancellation of neutral current harmonics under varying load conditions. The proposed system drastically improves the overall system performance and virtually eliminates transformer overheating due to harmonics. Experimental results from a prototype active power filter confirm the suitability of the proposed approach.

A method for the solution of the three dimensional Laplace equation is presented. The method applies to planar geometry cases, such as pixel detector devices, characterized by mixed boundary conditions. Through this algorithm the capacitances associated with pixel detectors are calculated. These capacitances, which are the pixel to substrate and the interpixel capacitances, are of great importance in the design of a pixel detector since they influence the noise and the cross talk effects between pixels. Capacitances for various pixel and interpixel dimensions are presented along with an analytical approximation for the calculation of the total pixel capacitance.

An improved version of a Newton-type algorithm is used for adaptively searching for the minimum eigenvector of the asymptotic matrix of data that includes sinusoids of white noise. The proof of convergence is developed by the assumption of a suitable initialization. The new algorithm exhibits faster convergence properties than the earlier version, especially in low SNR cases.

The paper proposes an extension of the Monte Carlo procedures to the solution of axisymmetric problems. The stochastic techniques are illustrated with specific practical applications to the solution of Laplace's and Poisson's equations. The method requires no input data and provides results as accurate as those obtained using the finite element method.

A method that determines exactly the two-dimensional capacitance per unit length of a single dielectrically-insulated interconnection line above a conducting plane is introduced. The technique, which is analogous to a Fourier series, is based on a solution of Laplace's equation using Bernoulli's approach and may be applied to more complex configurations. A comparison with its counterparts in the literature is also provided.

An improved floating-random-walk algorithm for solving the multi-dielectric Dirichlet problem is outlined. The improvement is achieved by using statistically generated Green's functions that are calculated before hand and stored as look-up tables. These tables have been used to solve the multi-dielectric Dirichlet problem for an arbitrary two dimensional geometry. The improved algorithm is also compared with the conventional floating-random-walk algorithm and is found to be at least two times more efficient. Results are presented for two types of parallel plate geometries.

Numerical solution methods of Laplace's equation Delta-V = 0 when boundary values of potential V are specified abound, and many computer programs employing relaxation techniques, finite-element techniques, etc. have been discussed in the literature. The finite-mesh relaxation method of numerical iteration is discussed in many physics and electrical engineering texts, but little attention is given to the error analysis, which, moreover, is incorrect more often than not in these texts. We show that the error in the iterated solution can be found by a relatively simple analysis, and discuss its implications.

In this paper, the Floquet theory is combined with harmonic balance for the in-depth analysis of a Chua's family circuit, exhibiting intermittence. Floquet multipliers are calculated along the periodic solution paths obtained through harmonic balance by means of a continuation algorithm. The analysis of both the stable and unstable solution sections enhances the information about the system and permits a better understanding of the different phenomena that take place. Index Terms--Continuation algorithm, Floquet multipliers, harmonic balance, intermittency, route to chaos.

The Variable Speed Air Conditioner (VSAC) is a large domestic distorting load. We investigate the impact of a large number of VSAC's on domestic harmonic levels. We present * a general method to build a harmonic numerical model of a passive filtered rectifier supplied by a distorted voltage, * a statistical method to assess the total harmonic currents produced by a large number of units running at various power levels and supplied by various distorted voltages. These two methods are applied to a rectifier used by many VSACS. We also present results for two other rectifiers. Index Terms--Analytical model, diversity, harmonic cancellation, single phase air conditioner, VSAC.

A synchronous-reference-frame (SRF)-based controller for the dominant harmonic active filter (DHAF) system has already been proposed by the authors. The SRF controller is designed to achieve harmonic isolation at the dominant harmonic frequencies (such as at the 5th and/or 7th) between the supply and load. This allows implementation of the DHAF system by square-wave inverters switching at the 5th or 7th harmonic frequency. Compared to conventional active filter systems which require high-switching-frequency pulsewidth modulation inverters, the square-wave-inverter-based DHAF system provides a viable and cost-effective solution to achieve harmonic isolation for high-power nonlinear loads (10 MW and above) or cluster of nonlinear loads, to meet the IEEE 519 recommended harmonic standard. In this paper, a new feedforward command of the SRF controller is proposed which provides better dynamic performance. The improved feedforward command of the SRF controller can suppress any system resonances at the dominant harmonic frequencies and meet IEEE 519 harmonic current limits. Experimental results are presented to validate the effectiveness of the SRF controller and the DHAF system. Index Terms--Active filter, dominant harmonic active filter, harmonic filtering, harmonic isolation, square-wave inverter, synchronous reference frame.

A new battery configuration technique and accompanying control circuitry, termed a Synergetic Battery Pack (SBP), is design to work with Lithium batteries, and can be used as both an inverter for an electric vehicle AC induction motor drive and a battery charger. In this paper, we compare the performance of the Synergetic Battery Pack as a battery charger with several simple conventional battery charging circuits via computer simulation. The factors of comparison were power factor, harmonic distortion, and circuit efficiency. The simulations showed that the SBP is superior to the conventional charging circuits since the power factor is unity and harmonic distortion is negligible.