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The present work has been able to relate the magnetic field produced to the basic physical ionization process and derive a general expression for the same starting from the fundamental retarded scalar and vector potentials (Leinard-Weichert potentials).

The performance analysis of the improved proportionate affine projection (IPAP) algorithm is performed in this brief. Based on the energy-conservation arguments, the steady-state analysis of the IPAP algorithm is performed, which provides a general expression of steady-state excess mean-square error for the proportionate-type affine projection algorithms. The tracking behavior is also studied and the step size that optimizes the tracking performance is provided. Simulation results confirm the accuracy of the proposed expressions under different operating scenarios.

An algorithm for the detection and frequency estimation of periodic forced oscillations in power systems is proposed. The method operates by comparing the periodogram of synchrophasor measurements to a detection threshold. This threshold is established by deriving a general expression for the distribution of the periodogram and is related to the algorithm's probabilities of false alarm and detection. Unlike classic detection algorithms designed for use with white Gaussian noise, the proposed algorithm uses a detection threshold that varies with frequency to account for the colored nature of synchrophasor measurements. Further, a detection method based on multiple segments of data is also proposed to improve the algorithm's performance as a monitoring tool in the online environment. A design approach that helps to ensure that the best-available probability of detection from any one detection segment is constantly increasing with the duration of the forced oscillation is also developed. Results from application of the detection algorithm to simulated and measured power system data suggest that the algorithm provides the expected detection performance and can be used to detect forced oscillations in practical monitoring of power systems.

In order to meet the exponentially increasing demand on mobile data traffic, self-backhaul ultra-dense networks (UDNs) combined with millimeter wave (mmWave) communications are expected to provide high spatial multiplexing gain and wide bandwidths for multi-gigabit peak data rates. In self-backhaul UDNs, how to make the radio access rates of small cells match their backhaul rates by user association and how to dynamically allocate bandwidth for the access links and backhaul links to balance two-hop link resources are two key problems on improving the overall throughputs. Based on this, a joint scheme of user association and resource allocation is proposed in self-backhaul ultra-dense networks. Because of the combinatorial and nonconvex features of the original optimization problem, it has been divided into two subproblems. Firstly, to make the radio access rates of small base stations match their backhaul rates and maximize sum access rates per Hz of all small cells, a proportional constraint is introduced, and immune optimization algorithm (IOA) is adopted to optimize the association indicator variables and the boresight angles of between users and base stations. Then, the optimal backhaul and access bandwidths are calculated by differentiating the general expression of overall throughput. Simulation results indicate that the proposed scheme increases the overall throughputs significantly compared to the traditional minimum-distance based association scheme.

This paper investigates the dependence of background limited performance (BLIP) temperature of quantum well infrared photodetectors (QWIPs) on doping density. In contrast to the generally accepted optimal doping condition EF=kBTBLIP, our theoretical prediction shows that lower doping densities should slightly increase the BLIP temperature TBLIP taking into account the temperature dependence of the Fermi energy EF, a factor neglected in the previous analyses. Numerical modeling results are used to reinterpret the reported TBLIP measurements for a series of QWIPs of typical design for 9 μm peak wavelength with different doping values. In addition, based on the same general expression for the Fermi energy, the optimized sheet doping concentration to achieve maximum detectivity is given by EF=1.37 kBT, a revision to the previous EF=2 kBT condition.

One of the factors limiting the performance of continuous-time sigma-delta modulators (CTSDMs) is clock jitter. This jitter can be classified as synchronous and accumulated/long-term jitter. A clock that is derived from a phase-lock loop contains both types of jitter. In this paper, we present a framework that can be used to obtain the output spectrum in the presence of jitter, either synchronous or accumulated or a combination of both. First, a general expression for the output power spectral density (PSD) of the CTSDM in the presence of clock jitter is derived. Based on this, analytical expressions for the output PSD are obtained for particular cases of synchronous and long-term jitter. These are validated against behavioral simulations. � 2009 IEEE.

This paper presents a generalized analysis model for fringe pattern profilometry. We mathematically derived a new analysis model that gives a more general expression of the relationship between projected and deformed fringe patterns. Meanwhile, based on the proposed generalized model, a new algorithm is presented to retrieve 3-D surfaces from nonlinearly distorted fringes. Without any prior knowledge about the projection system, we still can obtain very accurate measurement results by using a generalized analysis model and a proposed algorithm. Computer simulation and experimental results show that the generalized model and the proposed algorithm can significantly improve the 3-D reconstruction precision, especially when the projected fringe pattern is nonlinearly distorted.

Delivery Networks (CDNs) appeared at late 90's as a means of reducing response time experienced by Internet users by distributedly placing multiple servers, called surrogates, in the client network neighbourhood. Many companies have deployed their own propietary CDN hiding implementational aspects, which guides to a lack of a general open model that describes CDN behaviour from an analytical perspective. This article proposes a general expression for a CDN considering certain design parameters, such as caching hit rate, delay and number of clients and surrogates.

A model for determining the cross-correlation function of partially correlated noise is presented. In this model a strong interferer is included and represented by a periodic signal common to both channels of the correlator. A general expression for the correlation function is deduced and verified. The power spectrum of a calculated correlation function is compared with a simulation. The results presented in this paper form a base for the design of modern multi-bit correlators. These are part of future generation Radio Astronomy Receivers which increasingly have to cope with man-made interfering signals.

In 1977, Rosich and Wait (see Radio Science, vol.12, no.5, p.719-29, Sept./Oct. 1977) presented a general expression for a perturbation series solution to electromagnetic (EM) reflection from an imperfectly conducting periodic rough surface. This is the first known publication of such a general result. Although this expression was shown to be consistent with earlier published results, all questions concerning the convergence of the series were deferred. This paper takes a first step in addressing this oversight.

This letter is devoted to the analysis of the nonasymptotic behavior of beamforming for the bearing estimation of a single stochastic source impinging on an uniform linear array. An analytic expression of the maximum-likelihood mean-squared error is derived. This general expression is valid at any SNR and for any number of snapshots. Simulation results verify the analytically predicted performances.

For original paper see ibid., vol. 49, no. 6, p. 1094-1100 (2001). A general expression for the gain in terms of S-parameters, based on the physical concept of the input and output impedances of the self-terminated circuit, has been provided. This expression is mathematically equivalent to the one provided in terms of T-parameters in the aforementioned paper by Randall and Hock, and in the opinion of the commenter invalidates the S-parameter formulation provided by them in the paper. In reply, the authors state that Cascio's comments and S-parameter derivation touch on an important fundamental concept underlying the derivation described in their paper. They claim that their paper did not go into depth explaining some of the subtleties related to this, but they welcome the opportunity to do so now in this reply.

A general expression for the mean-square error (MSE) of the ESPRIT direction-of-arrival (DOA) estimation of narrowband far-field sources under random sensor perturbations is derived. Explicit solutions for the case of an arbitrary ESPRIT array geometry with one and two sources are given. Solutions for the case of a uniform linear array and arbitrary number of sources are found provided that the number of sensors is large. For this case, it is found that the MSE of ESPRIT with maximum aperture (i.e., maximum-overlapping subarrays) is lower than that of ESPRIT with nonoverlapping subarrays. A comparison with MUSIC suggests that the MSE for MUSIC is lower than that for ESPRIT. Furthermore, for the cases studied, it is shown that the MSE of ESPRIT depends only on sensor phase errors while that of MUSIC is dependent on both sensor grain and phase errors. >

Coding capacity is considered for a class of additive dimension-limited channels. The channels may be with or without memory, stationary or nonstationary. The constraint is partially given in terms of an increasing family of finite-dimensional subspaces. A general expression for the capacity is obtained, which depends on the family of subspaces and the relation between the noise covariance and the covariance giving the energy-frequency constraint on the transmitted signal. This result holds for all classical discrete-time Gaussian channels and for continuous-time Gaussian channels with fixed time of transmission, so long as a peak energy constraint is used on the codewords. The expression also provides upper bounds for a class of non-Gaussian channels. Several results are obtained that aid in calculation of capacity for specific applications. For this class of channels, it is shown that coding capacity is equal to information capacity. Error bounds are given for Gaussian channels. >

PRML channels for perpendicular magnetic recording with a ring head and a single layer magnetic media are investigated. The general expression of these PRML channels with dipulse-shaped signals is defined, and one PRML channel suitable for high-speed processing with a compact circuit is found. Simulations confirm that these PRML channels have better performance than for longitudinal magnetic recording.

A graphical method for the determination of semiconductor generation parameters has been developed. This technique is based on two graphs which are plotted from a general expression of capacitance-time (C-t) behavior and a measured C-t curve of a pulsed metal-insulator-semiconductor capacitor (MIS-C). The generation lifetime and the surface generation velocity obtained by this method agree very well with those obtained by the Zerbst technique. >

An approximate analysis of anisotropic aberrations in waveguides lenses on lithium niobate is presented. The causes of anisotropic aberrations are discussed. Anisotropic aberrations of a single refracting surface are studied and a general expression for an optical system consisting of m surfaces is derived. Numerical examples provided illustrate the anisotropic aberrations in various spherical aberration-corrected waveguide lenses. >

A mathematical analysis of the transient skin effect in tubular and flat conductors has led to the development of a theory of ideal heavy-current shunts immune to the measuring error caused by this effect. A general expression was derived for calculating a profile of the measuring circuit laid inside the shunt wall that would give a step response undistorted by the skin effect. A model of the new shunt ws examined with a current step; the recorded response followed the applied pulse form.

A new algebraic expression has been established for the critical sparkover voltage (CSOV) afair insulation submitted to positive switching impulses. By using the concept of the gap factor, the expression is found to be valid for all practical gap configurations in the distance range 1 to at least 30 m. Based on these considerations, an absolute limit of 2.4 MV is foreseen for the rated voltage of AC systems. Sparkover voltages under A.C. or lightning impulses are also predictable. Complementary investigations concerning the physics of discharge are needed for further improvements.

A general expression is derived for the tap settings of a linear transversal equalizer using the minimum mean-square error (MMSE) criterion when the class-4 partial-response (PR) signal is distorted by noise as well as carrier phase and timing errors. The values of the tap settings are used to reduce the carrier and timing phase errors.

Using 112 mm diameter, Harrison profile stainless steel polsihed electrodes, uniform field dc breakdown voltages are measured for N2O mixtures with SF6, CCl2F2, and CO2 in the pressure range of 0.02 to 1 MPa and gap lengths up to 20 mm. The results show that the breakdown strength (E8/P) of SF6, CCl2F2 and their mixtures decreases with pressure while it remains practically constant for N2O and N2O-CO2 mixtures over the investigated pressure range. From the breakdown data, limiting sparkover strengths (E8/P)lim are calculated for various mixtures which are expressed by a general expression (E8/P)lim = A+B (X)C, where X is the percentage content of SF6 in SF6-N2O mixtures, CCl2F2 in CCl2F2-N2O mixtures, and N2O in N2O-CO2 mixtures. Values of constants A, B, and C are given for the investigated gas mixtures.

A general model for conduction in polysilicon is presented for arbitrary applied voltage. The model incorporates the effect of mobile carrier redistribution under bias and accounts for the high field switching in amorphous grain boundary. Microscopic mobilities used for describing the carrier transport provides a physical basis for introducing the grain voltage across the unit cell of polysilicon. The voltage, in turn, distributes itself to preserve a constant current density therein. This new criterion yields a new voltage partitioning scheme, and a general expression for the corresponding current is derived in terms of pertinent system parameters.

We derive a rigorous expression for the three-dimensional point response function associated with the combined encoding-decoding process of coded aperture imaging. From this general expression we derive the two-dimensional point response function appropriate to a coded aperture imaging system which images a two-dimensional slice through a, three-dimensional source distribution. This point response function is then calculated numerically for a number of different aperture coding functions and decoding functions. The graphed results suggest that simple modifications of the decoding function can lead to significant improvements in the depth resolving capability of a coded aperture imaging system. Suggestions for future research are given.

Ferroresonance is defined in a way corresponding to the more general expression "jump resonance." An analytical method called the incremental describing-function method is applied to the problem of ferroresonance in power systems for a certain class of problems. In general, the method is applicable when the conditions can be shown to be essentially single phase.

A general expression is derived for the probability density function of the output of a cross-correlator, the inputs of which are assumed to consist of deterministic signals with a common frequency plus correlated stationary Gaussian noises. The correlator is composed of input bandpass filters, a multiplier, and postmultiplier low-pass filter. The general expression for the density function is later reduced to some special cases for comparison with previous results. Prior treatments of the problem, however, have omitted the case of correlated noise inputs except under more restrictive conditions.

Read's theory of the negative-resistance avalanche diode has been examined in detail for the small-signal case. The space-charge wave approach has been used in the analysis leading directly to a simple equivalent circuit and a general expression for the small-signal impedance which includes the significant design and operating parameters. The theory indicates that strong tuning effects will occur through variation of the dc avalanche current. This has been verified experimentally.

A technique is presented which can be utilized to establish a standardized procedure for performing conducted susceptibility testing on signal lines at the component and/or the subsystem level. Typical military specifications require that the test function be injected to the test lines via a susceptibility transformer, a coupling capacitor, or a standardized network, such as the line stabilization network (LSN). Although these methods may be adequate for testing of power line susceptibility, they present several disadvantages when utilized in signal lines, such as impedance loading, the requirement for physical insertion, and proximity to the load. These disadvantages become more pronounced at RF where the signal developed across the input of the test specimen may be considerably lower than the signal injected at the physical insertion point. A technique that overcomes these deficiencies utilizes a coupling jig that 1) does not require a physical connection, and 2) provides a known coupling across the input impedance of the package being tested-thus simulating, in a very realistic manner, interference coupling as it may occur in a system. A general expression for coupling prediction and a computer solution for various values of load impedances are presented.

The information storage density in digital magnetic recording is dependent on both the pulse resolution and the track definition. This paper is concerned with these two factors in the design of magnetic heads for noncontact recording.1 A concept of changed pole-tip geometry which led to a significant improvement of pulse resolution is introduced. A general expression based on ``single-pulse'' superposition is derived for various bit densities2 and data codes. In addition, several recording methods are discussed for achieving near-maximum track density2 under various head-repositioning error3 conditions. As shown, high-density heads for noncontact recording have been designed successfully by applying the concept and techniques developed. Good correlation has been realized between analytical and experimental results. Performance characteristics under simulated machine conditions are presented.

This paper discusses the use of computers in calculating the unserviceable probability of a class of telecommunication networks. The unserviceable probability for a pair of terminals in the network is derived and is so complicated that it is not feasible to calculate without the use of a computer. Under the condition that every junctor in the network has a small ratio of mean service time to mean time between failures, it is shown that the computer-aided methods available for calculating network unreliability and network blocking probability are also applicable to network unserviceable probability. For the general expression of the network unserviceable probability, no simple computer-aided method is yet known. However, no urgent need for a computer-aided method for the general expression of the network unserviceable probability is envisaged since practical networks usually have small ratios of mean service time to mean time between failures for each of its junctors.

The threshold scene brightness which a picture-reproducing device can record, a measure of its "operating sensitivity," depends not only upon the lens speed and the exposure time, but also upon the amount of detail in the recorded image. A general expression for the "operating sensitivity" of a picture-reproducing device is obtained which includes these factors together with the threshold number of quanta per picture element. This parameter characterizes the "true sensitivity" of the given device. The "true" and "operating" sensitivities of four types of television pickup tubes, photographic film, the human eye, and an ideal picture-reproducing device are obtained. Eye and film have of the order of one one-hundredth the "true sensitivity" of an ideal picture-reproducing device. Some recent television pickup tubes have of the order of one one-hundred-thousandth the "true sensitivity" of an ideal device. To compare "operating sensitivities," the same exposure time and equivalent lens systems are taken for the three devices. A television pickup tube which has a photoelectric response of 10 microamperes per lumen and makes full use of the storage principle can record scenes with no more illumination than that required by some of the "faster" photographic films. The relatively low "operating sensitivity" of film results from the large amount of intrinsic picture detail (a picture element is taken to be a single grain). The human eye has a range of "operating sensitivities" extending from that of film to a value several thousand times higher.

A review of various types of fluxgate sensors is given and they are divided into two major groups, parallel-and orthogonal-gated fluxgates. A theory for parallel and for orthogonal gating is presented and the gating characteristics for the two cases are calculated from measured B-H curves. The theory is verified by a close fit to the experimentally derived curves and finally a general expression for the output voltage from the two types of fluxgates is presented.

Consider a nonlinear system, with memory, which has two input ports and one output port. It is assumed that the system can be represented by a double Volterra series. Two results for such a system are stated in Part I. The first is a general expression for the sinusoidal components of the output y (t) when the two inputs x u (t) and x v (t) are sums of sinusoidal terms. The second result is an expression for the power spectrum of y (t) when x u (t) is a stationary Gaussian process and x v (t) = P cos pt. Part II is concerned with using results from the theory of Volterra series for multi-input systems to calculate the third-order distortion in an idealized frequency converter.

There are two topics covered here. First, asymmetrical locking properties of an injection-locked oscillator (ILO) are dealt with. It is shown that these properties can be partly explained by the asymmetry in the phase response of the oscillator tuned circuit. Second, the Shaw-Stover's locking figure of merit is briefly discussed. A general expression for the said figure is given. It can be used for optimization purposes when maximum locking figure of merit is the main goal of a particular design.

Subsidiary-resonance phenomena in single-crystal Mn-ZnY have been theoretically and experimentally investigated. Using the general expression for the first-order instability, the threshold fields have been calculated for material parameters (anisotropy field, saturation magnetization) appropriate to Mn-ZnY. Good agreement is shown between experimental data and theoretical predictions.

A general expression for Mason's gain U is derived and expressed in the linear two-port h parameters of a network. In a recent paper by S. Prasad et al. (ibid., vol.35, no.12, 1988, p.2288-94) an incorrect expression for U is presented. The commenter shows that the two expressions are equal at only one frequency, f/sub max/, i.e. when U is solved for U=1. >

The degradation of radar system sensitivities due to the TR tube and the TR limiter are calculated. A general expression relating to the various parameters of the TR tube and the TR limiter and noise figure of the receiver is derived from the condition that the TR limiter will be more sensitive than the TR tube with keep-alive, KA. In particular, the TR limiter may be less sensitive than the TR tube with KA due to the higher insertion loss of the TR limiter. The much longer life of the TR limiter, however, may be the deciding factor for its use in a radar receiver.

A numerical method of analysis is developed to determine the characteristics of a homogeneous dielectric antenna of arbitrary shape based on a general expression of electromagnetic wave scattering by a homogeneous dielectric body derived by Barrar and Dolph. This method is tested on a dielectric-disk antenna.

A general expression for oo such that cal (k,θ+θ0)= sal (k,θ) is obtained and a proof is given. This new form of θ0 is more direct and thus easier to use than other existing formulas.

A mode chart and a general expression for the unloaded quality factor of an elliptic microstrip resonator operating in transverse or radial TM modes are presented.

Most present-day reliability schemes using redundancy to mask the failure of individual logic modules employ majority voting with the assumption that the replicated modules have symmetrical failure characteristics. An analysis is presented of such schemes when the modules exhibit asymmetrical failure modes; that is, the probability that a module fails with a 0 output is not equal to the probability that it fails with a 1 output. A general expression is presented which gives the reliability of a network consisting of n identical modules feeding a k-out-of-n voter. It is shown that a simple majority element does not always represent the optimal choice. Plots illustrating the results are included.

A general expression is established which relates the output roundoff noise generated by a fixed-point multiplier in a digital filter to the sensitivity of the filter attenuation with respect to the corresponding multiplier coefficient. It confirms that filters with low sensitivity of the attenuation also produce less roundoff noise.