Comparison of Computed RF Current Flow on a Power Line With Full Scale Measurements

Reradiation of an MF/AM broadcast transmitter's signal by a power transmission line can cause serious pattern distortion. A computer model of a power line, developed and tested against scale model measurements over highly conductive ground, has been used to assess the pattern distortion to be expected from a power line proposed for construction, to identify those towers on an existing power line which carry strong RF currents, and to design "detuningn devices to suppress such currents. The accuracy of the computer model's "predictions" is tested in this paper against full-scale measured RF current flow on the skywires of a real power line. A toroidal current probe is described which is suitable in the MF band for current measurement on a large steel lattice structure such as a power line tower. Instrumentation is described for the measurement of either current magnitude only, or of both magnitude and phase. Thus the current flowing on a power line tower is readily measured by this method. Measurements of skywire current are compared with computations using a highly conductive "perfect" ground model, and using the Sommerfeld-Norton ground model for "lossy" ground of conductivity 10 millisiemens/metre and relative permittivity 15. The two ground models result in similar current distributions, with the peaks and minima in the standing wave pattern at the same positions on the skywire. The lossy ground model results in somewhat less current flow due to the damping introduced into the resonant behaviour of the power line.     

A Microcomputer Program for Predicting AM Broadcast Re-Radiation from Steel Tower Power Lines

Computations of the re-radiation of AM broadcast signals by steel tower power lines are carried out using a simplified method, and compared with computations by moment method. The simplified method is based on transmission line theory and was implemented on a microcomputer in BASIC using 32K of RAM. The computer program (AMPL) includes the effect of the lossy ground. Results show that this simplified method is useful for making an approximate but rapid and inexpensive assessment of the impact of a power line on an AM broadcast antenna's performance.     

Impedance, bandwidth, and Q of antennas

To address the need for fundamental universally valid definitions of exact bandwidth and quality factor (Q) of tuned antennas, as well as the need for efficient accurate approximate formulas for computing this bandwidth and Q, exact and approximate expressions are found for the bandwidth and Q of a general single-feed (one-port) lossy or lossless linear antenna tuned to resonance or antiresonance. The approximate expression derived for the exact bandwidth of a tuned antenna differs from previous approximate expressions in that it is inversely proportional to the magnitude |Z'/sub 0/(/spl omega//sub 0/)| of the frequency derivative of the input impedance and, for not too large a bandwidth, it is nearly equal to the exact bandwidth of the tuned antenna at every frequency /spl omega//sub 0/, that is, throughout antiresonant as well as resonant frequency bands. It is also shown that an appropriately defined exact Q of a tuned lossy or lossless antenna is approximately proportional to |Z'/sub 0/(/spl omega//sub 0/)| and thus this Q is approximately inversely proportional to the bandwidth (for not too large a bandwidth) of a simply tuned antenna at all frequencies. The exact Q of a tuned antenna is defined in terms of average internal energies that emerge naturally from Maxwell's equations applied to the tuned antenna. These internal energies, which are similar but not identical to previously defined quality-factor energies, and the associated Q are proven to increase without bound as the size of an antenna is decreased. Numerical solutions to thin straight-wire and wire-loop lossy and lossless antennas, as well as to a Yagi antenna and a straight-wire antenna embedded in a lossy dispersive dielectric, confirm the accuracy of the approximate expressions and the inverse relationship between the defined bandwidth and the defined Q over frequency ranges that cover several resonant and antiresonant frequency bands.     

Wire antennas over a lossy half-space

A recently developed technique for approximate but accurate evaluation of the various vector potential components associated with a current element radiating over a lossy ground is used to study the problem of antennas radiating over a lossy ground. A general integral equation for an arbitrarily shaped thin-wire antenna over a lossy half-space is derived, and the method of moments is employed to process this equation numerically. Illustrative numerical results are presented to demonstrate the effect of the lossy half-space on a number of antenna configurations.     

Improving signal integrity in circuit boards by incorporatingembedded edge terminations

Much attention has been paid toward signal and power integrity in devices, circuit boards and entire systems. Resonances set up between the power and ground planes due to multiple reflections from the edges of the circuit board will affect signal integrity. The impedance seen by a via passing between the power and ground planes can be very high at the resonant frequencies. This gives rise to the effects of crosstalk and simultaneous switching noise (SSN) which would adversely effect the operation of the device. An attempt has been made in this paper to cover all the topics in earlier papers (Shi et al., Proc. Electron. Comp. Technol. Conf., 2001, and Adsure et al., Proc. IPAC'01 Conf., 2001), which describe a method to incorporate lossy (absorbing) material at the edges of a circuit board to reduce the wave reflections. The "lossy material" is usually a material of very high resistivity but which shows large magnetic losses at UHF and microwave frequencies. Thus this material is suitable to be placed directly between the power and ground planes without introducing any DC leakage currents. Experiments were carried out on a bare copper circuit board with FR-4 dielectric. The absorber used in the experiments is available commercially in flexible, castable and hard dense forms. It is shown that it is possible to reduce the impedances at the resonant frequencies to quite an extent over a broad frequency band by applying the lossy material at the edges of the board. Various configurations of applying the material are also described     

On the modeling of conductor and substrate losses inmulticonductor, multidielectric transmission line systems

Most models used for the analysis of lossy, multiconductor, multidielectric transmission line systems (MCMDTLSs) are noncausal and fail to accurately predict the signal distortion on practical printed circuits. The authors review the method of analysis and assumptions made in these models and present more accurate models. The authors solve for the time-domain response of a single, lossy, perfectly matched conductor above a ground plane and immersed in a perfect dielectric, assuming transverse electromagnetic (TEM) propagation. The authors also solve for the same line, except that the line is assumed to be perfect while the dielectric is lossy. The TEM mode propagates in such lines and no errors result from this assumption. A brief generalization to MCMDTLSs is described to illustrate the theory, and numerical examples are presented     

Homogeneously broadened CW lasers with uniform distributed loss

The exact equations relating the CW output power to the parameters of a homogeneously broadened laser with distributed loss and its cavity are analytically intractable. In their place, simple approximate expressions are derived which permit convenient evaluation of the laser parameters from output power measurements in cavities with variable coupling, and conversely, of the maximum available oscillator power from small-signal gain and absorption-loss measurements. The approximate solutions have negligible error for lossy standing-wave lasers and are but slightly less accurate for lossy traveling-wave ring lasers.     

Influence of a lossy ground on lightning-induced voltages onoverhead lines

A comprehensive study on the effect of a lossy ground on the induced voltages on overhead power lines by a nearby lightning strike is presented. The ground conductivity plays a role in both the evaluation of the lightning radiated fields and of the line parameters. To be calculated by means of a rigorous theory, both fields and line constants need important computation time, which, for the problem of interest, is still prohibitive. The aim of this paper is to discuss and analyze the various simplified approaches and techniques that have been proposed for the calculation of the fields and the line constants when the ground cannot be assumed as a perfectly conducting plane. Regarding the radiated electromagnetic field, it is shown that the horizontal electric field, the component which is most affected by the ground finite conductivity, can be calculated in an accurate way using the Cooray-Rubinstein simplified formula. The presence of an imperfectly conducting ground is included in the coupling equations by means of two additional terms: the longitudinal ground impedance and the transverse ground admittance, which are both frequency-dependent. The latter can generally be neglected for typical overhead lines, due to its small contribution to the overall transverse admittance of the line. Regarding the ground impedance, a comparison between several simplified expressions used in the literature is presented and the validity limits of these expressions are established. It is also shown that for typical overhead lines the wire impedance can be neglected as regard to the ground impedance     

A Simple Model for the Line Parameters of a Lossy Coaxial Cable Filled With a Nondispersive Dielectric

This paper discusses a simple model for approximating the per-unit-length parameters of a lossy cable providing a smooth transition from low to high frequencies. Using Schelkunoff's classical expressions for the transmission-line parameters of a coaxial line, the simple model is postulated and used to provide approximate responses that can be compared with the rigorous solutions. This approximate model is shown to be accurate and offers an alternative to evaluating the Bessel function expressions for the line parameters     

Cooray–Rubinstein Formula for the Evaluation of Lightning Radial Electric Fields: Derivation and Implementation in the Time Domain

Ground conductivity plays an important role both in the evaluation of the electromagnetic (EM) fields due to a lightning event and in the calculation of the line parameters, which are, in turn, fundamental in the analysis of the lightning-induced voltages on overhead lines. The exact formulation of the EM fields over a lossy ground involves the numerical evaluation of the Sommerfeld integrals, which are slowly converging and can only be computed in the frequency domain. For this reason, a great effort has been devoted in the derivation of approximate formulas that can provide accurate results with low computational costs. The most popular one is the Cooray-Rubinstein formula, which has been proposed in the frequency domain. Here, its time-domain counterpart is mathematically derived, and an efficient algorithm for its implementation is presented together with some comparisons with the exact approach.     

Coupling coefficients of coupled laser cavities

We discuss certain properties of the coupling coefficients for a specific model consisting of two coupled resonant cavities separated by a lossy coupling gap. The coupling coefficients are here defined in the framework of time-dependent coupled-cavity theory-not as end-fire power coupling between traveling waves of two adjacent waveguides. In particular, we explore the validity of a heuristic formula for the coupling coefficients proposed in an earlier publication. It turns out that, in this example, the heuristic formula is directly applicable only if the coupling gap is lossless and off-resonance, but it becomes inapplicable if the lossless gap approaches resonance. The heuristic formula remains useful, but requires a correction if the coupling gap is lossy. The phase angle of the complex coupling coefficient is found to be linearly dependent on the width of the coupling gap, assuming the value 0 (to within multiples of 2π) for an off-resonant gap and the value ofpi/2for a resonant gap. It is not the purpose of this letter to explore properties of c³lasers or to specify their optimum operating conditions. Only the validity of the approximate coupling function is to be investigated.     

Application of the cavity model to lossy power-return plane structures in printed circuit boards

Power-return plane pairs in printed circuit boards are often modeled as resonant cavities. Cavity models can be used to calculate transfer impedance parameters used to predict levels of power bus noise. Techniques for applying the cavity model to lossy printed circuit board geometries rely on a low-loss assumption in their derivations. Boards that have been designed to damp power bus resonances (e.g., boards with embedded capacitance) generally violate this low-loss assumption. This paper investigates the validity of the cavity model when applied to printed circuit board structures where the board resonances are significantly damped. Cavity modeling results for sample lossy power-return plane structures are validated using a three-dimensional full wave numerical code. A simple method is also established to check the validity of the cavity model for a power-return plane structure with imperfect conductors and lossy dielectric substrates.     

有损土壤上的多导体传输线的时域分析

将多导体传输线（ＭＴＬ）的土壤复数阻抗拓展为土壤运算阻抗,采用Ｐａｄｅ展开法,提出了计及土壤影响的多导体传输线的时域模型,建立了该模型的时域有限差分（ＦＤＴＤ）算法。通过对计及土壤影响的架空单导体和双导体传输线的波过程计算,表明本文方法的正确性,并可以应用于超高压变电站高压母线和超高压输电线路的瞬态电磁干扰计算。     

Rigorous and approximate solutions for the three-conductor lossy transmission lines problem

The coupled first-order linear differential equations governing the voltage and the current on three-conductor lossy (identical) transmission lines are solved by two methods. One method is rigorous, and the other one is approximate and applies in the low- and high-frequency ranges. Although the rigorous solution is a numerical one, the approximate solution consists of explicit expressions that are easy to calculate and give physical insight into the coupling process. Experimental results that are available for two parallel identical lossy wires of finite length situated above a perfectly conducting ground (when only one of the wires is driven by a source) and previously published theoretical results compare satisfactorily with the results obtained by the two methods.<>     

The development of a closed-form expression for the input impedance of power-return plane structures

In multilayer printed circuit boards, the noise on the power bus is influenced by the impedance between the power and ground planes. Power-bus noise estimates require an accurate estimate of the power-bus input impedance. This paper develops a closed-form estimate of the input impedance for circular power-return plane structures. When the structure is lossy (e.g., boards employing embedded capacitance or densely populated boards), the energy reflected from the board edge does not significantly affect the input impedance. In general, the expressions developed here for circular structures can be used to estimate the impedance of lossy power-return plane structures of any shape.     

Some measurement results for frequency-dependent inductance of ICinterconnects on a lossy silicon substrate

Frequency dependent measurements of scattering (S) parameters using a vector network analyzer (VNA) have been performed on IC interconnects on a lossy silicon substrate. The multiline calibration method has been used to perform the de-embedding of the line parameters, from which the line inductance is extracted. A highly accurate closed-form approximation for frequency-dependent impedance per unit length of a lossy silicon substrate for IC interconnects has been used to compare with the measurements performed     

New high-frequency circuit model for coupled lossless and lossywaveguide structures

A coupled transmission line model describing the two fundamental modes of any two-conductor (above a ground plane or shielded) dispersive or nondispersive lossless waveguide system is given. The model is based on a power-current formulation of the impedances but does not need an a priori supposition about the power distribution over each transmission line. The analysis is extended to lossy structures and to the multiconductor situation. Impedance calculations for a typical coupled microstrip configuration are used to illustrate the approach     

Resonances of perfectly conducting wires and bodies of revolutionburied in a lossy dispersive half-space

The method of moments (MoM) is utilized to compute the complex resonant frequencies and modal currents of perfectly conducting wires and bodies of revolution buried in a lossy dispersive half space. To make such an analysis tractable computationally, the half-space Green's function is computed via the method of complex images, with appropriate modifications made to account for the complex frequencies characteristic of resonant modes. Results are presented for wires and bodies of revolution buried in lossy soil using frequency-dependent measured parameters for the complex permittivity, and we demonstrate that the resonant frequencies generally vary with target depth. In addition to presenting results, relevant issues are addressed concerning the numerical computation of buried-target resonant frequencies     

Ground effects on induced voltages from nearby lightning

The lightning induced voltage on overhead lines from return strokes and it's dependency of a lossy ground is analyzed using a new, analytical vector potential formulation. Norton's (1937) approximation and the surface impedance approach are used to take loss effects into account. The surface impedance method predicts in general induced voltages in good agreement with Norton's approximation, but the accuracy of the method is dependent on the variation of the current along the lightning channel. Norton's method is compared with the exact Sommerfeld solution, showing a deviation <10% even for low conducting grounds and distances from 100-1000 m. The effect of stroke location and line termination is also analyzed, showing that a line terminated by it's characteristic impedance and excited by a return stroke at the prolongation of the line is especially sensitive to lossy ground effects. Strokes near the mid-point of an overhead line gives less loss effect than strokes at the end of the line. The surface impedance approximation is derived from Norton's method and the necessary assumptions are outlined     

A Family of Single-Stage Resonant AC/DC Converters With PFC

A family of novel, single-stage, isolated, resonant-based ac/dc power supply circuits with inherently high power factor is presented in this paper. The three topologies in the family are transformer isolated; they contain a bulk energy storage capacitor to enable output voltage holdup, and they also contain a resonant circuit in which a resonant capacitor is connected directly across the mains input rectifier. The presence of this resonant circuit results in ac line current being drawn over much of the line cycle, as well as in soft switching of the power devices. The rectifier-compensated fundamental-mode approximation (RCFMA) method is used to provide an accurate yet simple analysis of the circuit. Experimental results for closed-loop operation of two of the topologies are also presented. This family of single-stage, high–power-factor converters provides for simple control and high-frequency operation, due to the resonant configuration of the power circuit, without the excessive conduction loss of fully resonant techniques.