Class-F power amplifiers with maximally flat waveforms

Class-F power amplifiers (PA's) employ harmonic-frequency resonators to shape their drain or collector waveforms to improve efficiency. Generally, the output network must present the drain with either an open or short circuit at the harmonic frequencies. At VHF and higher frequencies, the drain capacitance, lead inductance, lead length, and dispersion make implementation of reasonably ideal tuned circuits difficult. However it is possible to control the impedances at a finite number of harmonics. This note first derives the basic relationships among the Fourier coefficients of the waveforms and the performance of the amplifier. Fourier coefficients for maximally flat waveforms are then derived for inclusion of up to the fifth harmonic. Amplifier performance is then tabulated as a function of which harmonics are included in the voltage and current waveforms. Efficiency increases from 50% of class A toward 100% as harmonics are added. Power-output capability increases by up to 27%     

Mathematical models for the reflection coefficients of lossy dielectric half-spaces with application to transient responses of chirped pulses

Reflection coefficients are found at normal incidence for a large class of homogeneous lossy half-spaces with a one-dimensionally inhomogeneous or stratified lossy layer on top. Solutions are in terms of Hankel functions of complex argument to decrease cancellation error at high frequencies. One special case is that of layers on a homogeneous half-space where the dielectric constant in each layer may vary in a quite general manner. A Wronskian is used to insure the critical computations are correct. The reflection of chirped pulses is considered. Solutions are obtained by applying the fast Fourier transform. It is found that for a typical relatively long normalized "long" pulse the power reflected as a function of time is essentially the power reflection coefficient for the frequencies swept out, whereas for a relatively short "long" pulse, with the same relative change in frequency and the same number of oscillations there is only the uniform attenuation by the power reflection coefficient of the center frequency. By a "long" pulse we mean a pulse whose spatial length is long compared to the thickness of the reflecting layer.     

A closed-form formula for 2-D ohmic losses calculation in SMPStransformer foils

A new formula aimed at calculating ohmic losses in switch-mode power supply (SMPS) transformers is presented. It is based on intensive two-dimensional (2-D) finite element method (FEM) simulations, the results of which have been summarized in a closed-form formula following a “semi-empirical” approach. The main benefit of this new formula, specifically intended for industrial designers, is to combine the precision of 2-D models with the ease-of-use and speed of calculation of one-dimensional (1-D) models, on the whole frequency range. It accurately covers cases where the classical Dowell's formula significantly underestimated the losses, specifically those with significant edge effect in foil windings. Experimental validation and discussion of accuracy is provided. At the moment, the formula is only valid for one layer of foil located between a zero and a maximum of the magnetomotive force but a similar approach could be applied with success to other types of windings. Furthermore, the analytical expression proposed in the article, based on Maxwell equations, can be used as a stand-alone tool to model the real behavior of any type of winding. More accurate understanding of the 2-D field is also possible thanks to the direct link established between the losses and the geometrical data of the winding     

Analytical evaluation of harmonic distortion in PWM AC drives using the notion of stator flux ripple

This paper presents a method to evaluate harmonic distortion due to space vector-based pulse-width modulation (PWM) strategies for ac drives. The proposed method is general enough to deal with division of zero vector time as well as division of active vector time within a subcycle. The method is based on the notion of stator flux ripple, which is a measure of line current ripple. Expressions for RMS ripple over a subcycle are derived for six switching sequences in terms of magnitude and angle of the reference vector, and subcycle duration. The sequences considered include those involving division of active vector time within a subcycle. Further, analytical closed form expressions are derived for the total RMS harmonic distortion factor corresponding to six space vector-based synchronized PWM strategies, proposed recently, for high power drives. The square of the distortion factor turns out to be a quadratic polynomial in modulation index (M), and the coefficients differ with PWM strategies and pulse numbers. These expressions are validated through Fourier analysis as well as experimental measurements. The concept of stator flux ripple provides insight into current ripple as well as torque ripple corresponding to different sequences and strategies.     

A constrained notch Fourier transform

The paper presents a new sliding algorithm for estimating the amplitude and phase of the Fourier coefficients of noise corrupted harmonic signals given a priori knowledge of the signal frequencies. The proposed method is similar in principle to the notch Fourier transform (NFT) technique suggested by Tadokoro et al. [1987] except that it employs an infinite impulse response (IIR) rather than a finite impulse response (FIR) notch filter parameterization. This modification provides bandwidth controlled bandpass (BP) filters whose center frequencies are equally spaced in the frequency spectrum. In this sense, the proposed technique can be regarded as a constrained notch Fourier transform (CNFT). Sliding algorithms have been derived for both the NFT and CNFT for the purpose of estimating the Fourier coefficients of the sinusoidal components. The paper also proposes a similar algorithm to the CNFT for the signals containing sinusoids at arbitrary known frequencies. The main feature of the modified CNFT is that it uses second-order IIR BP filters whose bandwidth and center frequency can be adjusted independently. The bandwidth control aspect provides the user with an efficient means of achieving the required resolution as well as reducing spectral leakage. In general, the proposed approach leads to considerable reduction in terms of computational burden and memory storage     

Transmission theory of a parallel-two-wire-transmission-linecovered with three layer media

A parallel-two-wire-transmission-line covered by a three layer media has particular transmission characteristics. It is expected that this type of line might therefore be applied to new microwave circuits and antennas. Such lines have been analyzed by solving Laplace equations as a two dimensional boundary value problem. However, at higher frequencies, it is not appropriate to explain these particular properties using the quasi-TEM mode analysis. Transmission theory for these lines has to be solved using a rigorous three dimensional analysis. in this paper, we describe a new three dimensional analysis technique that is used to obtain more accurate propagation constants by considering the E_Z, H_Z components of the field. The assumed current distribution of the parallel-two-wire-line system is Fourier expanded over the angular coordinate &thetas;, and the boundary value problem is solved by the mode matching technique. It is found that mainly hybrid modes are transmitted via this type of transmission system and that the propagation constant varies discontinuously at frequencies where the dipole mode can exist on the three layer dielectric media itself. Numerical results are presented and compared with experimental data     

Design and precise realization of optimized current waveforms foran 8/6 switched reluctance drive

Optimized shaping of the stator current in the switched reluctance motor drive can be used to mitigate electromagnetic torque ripple and decrease the RMS current. Previously, optimal current waveshaping has been based upon defining the optimal current waveform as a set of discrete points and interpolating intermediate points. In this work, an alternate approach is employed in which the current waveform is treated as a set of harmonic coefficients, rather than as an array of discrete values. This has advantages in terms of computation speed and in programming of the microcontroller. A second feature of this new method is that it incorporates a multiple reference frame estimator/regulator that ensures each harmonic of the current converges to its commanded value thereby avoiding the degradation in performance associated with imperfect tracking that other methods are susceptible to. The experimental and simulated results demonstrate the optimality of the waveforms and the importance of the multiple reference frame estimator/regulator, particularly in mitigating torque ripple     

Current on an infinitely-long carbon nanotube antenna excited by a gap generator

The current on an infinitely-long carbon nanotube (CN) antenna fed by a delta-gap source is studied using a Fourier transform technique. The CN is modeled as an infinitely-thin tube characterized by a semi-classical conductance, appropriate for the frequencies of interest considered in this work. The CN's current is compared with the current on solid and tubular copper antennas having similar or somewhat larger radius values. It is found that for radius values on the scale of nanometers, CNs exhibit smaller losses than cylindrical copper antennas having the same dimensions, assuming the bulk value of copper conductivity. When one assumes a more realistic, reduced copper conductivity that accounts for the nanoscopic radius of the wire, the advantage of the CN over a metallic wire is increased.     

影响高压阳极铝箔隧道孔极限长度的因素

研究了高压阳极铝箔在HCl-H2SO4腐蚀体系中,H2SO4/HCl浓度比、Al3+浓度、温度和电流密度对隧道孔长度和铝箔芯层厚度的影响规律。结果表明:提高H2SO4/HCl浓度比、Al3+浓度温度和电流密度,均可缩短隧道孔长度和增加芯层厚度。提出隧道孔的生长受Al3+在隧道孔中的扩散和铝箔表面扩散层中的扩散共同控制,可以对上述因素的影响规律做出更合理的解释。     

Advanced spectrum estimation methods for signal analysis in power electronics

Modern frequency power converters generate a wide spectrum of harmonic components. Large converters systems can also generate noncharacteristic harmonics and interharmonics. Standard tools of harmonic analysis based on the Fourier transform assume that only harmonics are present and the periodicity intervals are fixed, while periodicity intervals in the presence of interharmonics are variable and very long. A novel approach to harmonic and interharmonic analysis, based on the "subspace" methods, is proposed. Min-norm harmonic retrieval method is an example of high-resolution eigenstructure-based methods. The Prony method as applied for signal analysis was also tested for this purpose. Both high-resolution methods do not show the disadvantages of the traditional tools and allow exact estimation of the interharmonics frequencies. To investigate the methods several experiments were performed using simulated signals, current waveforms at the output of a simulated frequency converter, and current waveforms at the output of an industrial frequency converter. For comparison, similar experiments were repeated using the fast Fourier transform (FFT). The comparison proved the superiority of the new methods. However, their computation is much more complex than FFT.     

铝衰减膜表面氧化对软X光透过率的影响与修正

对用不同方法制备的软Ｘ光激光实验用的Ａｌ衰减膜样品,用Ａｕｇｅｒ电子能谱（ＡＥＳ）结合氩离子束刻蚀进行了组分的表面和深度分布分析,结果表明表面氧化层主要由Ａｌ２Ｏ３组成,氧化达到饱和时的氧化层厚度≈７．５ｎｍ。由于在软Ｘ光波段内,氧的吸收系数比铝大一个多数量级,这一氧化层对软Ｘ光透过率的影响甚大。将ＡＥＳ测试结果作为参数,使用公式Ｉ＝Ｉ０·ｅｘｐ［－μ（Ｅ）·（ρｄ）］对Ｘ光透过强度进行修正。同步辐射软Ｘ光对样品透过率的直接测量表明,对于透过率大于２０％的Ａｌ膜,直接测量结果与按修正公式计算的结果在最大偏差１１％范围内符合。     

Millimeter wave semiconductor diode detectors, mixers, and frequency multipliers

The devices described include video detectors, mixers, harmonic mixers, and harmonic generators. A general discussion of the theoretical potential and limitations of these diodes is given, based on the equivalent circuit representation. This model is shown by experimental results to be valid up through 600 GHz. Diode materials, structures and forming techniques are described which have resulted in significantly improved electrical performance, as well as improved reliability and repeatability. Experimental results are quoted for detector sensitivities from 70 through 420 GHz, fundamental mixer conversion losses from 35 through 300 GHz, harmonic mixer conversion losses from 93 through 600 GHz, and harmonic generation efficiencies from fundamental frequencies of 60 through 140 GHz. The repeatability of mixer performance indicates that construction of balanced mixers is now feasible throughout the millimeter wavelength region. The improved harmonic mixer conversion losses permit construction of practical superheterodyne receivers at frequencies where local oscillator sources are impractical or unavailable. The harmonic generation capability at high frequencies (for example, at 140 GHz, one mW with diodes in the variable resistance mode and 15 mW with diodes in the varactor mode) is seen to permit the extension of frequencies for solid-state oscillators. If full advantage is taken of the capabilities of these devices, a large variety of millimeter wave systems can be assembled, including high resolution raders, high thermal sensitivity radiometers, broad bandwidth communication systems, as well as laboratory systems for mearsurement use or spectroscopic studies.     

Reducing IGBT losses in ZCS series resonant converters

The fundamental operational parameter that controls the losses in series resonant power converters was found to be the reflected DC voltage transfer ratio. Losses which are a function of the average current (such as conduction losses of insulated gate bipolar transistors and diodes) are independent of the switching frequency. Losses which are associated with the RMS current are a function of both the reflected DC voltage ratio and the switching frequency ratio. Universal and normalized graphs, derived in this paper, can be conveniently used to assess the expected RMS and average current conduction losses under any given operational conditions. The residual switching losses in zero-current-switching series resonant power converters operating in continuous current mode can be reduced by simple current snubbers placed in the commutation circuits. The experimental results of this paper confirm the theoretical predictions and demonstrate that the turn-on snubbers can reduce switching losses by about 1.5% at a switching frequency of 65 kHz     

Size effect in AC losses of superconducting cables

We calculate the dependence of the transverse coupling losses in cables, the most important contribution to AC losses in cables without central insulating layer. Two effects cause differences with respect to the infinite samples: (1) changed area of the loops between the strands, and (2) increased resistivity between them. At low frequencies, the transverse losses P for finite samples of length l are well-described by the formula P/P_∞=1-C₀l₀/l, where C₀ depends on the ratio b/c (b-cable width, c-thickness of normal layer between strands), l₀ is the cabling length and P _∞ the losses for corresponding infinite sample. We obtain α=1/C₀≈3 for b/c≈10 and α≈2 for b/c>50. The same formula applies for higher frequencies, with frequency dependent correction factor C(ω). This correction factor decreases and becomes even negative at higher frequencies. Thus, the losses in finite samples are higher than in the corresponding infinite cables. This effect could be therefore called the inverse size effect, appearing above ωτ>0.9 for b/c=10 and ωτ>1.53 for b/c=50. It may explain some experimental results where size effect was expected but not found in the loss measurements     

Modeling Active Microwave Remote Sensing of Snow Using Dense Media Radiative Transfer (DMRT) Theory With Multiple-Scattering Effects

Dense media radiative transfer (DMRT) theory is used to study the multiple-scattering effects in active microwave remote sensing. Simplified DMRT phase matrices are obtained in the 1-2 frame. The simplified expressions facilitate solutions of the DMRT equations and comparisons with other phase matrices. First-order, second-order, and full multiple-scattering solutions of the DMRT equations are obtained. To solve the DMRT equation, we decompose the diffuse intensities into Fourier series in the azimuthal direction. Each harmonic is solved by the eigen-quadrature approach. The model is applied to the active microwave remote sensing of terrestrial snow. Full multiple-scattering effects are important as the optical thickness for snow at frequencies above 10 GHz often exceed unity. The results are illustrated as a function of frequency, incidence angle, and snow depth. The results show that cross polarization for the case of densely packed spheres can be significant and can be merely 6 to 8 dB below copolarization. The magnitudes of the cross polarization are consistent with the experimental observations. The results show that the active 13.5-GHz backscattering coefficients still have significant sensitivity to snow thickness even for snow thickness exceeding 1 m     

Recent Developments in Fault Detection and Power Loss Estimation of Electrolytic Capacitors

This paper proposes a comparative study of current-controlled hysteresis and pulsewidth modulation (PWM) techniques, and their influence upon power loss dissipation in a power-factor controller (PFC) output filtering capacitors. First, theoretical calculation of low-frequency and high-frequency components of the capacitor current is presented in the two cases, as well as the total harmonic distortion of the source current. Second, we prove that the methods already used to determine the capacitor power losses are not accurate because of the capacitor model chosen. In fact, a new electric equivalent scheme of electrolytic capacitors is determined using genetic algorithms. This model, characterized by frequency-independent parameters, redraws with accuracy the capacitor behavior for large frequency and temperature ranges. Thereby, the new capacitor model is integrated into the converter, and then, software simulation is carried out to determine the power losses for both control techniques. Due to this model, the equivalent series resistance (ESR) increase at high frequencies due to the skin effect is taken into account. Finally, for hysteresis and PWM controls, we suggest a method to determine the value of the series resistance and the remaining time to failure, based on the measurement of the output ripple voltage at steady-state and transient-state converter working.      

Temperature rise measurement for power-loss comparison of an aluminum electrolytic capacitor between sinusoidal and square-wave current injections

DC-link capacitors are a major factor of degrading reliability of power electric converters because they usually have a shorter lifetime and higher failure rate than those of semiconductor devices or magnetic devices. Characteristics of the capacitors are usually evaluated by a single sinusoidal current waveform. However, actual current flowing out of the converter into the capacitor is a modulated square current waveform. This paper provides experimental comparison of the power loss dissipated in an aluminum electrolytic capacitor between sinusoidal and square-wave current injections. Power loss is estimated by temperature rise of the capacitor. Experimental results confirm that power losses of the square-wave current injection were always lower than those of the sinusoidal current injection by 10–20%. Moreover, the power losses of the square-wave current injection can be estimated by a synthesis of fundamental and harmonic currents based on the Fourier series expansion, which brings a high accuracy less than 1% when more than fifth harmonic current is introduced. This comparison will be useful for estimating power loss and life time of electrolytic capacitors.     

RMS Detector of Multiharmonic Signals

This paper presents a new realization of the implicit root‐mean‐square (RMS) detector, employing three second‐generation current conveyors and MOS transistors. The proposed circuit can be applied in measuring the RMS value of complex, periodic signals, represented in the form of the Fourier series. To verify the theoretical analysis, circuit Simulation Program with Integrated Circuit Emphasis simulations and experiment results are included, showing agreement with the theory.     

Azimuthal harmonic coefficients of the microwave backscattering from a non-Gaussian ocean surface with the first-order SSA model

In this paper, the first-order small slope approximation is applied to a rough sea surface with non-Gaussian statistics, for which the third- and the fourth-order statistics are taken into account in the calculation of the radar cross section. From the Cox and Munk slope distribution, the higher order statistic moments are derived, and behaviors of the corresponding correlation functions are assumed. We show that the fourth order (related to the peakedness or kurtosis) is isotropic, whereas the third order (related to the skewness) has a behavior as cos(/spl psi/), where /spl psi/ is the wave direction along the wind direction. Thus, using the Elfouhaily et al. sea height spectrum, related to the second-order statistics, we show that the normalized radar backscattering cross section (NRBCS) can be expanded as an even Fourier series in cos(n/spl phi/) (where n is a positive integer), for which the harmonic coefficients require only a single integration over the radial distance. This result is consistent with experimental data done for microwave frequencies. In addition, we show for microwave frequencies (like C- and Ku-bands) that the Fourier series can be truncated up to the second order, since the higher order harmonic coefficients vanish. The NRBCS is also compared with empirical backscattering models CMOD2-I3 and SASS-II, valid in C- and Ku-bands, according to the scattering angle and the wind direction. The first-order harmonic coefficient predicts the surface asymmetry along the upwind and downwind directions, whereas the second-order harmonic coefficient describes the surface asymmetry along the upwind and crosswind directions.     

金属结的三次谐波特性分析

基于金属结的势垒模型, 分析了金属结的再辐射过程, 详细分析了金属结上直流偏置电压的动态平衡过程.给出了到达平衡状态之后, 金属结上的三次谐波电流分量的表达式.此外, 从金属结的角度出发, 经过详细的数值分析, 讨论了金属结的再辐射特性中影响三次谐波电流分量大小的因素.理论和仿真结果表明:当金属结的势垒宽度较大、金属与氧化层的接触面积较小、或金属与氧化层接触面的势垒高度较大时, 能够获得较小的三次谐波电流分量.最后, 通过实验测试验证, 金属与氧化层的接触面积较小或金属与氧化物接触面的势垒高度较大时, 三次谐波明显减弱.