Table of z-Transforms

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RTL8201数据手册

2. SYSTEM APPLICATIONS................................................................................................................1
3. FEATURES ..........................................................................................................................................2
5.1. LEAD (PB)-FREE PACKAGE AND VERSION IDENTIFICATION ...........................................................4
6. PIN DESCRIPTION............................................................................................................................5
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Track ID: JATR-1076-21 Rev. 1.3
RTL8201BL Datasheet
Table of Contents
1. INTRODUCTION ..........................................................1
Pin8: DVDD25-> PWFBIN
2. Add pull-high resistor for MDIO 3. Modify ResetB circuit to meet wake-on-LAN application Cosmetic layout changes

数据的整编和分析

常用统计分析方法——SPSS应用General Method of Statistical AnalysisSPSS Application杜志渊编著前言《统计学》是一门计算科学，是自然科学在社会经济各领域中的应用学科，是许多学科的高校在校本科生的必修课程。

在统计学原理的学习和统计方法的实际应用中，经常需要进行大量的计算。

因此，统计分析软件问世使强大的计算机功能得到充分发挥，不仅能够减轻计算工作量，计算结果非常准确，而且还节省了统计分析时间。

因此，应用统计分析软件进行数据处理已经成为社会学家和科学工作者必不可少的工作内容。

为了使高校的学生能够更好的适应社会的发展和需求，学习和使用统计软件已经成为当前管理学、社会学、自然科学、生物医学、工程学、农业科学、运筹学等学科的本科生或研究生所面临的普遍问题。

为了使大学生和专业人员在掌握统计学原理的基础上能够正确地运用计算机做各种统计分析，掌握统计分析软件的操作是非常有必要的。

现将常用的SPSS统计分析软件处理数据和分析数据的基本方法编辑成册，供高校学生及对统计分析软件有兴趣的人员学习和参考，希望能够对学习者有所帮助。

本书以统计学原理为理论基础，以高等学校本科生学习的常用的统计方法为主要内容，重点介绍这些统计分析方法的SPSS 软件的应用。

为了便于理解，每一种方法结合一个例题解释SPSS软件的操作步骤和方法，并且对统计分析的输出结果进行相应的解释和分析。

同时也结合工业、农业、商业、医疗卫生、文化教育等实际问题，力求使学生对统计分析方法的应用有更深刻的认识和理解，以提高学生学习的兴趣和主动性。

另外，为了方便学习者的查询，将常用统计量的数学表达式作为附录1，SPSS 中所用的主要函数释义作为附录2，希望对学习者能够的所帮助。

编者目录第一章数据文件的建立及基本统计描述 (1)§1.1 SPSS的启动及数据库的建立 (1)§1.1.2 SPSS简介 (1)§1.1.2 启动SPSS软件包 (3)§1.1.3 数据文件的建立 (5)§1.2 数据的编辑与整理 (8)§1.2.1 数据窗口菜单栏功能操作 (8)§1.2.2 Date数据功能 (9)§1.2.3 Transform 变换及转换功能 (10)§1.2.4 数据的编辑 (12)§1.2.5 SPSS对变量的编辑 (20)§1.3 基本统计描述 (26)§1.3.1 描述统计分析过程 (26)§1.3.2 频数分析 (28)§1.4 交叉列联表分析 (44)§1.4.1 交叉列联表的形成 (44)§1.4.2 两变量关联性检验（Chi-square Test卡方检验） (47)第二章均值比较检验与方差分析 (54)§2.1 单个总体的t 检验（One-Sample T Test）分析 (55)§2.2 两个总体的t 检验 (58)§2.2.1 两个独立样本的t检验（Independent-sample T Test） (58)§2.2.2 两个有联系总体间的均值比较（Paired-Sample T Test） (61)§2.3 单因素方差分析 (64)§2.4 双因素方差（Univariate）分析过程 (69)第三章相关分析与回归模型的建立与分析 (80)§3.1 相关分析 (80)§3.1.1 简单相关分析 (81)§3.1.1.1 散点图 (81)§3.1.1.2 简单相关分析操作 (83)§3.1.2 偏相关分析 (85)§3.2 线性回归分析 (89)§3.3 曲线估计 (100)第四章时间序列分析 (111)§4.1 实验准备工作 (111)§4.1.1 根据时间数据定义时间序列 (111)§4.1.2 绘制时间序列线图和自相关图 (112)§4.2 季节变动分析 (118)§4.2.1 季节分析方法 (118)§4.2.2 进行季节调整 (121)第五章非参数检验 (125)§5.1 Chi-Square Test 卡方检验 (127)§5.2 一个样本的K-S检验 (131)§5.3 两个独立样本的检验（Test for Two Independent Sample） (135)§5.4 两个有联系样本检验（Test for Two related samples） (138)§5.6 多个样本的非参数检验（K Samples Test） (141)§5.6 游程检验（Runs Test） (148)附录1 部分常用统计量公式 (154)§6.1 数据的基本统计特征描述 (154)§6.2 总体均值检验统计量 (156)§6.3 方差分析中的统计量 (158)§6.4 回归分析模型 (161)§6.5 非参数检验 (168)附录2 SPSS函数 (175)第一章数据文件的建立及基本统计描述在社会各项经济活动和科学研究过程中，经常获得许多数据，而这些数据中包含着大量有用的信息。

齿轮翻译

Description:The model type Gear stage can be used for the conversion of rotational speed and torque during the transmission process. It models the meshing of the gears, taking the tooth stiffness and rotary backlash into account. It is suitable for modeling spur and helical gears. If required, the gear contact can be modeled as rigid.The radial and axial support behavior can be modeled externally and thus can be rigid or elastic. Force, spring, and pre-load models are possible.Figure 1: Coordinate systems of the Gear stage modelThe gear element transforms displacements, velocities, accelerations, and forces (torques) between the red connector coordinate systems and the green inner coordinate system at the tooth contact (indicated by I). The tooth contact model is described in the chapter Tooth Contact.Furthermore, the element is able to represent losses. The losses can be considered in the tooth contact and / or in the gear supports (at the rotational connectors).Parameters:GeometryIt is possible to use only constructional data for the parameterization of the gear (see Figure 1). These are in particular:∙the Normal Modulus,∙the Tooth Width ,∙the Number of Teeth z1 and z2 for the two gears,∙the Helix Angle (measured with respect to gear 1, see Figure 1),∙the Pressure Angle ,∙and the Rotary Backlash j t.All the mechanical parameters (stiffness, damping, overlap) can be calculated internally, if nothing else is specified. In addition each parameter (if known) can be altered manually in further parameter groups in order to precisely adjust the model to the situation to be simulated.Tooth ContactThe tooth contact can be modeled as rigid (see below) or elastic. If no values are given, SimulationX computes the tooth stiffness by an internal approach. Otherwise you can choose between an elastic or a rigid tooth contact model. Further information for parameterization, calculation and results of the tooth contact can be found in chapter Tooth Contact.The principal model of the gear stage is defined by the Rigid checkbox. It can behave as∙Spring-Damper-Backlash: The Rigid checkbox is deselected. The behavior is defined by the given or computed stiffness, damping, and backlash parameters. Within the backlash the stiffness and damping are always zero.∙Rigid End Stop: If the Rigid checkbox is selected, the model behaves as rigid. I.e., it consists of an ideal transformation with rigid connection between all connectors(kindR == "without Backlash") or an ideal transformation combined with a rigid end stop. The kind of impact can be specified by the user via the Tooth Contact parameter - in the same way as for the rigid end stop in the Linear Mechanics library. If abacklash is present, it is set via the Rotary Backlash parameter.∙If the checkbox Rigid is selected and if the Contact enumeration kindR is switched to "without Backlash", the gear stage as a transformer (transmission). In this case,forces will only be transferred via the right tooth flanks, no matter in which direction the power is transmitted. So, the right tooth flanks transfer tensile and compressive forces (tensile forces have a negative sign). In this case, the result variables for the forces of the left tooth flanks Fbnl and Ftl are deactivated.∙If Consideration of Stiffness Change is selected (only possible if Rigid is deselected) the element computes a variable toothing stiffness by an internal approach (seechapter Tooth Contact).Stiffness of Toothing and Damping of Toothing∙If Rigid is deselected, the properties dialog page Free Definition 1 provides parameters to define the elastic tooth contact model. Read more about theparameters and the calculation in the chapter Tooth Contact.Modified Profile / Contact RatioThis group provides further geometry parameters of the gear. If Consideration of Modified Profile is selected, it is possible to enter∙profile offset factors x1 and x2 for every gear. Based on this the effective radii for the force and motion quantity transformation between Tooth Contact and connectorcoordinate systems will be computed.∙the center distance a of the gears. Together with the tooth numbers, the effective transformation radii can be computed.∙Furthermore, the Input of an Addendum Modification is possible. The Addendum Modification kmn in the element Gear is an absolute value. If only an relative value k mn,rel is given, the absolute value can be computed using the normal modulus m n by:∙Finally the Total Contact Ratio can be specified. By default it is computed internally,but it is possible to enter a constant value for epsilon (, see chapter ToothContact) in order to consider different kinds of modified profiles. The total contactratio is used for the computation of the total stiffness by the specific stiffness of one pair of teeth (see also chapter Tooth Contact). Thus, this parameter is redundant if Summated Meshing Spring Stiffness is selected for kindS on page Free Definition 1.If you decide to enter a value for the total contact ratio, the addendum modificationis obsolete, because this modification is always considered within the total contactratio value.Losses (page Loses 1 and page Losses 2)There are three locations for the consideration of losses:∙the tooth contact,∙the gear bearing at gear 1 (ctrR1), and∙the gear bearing at gear 2 (ctrR2).Each loss location can be parameterized separately. All losses can be considered separately or in combination.If reliable data is only available for the whole gear stage, e.g., the overall efficiency, only the parameters in the box Toothing / Gear Stage on the dialog page Losses 1 have to be entered and will determine the overall efficiency.A detailed description of the loss models in gear stage elements ca be found in the chapter Losses in Gear Stages.Results:∙The gear model provides the normal forces, the tangential, radial, and axial forces, deformations and velocity differences of the tooth contact for the left and the right flank (see chapter Tooth Contact).The tangential, radial, and axial forces are acting as pressure forces w.r.t.the green coordinate system in Figure 1 on gear 2. So, a negative radialforce will move the gears appart.∙Furthermore the Total Meshing Spring Stiffness is computed during simulation and can be observed in the result variable kbt.∙If a spring-damper-backlash model (non-rigid model) of the tooth contact is selected, the Change of Potential Energy (the power flow into the spring in the contact) and the Power Loss (power dissipated in the damper) can be examined too.∙If there is a change of the contact surface, there is also a change in the place and direction where the spring stiffness, damping, and the normal force act.∙If Rigid is selected and kindR=="without backlash", the tooth contact forces Fbnl and Ftl are deactivated (see section Tooth Contact in this chapter).Periodic Steady State Simulation:The relative damping and Lehr's damping factor D as well as the spectral powers of the left and the right flank PSpecl and PSpecr, resp., are only taken into account in the Periodic Steady State Simulation. These parameters are described in some detail in sections Periodic Steady State Simulation (Parameters) and Periodic Steady State Simulation (Results) of the chapter Tooth Contact.Remarks:The gear element only calculates the deformation forces in the tooth engagement. The inertia properties, i.e. the moments of rotary inertia in the gears, have to be assigned to externally connected objects.The linear (translatory) connectors ctrT1x, ctrT1y, ctrT1z, ctrT2x, ctrT2y, and ctrT2z can be used to model support properties, as well as for example preloads, which are applied to the gear stage. Some examples on how to model such situations are given in the subsection Linear connections of the Gear.Table of Parameters and Result Quantities:。

encyclopediaofvibration

Encyclopedia of VibrationBraun, Simon GISBN-13: 9780122270857Table of ContentsAbsorbers, VibrationValder Steffen, Jr, and Domingo Rade, Federal University of Uberlandia, BrazilActive Control of Civil StructuresT T (Larry) Soong, MCEER, SUNY Buffalo, USA, and B F Spencer, Jr, USAActive Control of Vehicle VibrationMehdi Ahmadian, Virginia Polytechnic Institute & State University, USAActive IsolationSteve Griffin, AFRL/VSSV, USA, and Dino Sciulli, Virginia, USAActive Vibration SuppressionDaniel Inman, Virginia Polytechnic Institute & State University, USAActuators and Smart StructuresVictor Giurgiutiu, University of South Carolina, USAAdaptive FiltersStephen J Elliott, University of Southampton, UKAeroelastic ResponseJ E Cooper, University of Manchester, UKAveragingSimon Braun, Technion - Israel Institute of Technology, IsraelBalancingR Bigret, Drancy, FranceBasic PrinciplesGiora Rosenhouse, Technion City, IsraelBeamsRichard A Scott, University of Michigan, USABearing DiagnosticsK McKee and C James Li, Rensselaer Polytechnic Institute, USABearing VibrationsR Bigret, Drancy, FranceBeltsL Zhang and J W Zu, University of Toronto, CanadaBlades and Bladed DisksR Bigret, Drancy, FranceBoundary ConditionsGiora Rosenhouse, Technion City, IsraelBoundary Element MethodsFriedel Hartmann, University of Kassel, GermanyBridgesSingiresu S Rao, University of Miami, USACablesNoel C Perkins, University of Michigan, USACepstrum AnalysisBob Randall, University of New South Wales, AustraliaChaosPhilip J Holmes, Princeton University, USAColumnsIsaac Elishakoff, Florida Atlantic University, USA, and C W Bert, University of Oklahoma, USACommercial SoftwareGuy Robert, Liege, BelgiumComparison of Vibration Properties: Comparison of Spatial PropertiesMircea Rades, University Politechnica of Bucharest, RomaniaComparison of Vibration Properties: Comparison of Modal PropertiesMircea Rades, University Politechnica of Bucharest, RomaniaComparison of Vibration Properties: Comparison of Response PropertiesMircea Rades, University Politechnica of Bucharest, RomaniaComputation for Transient and Impact DynamicsDavid J Benson, University of California, San Diego, USA, and John Hallquist, Livermore Software Technology Corporation (LSTC), USAContinuous MethodsC W Bert, University of Oklahoma, USACorrelation FunctionsSimon Braun, Technion - Israel Institute of Technology, IsraelCrashVictor H Mucino, West Virginia University, USACritical DampingDaniel Inman, Virginia Polytechnic Institute & State University, USADamping in FE ModelsGeorge A Lesieutre, Pennsylvania State University, USADamping MaterialsEric E Ungar, Acentech, Inc, USADamping MeasurementD J Ewins, Imperial College of Science, Technology and Medicine, UKDamping ModelsDaniel Inman, Virginia Polytechnic Institute & State University, USADamping MountsJian-Qiao Sun, University of Delaware, USADamping, ActiveAmr Baz, University of Maryland, USAData AcquisitionBob Randall and M J Tordon, University of New South Wales, AustraliaDiagnostics and Condition Monitoring, Basic ConceptsM Sidahmed, UniversitÃ© de Compiegne, France, and Giorgio Dalpiaz, University of Bologna, Italy Digital FiltersTony Constantinides, Imperial College of Science, Technology and Medicine, UKDiscrete ElementsSingiresu S Rao, University of Miami, USADisksD J Ewins, Imperial College of Science, Technology and Medicine, UKDisplays of Vibration PropertiesMircea Rades, University Politechnica of Bucharest, RomaniaDynamic StabilityA Steindl, Vienna University of Technology, Austria, and Hans Troger, Vienna, Austria Earthquake Excitation and Response of BuildingsFarzad Naeim, John A Martin & Associates, Inc, USAEigenvalue AnalysisOliver Bauchau, Georgia Institute of Technology, USAElectrorheological and Magnetorheological FluidsR Stanway, The University of Sheffield, UKElectrostrictive MaterialsKenji Uchino, Pennsylvania State University, USA, and H S Tzou, University of Kentucky, USA Environmental Testing, ImplementationP S Varoto, Escola de Engenharia de Sao Carlos, USP, BrazilEnvironmental Testing, OverviewDavid Smallwood, Sandia National Laboratories, USAFatigueAlbert Kobayashi and M Ramula, University of Washington, USAFeed Forward Control of VibrationChristopher R Fuller, Virginia Polytechnic Institute & State University, USAFinite Difference MethodsSingiresu S Rao, University of Miami, USAFinite Element MethodsSingiresu S Rao, University of Miami, USAFluid/Structure InteractionSabih Hayek, Pennsylvania State University, USAFlutterJan Wright, University of Manchester, UKFlutter, Active ControlFrank H Gern, Virginia Polytechnic Institute & State University, USAForced ResponseN A J Lieven, Bristol University, UKFriction DampingRaouf Ibrahim, Wayne State University, USAFriction Induced VibrationsRaouf Ibrahim, Wayne State University, USAGear DiagnosticsC James Li, Rensselaer Polytechnic Institute, USAGround Transportation SystemsA K W Ahmed, Concordia University, CanadaHand-transmitted VibrationM Griffin, University of Southampton, UKHelicopter DampingNorman M Wereley, University of Maryland at College Park, USAHilbert TransformsM Feldman, Technion - Israel Institute of Technology, IsraelHybrid ControlKon-Well Wang, Pennsylvania State University, USAHysteretic DampingH T Banks, North Carolina State University, USA and G A Pinter, North Carolina State University, USA Identification, Fourier-based MethodsSimon Braun, Technion - Israel Institute of Technology, IsraelIdentification, Model Based MethodsSpilios D Fassois, University of Patras, GreeceInverse ProblemsY M Ram, Louisiana State University, USAKrylov-Lanczos MethodsRoy Craig, University of Texas, USALaser Based MeasurementsP Castellini, E P Tomasini, and G M Revel, UniversitÃ di Ancona, ItalyLinear AlgebraCharbel Farhat, University of Colorado, USA, and Daniel Rixen, Delft, BelgiumLinear Damping Matrix MethodsFai Ma, University of California, Berkeley, USALiquid SloshingRaouf Ibrahim, Wayne State University, USALocalizationChristophe Pierre, University of Michigan, USAMagnetostrictive MaterialsAlison Flatau, National Science Foundation, USAMembranesArthur W Leissa, Ohio State University, USAMEMs ApplicationsI Stiharu, Concordia University, CanadaMEMs, Dynamic ResponseI StiharuMEMs, General PropertiesI StiharuModal Analysis, Experimental: Basic PrinciplesD J Ewins, Imperial College of Science, Technology and Medicine, UKModal Analysis, Experimental: Measurement TechniquesJ M Silva, Institute Superior Technico, PortugalModal Analysis, Experimental: Parameter Extraction MethodsN M Maia, Institute Superior Technico, PortugalModal Analysis, Experimental: Construction of Models from TestsN M Maia, Institute Superior Technico, PortugalModal Analysis, Experimental: ApplicationsD J Ewins, Imperial College of Science, Technology and Medicine, UKMode of VibrationD J Ewins, Imperial College of Science, Technology and Medicine, UKModel Updating and ValidatingM Link, UniversitÃ¤t Gesamthoschule Kassel, GermanyMotion SicknessM Griffin, University of Southampton, UKNeural Networks, Diagnostic ApplicationsM Zacksenhouse, Technion - Israel Institute of Technology, IsraelNeural Networks, General PrinciplesB Dubuisson, La Croix Saint Ouen, FranceNoise, Noise Radiated from Elementary SourcesMichael Peter Norton and J Pan, University of Western Australia, AustraliaNoise, Noise Radiated by Baffled PlatesMichael Peter Norton and J pan, University of Western Australia, AustraliaNondestructive Testing, SonicScott Doebling and Charles Farrar, Los Alamos National Laboratory, USANondestructive Testing, UltrasonicL W Schmerr Jr, Iowa State University, USANonlinear Normal ModesAlexander Vakakis, University of Illinois, USANonlinear System IdentificationB F Feeny, Michigan State University, USANonlinear System Resonance PhenomenaAnil Bajaj and Charles M Krousgrill, Purdue University, USANonlinear Systems AnalysisAnil Bajaj, Purdue University, USANonlinear Systems, OverviewNoel C Perkins, University of Michigan, USAObject Oriented Programming in FE AnalysisIgor Klapka, UniversitÃ© de LiÃ¨ge, Belgium, Alberto Cardona, INTEC, Argentina, and Philipee Devloo, Universidade Estadual de Campinas, BrazilOptimal FiltersStephen J Elliott, University of Southampton, UKPackagingJorge Marcondes, San Jose University, USAParallel ProcessingDaniel Rixen, Delft, BelgiumParametric ExcitationAlexandra David and Subhash Sinha, Auburn University, USAPerturbation Techniques for Non-linear SystemsSteve Shaw, Michigan State University, USAPiezoelectric MaterialsH S Tzou, University of Kentucky, USA, and M C Natori, Institute of Space & Astronautical Science, JapanPipesSingiresu S Rao, University of Miami, USAPlatesArthur W Leissa, Ohio State University, USARandom ProcessesMikhail F Dimentberg, Worcester Polytechnic Institute, USARandom Vibration, Basic TheoryMikhail F Dimentberg, Worcester Polytechnic Institute, USAResonance and AntiresonanceMircea Rades, University Politechnica of Bucharest, RomaniaRobot VibrationsWayne Book, Georgia Institute of Technology, USARotating Machinery, Essential FeaturesR Bigret, Drancy, FranceRotating Machinery, Model CharacteristicsR Bigret, Drancy, FranceRotating Machinery, MonitoringR Bigret, Drancy, FranceRotor DynamicsR Bigret, Drancy, FranceRotorstator InteractionsR Bigret, Drancy, FranceSeismic Instruments, Environmental FactorsKenneth McConnell, Iowa State University, USASensors and ActuatorsH S Tzou, University of Kentucky, USA, and C S Chou, National Taiwan University, Republic of ChinaShape Memory AlloysM Baz, University of Maryland, USAShellsW Soedel, Purdue University, USAShip VibrationsWilliam S Vorus, University of New Orleans, USAShockJorge Marcondes, San Jose University, USAShock Isoloation SystemsMircea Rades, University Politechnia of Bucharest, RomaniaSignal Generation Models for DiagnosticsGiorgio Dalpiaz, University of Bologna, Italy, and M Sidahmed, UniversitÃ© de Compiegne, FranceSignal Integration and DifferentiationStuart Dyne, University of Southampton, UKSignal Processing, Model Based MethodsSimon Braun, Technion - Israel Institute of Technology, IsraelSpectral Analysis, Classical MethodsSimon Braun, Technion - Israel Institute of Technology, IsraelStandards for Vibrations of Machines and Measurement ProceduresJohn Niemkiewicz, Maintenance and Diagnostic (M&D) LLC, USAStochastic Analysis of Nonlinear SystemsY K Lin and C Q Cai, Florida Atlantic University, USAStochastic SystemsMikhail F Dimentberg, Worcester Polytechnic Institute, USAStructural Dynamic ModificationsA Sestieri, Universita Degli Studi di Roma, Italy, and W D'Amorogio, Universita Be L'Aquila, ItalyStructure-Acoustic Interaction, High FrequenciesA Sestieri, Universita Degli Studi di Roma, ItalyStructure-Acoustic Interaction, Low FrequenciesA Sestieri, Universita Degli Studi di Roma, ItalyTesting, Non-linear SystemsAlan Haddow, Michigan State University, USATheory of Vibration, FundamentalsBingen Yang, University of Southern California, USATheory of Vibration, SuperpositionM G Prasad, Stevens Institute of Technology, USATheory of Vibration, Duhamel's Principle and ConvolutionG Rosenhouse, Technion - Israel Institute of Technology, IsraelTheory of Vibration, Energy MethodsSingiresu S Rao, University of Miami, USATheory of Vibration, Equations of MotionJonathan Wickert, Carnegie Mellon University, USATheory of Vibration, SubstructuringMehmet Sunar, King Fahd University of Petroleum and Minerals, Saudi ArabiaTheory of Vibration, Impulse Response FunctionRakesh Kapania, Virginia Polytechnic Institute & State University, USATheory of Vibration, Variational MethodsSingiresu S Rao, University of Miami, USATime-Frequency MethodsPaul White, University of Southampton, UKTire VibrationsG D Shteinhauz, The Goodyear Tire & Rubber Company, USATool Wear MonitoringM Sidahmed, UniversitÃ© de Compiegne, FranceTransducers for Absolute MotionKenneth McConnell, Iowa State University, USATransducers for Relative MotionKenneth McConnell, Iowa State University, USA, Simon Braun, Technion - Israel Institute of Technology, Israel, and Gene E Maddux, Tipp City, USATransform MethodsSimon Braun, Technion - Israel Institute of Technology, IsraelTransforms, WaveletsPaul White, University of Southampton, UKUltrasonicsM J S Lowe, Imperial College of Science, Technology and Medicine, UKVibration Generated Sound, FundamentalsMichael Peter Norton and S J Drew, University of Western Australia, AustraliaVibration Generated Sound, Radiation by Flexural ElementsMichael Peter Norton and S J Drew, University of Western Australia, AustraliaVibration IntensitySabih Hayek, Pennsylvania State University, USAVibration Isolation, Applications and CriteriaE Rivin, Wayne State University, USAVibration Isolation TheoryE Rivin, Wayne State University, USAVibration TransmissionSabih I Hayek, Pennsylvania State University, USAVibro-impact SystemsF Peterka, Academy of Sciences of the Czech Republic, Czech RepublicViscous DampingFarhan Gandhi, Pennsylvania State University, USAWave Propagation, Waves in an Unbound MediumM J S Lowe, Imperial College of Science, Technology and Medicine, UKWave Propagation, Interaction of Waves with BoundariesM J S Lowe, Imperial College of Science, Technology and Medicine, UKWave Propagation, Guided Waves in StructuresM J S Lowe, Imperial College of Science, Technology and Medicine, UKWhole-body VibrationM Griffin, University of Southampton, UKWind-Induced VibrationsAhsan Kareem, University of Notre Dame, USAWindowsSimon Braun, Technion - Israel Institute of Technology, Israel。

ADXL345数据手册_引脚图_参数

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LaTeX符号表

The Comprehensive L A T E X Symbol ListScott Pakin<pakin@>∗29September2003AbstractThis document lists2826symbols and the corresponding L A T E X commands that produce them.Some of these symbols are guaranteed to be available in every L A T E X2εsystem;others require fonts and packagesthat may not accompany a given distribution and that therefore need to be installed.All of the fontsand packages used to prepare this document—as well as this document itself—are freely available from theComprehensive T E X Archive Network().Contents1Introduction61.1Document Usage (6)1.2Frequently Requested Symbols (6)2Body-text symbols7 Table1:L A T E X2εEscapable“Special”Characters (7)Table2:L A T E X2εCommands Deﬁned to Work in Both Math and Text Mode (7)Table3:Predeﬁned L A T E X2εText-mode Commands (7)Table4:Non-ASCII Letters(Excluding Accented Letters) (8)Table5:Letters Used to Typeset African Languages (8)Table6:Punctuation Marks Not Found in OT1 (8)Table7:pifont Decorative Punctuation Marks (8)Table8:wasysym Phonetic Symbols (8)Table9:tipa Phonetic Symbols (8)Table10:wsuipa Phonetic Symbols (10)Table11:phonetic Phonetic Symbols (10)Table12:Text-mode Accents (11)Table13:tipa Text-mode Accents (11)Table14:wsuipa Text-mode Accents (12)Table15:phonetic Text-mode Accents (13)Table16:wsuipa Diacritics (13)Table17:textcomp Diacritics (13)Table18:textcomp Currency Symbols (13)Table19:marvosym Currency Symbols (14)Table20:wasysym Currency Symbols (14)Table21:eurosym Euro Signs (14)Table22:textcomp Legal Symbols (14)Table23:textcomp Old-style Numerals (14)Table24:Miscellaneous textcomp Symbols (15)Table25:Miscellaneous wasysym Text-mode Symbols (15)Table26:A M S Commands Deﬁned to Work in Both Math and Text Mode (15)∗The original version of this document was written by David Carlisle,with several additional tables provided by Alexander Holt.See Section7.6on page69for more information about who did what.13Mathematical symbols16 Table27:Binary Operators (16)Table28:A M S Binary Operators (16)Table29:stmaryrd Binary Operators (17)Table30:wasysym Binary Operators (17)Table31:txfonts/pxfonts Binary Operators (17)Table32:mathabx Binary Operators (18)Table33:ulsy Geometric Binary Operators (18)Table34:mathabx Geometric Binary Operators (18)Table35:Variable-sized Math Operators (18)Table36:A M S Variable-sized Math Operators (19)Table37:stmaryrd Variable-sized Math Operators (19)Table38:wasysym Variable-sized Math Operators (19)Table39:mathabx Variable-sized Math Operators (19)Table40:txfonts/pxfonts Variable-sized Math Operators (20)Table41:esint Variable-sized Math Operators (20)Table42:Binary Relations (21)Table43:A M S Binary Relations (21)Table44:A M S Negated Binary Relations (21)Table45:stmaryrd Binary Relations (21)Table46:wasysym Binary Relations (21)Table47:txfonts/pxfonts Binary Relations (22)Table48:txfonts/pxfonts Negated Binary Relations (22)Table49:mathabx Binary Relations (22)Table50:mathabx Negated Binary Relations (23)Table51:trsym Binary Relations (23)Table52:trfsigns Binary Relations (23)Table53:Subset and Superset Relations (23)Table54:A M S Subset and Superset Relations (23)Table55:stmaryrd Subset and Superset Relations (24)Table56:wasysym Subset and Superset Relations (24)Table57:txfonts/pxfonts Subset and Superset Relations (24)Table58:mathabx Subset and Superset Relations (24)Table59:Inequalities (24)Table60:A M S Inequalities (24)Table61:wasysym Inequalities (25)Table62:txfonts/pxfonts Inequalities (25)Table63:mathabx Inequalities (25)Table64:A M S Triangle Relations (25)Table65:stmaryrd Triangle Relations (25)Table66:mathabx Triangle Relations (25)Table67:Arrows (26)Table68:Harpoons (26)Table69:textcomp Text-mode Arrows (26)Table70:A M S Arrows (26)Table71:A M S Negated Arrows (26)Table72:A M S Harpoons (26)Table73:stmaryrd Arrows (27)Table74:txfonts/pxfonts Arrows (27)Table75:mathabx Arrows (27)Table76:mathabx Negated Arrows (27)Table77:mathabx Harpoons (28)Table78:chemarrow Arrows (28)Table79:ulsy Contradiction Symbols (28)Table80:Extension Characters (28)Table81:stmaryrd Extension Characters (28)Table82:txfonts/pxfonts Extension Characters (28)2Table83:mathabx Extension Characters (28)Table84:Log-like Symbols (29)Table85:A M S Log-like Symbols (29)Table86:Greek Letters (29)Table87:A M S Greek Letters (29)Table88:txfonts/pxfonts Upright Greek Letters (30)Table89:upgreek Upright Greek Letters (30)Table90:txfonts/pxfonts Variant Latin Letters (30)Table91:A M S Hebrew Letters (30)Table92:Letter-like Symbols (30)Table93:A M S Letter-like Symbols (31)Table94:txfonts/pxfonts Letter-like Symbols (31)Table95:mathabx Letter-like Symbols (31)Table96:trfsigns Letter-like Symbols (31)Table97:A M S Delimiters (31)Table98:stmaryrd Delimiters (31)Table99:mathabx Delimiters (31)Table100:nath Delimiters (31)Table101:Variable-sized Delimiters (32)Table102:Large,Variable-sized Delimiters (32)Table103:Variable-sized stmaryrd Delimiters (32)Table104:mathabx Variable-sized Delimiters (32)Table105:nath Variable-sized Delimiters(Double) (33)Table106:nath Variable-sized Delimiters(Triple) (33)Table107:textcomp Text-mode Delimiters (33)Table108:Math-mode Accents (34)Table109:A M S Math-mode Accents (34)Table110:yhmath Math-mode Accents (34)Table111:trfsigns Math-mode Accents (34)Table112:Extensible Accents (35)Table113:overrightarrow Extensible Accents (35)Table114:yhmath Extensible Accents (35)Table115:A M S Extensible Accents (35)Table116:chemarr Extensible Accents (36)Table117:chemarrow Extensible Accents (36)Table118:mathabx Extensible Accents (36)Table119:esvect Extensible Accents (37)Table120:undertilde Extensible Accents (37)Table121:Dots (37)Table122:A M S Dots (37)Table123:mathdots Dots (38)Table124:yhmath Dots (38)Table125:Miscellaneous L A T E X2εSymbols (38)Table126:Miscellaneous A M S Symbols (38)Table127:Miscellaneous wasysym Symbols (38)Table128:Miscellaneous txfonts/pxfonts Symbols (38)Table129:Miscellaneous mathabx Symbols (39)Table130:Miscellaneous textcomp Text-mode Math Symbols (39)Table131:mathcomp Math Symbols (39)Table132:gensymb Symbols Deﬁned to Work in Both Math and Text Mode (39)Table133:mathabx Mayan Digits (39)Table134:marvosym Math Symbols (39)Table135:Math Alphabets (40)34Science and technology symbols41 Table136:wasysym Electrical and Physical Symbols (41)Table137:ifsym Pulse Diagram Symbols (41)Table138:ar Aspect Ratio Symbol (41)Table139:textcomp Text-mode Science and Engineering Symbols (41)Table140:wasysym Astronomical Symbols (41)Table141:marvosym Astronomical Symbols (42)Table142:mathabx Astronomical Symbols (42)Table143:wasysym Astrological Symbols (42)Table144:marvosym Astrological Symbols (42)Table145:mathabx Astrological Symbols (42)Table146:wasysym APL Symbols (42)Table147:wasysym APL Modiﬁers (42)Table148:marvosym Computer Hardware Symbols (43)Table149:ascii Control Characters(IBM) (43)Table150:marvosym Communication Symbols (43)Table151:marvosym Engineering Symbols (43)Table152:wasysym Biological Symbols (43)Table153:marvosym Biological Symbols (43)Table154:marvosym Safety-related Symbols (44)5Dingbats45 Table155:bbding Arrows (45)Table156:pifont Arrows (45)Table157:marvosym Scissors (45)Table158:bbding Scissors (45)Table159:pifont Scissors (45)Table160:dingbat Pencils (45)Table161:bbding Pencils and Nibs (46)Table162:pifont Pencils and Nibs (46)Table163:dingbat Hands (46)Table164:bbding Hands (46)Table165:pifont Hands (46)Table166:bbding Crosses and Plusses (46)Table167:pifont Crosses and Plusses (46)Table168:bbding Xs and Check Marks (46)Table169:pifont Xs and Check Marks (47)Table170:wasysym Xs and Check Marks (47)Table171:pifont Circled Numbers (47)Table172:wasysym Stars (47)Table173:bbding Stars,Flowers,and Similar Shapes (47)Table174:pifont Stars,Flowers,and Similar Shapes (48)Table175:wasysym Geometric Shapes (48)Table176:ifsym Geometric Shapes (48)Table177:bbding Geometric Shapes (49)Table178:pifont Geometric Shapes (49)Table179:universa Geometric Shapes (49)Table180:manfnt Dangerous Bend Symbols (49)Table181:skull Symbols (49)Table182:Non-Mathematical mathabx Symbols (49)Table183:marvosym Information Symbols (49)Table184:Miscellaneous dingbat Dingbats (50)Table185:Miscellaneous bbding Dingbats (50)Table186:Miscellaneous pifont Dingbats (50)46Other symbols51 Table187:textcomp Genealogical Symbols (51)Table188:wasysym General Symbols (51)Table189:wasysym Musical Notes (51)Table190:wasysym Circles (51)Table191:Miscellaneous manfnt Symbols (51)Table192:marvosym Navigation Symbols (52)Table193:marvosym Laundry Symbols (52)Table194:Other marvosym Symbols (52)Table195:Miscellaneous universa Symbols (52)Table196:ifsym Weather Symbols (53)Table197:ifsym Alpine Symbols (53)Table198:ifsym Clocks (53)Table199:Other ifsym Symbols (53)Table200:skak Chess Informator Symbols (54)7Additional Information557.1Symbol Name Clashes (55)7.2Where can Iﬁnd the symbol for...? (55)7.3Math-mode spacing (64)7.4Bold mathematical symbols (65)7.5ASCII and Latin1quick reference (66)7.6About this document (69)References69 Index7151IntroductionWelcome to the Comprehensive L A T E X Symbol List!This document strives to be your primary source of L A T E X symbol information:font samples,L A T E X commands,packages,usage details,caveats—everything needed to put thousands of diﬀerent symbols at your disposal.All of the fonts covered herein meet the following criteria:1.They are freely available from the Comprehensive T E X Archive Network().2.All of their symbols have L A T E X2εbindings.That is,a user should be able to access a symbol by name,not just by\char number .These are not particularly limiting criteria;the Comprehensive L A T E X Symbol List contains samples of2826 symbols—quite a large number.Some of these symbols are guaranteed to be available in every L A T E X2εsystem; others require fonts and packages that may not accompany a given distribution and that therefore need to be installed.See /cgi-bin/texfaq2html?label=instpackages+wherefiles for help with installing new fonts and packages.1.1Document UsageEach section of this document contains a number of font tables.Each table shows a set of symbols,with the corresponding L A T E X command to the right of each symbol.A table’s caption indicates what package needs to be loaded in order to access that table’s symbols.For example,the symbols in Table23,“textcomp Old-Style Numerals”,are made available by putting“\usepackage{textcomp}”in your document’s preamble.“A M S”means to use the A M S packages,viz.amssymb and/or amsmath.Notes below a table provide additionalinformation about some or all the symbols in that table.One note that appears a few times in this document,particularly in Section2,indicates that certain symbols do not exist in the OT1font encoding(Donald Knuth’s original,7-bit font encoding,which is the default font encoding for L A T E X)and that you should use fontenc to select a diﬀerent encoding,such as T1 (a common8-bit font encoding).That means that you should put“\usepackage[ encoding ]{fontenc}”in your document’s preamble,where encoding is,e.g.,T1or LY1.To limit the change in font encoding to the current group,use“\fontencoding{ encoding }\selectfont”.Section7contains some additional information about the symbols in this document.It shows which symbol names are not unique across packages,gives examples of how to create new symbols out of existing symbols, explains how symbols are spaced in math mode,presents a L A T E X ASCII and Latin1tables,and provides some information about this document itself.The Comprehensive L A T E X Symbol List ends with an index of all the symbols in the document and various additional useful terms.1.2Frequently Requested SymbolsThere are a number of symbols that are requested over and over again on comp.text.tex.If you’re looking for such a symbol the following list will help youﬁnd it quickly.,as in“Spaces signiﬁcant.” (7)´ı,`ı,¯ı,ˆı,etc.(versus´i,`i,¯i,andˆi) (11)¢ (13)e (14)©,®,and™ (14)‰ (15) (20)∴ (21)and (22)and (24)... (38)°,as in“180°”or“15℃” (39)L,F,etc (40)N,Z,R,etc (40)−R (58)´¯a,`ˆe,etc.(i.e.,several accents per character)60 <,>,and|(instead of¡,¿,and—) (66)ˆand˜(or∼) (67)62Body-text symbolsThis section lists symbols that are intended for use in running text,such as punctuation marks,accents, ligatures,and currency symbols.Table1:L A T E X2εEscapable“Special”Characters$\$%\%\_∗}\}&\&#\#{\{∗The underscore package redeﬁnes“_”to produce an underscore in text mode(i.e.,itmakes it unnecessary to escape the underscore character).Table2:L A T E X2εCommands Deﬁned to Work in Both Math and Text Mode$\$\_‡\ddag{\{¶\P c○©\copyright...\dots}\}§\S†\dag£\poundsWhere two symbols are present,the left one is the“faked”symbol that L A T E X2εprovides by default,and the right one is the“true”symbol that textcomp makesavailable.Table3:Predeﬁned L A T E X2εText-mode Commandsˆ\textasciicircum<\textless˜\textasciitilde aª\textordfeminine∗\textasteriskcentered oº\textordmasculine\\textbackslash¶\textparagraph|\textbar·\textperiodcentered{\textbraceleft¿\textquestiondown}\textbraceright“\textquotedblleft•\textbullet”\textquotedblrightc○©\textcopyright‘\textquoteleft†\textdagger’\textquoteright‡\textdaggerdbl r○®\textregistered$\textdollar§\textsection...\textellipsis£\textsterling—\textemdash TM™\texttrademark–\textendash\textunderscore¡\textexclamdown\textvisiblespace>\textgreaterWhere two symbols are present,the left one is the“faked”symbol that L A T E X2εprovides by default,and the right one is the“true”symbol that textcomp makesavailable.7Table4:Non-ASCII Letters(Excluding Accented Letters)˚a\aaÐ\DH∗ L\Lø\oß\ss˚A\AAð\dh∗ l\lØ\O SS\SSÆ\AEÐ\DJ∗Ŋ\NG∗Œ\OEÞ\TH∗æ\aeđ\dj∗ŋ\ng∗œ\oeþ\th∗∗Not available in the OT1font e the fontenc package to select analternate font encoding,such as T1.Table5:Letters Used to Typeset African LanguagesÐ\B{D}°\m{c}¤\m{f}¨\m{k}»\M{t} \m{Z}\B{d} \m{D} \m{F} \m{N} \M{T}Â\T{E}\B{H}ð\M{d} \m{G}\m{n}º\m{t}â\T{e}§\B{h}Ð\M{D}¦\m{g}ª\m{o} \m{T}Å\T{O}·\B{t}¡\m{d}À\m{I} \m{O}®\m{u}∗å\T{o}\B{T} \m{E}à\m{i} \m{P} \m{U}∗\m{b}¢\m{e} \m{J}±\m{p} \m{Y}\m{B} \M{E}©\m{j}¬\m{s}¯\m{y}\m{C}£\M{e} \m{K} \m{S}¶\m{z}These characters all need the T4font encoding,which is provided by the fc package.∗\m{v}and\m{V}are synonyms for\m{u}and\m{U}.Table6:Punctuation Marks Not Found in OT1«\guillemotleft‹\guilsinglleft…\quotedblbase"\textquotedbl »\guillemotright›\guilsinglright‚\quotesinglbaseTo get these symbols,use the fontenc package to select an alternate font encoding,such as T1.Table7:pifont Decorative Punctuation Marks❛\ding{123}❝\ding{125}❡\ding{161}❣\ding{163}❜\ding{124}❞\ding{126}❢\ding{162}Table8:wasysym Phonetic SymbolsD\DH \dh \openoÞ\Thorn \inveþ\thornTable9:tipa Phonetic Symbols8È\textbabygamma P\textglotstopï\textrtailnb\textbarb;\texthalflengthó\textrtailrc\textbarc»\texthardsignù\textrtailsd\textbard#\texthooktopú\textrtailté\textbardotlessjá\texthtbü\textrtailzg\textbargê\texthtbardotlessj$\textrthookÜ\textbarglotstopÁ\texthtcÀ\textsca1\textbariâ\texthtdà\textscbª\textbarlä\texthtg¤\textsce8\textbaro H\texththå\textscgÝ\textbarrevglotstopÊ\texththengË\textsch0\textbaruÎ\texthtk@\textschwaì\textbeltlÒ\texthtp I\textsciB\textbetaÓ\texthtq¨\textscjò\textbullseye£\texthtrtaildÏ\textscl \textceltpalÉ\texthtscgð\textscnX\textchiÖ\texthtt×\textscoeligÅ\textcloseepsilonÿ\texthvlig±\textscomegaÑ\textcloseomegaÛ\textinvglotstopö\textscrÆ\textcloserevepsilon K\textinvscr A\textscriptaÞ\textcommatailzÌ\textiota g\textscriptg^\textcorner«\textlambda V\textscriptv\textcrb:\textlengthmarkÚ\textscu¡\textcrd³\textlhookt Y\textscyg\textcrg¦\textlhtlongi \textsecstressè\textcrh¶\textlhtlongyº\textsoftsignÛ\textcrinvglotstopÔ\textlonglegrÂ\textstretchc¬\textcrlambda½\textlptr t C\texttctclig2\textcrtwo M\textltailmÙ\textteshligC\textctcñ\textltailn T\texttheta¢\textctdë\textltildeþ\textthorn¢ý\textctdctzligÐ\textlyoghlig¿\texttoneletterstem ²\textcteshÍ\textObardotlessjµ\texttsligJ\textctj\textOlyoghlig5\textturna®\textctn°\textomega¯\textturncelig´\textctt_\textopencorner4\textturnh´C\textcttctclig O\textopeno©\textturnk¸\textctyogh%\textpalhookÕ\textturnlonglegr ý\textctz F\textphi W\textturnmdý\textdctzlig|\textpipeî\textturnmrlegS\textdoublebaresh"\textprimstressô\textturnr}\textdoublebarpipe¼\textraiseglotstopõ\textturnrrtail=/\textdoublebarslash§\textraisevibyi6\textturnscripta {\textdoublepipe7\textramshornsØ\textturnt\textdoublevertline\\textrevapostrophe2\textturnv\textdownstep9\textreveû\textturnwÃ\textdyoghlig3\textrevepsilon L\textturnyd z\textdzlig Q\textrevglotstop U\textupsilonE\textepsilon¹\textrevyogh \textupstepS\texteshÇ\textrhookrevepsilon \textvertlineR\textfishhookrÄ\textrhookschwa§\textvibyi¥\textg~\textrhoticity·\textvibyyG\textgamma¾\textrptrß\textwynn\textglobfallã\textrtaild Z\textyogh(continued on next page)9(continued from previous page)\textglobrise í\textrtailltipa deﬁnes shortcut characters for many of the above.It also deﬁnes a command \tone for denoting tone letters (pitches).See the tipa documentation for more information.Table 10:wsuipa Phonetic Symbols3\babygamma V \eng R \labdentalnas !\schwa ¦\barb "\er G \latfric B \sci \bard w \esh T \legm X \scn 9\bari \eth i \legr t \scrF \barl h \flapr I \lz¡\scripta `\baro \glotstop ¢\nialpha (\scriptg e \barp ¨\hookb ©\nibeta \scriptv C \barsci \hookd \nichi\scu \barscu )\hookg $\niepsilon \scy \baru 6\hookh 1\nigamma §\slashb Y \clickb 7\hookhengA \niiota \slashc \clickc &\hookrevepsilon P \nilambda \slashd \clickt4\hv b \niomega \slashu c \closedniomega \inva g \niphi \taild '\closedrevepsilon D \invfy \nisigma r \tailinvr ¥\crossb d \invglotstop \nitheta H \taill \crossd 8\invh \niupsilon W \tailn 5\crosshs \invlegr U \nj p \tailr Q \crossnilambda S \invm d \oo v \tails \curlyc q \invr a \openo \tailt x \curlyesh u \invscr#\reve\tailz \curlyyogh £\invscripta f \reveject \tesh \curlyz ¤\invv %\revepsilon f \thorn @\dlbari \invw \revglotstop E \tildel \dz\invy\scd\yoghe\ejective2\ipagamma\scgTable 11:phonetic Phonetic Symbolsj \barjf \flap i ¯\ibar e \rotvara i \vari¡\barlambda c \glottal \openo w \rotw ¨\varomega w \emgma f \hausaB ¯h \planck y \roty g \varopeno n \engma \hausab \pwedge e \schwa v ˚\vodx \enya h \hausad ¢\revD p \thorn h \voicedh 4\epsi \hausaD \riota u \ubar x\yoghs \esh k \hausak m \rotmu \udesc d \eth u \hausaK \rotOmega \vara p\fjh\hookdr\rotr q\varg10Table 12:Text-mode Accents¨A¨a \"{A}\"{a}`A`a \‘{A}\‘{a}˝A˝a \H{A}\H{a}˘A˘a \u{A}\u{a}´A´a \’{A}\’{a}A ¯a ¯\b{A}\b{a}Ąą\k{A}\k{a}†ˇAˇa \v{A}\v{a}˙A˙a \.{A}\.{a}A ¸¸a \c{A}\c{a}˚A ˚a \r{A}\r{a}˜A˜a \~{A}\~{a}¯A¯a \={A}\={a}A .a .\d{A}\d{a} A a \t{A}\t{a}ˆAˆa \^{A}\^{a} A a\G{A}\G{a}‡¼A¼a \U{A}\U{a}‡ Aa \newtie{A}\newtie{a}∗A ○a ○\textcircled{A}\textcircled{a}∗Requires the textcomp package.†Not available in the OT1font e the fontenc package to select an alternate font encoding,such as T1.‡Requires the T4font encoding,provided by the fc package.Also note the existence of \i and \j ,which produce dotless versions of “i”and “j”(viz.,“ı”and “j”).These are useful when the accent is supposed to replace the dot.For example,“na\"{\i}ve ”produces a correct “na¨ıve”,while “na\"{i}ve ”would yield the rather odd-looking “na ¨ive”.(“na\"{i}ve ”does work in encodingsother than OT1,however.)Table 13:tipa Text-mode Accents¡©A ¡©a \textacutemacron{A}\textacutemacron{a}¡§A ¡§a \textacutewedge{A}\textacutewedge{a}A 0a 0\textadvancing{A}\textadvancing{a}A `a `\textbottomtiebar{A}\textbottomtiebar{a}¨©A ¨©a \textbrevemacron{A}\textbrevemacron{a} A a \textcircumacute{A}\textcircumacute{a}¢ A ¢ a \textcircumdot{A}\textcircumdot{a} A a \textdotacute{A}\textdotacute{a} ¨A ¨a\textdotbreve{A}\textdotbreve{a}¨A ¨a \textdotbreve{A}\textdotbreve{a}A a \textdoublegrave{A}\textdoublegrave{a}A a \textdoublevbaraccent{A}\textdoublevbaraccent{a} A a \textgravecircum{A}\textgravecircum{a} A a \textgravedot{A}\textgravedot{a}©A ©a \textgravemacron{A}\textgravemacron{a} A a \textgravemid{A}\textgravemid{a}A a \textinvsubbridge{A}\textinvsubbridge{a}A )a )\textlowering{A}\textlowering{a} A a \textmidacute{A}\textmidacute{a}$A $a\textovercross{A}\textovercross{a}(continued on next page)(continued from previous page)" A "a\textoverw{A}\textoverw{a}A a \textpolhook{A}\textpolhook{a}A(a(\textraising{A}\textraising{a}A1a1\textretracting{A}\textretracting{a}¦©A¦©a\textringmacron{A}\textringmacron{a} A a\textroundcap{A}\textroundcap{a}A#a#\textseagull{A}\textseagull{a}A a\textsubacute{A}\textsubacute{a}A a\textsubarch{A}\textsubarch{a}A©a©\textsubbar{A}\textsubbar{a}A a \textsubbridge{A}\textsubbridge{a}A ¢a¢\textsubcircum{A}\textsubcircum{a}A a\textsubdot{A}\textsubdot{a}A a\textsubgrave{A}\textsubgrave{a}A!a!\textsublhalfring{A}\textsublhalfring{a} A'a'\textsubplus{A}\textsubplus{a}A a\textsubrhalfring{A}\textsubrhalfring{a}A ¦a¦\textsubring{A}\textsubring{a}A a \textsubsquare{A}\textsubsquare{a}A £a£\textsubtilde{A}\textsubtilde{a}A ¤a¤\textsubumlaut{A}\textsubumlaut{a}A"a"\textsubw{A}\textsubw{a}A §a§\textsubwedge{A}\textsubwedge{a}A8a8\textsuperimposetilde{A}\textsuperimposetilde{a}A 4a4\textsyllabic{A}\textsyllabic{a}£ A£ a\texttildedot{A}\texttildedot{a}bA b a\texttoptiebar{A}\texttoptiebar{a}A a\textvbaraccent{A}\textvbaraccent{a}tipa deﬁnes shortcut sequences for many of the above.See the tipa documentation for more information.Table14:wsuipa Text-mode AccentsA g a g\dental{A}\dental{a}A a \underarch{A}\underarch{a}Table 15:phonetic Text-mode AccentsA {a {\hill{A}\hill{a}©A ©a \rc{A}\rc{a}A ˜a˜\ut{A}\ut{a}A ˚a ˚\od{A}\od{a}Aa \syl{A}\syl{a}{A {a\ohill{A}\ohill{a}A ..a ..\td{A}\td{a}The phonetic package provides a few additional macros for linguistic accents.\acbar and \acarc compose characters with multiple accents;for example,\acbar{\’}{a}produces “´¯a ”and \acarc{\"}{e}produces “¨¯e ”.\labvel joinstwo characters with an arc:\labvel{mn}→“ mn”.\upbar is intended to gobetween characters as in “x\upbar{}y’’→“x y”.Lastly,\uplett behaves like \textsuperscript but uses a smaller font.Contrast “p\uplett{h}’’→“p h ”with “p\textsuperscript{h}’’→“p h ”.Table 16:wsuipa Diacriticss \ain v \leftp x \overring h \stress }\underwedge k \corner n \leftt ~\polishhook j \syllabic t \upp u \downp q \length w \rightp r \underdots l\uptm \downt{\midtilde o \rightt y \underring p\halflengthz\openi\secstress|\undertildeThe wsuipa package deﬁnes all of the above as ordinary characters,not as accents.However,it does provide \diatop and \diaunder commands,which are used to compose diacritics with other characters.For example,\diatop[\overring|a]produces “x a ”,and \diaunder[\underdots|a]produces “r a ”.See the wsuipa doc-umentation for more information.Table 17:textcomp Diacritics˝\textacutedbl ˇ\textasciicaron ¯\textasciimacron ´\textasciiacute ¨\textasciidieresis ̏\textgravedbl˘\textasciibreve`\textasciigraveThe textcomp package deﬁnes all of the above as ordinary characters,not as accents.Table 18:textcomp Currency Symbols฿\textbaht $\textdollar\textguarani ₩\textwon ¢\textcent$\textdollaroldstyle ₤\textlira ¥\textyen¢\textcentoldstyle ₫\textdong ₦\textnaira ₡\textcolonmonetary €\texteuro \textpeso¤\textcurrencyƒ\textflorin£\textsterlingTable19:marvosym Currency Symbols¢\Denarius e\EUR D\EURdig e\EURtm£\Pfund\Ecommerce d\EURcr c\EURhv¦\EyesDollar¡\Shilling The diﬀerent euro signs are meant to be compatible with diﬀerent fonts—Courier (\EURcr),Helvetica(\EURhv),Times(\EURtm),and the marvosym digits listed in Table134(\EURdig).Table20:wasysym Currency Symbols¢\cent¤\currencyTable21:eurosym Euro SignsA C\geneuroB C\geneuronarrow C\geneurowide e\officialeuro\euro is automatically mapped to one of the above—by default,\officialeuro—based on a eurosym package option.See the eurosym documentation for more information.The\geneuro...characters are generated from the current body font’s“C”character and therefore may not appear exactly as shown.Table22:textcomp Legal Symbols℗\textcircledP c○©\textcopyright℠\textservicemark \textcopyleft r○®\textregistered TM™\texttrademarkWhere two symbols are present,the left one is the“faked”symbol that L A T E X2εprovides by default,and the right one is the“true”symbol that textcomp makes available.See /cgi-bin/texfaq2html?label=tradesyms for solu-tions to common problems that occur when using these symbols(e.g.,getting a“r○”when you expected to get a“®”).Table23:textcomp Old-style Numerals0\textzerooldstyle4\textfouroldstyle8\texteightoldstyle1\textoneoldstyle5\textfiveoldstyle9\textnineoldstyle2\texttwooldstyle6\textsixoldstyle3\textthreeoldstyle7\textsevenoldstyleRather than use the bulky\textoneoldstyle,\texttwooldstyle,mands shown above,consider using\oldstylenums{...}to typeset an old-style number.。

Laplace_Transforms

A Useful Analogy.
To understand the Laplace transform, use of the Laplace to solve differential equations, and the relationship between the s-domain and the time doห้องสมุดไป่ตู้ain it is useful to consider the logarithm function.
An Important Limitation.
The Laplace transform and techniques related to it are only applicable to systems described by linear constant-coefficient models.
Using the Laplace Transform.
In order to apply the technique described above, it is necessary to be able to do the forward and inverse Laplace transforms. Although in principle, you could do the necessary integrals, people have been doing those integrals for centuries. They have them pretty well figured out by now, and you’ve got better things to do. So a better plan is to use a table of Laplace transforms. The book has a pretty good table, but we’ll provide a larger table. The table is used primarily for the inverse transform, and for transforming inputs. For other parts of your equation(s), it is only necessary to know a few properties of the Laplace transform. Some of these are derived in Appendix II, but you only need to be able to use them, not derive them. Linearity: (both superposition and homogeneity):

[数学]拉普拉斯变换 Laplace Transform

Poularikas A. D. “Laplace Transforms” The Handbook of Formulas and Tables for Signal Processing. Ed. Alexander D. Poularikas Boca Raton: CRC Press LLC,1999
0
∫ F(s ′) ds ′
s T − st
∞
15.
f (t) periodic
∫e L { f (t )} =
f (t ) dt f (t ) = f (t + T )
1 − e − sT
2.2.2 Methods of Finding the Laplace Transform
1. 2. 3. 4. Direct method by solving (2.1.1). Expand f (t) in power series if such an expansion exists. Differentiation with respect to a parameter. Use of tables.
F( s) =
∫ f (t ) e
0
∞
− st
dt
s = σ + jω
f (t) = piecewise continuous and of exponential order
2 Transform
f (t ) = 1 2 πj
σ+ j ∞
σ− j ∞
∫ F( s) e
st
ds
where the integration is within the regions of convergence which is a vertical strip σ1 < Re{s} < σ2.

Laplace_Table

0 ¥
If n is a positive integer then,
G ( n + 1) = n !
The Gamma function is an extension of the normal factorial function. Here are a couple of quick facts for the Gamma function G ( p + 1) = pG ( p ) p ( p + 1)( p + 2 )L ( p + n - 1) = æ1ö Gç ÷ = p è2ø G ( p + n) G( p)
2
+ b2 -b
n +1 2
(s - a)
2
+ b2 - b2
b
s-a
(s - a)
2
(s - a)
2
n!
(s - a)
1 æsö Fç ÷ c ècø e - cs e - cs L { g ( t + c )}
uc ( t ) f ( t - c ) ect f ( t ) 1 f (t ) t
(s
+ a2 )
10. 12.
(s
+ a2 )
2
13. 15. 17. 19. 21. 23. 25. 27. 29. 31. 33. 35. 37.
(s + a ) s (s - a ) (s + a )
2 2 2 2 2 2 2 2
2a 3
14. 16. 18. 20. 22. 24. 26. 28. 30. 32. 34. 36.
© 2004 Paul Dawkins

PolesandZerosofTransferFunctions：传递函数的零点和极点

Poles and Zeros of Transfer FunctionsMost circuits we consider, in practice, are discrete (circuit parameters such as R s, L s and C s, appear in discrete lumps, rather than smears, as they do intransmission lines), time invariant (the values of circuit parameters such as R s, L s and C s, so not change with time), and linear (the i-v relationships of the circuit elements, such as R s, L s and C s, are given by mathematically linear relations of i , v and their derivatives). For such ordinary circuits, all transfer functions can be written as the ratio of polynomials in the variable, s :()()()N s T s D s = where ()N s is the numerator polynomial and ()D s is the denominator polynomial.A function such as ()T s which can be expressed as a ratio of polynomials iscalled a rational function . A polynomial in s , recall, is a weighted sum of the powers of s up to some finite maximum power of s . For example,()212102P s s s =++is a polynomial. Because its highest power of s is 2, this particular polynomial is said to be a second-degree polynomial. (The function s e -, as an example, is not a polynomial because its Taylor series expansion is an infinite series of terms of increasingly higher powers of s .)The degree of the denominator polynomial, ()D s , for a transfer function basically is given by the number of energy storage elements (inductors and capacitors) in the circuit, although series or parallel combinations of inductors or capacitors that can be reduced to a single element count only once. The degree of the numerator polynomial, ()N s , is usually less than or equal to the degree of the denominator polynomial.Any polynomial of degree n can be factored into the product of n terms of the form ()s a +, where a is a constant. For example, we can factor thepolynomial ()212102P s s s =++ as follows:()()()212102223P s s s s s =++=++In this example, the constants in each factor are real integers. This circumstance is atypical. Often, the constants are complex irrational numbers. For example, the polynomial ()21P s s s =-+ requires complex constants in its factors:()211122P s s s s s ⎛=-+=-+-- ⎝⎭⎝⎭ If ()N s is a polynomial of degree m and if ()D s is a polynomial of degree n , then we can write transfer functions in factored form:()()()()()()()1212m n s z s z s z T s K s p s p s p --⋅⋅⋅-=--⋅⋅⋅- where the constants 12,,...,m z z z are called the zeros of the transfer function, ()T s , the constants 12,,...,n p p p are called the poles of the transfer function and K is some constant. The poles and zeros are not necessarily unique. That is,some factors may be repeated. Note that ()T s is completely specified by its poles, its zeros and the constant K . That is, ()T s can be reconstructed exactly if we know these 1m n ++ quantities.Should the value of s ever equal any one of the zeros, 12,,...,m z z z , say k z , of ()T s , note that()0k T z =Hence, the name zeros. Of course some of the zeros may be complex, so for these, ()T s achieves zero value only when s takes on complex values. We thus will find it necessary to consider s to be a complex variable. That is, it can take on values in the complex s -plane, a plane with real and imaginary axes. In thiscomplex s-plane, for example, we can plot the zeros112z j =+ 212z=-that we found earlier for the polynomial ()211122P s s s s s ⎛=-+=-+-- ⎝⎭⎝⎭as follows:In this example, note that the two zeros of ()P s lie in symmetric positions with respect to the horizontal axis. In the language of complex numbers, z 1 and z 2 are said to be complex conjugates : their real parts are identical and their imaginary parts have the same magnitude but opposite signs. If two numbers, z 1 and z 2, are complex conjugates, the customary notation is that 21*z z = or, of course, 12*z z =. If we think of conjugation as an operator, it has the effect of reversing the sign ofthe imaginary part of a complex number. For example, if112z j =+and 212z =-then12*11*2222z j j z ⎛=+=- ⎝⎭We now demonstrate an important result known as the conjugate law for transfer functions : the poles and zeros of a transfer function,()()()N s T s D s = either (1) lie on the real axis of the s -plane or (2) occur in complex conjugate pairs.To begin demonstration of this result, note that the coefficients of s in ()N s and ()D s are real numbers because they are just combinations of the various (real) circuit parameters (R s, L s, Cs and so forth). For any polynomial, ()P s , with real coefficients for the powers of s , it is true that()()**P s P s = For a specific example, suppose()246116P s s s =++in which, we note, all coefficients of s are real. Thus, we see()()()2***46116P s s s =++ ()()**246116P s s s =++()()()()***P s P s P s =≡ The key to obtaining this result is that the coefficients of s in the polynomial are real.We now apply this result separately to the polynomials ()N s and ()D s . For any of the zeros of the transfer function, say, k z , we have()0k N z =If we take the complex conjugate of this equation, we see()*0k N z =From the conjugate law, we have()*0k N z = Thus, we have the result that if k z is a zero of ()T s , then *k z also is a zero of()T s . Thus, unless k z is real, it is a member of a complex conjugate pair of zeros. We conclude that the zeros of ()T s either are real or occur in complex conjugate pairs.What about the poles of ()T s ? For any of the poles, say, k p , we have()0k D p =If we take the complex conjugate of this equation, we see()*0k D p =From the conjugate law, we have()*0k D p =Thus, we have the result that if k p is a pole of ()T s , then *k p also is a pole of ()T s . Thus, unless k p is real, it is a member of a complex conjugate pair of poles.We conclude that the poles of ()T s either are real or occur in complex conjugate pairs.These two results, for the poles and zeros of ()T s , demonstrate the conjugate law for ()T s . Because of the conjugate law, a plot in the s -plane of the locations of the poles and zeros of ()T s are always symmetric about the real axis in the s -plane. Consider, for example,Because a pole-zero plot such as this shows the location of all poles and zeros of ()T s and because ()T s can be constructed from its poles and zeros (plus the constant, K , which can be determined if the value of ()T s is known for a single value of s ), the pole-zero plot can serve as an alternative representation to the rational (ratio of polynomials) function representation of ()T s .We have already mentioned that inverting ()out V s to obtain ()out v t can involve a lot of effort. This difficulty provides strong motivation to learn as much as possible about the behavior of ()out v t from investigating ()out V s without going through the trouble of inverting it. After all, ()out V s contains precisely the same information as ()out v t since ()out v t can be reconstructed from ()out V s . Laplace transform theoryprovides two results, the initial value and the final value theorems, that give bits of information about ()out v t directly from ()out V s : ()()0lim out out s v sV s +→∞= ()()0lim out out s v sV s +→∞=These results, valid when the limits exist, give the initial and final values of ()out v t directly from ()out V s without inverting ()out V s . The final value theorem can give information about the ultimate stability of an amplifier – if ()out v ∞→∞, then the amplifier clearly is unstable. Unfortunately, the output of unstable amplifiers typically is an exponentially growing sinusoid, which oscillates between ±∞. In such cases, the limit in the final value theorem does not exist, so that theorem provides no information. We obtain a more useful test for stability by applying a partial fraction expansion to ()out V s .For present purposes, we consider an amplifier to be stable if, in response to an impulse, ()t δ, to its input, the output, ()out v t , of the amplifier eventuallyapproaches zero. By applying an impulse to the input, we are applying all possible frequencies simultaneously. We will therefore excite any instability in the amplifier, regardless of its frequency. If the input is an impulse at 0t =, then we have()(){}(){}1in in V s L v t L t δ===where {}L ⋅ indicates Laplace transformation. Thus, for the purpose of examining stability of an amplifier, we have:()()()()()()()()()()1212m out in n s z s z s z V s T s V s T s K s p s p s p --⋅⋅⋅-===--⋅⋅⋅- The idea of a partial fraction expansion is that a rational function, such as ()T s , can be expanded as the sum of simpler rational functions, each of which has only one pole (although, in certain cases the pole can be repeated). If, for simplicity, we assume that none of the poles of ()T s is repeated, its partial fraction expansion takes the form()1212......k n k nA A A A T s s p s p s p s p ≡+++++---- where ,1,2,...,k A k n =, are complex constants that are chosen so that the identity holds for all s . If ()T s has repeated poles, then its partial fractionexpansion is slightly more complicated, but our main results do not change. As we’ve seen, each of the poles 12,,...,n p p p can have both real and imaginaryparts: k k k p j οω=+Thus, we can write()121122......k n out k k n nA A A A V s s j s j s j s j οωοωοωοω=+++++-------- By taking the inverse Laplace transform (from a table of transforms), we see()112212......k k n n t j t t j t t j t t j t out k n v t Ae A e A e A e οωοωοωοω++++=+++++ Because the poles of ()T s are either real or occur in complex conjugate pairs, more detailed calculations show that the terms can be grouped to show explicitly that the right hand side of this equation is real, as required (since ()out v t must be real). Those details are of little concern to our stability analysis, however. We note that if all of the 0,1,2,...,k k n ο<=, then each term produces damped oscillations, so that the output, ()out v t , approaches zero for long times. That is, an amplifier is stable if all poles of its transfer function, ()T s , lie in the left half of the s-plane . If even one 0k ο≥, however, then the corresponding term produces exponentially growing oscillations for long times. That is , an amplifier is unstable if at least one pole of its transfer function lies in the right half s-plane . Incidentally, we consider a transfer function with poles on the imaginary axis to be unstable, even though the corresponding terms do not approach infinity because ()out v t does not approach zero after long times. It oscillates.。

常见函数的拉普拉斯变换

s2 (s2 − a2 )2
s3 (s2 − a2 )2
s2 (s2 − a2)3/2
1 (s2 + a2 )3
s (s2 + a2 )3
s2 (s2 + a2 )3
s3 (s2 + a2 )3
F(t)
ebt cosh at
ebt − eat b− a
bebt − aeat b− a
sin at − at cos at 2a3ቤተ መጻሕፍቲ ባይዱ
1 s−a +b
F(t)
eat /2 ⎧
3a
⎨cos ⎩
3at 2
+
3 sin
3at 2
−
e−3at
/
2
⎫ ⎬
⎭
1 3
⎛ ⎝⎜e
−
at
+
2eat /2
cos
3at⎞ 2 ⎠⎟
e−at / 2 3a2
⎧ ⎨e3at /2 ⎩
−
cos
3at 2
−
3 sin
3at ⎫
2
⎬ ⎭
e−at /2 ⎧
3a
⎨ ⎩
3 sin
F(n)(t)
33.10.
f ′(s)
–tF(t)
33.11. 33.12. 33.13.
33.14.
f ′′(s)
f (n)(s)
f (s) s
f (s) sn
t2F(t)
(–1)nt nF(t)
t
∫0 F(u)du
∫ ∫ ∫ t 0
t
F(u)dun =
0
t (t − u)n−1 0 (n − 1)! F(u)du

DB33∕T 1136-2017 建筑地基基础设计规范

5
地基计算 ....................................................................................................................... 14 5.1 承载力计算......................................................................................................... 14 5.2 变形计算 ............................................................................................................ 17 5.3 稳定性计算......................................................................................................... 21
主要起草人：施祖元刘兴旺潘秋元陈云敏王立忠李冰河（以下按姓氏拼音排列）蔡袁强陈青佳陈仁朋陈威文陈舟樊良本胡凌华胡敏云蒋建良李建宏王华俊刘世明楼元仓陆伟国倪士坎单玉川申屠团兵陶琨叶军徐和财许国平杨桦杨学林袁静主要审查人：益德清龚晓南顾国荣钱力航黄茂松朱炳寅朱兆晴赵竹占姜天鹤赵宇宏童建国浙江大学参编单位：（排名不分先后）浙江工业大学温州大学华东勘测设计研究院有限公司浙江大学建筑设计研究院有限公司杭州市建筑设计研究院有限公司浙江省建筑科学设计研究院汉嘉设计集团股份有限公司杭州市勘测设计研究院宁波市建筑设计研究院有限公司温州市建筑设计研究院温州市勘察测绘院中国联合工程公司浙江省电力设计院浙江省省直建筑设计院浙江省水利水电勘测设计院浙江省工程勘察院大象建筑设计有限公司浙江东南建筑设计有限公司湖州市城市规划设计研究院浙江省工业设计研究院浙江工业大学工程设计集团有限公司中国美术学院风景建筑设计研究院华汇工程设计集团股份有限公司

OB5269 65W Demo Board Manual

No load standby power under 100mW@264VacAveraged efficiency more than 88%@115/230Vac at AWG18 cable endTurn on Delay Time<500mSecProgrammable OTP/OVP with latch shutdowno nf i de nt i al toKContents Index1Adapter Module Specification...........................................................................................................4 1.1 Input Characteristics.....................................................................................................................4 1.2 Output Characteristics..................................................................................................................4 1.3 Performance Specifications..........................................................................................................4 1.4 Protection Features......................................................................................................................4 1.5 Environments.. (4)2 Adapter Module Information (5)2.1 Schematic.....................................................................................................................................5 2.2 Bill of material.................................................................................................................................5 2.3 PCB Gerber File..............................................................................................................................7 2.4 Transformer Design......................................................................................................................8 2.4.1 Transformer Specification........................................................................................................8 2.4.2 Transformer Winding data.......................................................................................................8 2.2 Adapter Module Snapshot (9)3 Performance Evaluation (10)3.1 Input Characteristics....................................................................................................................11 3.1. 1 Input current and Standby power............................................................................................11 3.1. 2 Efficiency.................................................................................................................................11 3.2 Output Characteristics.................................................................................................................11 3.2.1 Line Regulation & Load Regulation..........................................................................................11 3.2.2 Ripple & Noise.........................................................................................................................12 3.2.3 Overshoot & Undershoot.......................................................................................................13 3.2.4 Dynamic Test.........................................................................................................................14 3.2.5 Time Sequence......................................................................................................................14 3.3 Protections..................................................................................................................................15 3.3.1 Over Current Protection (OCP).............................................................................................15 3.3.2 Over Voltage Protection (OVP)..............................................................................................15 3.3.3 Over Load Protection (OLP)..................................................................................................16 3.3.4 Over Temperature Protection (OTP)......................................................................................16 3.4 EMI Test......................................................................................................................................17 3.4.1 Conduction EMI Test..................................................................................................................17 3.4.2 Radiation EMI Test.....................................................................................................................19 3.5 Thermal Test. (20)4 Other important waveform (20)4.1 CS, FB, Vdd & Vds waveform at no load/full load......................................................................20 4.2 Vds waveform at full load, start/normal/output short..................................................................21 4.2.1 VDS at full load, start/normal/output short..............................................................................21 4.2.2 Vds at full load, start waveform...............................................................................................21 4.2.3 Vds at full load, normal waveform...........................................................................................21 4.2.4 Vds at full load, output short waveform.. (21)On -B ri g ht Co nf i de nt i a l toKt ecFigures IndexFig. 1 R&N waveform@90Vac; no load CH2:Vout_Ripple,..................................................................12 Fig. 2 R&N waveform@90Vac; full load, CH2:Vout_Ripple....................................................................12 Fig. 3 R&N waveform@264Vac; no load, CH2:Vout_Ripple...................................................................12 Fig. 4 R&N waveform@264Vac; full load, CH2:Vout_Ripple..................................................................12 Fig. 5 Overshoot waveform@90Vac; full load, CH2:Vout........................................................................13 Fig. 6 Overshoot waveform @90Vac; no load, CH2:Vout.......................................................................13 Fig. 7 Overshoot waveform @264Vac; full load, CH2:Vout ....................................................................13 Fig. 8 Overshoot waveform @264Vac; no load, CH2:Vout.....................................................................13 Fig. 9 Undershoot waveform@90Vac; full load,, CH2:Vout ....................................................................13 Fig. 10 Undershoot waveform @264Vac; full load, CH2:Vout ................................................................13 Fig. 11 Dynamic waveform@90Vac input, CH1;Vout..............................................................................14 Fig. 12 Dynamic waveform@264Vac input, CH1;Vout............................................................................14 Fig. 13 Turn on delay waveform @90Vac; full load,CH1:Vout,CH2:Vin..................................................14 Fig. 14 Hold up time waveform @100Vac; full load, CH1:Vout,CH2:Vin ................................................15 Fig. 15 Hold up time waveform @240Vac; full load, CH1:Vout,CH2:Vin ................................................15 Fig. 16 OVP waveform @90Vac; no load,CH1:Vout,CH2:Vdd................................................................15 Fig. 17 OVP waveform @264Vac;no load, CH1:Vout,CH2:Vdd..............................................................15 Fig. 18 OLP waveform @90Vac; over load,CH1:FB,CH2:Vds,CH3:Vdd,CH4:Vcs.................................16 Fig. 19 OLP waveform @264Vac;over load, CH1:FB,CH2:Vds,CH3:Vdd,CH4:Vcs............................16 Fig. 20 CS,FB,Vdd&Vdswave form@90Vac; no load, CH1:FB,CH2:Vds,CH3:Vdd,CH4:Vcs................20 Fig. 21 CS,FB,Vdd&Vdswave form@90Vac; full load, CH1:FB,CH2:Vds,CH3:Vdd,CH4:Vcs................20 Fig. 22 CS,FB,Vdd&Vdswave form@264Vac; no load, CH1:FB,CH2:Vds,CH3:Vdd,CH4:Vcs..............20 Fig. 23 CS,FB,Vdd&Vdswave form@264Vac; full load, CH1:FB,CH2:Vds,CH3:Vdd,CH4:Vcs..............20 Fig. 24 Vds start waveform@264Vac; full load,CH2:Vds........................................................................21 Fig. 25 Vds Normal waveform@264Vac; full load, CH2:Vds..................................................................21 Fig. 26 Vds ,CS output short waveform@264Vac; full load,. (21)Tables IndexTable 1 Input current at full load...............................................................................................................11 Table 2 Standby power at no load............................................................................................................11 Table 3 Efficiency......................................................................................................................................11 Table 4 Line Regulation & Load Regulation.............................................................................................11 Table 5 Ripple & Noise measure results .................................................................................................12 Table 6 Overshoot/undershoot measurement results..............................................................................13 Table 7 Output voltage under dynamic test.............................................................................................14 Table 8 Turn-on delay /hold-up/Rise time measurement results.............................................................14 Table 9 OCP value vs. input voltage........................................................................................................15 Table 10 Load OVP test result.. (15)On -B ri g ht Co nf i de nt i a l toKt ec1 Adapter Module Specification1.1 Input CharacteristicsAC input voltage rating 100Vac ~ 240Vac AC input voltage range 90Vac ~ 264Vac AC input frequency range 47Hz ~ 63Hz Input current1.8 Arms max.1.2 Output CharacteristicsOutput Voltage19.0VOutput Tolerance ±5% Min. load current 0A Max. load current3.42A1.3 Performance SpecificationsMax. Output Power 65WStandby Power <100mW @ 264V/50Hz, no loadEfficiency >87%，Meet EPS2.0 level 5Line Regulation ±2% Load Regulation ±5%Ripple and Noise <200mVpk-pkHold up Time10mSec. Min. @100Vac with full loadTurn on Delay Time500mSec. Max. @90Vac with full load1.4 Protection FeaturesShort Circuit Protection Output shut down with auto-recovery Over Voltage Protection Output shut down with latch Over Current Protection Output shut down with auto-recovery Over Temperature ProtectionOutput shut down with latch1.5 EnvironmentsOperating Temperature 0℃ to +40℃ Operating Humidity 20% to 90% R.H. Storage Temperature -40℃ to +60℃Storage Humidity0% to 95% R.H.On -B ri g ht Co nf i de nt i a l toKt ecnt i a l toKt ec2.3 PCB Gerber FileOn -B ri g ht Co nf i de nt i a l toKt ec2.4.2 Transformer Winding dataWinging MaterialTurns 1 N1 0.5 2UEW 19 TAPE TAPE W=10.5mm (Y) 2 3 N2 Φ0.20*6 2UEW 7 TAPE TAPE W=10.5mm (Y) 2 5 N3 Φ0.45*2 triple insulated TAPE TAPE W=10.5mm (Y) 7 N4 0.45*2 triple insulated 8 TAPE TAPE W=10.5mm (Y) 9 N5 Φ0.20*6 2UEW NC 10 TAPE TAPE W=10.5mm (Y) 11 N6 0.5 2UEW 12 TAPE TAPE W=10.5mm (Y) 13 N7 0.23 2UEW 10 14 TAPE TAPE W=10.5mm (Y) Notes: Core connected to GND(PIN3)n -B ri g ht Co nf i dl to2.2 Adapter Module SnapshotOn -B ri g h t C o n f i de nt i a l toKt ecCH2:Vout_Ripplen -B ri g ht Co nf i de nAc input switches ON for overshoot and OFF for undershoot Overshoot/undershoot measurement resultsItem Measure Data (%) Waveformovershoot 2.5 Fig.5undershoot 2.1 Fig.6overshoot 1.7 Fig.7undershoot overshoot 2.5 Fig.8undershoot 1.3 Fig.9overshoot 1.7 Fig.10undershoot Fig. 5 Overshoot waveform@90Vac; full load, CH2:VoutFig. 6 Undershoot waveform @90Vac; Full load, CH2:Vout Fig. 7 Overshoot waveform @90Vac; No load, CH2:VoutFig. 8 Overshoot waveform @264Vac; Full load, CH2:Vout Fig. 9 Undershoot waveform@264Vac; full load,, CH2:VoutFig. 10 Undershoot waveform @264Vac; No load, CH2:Voutn -B ri g ht Co nf i de nt i a l toKt ecDynamic waveformFig. 11 Dynamic waveform@90Vac input, CH1;VoutFig. 12 Dynamic waveform@264Vac input, CH1;Vout3.2.5 Time SequenceLoad condition: Full load Table 8 Turn-on delay /hold-up/Rise time measurement resultsItem Input voltage Meas. Data (S)Remark Turn-on delay time 90V/60Hz 430mS Fig.13 Hold-up time 100V/60Hz 11.1mS Fig.14 Hold-up time 240V/60Hz 97.4mSFig.15Time sequence waveformFig. 13 Turn on delay waveform @90Vac; full load,CH1:Vout,CH2:Vinn -B r i g h t Co n f i de nt i al toKFig. 14 Hold up time waveform @100Vac; full load, CH1:Vout,CH2:Vin Fig. 15 Hold up time waveform @240Vac; full load, CH1:Vout,CH2:Vin3.3 Protections3.3.1 Over Current Protection (OCP)The power supply will shut down auto-recovery when output current exceeds 4.3～5.0A, and it should recover when the over current condition is removed.Table 9 OCP value vs. input voltage 115V/60Hz230V/50Hz 264V/50Hz 4.56A 4.66A 4.77A4.53A4.65A 4.76A3.3.2 Over Voltage Protection (OVP)The power supply will shut down and latch when feedback circuit is disabled, and the output voltage can not be over 31V. The unit should recover when the protection condition is removed and restart input.OVP Trigger Voltage (V)No Load90V/60Hz 29.3264V/50Hz 30.6Fig. 16 OVP waveform @90Vac; no load,CH1:Vout,CH2:VddFig. 17 OVP waveform @264Vac;no load, CH2:Vout,CH3:Vddn -B ri ghf i de nt i al toKt ec3.3.3 Over Load Protection (OLP)The power supply will shut down auto-recovery when output current exceeds OCP and it should recover when the over current condition is removed.Fig. 18 OLP waveform @90Vac; overload,CH1:FB,CH2:Vds,CH3:Vdd,CH4:Vcs Fig. 19 OLP waveform @264Vac;over load, CH1:FB,CH2:Vds,CH3:Vdd,CH4:Vcs3.3.4 Over Temperature Protection (OTP)The power supply will shut down and latch when the voltage of RT pin is under 1.0V(OTP), and the unit should recover when the protection condition is removed and restart input.On -B ri g ht Co nf i de nt i a l toKt ec3.4 EMI TestThe Power supply passed EN55022 Class B & FCC class B EMI requirement with more than 6dB margin3.4.1 Conduction EMI TestEN55022 CLASS B @ full load reportOn -B ri g ht Co nf i de nt i al t oKt ecFCC CLASS B @ full load reportOn -B ri g ht Co nf i de nt i a l toKt ec3.4.2 Radiation EMI TestEN55022 CLASS B @ full load reportFCC CLASS B @ full load reportOn -B ri g ht Co nf i de nt i a l toKt ecFig. 20 CS,FB,Vdd&Vds waveform@90Vac; no load, CH1:FB,CH2:Vds,CH3:Vdd,CH4:VcsFig. 21 CS,FB,Vdd&Vds waveform@90Vac; full load, CH1:FB,CH2:Vds,CH3:Vdd,CH4:VcsFig. 22 CS,FB,Vdd&Vds waveform@264Vac; no load, CH1:FB,CH2:Vds,CH3:Vdd,CH4:Vcs Fig. 23 CS,FB,Vdd&Vds waveform@264Vac; full load, CH1:FB,CH2:Vds,CH3:Vdd,CH4:Vcsn -B ri g ht Co nf i de nt i aFig. 24 Vds start waveform@264Vac; full load,CH2:Vds4.2.3 Vds at full load, normal waveformFig. 25 Vds Normal waveform@264Vac; full load, CH2:Vds4.2.4 Vds at full load, output short waveformFig. 26 Vds output short waveform@264Vac; full load,n -B ri g ht Co nf i deDisclaimerOn-Bright Electronics reserves the right to make corrections, modifications, enhancements, improvements, and other changes to its documents, products and services at any time and to discontinue any product or service without notice. Customers should obtain the latest relevant information before placing orders and should verify that such information is current and complete.This document is under copy right protection. None of any part of document could be reproduced, modified without prior written approval from On-Bright Electronics.On -B ri g ht Co nf i de nt i a l toKt ec。

Z-Transform(Z变换).

49Chapter 10 The Z -Transform10.1 The Z-Transform （Z 变换）10.2 The Region of Convergence for theProperty 2: The ROC does not contain any poles.ROC 内不包括任何极点。

Property 6: If x [n ] is two sided, and if the circle |z |= r 0 is in the ROC, then the ROC will consist of a ring in the z-plane that includes the circle |z |= r 0 . 如果x (t )是双边序列，而且如果|z |= r 0的圆位于ROC 内，那么该ROC 就一定是由包括|z |= r 0的圆环所组成。

50Z-Transform （Z 变换收敛域）10.3 The Inverse Z-Transform （Z 反变换）.111)(][R ROC z X n x ZT =−→←222)(][R ROC z X n x ZT =−−→←R ROC z X n x ZT=−→←)(][10.4 Geometric Evaluation of the Fourier Transform from the Pole-Zero Plot (由零极点图对傅立叶变换进行几何求值)10.7 Analysis and Characterization of LTI Systems Usingthe Z-Transform (利用Z 变换分析和表征LTI 系统)2. Stability (稳定性))()()(z H z X z Y =521. Systems functions for interconnections of LTI systems 10.8 System Function Algebra and Block Diagram Representations （系统函数的代数属性与方框图表示）53。

z变换到差分方程

z变换到差分方程z变换（Z-transform）是一种在数字信号处理中广泛应用的数学工具，用于将离散时间域中的信号转换为连续时间域中的信号，从而更方便地对信号进行分析与处理。

通常情况下，我们可以将差分方程（difference equation）通过Z变换来求解，从而得到其对应的Z变换函数（Z-transform function）。

具体地说，对于给定的差分方程：y(n) + a1*y(n-1) + a2*y(n-2) + ... + ak*y(n-k) = b0*x(n) + b1*x(n-1) + b2*x(n-2) + ... + bm*x(n-m)其中，y(n)和x(n)分别表示输出和输入信号在时间点n的取值，a1、a2、…、ak和b0、b1、…、bm为常数系数，k和m为差分方程的阶数。

我们可以通过将差分方程中的所有项进行变换，得到其对应的Z变换函数：Y(z) + a1*Y(z)*z^{-1} + a2*Y(z)*z^{-2} + ... + ak*Y(z)*z^{-k} =b0*X(z) + b1*X(z)*z^{-1} + b2*X(z)*z^{-2} + ... + bm*X(z)*z^{-m}其中，Y(z)和X(z)分别表示输出和输入信号的Z变换函数，z^{-n}表示Z域中的时间延迟，也可以将其视为离散时间域中的退化因子，它对应的函数形式为z^{-n} = e^{-jwn}，其中w为频率。

通过对上述等式进行变换和整理，我们可以将Y(z)和X(z)表示为如下形式：Y(z) = [b0*X(z) + b1*X(z)*z^{-1} + b2*X(z)*z^{-2} + ... +bm*X(z)*z^{-m}] / [1 + a1*z^{-1} + a2*z^{-2} + ... + ak*z^{-k}]X(z) = [X(z) + X(z)*z^{-1} + X(z)*z^{-2} + ... + X(z)*z^{-m}] / [m0 + b1*z^{-1} + b2*z^{-2} + ... + bm*z^{-m}]其中，Y(z)表示差分方程的输出信号的Z变换函数，X(z)表示差分方程的输入信号的Z变换函数。

关于卧室的英语作文

关于卧室的英语作文As the sun dips below the horizon, casting a warm glow through the curtains, my bedroom transforms into a haven of tranquility. This is not just a place where I sleep, but a space that reflects my personality and serves as a sanctuary for relaxation and rejuvenation.The room is adorned with a comfortable queen-sized bed, dressed in soft, pastel-colored linens that invite sweet dreams. A collection of fluffy pillows, each with a unique pattern, adds a touch of whimsy and comfort. Above the bed, a vintage wooden headboard serves as a statement piece, its intricate carvings a testament to craftsmanship.To the right of the bed, a floor-to-ceiling bookshelf stands proudly, its shelves laden with an eclectic mix of novels, biographies, and coffee table books. A small reading nook, complete with a plush armchair and a floor lamp, is tucked into the corner, providing the perfect spot for late-night reads.Opposite the bed, a large window allows natural light toflood the room, while a set of sheer and blackout curtains ensure privacy and control over the room's ambiance. During the day, the sheer curtains billow gently with the breeze, creating a serene atmosphere.A small writing desk by the window is where I pen my thoughtsand plan my days. It's a simple yet functional space, with a laptop, a stack of notebooks, and a few inspirational quotes framed on the wall above.The walls of my bedroom are a soothing shade of blue, reminiscent of a cloudless sky, and they are adorned with afew pieces of abstract art that I've collected over the years. Each piece has a story, and they add a personal touch to the room.In the corner opposite the bookshelf, a small area is dedicated to yoga and meditation. A soft rug, a couple of candles, and a small table with a singing bowl create a peaceful space for mindfulness and self-care.The room is not overly large, but it's designed in a way that maximizes the use of space without feeling cluttered. Every piece of furniture, every decoration, has a purpose and contributes to the overall atmosphere of calm and contentment.In essence, my ideal bedroom is a harmonious blend of comfort, functionality, and personal expression. It's a place where I can escape the hustle and bustle of the world outside, andit's a space that inspires both relaxation and creativity.。

擦桌子的作文

擦桌子的作文英文回答：Cleaning the table is a seemingly mundane task, but it can be transformed into a mindful act by paying attention to the present moment and focusing on the sensations involved. 。

As I reach for the damp cloth, I feel its cool,slightly rough texture against my fingertips. The cloth slides effortlessly across the smooth surface of the table, leaving behind a streak-free shine. The rhythmic motion of my hand becomes hypnotic, and I find myself lost in the process. 。

The faint scent of polish fills the air, reminding me of the many hands that have touched this table before me. I imagine the conversations that have taken place over its surface, the laughter and tears that have been shared. The table becomes more than just a piece of furniture; ittransforms into a repository of stories and memories. 。