Ch5 Elasticity and Its__ Application

ⅠFill-in-the-Blank2. C12 has 6 protons（质子）. How many protons does C13 （中子）does C13 have? _7_ Nitrogen-14 (N14) has 6 protons and 8 neutrons: true or false?_false_4. The type of metamorphism that occurs over large areas, commonly at convergent platedisturbed after lithification.ⅡShort Answer Question1.What is the difference between an active volcano and a dormant volcano?2.What does a porphyritic texture tell about the history of an igneous rock?3.Briefly explain why the study of sedimentary environments is important in the studyof historical geology.4.What is the difference between slate and phyllite?5.What kind of rocks (igneous, sedimentary, metamorphic) have been most importantin determining absolute age dates for the geologic time scale? Explain why.6.What are the six fundamental geologic principles which are used in relative dating?7.Explain the differences between the magnitude and the intensity of an earthquake, interms of how each is measured or observed.8.What is the difference between elastic and plastic deformation?9.What does compression stress result from?10.What causes submarine hydrothermal vents?ⅢShort Answer Essay Questions1.How do a rock and a mineral differ?2.When looking at a hand sample of an igneous rock, how would you tell if it is plutonic or volcanic?3.How does elastic rebound theory explain when earthquakes occur?4.What are some uses of metamorphic rocks such as marble, slate, sulfide ore, talc, graphite, and clay?5.Briefly explain why, according to the principle of isostasy, continental crust should be thicker than oceanic crust.• Earth is a dynamic and evolving planet.• Plate tectonic theory: The lithosphere is composed of rigid plates that diverge, converge, orslide sideways past one another as they move over the asthenosphere.• Volcanoes and earthquakes occur at the boundaries between the plates.• The rock cycle illustrates theinteractions betweenEarth’s internal andexternal processesandhow the threerock groups areinterrelated.• Geology is the study of the Earth–Physical geology is concernedwith the materials and processes whichcompose and operate onthe surface of,and within, Earth.–Historical geology is concernedwith the origin and evolution of Earth'scontinents, oceans, atmosphere, and life.• The principal subsystems of the earth:Atmosphere / Biosphere / Hydrosphere / Lithosphere / Mantle / Core.• 十大环境问题：气候变暖、臭氧层破坏、生物多样性减少、酸雨蔓延、森林锐减、土地荒漠化、大气污染、水体污染、海洋污染、固体废物污染。

一.命名规则学习建模过程，可以使用示例中的命名规则，设计标准模型参见标准模型创建方法二.确定构件使用的坐标系构件坐标系是应该首先确定并记录的信息，以方便后续确定参考点坐标。

本例中坐标轴Z轴沿模型截面中心向上，X轴为荷载施加方向，荷载沿X轴正向施加。

Y轴与模型侧面垂直。

如图所示。

三.材料定义1混凝土材料的定义相关文献：http://127.0.0.1:2180/v6.13/books/usi/default.htmhttp://127.0.0.1:2180/v6.13/books/usb/default.htm?startat=pt05ch23s06abm39 .html#usb-mat-cconcretedamagedhttp://127.0.0.1:2180/v6.13/books/usi/default.htm?startat=pt03ch12s09s02.ht mlhttp://127.0.0.1:2180/texis/search/?query=concrete+damage+plasticity&submit .x=48&submit.y=6&group=bk&CDB=v6.131.1.密度/DensityMass Density=2.5e-9 tone/mm³（=2500kg/m³）1.2.弹性/ElasticMachanical/Elasticity/Elastic定义参数：杨氏模量：Young’s Modulus=34500 N/mm²；泊松比：Poisson’s Ratio=0.21.3.塑性/Concrete Damage PlasticityMechanical/Plasticity/Concrete Damage PlasticityAbaqus/CAE User’s Guide 12.9.2_Defining concrete damage plasticity************************************************************** Dilation AngleDilation angle, , in the p–q plane. Enter the value in degrees.EccentricityFlow potential eccentricity, . The eccentricity is a small positive number that defines the rate at which the hyperbolic flow potential approaches its asymptote. The default is .fb0/fc0, the ratio of initial equibiaxial compressive yieldstress to initial uniaxial compressive yield stress. The default value isK, the ratio of the second stress invariant on the tensile meridian, , to that on the compressive meridian, , at initial yield for any given value of the pressure invariant p suchthat the maximum principal stress is negative, . It must satisfy the condition . The default value is .Viscosity ParameterViscosity parameter, , used for the visco-plastic regularization of the concrete constitutive equations inAbaqus/Standard analyses. This parameter is ignored inAbaqus/Explicit. The default value is . (Units of .) TempTemperature.Field nPredefined field variables.*************************************************************** 定义参数：扩散角：Dilation Angle=38°；偏心率：Eccentricity=0.1；（默认值）双轴压缩屈服应力与单轴压缩屈服应力的比值：fb0/fc0=1.16；（默认值）拉伸子午面与压缩子午线的第二应力不变量之比：K（K c）=2/3;粘度系数：Viscosity Parameter=默认的参数为0.0s，选取值为0.00001s一般而言，粘性系数取值越小，分析越不容易收敛。

DATASHEETModbus Master/SlaveCommunication ModuleMVI56E-MCM/MCMXTThe MVI56E Communication Module allows for Modbus Master and/or Slaveconnectivity from Rockwell Automation® ControlLogix® processors to ModbusRTU/ASCII devices. Each MVI56E port can be configured as a Master or Slave.The MVI56E-MCM and MVI56E-MCMXT act as input/output modules on theControlLogix backplane, making Modbus data appear as I/O data to the processor.Two independently configurable serial ports can operate on the same or differentModbus networks. The MVI56E-MCM is designed for standard processapplications and the MVI56E-MCMXT is designed for the Logix-XT™ controlplatform, allowing it to operate in extreme environments. It can tolerate higheroperating temperatures, and has conformal coating to protect it from harsh orcaustic conditions.Features BenefitsBackward Compatibility ♦All MVI56E products are backward-compatible with earlier MVI56 modules allowing directreplacement without the need to change existing controller programs10,000 Word Database ♦Allows you to gather more data from your devices, which improves operationalperformance♦Enjoy Enhanced features and flexibility without incurring expensive reprogramming costs Add-On Instruction ♦Module configuration stored within the RSLogix™ 5000 project (ACD file)♦No additional programming or configuration software is required♦Add-On Instruction for RSLogix 5000 version 16 or higher cuts development time andcostsCIPconnect® Enabled ♦Facilitates remote user access across the ControlLogix backplane through RockwellAutomation’s 1756-ENBT module♦Configure, diagnose, and analyze process data and communications status♦Bridge through multiple ENBT/CNBT links to connect to MVI56E-MCMs installed in remotechassis for configuration and diagnosticsAdd-On Profile ♦Simplifies adding the module in an RSLogix 5000 projectConfigurationThe module configuration is defined in the Add on Instruction. The AOI is fullycommented, and includes user-defined data types, ladder rungs and controller tags. TheAOI can be used without modification for most application.The MVI56E-MCM User Manual and sample configuration provide a quick and easyexample with step-by-step instructions on how to move data through the module fromthe Modbus network to the processor.General Specifications∙Backward-compatible with previous MVI56-MCM version∙Single Slot - 1756 ControlLogix® backplane compatible∙10/100 MB Ethernet port for network configuration and diagnostics with Auto Cable Crossover Detection∙User-definable module data memory mapping of up to 10,000 16-bit registers∙4-character, scrolling, alphanumeric LED display of status and diagnostic data in plain English∙ProSoft Discovery Service (PDS) software finds the module on the network and assigns a temporary IP address to facilitate module accessFunctional SpecificationsThe MVI56E-MCM will operate on a Local or Remote rack (For remote rack applications with smaller data packet size please refer to the MVI56E-MCMR product)∙Supports Enron version of Modbus protocol for floating-point data transactions∙PCB includes powerful Modbus network analyzer∙Special functions (command control, event commands, status, and so on) are supported by message transfer (unscheduled) using the MSG instruction∙Error codes, network error counters, and port status data available in user data memorySlave SpecificationsThe MVI56E-MCM module accepts Modbus function code commands of 1, 2, 3, 4, 5, 6, 8, 15, 16, 17, 22, and 23 from an attached Modbus Master unit. A port configured as a Modbus Slave permits a remote Master to interact with all data contained in the module. This data can be derived from other Modbus Slave devices on the network, through a Master port, or from the ControlLogix processor.Master SpecificationsA port configured as a virtual Modbus Master device on the MVI56E-MCM module actively issues Modbus commands to other nodes on the Modbus network. Up to 325 commands are supported on each port. Additionally, the Master ports have an optimized polling characteristic that polls Slaves with communication problems less frequently. The ControlLogix processor ladder logic can issues commands directly from ladder logic or actively select commands from the command list to execute under ladder logic control.ControlLogix™ Modbus IntegrationGeneral Modbus SpecificationsCommunication Parameters Baud Rate: 110 baud to 115.2 kbpsStop Bits: 1 or 2Data Size: 7 or 8 bitsParity: None, Even, OddRTS Timing delays: 0 to 65535 milliseconds Modbus Modes RTU mode (binary) with CRC-16ASCII mode with LRC error checkingFloating Point Data Floating point data movement supported, includingconfigurable support for Enron and DanielimplementationsModbus Function Codes 1: Read Coils Status2: Read Input Status3: Read Holding Registers4: Read Input Registers5: Force (Write) Single Coil6: Preset (Write) Single Register8: Diagnostics15: Force (Write) Multiple Coils16: Preset (Write) Multiple Data Registers17: Report Slave ID22: Mask Write 4x Register23: Read/Write 4x RegistersModbus Master SpecificationsCommand List Up to 325 commands per Master port, each fullyconfigurable for function code, slave address, registerto/from addressing and word/bit count.Optimized Polling Configuration options allow Master ports andcommands to be optimized to poll slaves withcommunication problems less frequently.Command Status/Error Monitoring Command Status or Error codes are generated for each command as it executes, allowing careful monitoring of communication health between the Master and its Slaves.Slave Polling Control Master Port maintains a Slave Status list of all networkSlaves. Polling of each Slave may be disabled andenabled using this list.Modbus Slave SpecificationsFull Memory Access A port configured as a Modbus Slave permits a remoteMaster to read from or write to any of the 10,000registers that make up the user memory database. Multi-source Slave Data Data presented at the Slave port can be derived fromother Modbus Slave devices on a different networkthroug h the module’s Master port or from the processortag database.Node Address 1 to 247 (software selectable)Status Data Slave port error codes, counters and statuses areavailable separately for each port when configured as aSlave® products areHardware SpecificationsGeneralSpecification DescriptionBackplane Current Load 800 mA @ 5 Vdc3 mA @ 24 VdcOperating Temperature 0°C to 60°C (32°F to 140°F) - MVI56E-MCM-25°C to 70°C (-13°F to 158°F) - MVI56E-MCMXT Storage Temperature -40°C to 85°C (-40°F to 185°F)Extreme/Harsh Environment MVI56E-MCMXT comes with conformal coating Shock 30 g operational50 g non-operationalVibration: 5 g from 10 to 150 HzRelative Humidity 5% to 95% (without condensation)LED Indicators Battery Status (ERR)Application Status (APP)Module Status (OK)4-Character, Scrolling, Alpha-Numeric LED Display Shows Module, Version, IP, Port Master/Slave Setting, Port Status, and Error InformationDebug/Configuration Ethernet port (E1 - Config)Ethernet Port 10/100 Base-T, RJ45 Connector, for CAT5 cableLink and Activity LED indicatorsAuto-crossover cable detectionSerial Application ports (P1 & P2)Full hardware handshaking control, providing radio, modem, and multi-drop supportSoftware configurable communication parameters Baud rate: 110 baud to 115.2 kbpsRS-232, 485 and 422Parity: none, odd or evenData bits: 5, 6, 7, or 8Stop bits: 1 or 2RTS on/off delay: 0 to 65535 millisecondsSerial Applications Ports (P1, P2) RJ45 (DB-9M with supplied adapter cable) Configurable RS-232 hardware handshaking500V Optical isolation from backplaneRS-232, RS-422, RS-485 jumper-select, each port RX (Receive) and TX (Transmit) LEDs, each portShipped with Unit RJ45 to DB-9M cables for each serial port5 foot Ethernet Straight-Thru Cable (Gray) Agency Approvals and CertificationsAgencyRoHSATEXCSACECSA CB SafetycULusGOST-RLloyds® offers a full。

CATTI2004年5月英语二级笔译综合能力试题及答案试题部分：Section 1: Vocabulary and Grammar (25 points)This section consists of 3 parts. Read the directions for each part before answering the questions. The time for this section is 25 minutes.Part 1 Vocabulary SelectionIn this part, there are 20 incomplete sentences. Below each sentence, there are 4 choices respectively marked by letters A, B, C and D. Choose the word or phrase which best completes each sentence. There is only ONE right answer. Blacken the corresponding letter as required on your Machine-scoring ANSWER SHEET.1. The explanation given by the manager yesterday was not at all _____ to us.A. satisfyB. satisfiedC. satisfactoryD. satisfying2. Part of the funds will be used to _____ that old library to its original splendor.A. restB. recoverC. replaceD. restore3. This silk has gone right _____ and we have not sold a single piece of it for weeks.A. out of fadB. out of patternC. out of customD. out of fashion4. The new Personal Digital Assistance contained a large _____ of information about an individual life.A. dealB. amountC. numberD. account5. Primitive superstitions that feed racism should be _____ through education.A. ignoredB. exaltedC. eradicatedD. canceled6. _____ pollution control measures are expensive, many local governments hesitate to adopt them.A. AlthoughB. HoweverC. BecauseD. Moreover7. The less the surface of the ground yields to the weight of the body of a runner, _____ to the body.A. the stress it is greaterB. greater is the stressC. greater stress isD. the greater the stress8. Annie Jump Cannon, _____ discovered so many stars that she was called “the census taker of the sky.”A. a leading astronomer,B. who, as a leading astronomer,C. was a leading astronomer,D. a leading astronomer who9. Kingdom of Wonders, _____ in 1995 in Fremont, Calif., became an industry legend for two toys: a talking bear and a ray-gun game.A. findB. foundC. foundedD. founding10. Over a very large number of trials, the probability of an event _____ is equal to the probability that it will not occur.A. occurringB. to occurC. occursD. occur11. Only one-fifth of Americans saw oil as the chief reason that the U.S. madea war on Iraq, but 75 percent of the French and of the Russians believed_____.A. toB. soC. goD. do12. Sadly, while the academic industry thrives, the practice of translation continues to _____.A. stackB. stageC. stagnateD. stamp13. Your blunt treatment of disputes would put other people in a negative frame of _____, with the result that they would not be able to accept your proposal.A. mindB. ideaC. intentionD. wish14. If you are an energetic person with strong views as to the right way of doing things, you find yourself _____ under pressures.A. variablyB. invariablyC. invaluablyD. invalidly15. Uncle Vernon, quite unlike Harry Potter who looked nothing like the rest of the family, was large, very fat, and _____, with an enormous black mustache.A. neck-lessB. neck-laceC. recklessD. rack-less16. Home to _____ and gangsters, officials and laborers, refugees and artists, the city was, in its prime, a metropolis that exhibited all the hues of the human character.A. magnatesB. magnetsC. machinesD. magnitudes17. His _____ behavior made everyone nervous. He was always rushing to open doors and perform other small tasks, apologizing unnecessarily for any inconvenience that he might have caused.A. obliviousB. observantC. obsequiousD. obsolescent18. He was completely __________ by her tale of hardship.A. taken awayB. taken downC. taken inD. taken up19. Americans who consider themselves _____ in the traditional sense do not usually hesitate to heap criticism in domestic matters over what they believe is oppressive or wasteful.A. pedestrianB. penchantC. patriarchD. patriotic20. As technological advances put more and more time between early school life and the young person's final access to specialized work, the stage of_____ becomes an even more marked and conscious period.A. adolescenceB. adjacencyC. advantageD. adventurePart 2 Vocabulary ReplacementThis part consists of 15 sentences in which one word or phrase is underlined. Below each sentence, there are 4 choices respectively marked by letters A, B, C and D. Choose the word or phrase that can replace the underlined part without causing any grammatical error or changing the basic meaning of the sentence. There is only ONE right answer. Blacken the corresponding letter as required on your Machine-scoring ANSWER SHEET.21. That boy is suffering from unrequited love and pines away.A. ferventB. obsessiveC. secretD. unreturned22. For a long time in that vast region, this law was in abeyance.A. in active useB. in doubtC. in discussionD. in disuse23. A court-martial has but recently decided to acquit him.A. declare he is not guiltyB. pardon himC. condemn himD. persecute him24. There are more people who are obese today than 20 years ago.A. gainfully employedB. upwardly mobileC. excessively overweightD. privately educated25. As a conductor, Leonard Bernstein is famous for his intensely vigorous and exuberant style.A. enthusiasticB. nervousC. painfulD. extreme26. When insects feed on decaying plant material in a compost pile, they help turn it into useful garden soil.A. availableB. organicC. distastefulD. decomposing27. Researchers have discovered that dolphins are able to mimic human speech.A. importB. imitateC. impairD. humor28. The dichotomy postulated by many between idealism and realism is one of the standard clichés of the ongoing debate over international affairs.A. division into two partsB. combination of two partsC. disparityD. contradiction29. Attempts have been made for nearly three decades to increase the amount of precipitation from clouds by seeding them with salt or silver iodide.A. DevicesB. HypothesesC. EffortsD. Suggestions30. Justices of the peace have jurisdiction over the trials of some civil suits and of criminal cases involving minor offenses.A. supremacyB. authorityC. guidanceD. obedience31. The feeling of competition among the students in all the classrooms where the test was going on was noticeable to everyone.A. discordB. discoveryC. rivalryD. cooperation32. The artist spent years on his monumental painting, which covered the whole roof of the church, the biggest in the country.A. archaicB. sentimentalC. outstandingD. entire33. Many of the electric and electronic products we purchase and consume today are what some industrial experts call “homogeneous toys.”A. identicalB. homosexualC. unrelatedD. distinguishable34. Anthropologist Barbara Myerhoff furthered her reputation as an authority on Native American culture with her study of the symbols, myths, and rituals of the Huichol people.A. deservedB. retainedC. renewedD. advanced35. This reflects the priority being attached to economic over political activity, partly caused by a growing reluctance to enter a calling blighted by relentless publicity that all too often ends in destroying careers and reputations.A. powerfulnessB. unwillingnessC. renaissanceD. apologeticnessPart 3 Error CorrectionThis part consists of 15 sentences in which there is an underlined part that indicates a grammatical error. Below each sentence, there are 4 choices respectively marked by letters A, B, C and D. Choose the word or phrase that can replace the underlined part so that the error is corrected. There is only ONE right answer. Blacken the corresponding letter as required on your Machine-scoring ANSWER SHEET.36. An epigram is usually defined being a bright or witty thought that is tersely andingeniously expressed.A. asB. as beC. as beenD. to being37. Upon completing his examination over the patient, the doctor offered his judgment of her conditions.A. ofB. offC. aboutD. around38. If they spend some time on Chinese history, they will be more able to predict China’s future.A. moreB. be ableC. betterD. better able39. When she returned back by abroad, she told us all about her experience as an illegal immigrant.A. byB. backC. fromD. back from40. He was looking impatient at the visiting salesman, who showed no signs of getting ready to leave.A. patientB. patienceC. impatienceD. impatiently41. The recent conference on the effective use of the seas and oceans was another attempt resolving major differences among countries with conflicting interests.A. resolveB. resolvesC. to resolveD. being resolved42. Life insurance, before available only to young, healthy persons, can now be obtained for old people, and even for pets.A. before young, healthy persons available only,B. available only to young, healthy persons before,C. available only to persons young, but more healthy,D. before young and healthy persons only available to,43. Following a year of fast development, by the first quarter of this year, China has had about 1,100 e-commerce websites.A. China had about 1,100 e-commerce websites by the end of last MarchB. by the end of the first quarter of this year, China has had about 1,100e-commerce websitesC. by the end of this recent past March, China has about 1,100 e-commerce websitesD. by the end of this first quarter, China had about 1,100 or so e-commerce websites44. Sino-foreign educational program on business is popular in China now, and the demand for high level interpretation is great.A. programs in enterprises / high level interpretersB. programs in international business / senior interpretersC. program in international biz / senior interpretationsD. programs of business / high-level interpretations45. Many students agreed to come, but some students against because they said they don’t have time.A. were against because they said they did notB. were against because they say they don’tC. were against it because they said they did notD. were agains t coming because they said they don’t46. While it is essential that the text covers the subject adequately, it is also important that it is neither too detailed or too complex for the intended reader.A. forB. norC. noD. not47. Consumer porcelains in Jingdezhen are not selling well in export market as compared with those made in Liling, Hunan Province and Zibo, Shandong Province.A. on export marketB. in exporting marketC. in exported marketD. in the export market48. It is a market which sales value might be more than 10 billion yuan.A. a market with a sales value that might beB. a market which might be sales valueC. a market with sale value might beD. market with sales might be a value49. As an English major student, I think business English is more practical than other fields.A. a English student / fieldB. a English major student / regionsC. an English major / coursesD. an English student major /sciences50. We should let more young parents and their children can enjoy scientific early education.A. provide more young parents and their children to enjoy early educationB. provide more young parents and their children to enjoy early education and scientificC. provide young parents and their children enjoy more scientific early educationD. provide young parents and their children with more early education services Section 2: Reading Comprehension (50 points)In this section you will find after each of the passages a number of questions or unfinished statements about the passage, each with 4 (A, B, C and D) choices to complete the statement. You must choose the one which you think fits best. Then blacken the corresponding letter as required on your Machine-scoringANSWER SHEET. The time for this section is 70 minutes.Questions 51－60 are based on the following passage.Social control refers to social processes, planned or unplanned, by which people are taught, persuaded, or forced to conform to norms. In every society, some punishments or negative sanctions are established for deviant behavior. Without deviant behavior there would not be need for social control and without social control there would not be a way of recognizing the boundary between the acceptable and the unacceptable.Social control may be either formal or informal. Informal mechanisms include expressions of disapproval by significant others and withholding of positive rewards for disapproved behavior. Most people internalize norms in the course of socialization. This is any group’s most powerful protection against deviance, in th at the individual’s own conscience operates as an agent of social control. When informal sanctions fail, formal agents of social control may be called upon. In contemporary society, such formal agents and agencies include psychiatry and other mental health professions; mental hospitals; police and courts of law; prisons; and social welfare agencies. All these formal agents function to limit, correct, and control violation of norms. Conflict theorists would also point out that social control agents and systems tend, in any society, to serve the interests of powerful groups and to enforce the norms most beneficial to those who make the rules and who, therefore, define unacceptable behavior.Social control, whether formal or informal, has a dual function. First, it punishes the wrongdoer and reaffirms the boundaries of acceptable behavior. Second, and less recognized, it regulates the manner in which deviants are treated.51. Social control refers to processes by which .A. norms are developedB. norms are enforcedC. people are educated and trainedD. people are rewarded and punished52. Every society has its own .A. planned systemsB. controlled normsC. recognized boundaryD. established sanctions53. Informal mechanisms of social control include the following except .A. a high level of interest in ensuring conformityB. expression of disapproval by significant othersC. withholding of positive rewards for the deviantsD. people’s internalization of norms in socialization54. The most powerful protection against deviance is .A. negative sanctionsB. severe punishmentsC. the individual’s conscienceD. unrestrained suppression55. Formal agents of social control include the following except .A. police stationsB. mental hospitalsC. welfare agenciesD. vocational schools56. The purpose of formal agents is .A. to make beneficial rulesB. to preserve social ordersC. to control violation of normsD. to define acceptable behavior57. Which statement about social control agents is not true?A. They tend to serve the interest of those who enforce the norms.B. They tend to serve the interest of those who receive a benefit.C. They tend to serve the interest of those who make the rules.D. They tend to serve the interest of those who are powerful.58. According to conflict theorists, social control agents and systems are .A. liberalB. partialC. neutralD. overall59. In the third paragraph, “a dual function” refers to .A. formal and informB. rewards and penaltiesC. approval and disapprovalD. clarification and regulation60. The perspective from which the author discusses social control is .A. biologicalB. sociologicalC. psychologicalD. anthropologicalQuestions 61－70 are based on the following passage.Every group has a culture, however uncivilized it may seem to us. To the professional anthropologist, there is no intrinsic superiority of one culture over another, just as to the professional linguist, there is no intrinsic hierarchy among languages.People once thought of the languages of backward groups as undeveloped. While it is possible that language in general began as a series of grunts and groans, it is a fact established by the study of “backward” languages that no spoken tongue answers that description today. Most languages of uncivilized groups are, by our most severe standards, extremely complex. They differ from Western languages not in their sound patterns or grammatical structures, which usually are fully adequate for all language needs, but only in their vocabularies, which reflect the objects and activities known to their speakers. Even in this aspect, two things are to be noted. First, all languages seem to possess the machinery for vocabulary expansion, either by putting together words already in existence or by borrowing them from other languages and adapting them to their own system. Second, the objects and activities requiring names and distinctions in “backward” languages, while different from the West, are often surprisingly numerous and complicated. A Western language distinguishes merel y between two degrees of remoteness (“this” and “that”). But some languages of the American Indians distinguish between what isclose to the speaker, or to the person addressed, or removed from both, or out of sight, or in the past, or in the future.61. Every group of human beings .A. has its own set of ideas, beliefs and ways of lifeB. has an extremely complex and delicate languageC. has its own elegant music, literature, and other artsD. has the process of growing crops or raising animals62. To the professional linguists, .A. there is no intrinsic superiority of culturesB. there is no intrinsic hierarchy of languagesC. all languages came from grunts and groansD. all languages are most severe and standard63. Most languages of uncivilized groups are .A. adequateB. numerousC. ingeniousD. ingenuous64. “Backward” languages fall behind Western languages in .A. structuresB. vocabulariesC. written formsD. sound patterns65. All languages, whether civilized or not, have .A. their own ways to transfer ideasB. their own forms to satisfy needsC. their own abilities to answer descriptionD. their own systems to expand vocabulary66. Which of the following statements is implied in the passage?A. Anthropologists have nothing to do with linguists.B. Linguists have nothing to do with anthropologists.C. The study of languages casts light upon the study of cultures.D. The study of cultures casts no light upon the study of languages.67. It is implied that all cultures have to be viewed .A. profoundlyB. intrinsicallyC. independentlyD. professionally68. According to this passage, to learn a foreign language would require one .A. to do more activitiesB. to learn about a new cultureC. to meet more peopleD. to need more names69. The author’s attitude shown in this passage toward “backward” languages is .A. restrainedB. subjectiveC. objectiveD. resolute70. This passage is on the whole .A. narrativeB. instructiveC. prescriptiveD. argumentativeQuestions 71－80 are based on the following passage.The field of medicine has always attracted its share of quacks and charlatans — disreputable women and men with little or no medical knowledge who promise quick cures at cheap prices. The reasons why quackery thrives even in modern times are easy to find. To begin with, pain seems to be a chronic human condition. A person whose body or mind “hurts” will often pay any amount of money for the promise of relief. Second, even the best medical treatment cannot cure all the ills that beset men and women. People who mistrust or dislike the truths that their physicians tell them often turn to more sympathetic ears.Many people lack the training necessary to evaluate medical claims. Given the choice between (a) a reputable physician who says a cure for cancer will be long, expensive and may not work at all, and (b) a salesperson who says that several bottles of a secret formula “snake oil” will cure not only cancer but tuberculosis as well, some individuals will opt for “snake oil”.Many “snake oil” remedies are h ighly laced with alcohol or narcotic drugs. Anyone who drinks them may get so drunk or stoned that they drown their pains in the rising tide of pleasant intoxication. Little wonder that “snake oil” is a popular cure-all for minor aches and hurts! But let there be no misunderstandings. A very few “home remedies” actually work. However, most remedies sold by quacks are not only useless, but often can be harmful as well.71. In this passage, a quack or a charlatan is .A. someone who has a special abilityB. someone who has little knowledgeC. someone who is not a good doctorD. someone who pretends to be a doctor72. The sentence “pain seems to be a chronic human condition” means .A. pain seems to be very seriousB. pain seems to be very difficultC. pain seems to last for a long timeD. pain seems to be always happening73. Quackery thrives even in modern times because .A. patients pay any amount of moneyB. patients do not like their physiciansC. quacks say that they can help patientsD. best medical treatment costs very much74. People who seek the advice of quacks and charlatans are .A. those who are poorly educatedB. those who are highly educatedC. those who dislike medical treatmentsD. those who mistrust physicians’ truths75. To evaluate medical claims, one must .A. turn to reputable doctorsB. make an adequate choiceC. have the necessary trainingD. disbelieve promise of relief76. According to the author, a very few home remedies are .A. uselessB. harmfulC. pleasantD. effective77. Which of the following statements is not true?A. quacks are really sympatheticB. “snake oil” does not workC. doctors cannot cure all illsD. patients are often impatient78. Many individuals opt for “snake oil” because .A. they are misled by a secret formulaB. they cannot afford a treatmentC. they lack medical knowledgeD. they do not trust physicians79. “Snake oil” is a popular cure-all for minor aches and hurts because .A. it has actually workedB. it has some fruit stonesC. it has been misunderstoodD. it has alcohol or narcotic drugs80. Which of the following would be the best title of this passage?A. Distrust of PhysiciansB. Medical TreatmentC. Snake Oil RemediesD. Guard Against QuackeryQuestions 81－90 are based on the following passage.Modern industrial society grants little status to old people. In fact, such a society has a system of built-in obsolescence. There is no formal system for continuing our education throughout our life in order to keep up with rapidly changing knowledge. When our education and job skills have grown obsolete, we are treated exactly like those who have never gained an education or job skills and are not encouraged or given the opportunity to begin anew.As a society becomes more highly developed, the overall status of older people diminishes. Improved health technology creates a large pool of old people, who compete for jobs with the young. However, economic technology lowers the demand for workers and creates new jobs for which the skills of the aged are obsolete, forcing older people into retirement. At the same time, young people are being educated in the new technology and are keeping pace with rapid changes in knowledge. Finally, urbanization creates age-segregated neighborhoods. Because the old live on fixed incomes, they must often live in inferior housing. All these factors — retirement, obsolete knowledge and skills, inferior standards of living — lower the status of the aged in society. A century ago, when one could expect to live only to 50 or so, the life span more or less coincided with the occupation and family cycle. But today the average life span allows for fifteen to twenty years of life after these cycles. It appears that our life span is outpacing our usefulness in society.81. By “a system of built-in o bsolescence” the author means .A. no formal systems exists in modern industrial societyB. old people have no status in modern industrial societyC. young people have chances in modern industrial societyD. knowledge changes rapidly in modern industrial society82. According to the first paragraph, which of the following is true?A. People don’t have to gain educationB. People don’t have to learn job skillsC. People don’t have to be treated as equalsD. People don’t have chances to begin anew83. The more highly developed a society is, .A. the more advanced technology will beB. the larger the number of people will beC. the more diminished old people’s status will beD. the lower the overall status of the people will be84. The high development of economic technology .A. makes job skills out of fashionB. lowers the demand for workersC. forces old people into retirementD. creates new jobs for older people85. Which of the following statements is not true?A. Retired people could only live on fixed incomesB. Retired people are more skillful than young peopleC. Young people are educated in the new technologyD. Young people are keeping pace with rapid changes86. According to this passage, the status of the aged is lowered by .A. their forced retirementB. their inferior housingC. their longer life spanD. their fixed incomes87. The sentence “our life span outpaces our usefulness” means .A. we can live longer and make progressB. we can live longer and do more workC. we can live longer but move slowlyD. we can live longer but become useless88. The author’s attitude toward the aged is .A. realisticB. optimisticC. pessimisticD. sympathetic89. It can be deduced from this passage that .A. one should learn new skillsB. one should be open-mindedC. one should have a good personalityD. one should keep pace with the times90. Which of the following would be the best title for this passage?A. The Problem of AgingB. Social StructuresC. Economic TechnologyD. Continuing EducationQuestions 91－100 are based on the following passage.When you first drift off into slumber, your eyes will roll about a bit, your temperature will drop slightly, your muscles will relax, and your breathing will become quite regular. Your brain waves slow down a bit, with the alpha rhythm predominating for the first few minutes. This is the first stage of sleep. For the next 30 minutes or so, you will drift down through Stage 2 and Stage 3. The lower your stage of sleep, the slower your brain waves will be. About 40-60 minutes after you lose consciousness, you will reach the last stage. Your brain waves will show the delta rhythm. You may think that you stay at this deep stage all the rest of the night, but that turns out not to be the case. About 80 minutes after you fall into slumber, your activity cycle will increase slightly. The delta rhythm will disappear, to be replaced by the activity pattern of brain waves. Your eyes will begin to dart around under your closed eyelids. This period of Rapid Eye Movements lasts for 8-15 minutes and is called REM sleep.During both light and deep sleep, the muscles in your body are relaxed but capable of movement. As you slip into REM sleep, a very odd thing occurs —most of the voluntary muscles in your body become paralyzed. Although your brain shows very rapid bursts of neural activity during REM sleep, your body is incapable of moving. REM sleep is accompanied by extensive muscular inhibition.91. On the part of an average sleeper, of sleep in cycles.A. there is one stageB. there are two stagesC. there are six stagesD. there are four stages92. When a person falls into the state of sleep, .A. his eyeballs will roll about a bitB. his mind will relax more and moreC. his breathing will slow for minutesD. his temperature will increase slightly93. The lower your stage of sleep, .A. the faster your eyes will roll aboutB. the quieter your breath will becomeC. the slower your brain waves will beD. the higher your temperature will be94. After you have reached the deepest sleep, .A. you will stay at the fourth stage the rest of the nightB. you will lose your consciousness for 40－60 minutesC. your brain waves will show the delta rhythmD. your brain waves will show the alpha rhythm95. In the REM sleep, .A. the delta rhythm will disappearB. the activity pattern will appearC. something will occur in front of you。

Economics: the study of how society manages its scarce resources, e.g.how people decide what to buy,how much to work, save, and spendhow firms decide how much to produce,how many workers to hirehow society decides how to divide its resources between national defense, consumer goods, protecting the environment, and otherneedsTen Principles of Economics1.People face trade-offsEfficiency vs. Equality2.The cost of something is what you give up to get itOpportunity cost: whatever must be given up to obtain some item.3.Rational people think at the margin4.People respond to incentives.5.Trade can make everyone better off6.Markets are usually a good way to organize economic activityernments can sometimes improve market outcomes8.A country’s standard of living depends on its ability to produce goodsand services9.Price Rise When the Government Prints Too Much Money10.Society Face a Short-Run Trade-off between Inflation andUnemploymentEconomists play two roles:1.Scientists: they make appropriate assumptions and build simplifiedmodels to understand the world around them.2.Policy advisors: try to improve the world. They often offer conflictingadvice either because of difference in scientific judgment or becauseof differences in values.The Circular-Flow DiagramThe Production Possibilities FrontierSociety faces a tradeoff: getting more of one good requires sacrificing some of the other.The slope of the PPF tells you the opportunity cost of one good in terms of the other.Microeconomics and MacroeconomicsMicroeconomics is the study of how households and firms make decisions and how they interact in markets.Macroeconomics is the study of economy-wide phenomena, including inflation, unemployment, and economic growth.Positive statement and Normative StatementA positive statement is an assertion about how the world is whichcan be confirmed or refuted.A normative statement is an assertion about how the world oughtto be.Interdependence and trade allow everyone to enjoy a greater quantity and variety of goods & services.Comparative Advantage and Absolute AdvantageComparative advantage means being able to produce a good at a lower opportunity cost.Absolute advantage means being able to produce a good with fewer inputs.Trade makes everyone better off because it allows people to specialize in those activities in which they have a comparative advantage.The price of the trade: for both parties to gain from trade, the price at which they trade must lie between the two opportunity costs.Markets and CompetitionA market is a group of buyers and sellers of a particular product.A competitive market is one with many buyers and sellers, each hasa negligible effect on price.In a perfectly competitive market:All goods exactly the sameBuyers & sellers so numerous that no one can affect market price—each is a “price taker”The Demand CurveThe quantity demanded of any good is the amount of the good that buyers are willing and able to purchase.Law of demand: the claim that the quantity demanded of a good falls when the price of the good rises, other things equal.The Demand Curve Shifters:1.Number of BuyersIncrease in # of buyers, increases quantity demanded at each price,shifts D curve to the right.2.IncomeDemand for a normal good is positively related to income.Increase in income causes increase in quantity demanded at eachprice, shifts D curve to the right.Demand for an inferior good is negatively related to income. An increase in income shifts D curves for inferior goods to the left.3.Prices of Related GoodsTwo goods are substitutes if an increase in the price of one causes an increase in demand for the other.Two goods are complements if an increase in the price of one causes a fall in demand for the other.4.Tastes5.ExpectationsSupply CurveThe quantity supplied of any good is the amount that sellers are willing and able to sell.Law of supply: the claim that the quantity supplied of a good rises when the price of the good rises, other things equal.The Supply Curve Shifters:1.Input PricesA fall in input prices makes production more profitable at each outputprice, so firms supply a larger quantity at each price, and the S curveshifts to the right.2.Technology3.Expectations4.Number of sellersEquilibriumMarket equilibrium is a situation in which the market price has reached the levels at which quantity supplied equals quantitydemanded.The behavior of buyers and sellers naturally drives markets toward their equilibrium.Surplus: quantity supplied is greater than quantity demanded.Shortage : quantity demanded is greater than quantity suppliedChange in Demand vs. Change in Quantity demandedChange in demand: a shift in the D curve occurs when a non-price determinant of demand changes (like income or # ofbuyers)Change in the quantity demanded: a movement along a fixed D curve occurs when P changesCh.5The price elasticity of demand and its determinantsPrice elasticity of demand =Price elasticity of demand measures how much Q d responds to a change in P.Midpoint MethodPrice elasticity of demand = ( )/[]( )/[]DeterminantsPrice elasticity is higher when close substitutes are available.Price elasticity is higher for narrowly defined goods than broadly defined ones.Price elasticity is higher for luxuries than for necessities.Price elasticity is higher in the long run than the short run. The variety of demand curves1.Perfectly inelastic demand2.Inelastic demand3.Unit elastic demand4.Elastic demand5.Perfectly elastic demandTotal revenue and the price elasticity of demandFor inelastic demand curves, total revenue moves in the same direction as the price.For elastic demand curves, total revenue moves in the opposite direction as the price.Other elasticitiesIncome elasticity of demand: measures the response of Q d to a change in consumer incomeFor normal goods, income elasticity > 0.For inferior goods, income elasticity < 0.Cross-price elasticity of demand: measures the response of demand for one good to changes in the price of another good For substitutes, cross-price elasticity > 0(e.g., an increase in price of beef causes an increase indemand for chicken)For complements, cross-price elasticity < 0(e.g., an increase in price of computers causes decrease indemand for software)Ch. 6Price controlsPrice ceiling: a legal maximum on the price of a good or service Example: rent controlPrice floor: a legal minimum on the price of a good or service Example: minimum wageA Tax on BuyersA Tax on SellersNote: The effects on P and Q, and the tax incidence are the same whether the tax is imposed on buyers or sellers!Elasticity and Tax IncidenceWhen supply is elastic and demand is inelastic, the largest share of the tax burden falls on consumers.When supply is inelastic and demand is elastic, the largest share of the tax burden falls on producers.In general, a tax burden falls more heavily on the side of the market that is less elastic.A small elasticity of demand means that buyers do not havegood alternatives to consuming this product.A small elasticity of supply means that sellers do not havegood alternatives to producing this particular good.Ch.7Welfare economics studies how the allocation of resources affects economic well-being.Consumer SurplusThe height of the D curve reflects the value of the good to buyers—their willingness to pay for it.Consumer surplus is the amount a buyer is willing to pay minus the amount the buyer actually pays:CS = WTP – PProducer SurplusThe height of the S curve is sellers’ cost of producing the good.Sellers are willing to sell if the price they get is at least as high astheir cost.Producer surplus (PS): the amount a seller is paid for a good minus the seller’s costPS = P – costMarket EfficiencyTotal Surplus = Consumer surplus + Producer Surplus= total gains from trade in a market= (value to buyers) – (cost to sellers)An allocation of resources is efficient if it maximizes total surplus.Efficiency means:The goods are consumed by the buyers who value them most highly.The goods are produced by the producers with the lowest costs.Raising or lowering the quantity of a good would not increase total surplus.Under perfect competition, the market outcome is efficient.Altering it would reduce total surplus.Ch.8The Deadweight Loss of TaxationTaxes have deadweight losses because they cause buyers to consume less and sellers to produce less, and these changes inbehavior shrink the size of the market below the level thatmaximizes total surplus.Because the elasticities of supply and demand measure how much market participants respond to market conditions, largerelasticities imply larger deadweight losses.Deadweight Loss and Tax Revenue as Tax VaryWhen a tax increases, DWL rises even moreAn increase in the size of a tax causes revenue to rise at first, but eventually revenue falls because the tax reduces the size of themarket.Ch.9The World Price and Comparative AdvantageIf P D < P W,country has comparative advantage in the goodunder free trade, country exports the goodIf P D > P W,country does not have comparative advantageunder free trade, country imports the goodThe Winners and Losers from TradeThe Small Economy Assumption: A small economy is a price taker in world markets: its actions have no effect on P W.The Gains and Losses of an Exporting CountryWelfare without tradea. Consumer surplus is equal to: A + B.b. Producer surplus is equal to: C.c. Total surplus is equal to: A + B + C.Welfare with tradea. Consumer surplus is equal to: A.b. Producer Surplus is equal to: B + C + D.c. Total surplus is equal to: A + B + C + D.When a country exports a good, domestic producers of the good are better off and domestic consumers of the good are worse off.When a country exports a good, total surplus is increased and the economic well-being of the country rises.The Gains and Losses of an Importing CountryWelfare without tradea. Consumer surplus is equal to: A.b. Producer surplus is equal to: B + C.c. Total surplus is equal to: A + B + C.Welfare with tradea. Consumer surplus is equal to: A + B + D.b. Producer surplus is equal to: C.c. Total surplus is equal to: A + B + C + D.When a country imports a good, domestic consumers of the good are better off and domestic producers of the good are worse off.When a country imports a good, total surplus is increased and the economic well-being of the country rises.Note: whether a good is imported or exported, trade creates winners and losers. But the gains exceed the lossesThe Effects of a TariffTariff: a tax on goods produced abroad and sold domestically.A tariff raises the price above the world price. Thus, the domesticprice of textiles will rise to the world price plus the tariff.As the price rises, the domestic quantity of textiles demanded will fall and the domestic quantity of textiles supplied will rise. Thequantity of imports will fall and the market will move closer to thedomestic market equilibrium that occurred before trade.Welfare before the tariff (with trade)a. Consumer surplus is equal to: A + B + C + D + E + F.b. Producer surplus is equal to: G.c. Government revenue is equal to: zero.d. Total surplus is equal to: A + B + C + D + E + F + G.Welfare after the tariffa. Consumer surplus is equal to: A + B.b. Producer surplus is equal to: C + G.c. Government revenue is equal to: E.d. Total surplus is equal to: A + B + C + E + G.Deadweight loss of tariff : D+FD = deadweight loss from the overproduction of shirtsF = deadweight loss from the under-consumption of shirts。

INTERNATIONAL JOURNAL OF CIRCUIT THEORY AND APPLICATIONSInt.J.Circ.Theor.Appl.2006;34:559–582Published online in Wiley InterScience().DOI:10.1002/cta.375A wavelet-based piecewise approach for steady-state analysisof power electronics circuitsK.C.Tam,S.C.Wong∗,†and C.K.TseDepartment of Electronic and Information Engineering,Hong Kong Polytechnic University,Hong KongSUMMARYSimulation of steady-state waveforms is important to the design of power electronics circuits,as it reveals the maximum voltage and current stresses being imposed upon specific devices and components.This paper proposes an improved approach tofinding steady-state waveforms of power electronics circuits based on wavelet approximation.The proposed method exploits the time-domain piecewise property of power electronics circuits in order to improve the accuracy and computational efficiency.Instead of applying one wavelet approximation to the whole period,several wavelet approximations are applied in a piecewise manner tofit the entire waveform.This wavelet-based piecewise approximation approach can provide very accurate and efficient solution,with much less number of wavelet terms,for approximating steady-state waveforms of power electronics circuits.Copyright2006John Wiley&Sons,Ltd.Received26July2005;Revised26February2006KEY WORDS:power electronics;switching circuits;wavelet approximation;steady-state waveform1.INTRODUCTIONIn the design of power electronics systems,knowledge of the detailed steady-state waveforms is often indispensable as it provides important information about the likely maximum voltage and current stresses that are imposed upon certain semiconductor devices and passive compo-nents[1–3],even though such high stresses may occur for only a brief portion of the switching period.Conventional methods,such as brute-force transient simulation,for obtaining the steady-state waveforms are usually time consuming and may suffer from numerical instabilities, especially for power electronics circuits consisting of slow and fast variations in different parts of the same waveform.Recently,wavelets have been shown to be highly suitable for describingCorrespondence to:S.C.Wong,Department of Electronic and Information Engineering,Hong Kong Polytechnic University,Hunghom,Hong Kong.†E-mail:enscwong@.hkContract/sponsor:Hong Kong Research Grants Council;contract/grant number:PolyU5237/04ECopyright2006John Wiley&Sons,Ltd.560K.C.TAM,S.C.WONG AND C.K.TSEwaveforms with fast changing edges embedded in slowly varying backgrounds[4,5].Liu et al.[6] demonstrated a systematic algorithm for approximating steady-state waveforms arising from power electronics circuits using Chebyshev-polynomial wavelets.Moreover,power electronics circuits are piecewise varying in the time domain.Thus,approx-imating a waveform with one wavelet approximation(ing one set of wavelet functions and hence one set of wavelet coefficients)is rather inefficient as it may require an unnecessarily large wavelet set.In this paper,we propose a piecewise approach to solving the problem,using as many wavelet approximations as the number of switch states.The method yields an accurate steady-state waveform descriptions with much less number of wavelet terms.The paper is organized as follows.Section2reviews the systematic(standard)algorithm for approximating steady-state waveforms using polynomial wavelets,which was proposed by Liu et al.[6].Section3describes the procedure and formulation for approximating steady-state waveforms of piecewise switched systems.In Section4,application examples are presented to evaluate and compare the effectiveness of the proposed piecewise wavelet approximation with that of the standard wavelet approximation.Finally,we give the conclusion in Section5.2.REVIEW OF WA VELET APPROXIMATIONIt has been shown that wavelet approximation is effective for approximating steady-state waveforms of power electronics circuits as it takes advantage of the inherent nature of wavelets in describing fast edges which have been embedded in slowly moving backgrounds[6].Typically,power electronics circuits can be represented by a time-varying state-space equation˙x=A(t)x+U(t)(1) where x is the m-dim state vector,A(t)is an m×m time-varying matrix,and U is the inputfunction.Specifically,we writeA(t)=⎡⎢⎢⎢⎣a11(t)a12(t)···a1m(t)............a m1(t)a m2(t)···a mm(t)⎤⎥⎥⎥⎦(2)andU(t)=⎡⎢⎢⎢⎣u1(t)...u m(t)⎤⎥⎥⎥⎦(3)In the steady state,the solution satisfiesx(t)=x(t+T)for0 t T(4) where T is the period.For an appropriate translation and scaling,the boundary condition can be mapped to the closed interval[−1,1]x(+1)=x(−1)(5) Copyright2006John Wiley&Sons,Ltd.Int.J.Circ.Theor.Appl.2006;34:559–582A WA VELET-BASED PIECEWISE APPROACH FOR STEADY-STATE ANALYSIS561 Assume that the basic time-invariant approximation equation isx i(t)=K T i W(t)for−1 t 1and i=1,2,...,m(6) where W(t)is any wavelet basis of size2n+1+1(n being the wavelet level),K T i=[k i,0,...,k i,2n+1] is a coefficient vector of dimension2n+1+1,which is to be found.‡The wavelet transformedequation of(1)isKD W=A(t)K W+U(t)(7)whereK=⎡⎢⎢⎢⎢⎢⎢⎢⎣k1,0k1,1···k1,2n+1k2,0k2,1···k2,2n+1............k m,0k m,1···k m,2n+1⎤⎥⎥⎥⎥⎥⎥⎥⎦(8)Thus,(7)can be written generally asF(t)K=−U(t)(9) where F(t)is a m×(2n+1+1)m matrix and K is a(2n+1+1)m-dim vector,given byF(t)=⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣a11(t)W T(t)−W T(t)D T···a1i(t)W T(t)···a1m W T(t)...............a i1(t)W T(t)···a ii(t)W T(t)−W T(t)D T···a im W T(t)...............a m1(t)W T(t)···a mi(t)W T(t)···a mm W T(t)−W T(t)D T⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦(10)K=[K T1···K T m]T(11)Note that since the unknown K is of dimension(2n+1+1)m,we need(2n+1+1)m equations. Now,the boundary condition(5)provides m equations,i.e.[W(+1)−W(−1)]T K i=0for i=1,...,m(12) This equation can be easily solved by applying an appropriate interpolation technique or via direct numerical convolution[11].Liu et al.[6]suggested that the remaining2n+1m equations‡The construction of wavelet basis has been discussed in detail in Reference[6]and more formally in Reference[7].For more details on polynomial wavelets,see References[8–10].Copyright2006John Wiley&Sons,Ltd.Int.J.Circ.Theor.Appl.2006;34:559–582562K.C.TAM,S.C.WONG AND C.K.TSEare obtained by interpolating at2n+1distinct points, i,in the closed interval[−1,1],and the interpolation points can be chosen arbitrarily.Then,the approximation equation can be written as˜FK=˜U(13)where˜F= ˜F1˜F2and˜U=˜U1˜U2(14)with˜F1,˜F2,˜U1and˜U2given by˜F1=⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣[W(+1)−W(−1)]T(00···0)···(00···0)(00···0)[W(+1)−W(−1)]T···(00···0)............(00···0)2n+1+1columns(00···0)···[W(+1)−W(−1)]T(2n+1+1)m columns⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦⎫⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎬⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎭m rows(15)˜F2=⎡⎢⎢⎢⎢⎢⎢⎢⎢⎣F( 1)F( 2)...F( 2n+1)(2n+1+1)m columns⎤⎥⎥⎥⎥⎥⎥⎥⎥⎦⎫⎪⎪⎪⎪⎪⎪⎪⎪⎬⎪⎪⎪⎪⎪⎪⎪⎪⎭2n+1m rows(16)˜U1=⎡⎢⎢⎢⎣...⎤⎥⎥⎥⎦⎫⎪⎪⎪⎬⎪⎪⎪⎭m elements(17)˜U2=⎡⎢⎢⎢⎢⎢⎣−U( 1)−U( 2)...−U( 2n+1)⎤⎥⎥⎥⎥⎥⎦⎫⎪⎪⎪⎪⎪⎬⎪⎪⎪⎪⎪⎭2n+1m elements(18)Finally,by solving(13),we obtain all the coefficients necessary for generating an approximate solution for the steady-state system.Copyright2006John Wiley&Sons,Ltd.Int.J.Circ.Theor.Appl.2006;34:559–582A WA VELET-BASED PIECEWISE APPROACH FOR STEADY-STATE ANALYSIS5633.WA VELET-BASED PIECEWISE APPROXIMATION METHODAlthough the above standard algorithm,given in Reference[6],provides a well approximated steady-state solution,it does not exploit the piecewise switched nature of power electronics circuits to ease computation and to improve accuracy.Power electronics circuits are defined by a set of linear differential equations governing the dynamics for different intervals of time corresponding to different switch states.In the following,we propose a wavelet approximation algorithm specifically for treating power electronics circuits.For each interval(switch state),we canfind a wavelet representation.Then,a set of wavelet representations for all switch states can be‘glued’together to give a complete steady-state waveform.Formally,consider a p-switch-state converter.We can write the describing differential equation, for switch state j,as˙x j=A j x+U j for j=1,2,...,p(19) where A j is a time invariant matrix at state j.Equation(19)is the piecewise state equation of the system.In the steady state,the solution satisfies the following boundary conditions:x j−1(T j−1)=x j(0)for j=2,3,...,p(20) andx1(0)=x p(T p)(21)where T j is the time duration of state j and pj=1T j=T.Thus,mapping all switch states to the close interval[−1,1]in the wavelet space,the basic approximate equation becomesx j,i(t)=K T j,i W(t)for−1 t 1(22) with j=1,2,...,p and i=1,2,...,m,where K T j,i=[k1,i,0···k1,i,2n+1,k2,i,0···k2,i,2n+1,k j,i,0···k j,i,2n+1]is a coefficient vector of dimension(2n+1+1)×p,which is to be found.Asmentioned previously,the state equation is transformed to the wavelet space and then solved by using interpolation.The approximation equation is˜F(t)K=−˜U(t)(23) where˜F=⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣˜F˜F1˜F2...˜Fp⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦and˜U=⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣˜U˜U1˜U2...˜Up⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦(24)Copyright2006John Wiley&Sons,Ltd.Int.J.Circ.Theor.Appl.2006;34:559–582564K.C.TAM,S.C.WONG AND C.K.TSEwith ˜F0,˜F 1,˜F 2,˜F p ,˜U 0,˜U 1,˜U 2and ˜U p given by ˜F 0=⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣F a 00···F b F b F a 0···00F b F a ···0...............00···F b F a (2n +1+1)×m ×p columns⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦⎫⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎬⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎭m ×p rows (F a and F b are given in (33)and (34))(25)˜F 1=⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣F ( 1)0 0F ( 2)0 0............F ( 2n +1) (2n +1+1)m columns 0(2n +1+1)m columns···0 (2n +1+1)m columns(2n +1+1)×m ×p columns⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦⎫⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎬⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎭2n +1m rows(26)˜F 2=⎡⎢⎢⎢⎢⎢⎢⎢⎢⎣0F ( 1)···00F ( 2)···0............0(2n +1+1)m columnsF ( 2n +1)(2n +1+1)m columns···(2n +1+1)m columns⎤⎥⎥⎥⎥⎥⎥⎥⎥⎦(27)˜F p =⎡⎢⎢⎢⎢⎢⎢⎢⎢⎣0···0F ( 1)0···0F ( 2)...... 0(2n +1+1)m columns···(2n +1+1)m columnsF ( 2n +1)(2n +1+1)m columns⎤⎥⎥⎥⎥⎥⎥⎥⎥⎦(28)˜U0=⎡⎢⎢⎢⎣0 0⎤⎥⎥⎥⎦⎫⎪⎪⎪⎬⎪⎪⎪⎭m ×p elements(29)Copyright 2006John Wiley &Sons,Ltd.Int.J.Circ.Theor.Appl.2006;34:559–582A WA VELET-BASED PIECEWISE APPROACH FOR STEADY-STATE ANALYSIS565˜U1=⎡⎢⎢⎢⎢⎢⎣−U( 1)−U( 2)...−U( 2n+1)⎤⎥⎥⎥⎥⎥⎦⎫⎪⎪⎪⎪⎪⎬⎪⎪⎪⎪⎪⎭2n+1m elements(30)˜U2=⎡⎢⎢⎢⎢⎣−U( 1)−U( 2)...−U( 2n+1)⎤⎥⎥⎥⎥⎦(31)˜Up=⎡⎢⎢⎢⎢⎢⎣−U( 1)−U( 2)...−U( 2n+1)⎤⎥⎥⎥⎥⎥⎦(32)F a=⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣[W(−1)]T0 00[W(−1)]T 0............00···[W(−1)]T(2n+1+1)m columns⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦⎫⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎬⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎭m rows(33)F b=⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣[−W(+1)]T0 00[−W(+1)]T 0............00···[−W(+1)]T(2n+1+1)m columns⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦⎫⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎬⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎭m rows(34)Similar to the standard approach outlined in Section2,all the coefficients necessary for gener-ating approximate solutions for each switch state for the steady-state system can be obtained by solving(23).It should be noted that the wavelet-based piecewise method can be further enhanced for approx-imating steady-state solution using different wavelet levels for different switch states.Essentially, Copyright2006John Wiley&Sons,Ltd.Int.J.Circ.Theor.Appl.2006;34:559–582566K.C.TAM,S.C.WONG AND C.K.TSEwavelets of high levels should only be needed to represent waveforms in switch states where high-frequency details are present.By using different choices of wavelet levels for different switch states,solutions can be obtained more quickly.Such an application of varying wavelet levels for different switch intervals can be easily incorporated in the afore-described algorithm.4.APPLICATION EXAMPLESIn this section,we present four examples to demonstrate the effectiveness of our proposed wavelet-based piecewise method for steady-state analysis of switching circuits.The results will be evaluated using the mean relative error (MRE)and mean absolute error (MAE),which are defined byMRE =12 1−1ˆx (t )−x (t )x (t )d t (35)MAE =12 1−1|ˆx (t )−x (t )|d t (36)where ˆx (t )is the wavelet-approximated value and x (t )is the SPICE simulated result.The SPICE result,being generated from exact time-domain simulation of the actual circuit at device level,can be used for comparison and evaluation.In discrete forms,MAE and MRE are simply given byMRE =1N Ni =1ˆx i −x i x i(37)MAE =1N Ni =1|ˆx i −x i |(38)where N is the total number of points sampled along the interval [−1,1]for error calculation.In the following,we use uniform sampling (i.e.equal spacing)with N =1001,including boundary points.4.1.Example 1:a single pulse waveformConsider the single pulse waveform shown in Figure 1.This is an example of a waveform that cannot be efficiently approximated by the standard wavelet algorithm.The waveform consists of five segments corresponding to five switch states (S1–S5),and the corresponding state equations are given by (19),where A j and U j are given specifically asA j =⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩0if 0 t <t 10if t 1 t <t 21if t 2 t <t 30if t 3 t <t 40if t 4 t T(39)Copyright 2006John Wiley &Sons,Ltd.Int.J.Circ.Theor.Appl.2006;34:559–582A WA VELET-BASED PIECEWISE APPROACH FOR STEADY-STATE ANALYSIS567S1S2S3S4S50t1t2t3t4THFigure 1.A single pulse waveform consisting of 5switch states.andU j =⎧⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎩0if 0 t <t 1H /(t 2−t 1)if t 1 t <t 2−Hif t 2 t <t 3−H /(t 4−t 3)if t 3 t <t 40if t 4 t T(40)where H is the amplitude (see Figure 1).Switch states 2(S2)and 4(S4)correspond to the rising edge and falling edge,respectively.Obviously,when the widths of rising and falling edges are small (relative to the whole switching period),the standard wavelet method cannot provide a satisfactory approximation for this waveform unless very high wavelet levels are used.Theoretically,the entire pulse-like waveform can be very accurately approximated by a very large number of wavelet terms,but the computational efforts required are excessive.As mentioned before,since the piecewise approach describes each switch interval separately,it yields an accurate steady-state waveform description for each switch interval with much less number of wavelet terms.Figures 2(a)and (b)compare the approximated pulse waveforms using the proposed wavelet-based piecewise method and the standard wavelet method for two different choices of wavelet levels with different widths of rising and falling edges.This example clearly shows the benefits of the wavelet-based piecewise approximation using separate sets of wavelet coefficients for the different switch states.Copyright 2006John Wiley &Sons,Ltd.Int.J.Circ.Theor.Appl.2006;34:559–582568K.C.TAM,S.C.WONG AND C.K.TSE0−0.2−0.4−0.6−0.8−1−20−15−10−50.20.40.60.81−0.2−0.4−0.6−0.8−10.20.40.60.81(a)051015(b)Figure 2.Approximated pulse waveforms with amplitude 10.Dotted line is the standard wavelet approx-imated waveforms using wavelets of levels from −1to 5.Solid lines are the actual waveforms and the wavelet-based piecewise approximated waveforms using wavelets of levels from −1to 1:(a)switch states 2and 4with rising and falling times both equal to 5per cent of the period;and (b)switch states 2and 4with rising and falling times both equal to 1per cent of the period.4.2.Example 2:simple buck converterThe second example is the simple buck converter shown in Figure 3.Suppose the switch has a resistance of R s when it is turned on,and is practically open-circuit when it is turned off.The diode has a forward voltage drop of V f and an on-resistance of R d .The on-time and off-time equivalent circuits are shown in Figure 4.The basic system equation can be readily found as˙x=A (t )x +U (t )(41)where x =[i L v o ]T ,and A (t )and U (t )are given byA (t )=⎡⎢⎣−R d s (t )L −1L 1C −1RC⎤⎥⎦(42)U (t )=⎡⎣E (1−s (t ))+V f s (t )L⎤⎦(43)Copyright 2006John Wiley &Sons,Ltd.Int.J.Circ.Theor.Appl.2006;34:559–582Figure3.Simple buck convertercircuit.Figure4.Equivalent linear circuits of the buck converter:(a)during on time;and(b)during off time.Table ponent and parameter values for simulationof the simple buck converter.Component/parameter ValueMain inductance,L0.5mHCapacitance,C0.1mFLoad resistance,R10Input voltage,E100VDiode forward drop,V f0.8VSwitching period,T100 sOn-time,T D40 sSwitch on-resistance,R s0.001Diode on-resistance,R d0.001with s(t)defined bys(t)=⎧⎪⎨⎪⎩0for0 t T D1for T D t Ts(t−T)for all t>T(44)We have performed waveform approximations using the standard wavelet method and the proposed wavelet-based piecewise method.The circuit parameters are shown in Table I.We also generate waveforms from SPICE simulations which are used as references for comparison. The approximated inductor current is shown in Figure5.Simple visual inspection reveals that the wavelet-based piecewise approach always gives more accurate waveforms than the standard method.Copyright2006John Wiley&Sons,Ltd.Int.J.Circ.Theor.Appl.2006;34:559–582−0.5−10.51−0.5−10.51012345670123456712345671234567(a)(b)(c)(d)Figure 5.Inductor current waveforms of the buck converter.Solid line is waveform from piecewise wavelet approximation,dotted line is waveform from SPICE simulation and dot-dashed line is waveform using standard wavelet approximation.Note that the solid lines are nearly overlapping with the dotted lines:(a)using wavelets of levels from −1to 0;(b)using wavelets of levels from −1to 1;(c)using wavelets oflevels from −1to 4;and (d)using wavelets of levels from −1to 5.Table parison of MREs for approximating waveforms for the simple buck converter.Wavelet Number of MRE for i L MRE for v C CPU time (s)MRE for i L MRE for v C CPU time (s)levels wavelets (standard)(standard)(standard)(piecewise)(piecewise)(piecewise)−1to 030.9773300.9802850.0150.0041640.0033580.016−1to 150.2501360.1651870.0160.0030220.0024000.016−1to 290.0266670.0208900.0320.0030220.0024000.046−1to 3170.1281940.1180920.1090.0030220.0024000.110−1to 4330.0593070.0538670.3750.0030220.0024000.407−1to 5650.0280970.025478 1.4380.0030220.002400 1.735−1to 61290.0122120.011025 6.1880.0030220.0024009.344−1to 72570.0043420.00373328.6410.0030220.00240050.453In order to compare the results quantitatively,MREs are computed,as reported in Table II and plotted in Figure 6.Finally we note that the inductor current waveform has been very well approximated by using only 5wavelets of levels up to 1in the piecewise method with extremelyCopyright 2006John Wiley &Sons,Ltd.Int.J.Circ.Theor.Appl.2006;34:559–582123456700.10.20.30.40.50.60.70.80.91M R E (m e a n r e l a t i v e e r r o r )Wavelet Levelsinductor current : standard method inductor current : piecewise methodFigure parison of MREs for approximating inductor current for the simple buck converter.small MREs.Furthermore,as shown in Table II,the CPU time required by the standard method to achieve an MRE of about 0.0043for i L is 28.64s,while it is less than 0.016s with the proposed piecewise approach.Thus,we see that the piecewise method is significantly faster than the standard method.4.3.Example 3:boost converter with parasitic ringingsNext,we consider the boost converter shown in Figure 7.The equivalent on-time and off-time circuits are shown in Figure 8.Note that the parasitic capacitance across the switch and the leakage inductance are deliberately included to reveal waveform ringings which are realistic phenomena requiring rather long simulation time if a brute-force time-domain simulation method is used.The state equation of this converter is given by˙x=A (t )x +U (t )(45)where x =[i m i l v s v o ]T ,and A (t )and U (t )are given byA (t )=A 1(1−s (t ))+A 2s (t )(46)U (t )=U 1(1−s (t ))+U 2s (t )(47)Copyright 2006John Wiley &Sons,Ltd.Int.J.Circ.Theor.Appl.2006;34:559–582Figure7.Simple boost convertercircuit.Figure8.Equivalent linear circuits of the boost converter including parasitic components:(a)for on time;and(b)for off time.with s(t)defined earlier in(44)andA1=⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣−R mL mR mL m00R mL l−R l+R mL l−1L l1C s−1R s C s000−1RC⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦(48)A2=⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣−R mR dL mR m R dL m0−R mL m d mR m R dL l−R mR d+R lL l−1L lR mL l d m1C s00R mC(R d+R m)−R mC(R d+R m)0−R+R m+R dC R(R d+R m)⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦(49)Copyright2006John Wiley&Sons,Ltd.Int.J.Circ.Theor.Appl.2006;34:559–582U1=⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣EL m⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦(50)U2=⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣EL m−R m V fL m d mR m V fL l(R d+R m)−V f R mC(R d m⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦(51)Again we compare the approximated waveforms of the leakage inductor current using the proposed piecewise method and the standard wavelet method.The circuit parameters are listed in Table III.Figures9(a)and(b)show the approximated waveforms using the piecewise and standard wavelet methods for two different choices of wavelet levels.As expected,the piecewise method gives more accurate results with wavelets of relatively low levels.Since the waveform contains a substantial portion where the value is near zero,we use the mean absolute error(MAE)forTable ponent and parameter values for simulation ofthe boost converter.Component/parameter ValueMain inductance,L m200 HLeakage inductance,L l1 HParasitic resistance,R m1MOutput capacitance,C200 FLoad resistance,R10Input voltage,E10VDiode forward drop,V f0.8VSwitching period,T100 sOn-time,T D40 sParasitic lead resistance,R l0.5Switch on-resistance,R s0.001Switch capacitance,C s200nFDiode on-resistance,R d0.001Copyright2006John Wiley&Sons,Ltd.Int.J.Circ.Theor.Appl.2006;34:559–5820−0.2−0.4−0.6−0.8−1−50.20.40.60.815100(a)(b)−50.20.40.60.81510Figure 9.Leakage inductor waveforms of the boost converter.Solid line is waveform from wavelet-based piecewise approximation,dotted line is waveform from SPICE simulation and dot-dashed line is waveform using standard wavelet approximation:(a)using wavelets oflevels from −1to 4;and (b)using wavelets of levels from −1to 5.Table IV .Comparison of MAEs for approximating the leakage inductor currentfor the boost converter.Wavelet Number MAE for i l CPU time (s)MAE for i l CPU time (s)levels of wavelets(standard)(standard)(piecewise)(piecewise)−1to 3170.4501710.1250.2401820.156−1to 4330.3263290.4060.1448180.625−1to 5650.269990 1.6410.067127 3.500−1to 61290.2118157.7970.06399521.656−1to 72570.13254340.6250.063175171.563evaluation.From Table IV and Figure 10,the result clearly verifies the advantage of using the proposed wavelet-based piecewise method.Furthermore,inspecting the two switch states of the boost converter,it is obvious that switch state 2(off-time)is richer in high-frequency details,and therefore should be approximated with wavelets of higher levels.A more educated choice of wavelet levels can shorten the simulationCopyright 2006John Wiley &Sons,Ltd.Int.J.Circ.Theor.Appl.2006;34:559–582345670.050.10.150.20.250.30.350.40.450.5M A E (m e a n a b s o l u t e e r r o r )Wavelet Levelsleakage inductor current : standard method leakage inductor current : piecewise methodFigure parison of MAEs for approximating the leakage inductor current for the boost converter.time.Figure 11shows the approximated waveforms with different (more appropriate)choices of wavelet levels for switch states 1(on-time)and 2(off-time).Here,we note that smaller MAEs can generally be achieved with a less total number of wavelets,compared to the case where the same wavelet levels are employed for both switch states.Also,from Table IV,we see that the CPU time required for the standard method to achieve an MAE of about 0.13for i l is 40.625s,while it takes only slightly more than 0.6s with the piecewise method.Thus,the gain in computational speed is significant with the piecewise approach.4.4.Example 4:flyback converter with parasitic ringingsThe final example is a flyback converter,which is shown in Figure 12.The equivalent on-time and off-time circuits are shown in Figure 13.The parasitic capacitance across the switch and the transformer leakage inductance are included to reveal realistic waveform ringings.The state equation of this converter is given by˙x=A (t )x +U (t )(52)where x =[i m i l v s v o ]T ,and A (t )and U (t )are given byA (t )=A 1(1−s (t ))+A 2s (t )(53)U (t )=U 1(1−s (t ))+U 2s (t )(54)Copyright 2006John Wiley &Sons,Ltd.Int.J.Circ.Theor.Appl.2006;34:559–5820−0.2−0.4−0.6−0.8−1−6−4−20.20.40.60.81024680−0.2−0.4−0.6−0.8−1−6−4−20.20.40.60.81024680−0.2−0.4−0.6−0.8−1−6−4−20.20.40.60.81024680−0.2−0.4−0.6−0.8−1−6−4−20.20.40.60.8102468il(A)il(A)il(A)il(A)(a)(b)(c)(d)Figure 11.Leakage inductor waveforms of the boost converter with different choice of wavelet levels for the two switch states.Dotted line is waveform from SPICE simulation.Solid line is waveform using wavelet-based piecewise approximation.Two different wavelet levels,shown in brackets,are used for approximating switch states 1and 2,respectively:(a)(3,4)with MAE =0.154674;(b)(3,5)withMAE =0.082159;(c)(4,5)with MAE =0.071915;and (d)(5,6)with MAE =0.066218.Copyright 2006John Wiley &Sons,Ltd.Int.J.Circ.Theor.Appl.2006;34:559–582。