A design method for Quasi-Symmetrical Wide Angle Systems

International Journal of Mechanical Sciences 43(2001)2103–2123Quasi-static axial compression of thin-walled circular aluminium tubesS.R.Guillow a ,G.Lu a ;∗,R.H.Grzebieta ba School of Engineering and Science,Swinburne University of Technology,PO Box 218,Hawthorn,Victoria 3122,Australiab Department of Civil Engineering,Monash University,Clayton,Victoria 3168,AustraliaReceived5October 2000;receivedin revisedform 26March 2001AbstractThis paper presents further experimental investigations into axial compression of thin-walledcircular tubes,a classical problem studied for several decades.A total of 70quasi-static tests were conducted on circular 6060aluminium tubes in the T5,as-receivedcond ition.The range of D=t considered was expanded over previous studies to D=t =10–450.Collapse modes were observed for L=D 610anda mod e classiÿcation chart developed.The average crush force,F AV ,was non-d imensionalisedandan empirical formula establishedas F AV =M P =72:3(D=t )0:32.It was foundthat test results for both axi-symmetric and non-symmetric modes lie on a single prehensive comparisons have been made between existing theories andour test results for F AV .This has revealedsome shortcomings,suggesting that further theoretical work may be required.It was found that the ratio of F MAX =F AV increasedsubstantially with an increase in the D=t ratio.The e ect of ÿlling aluminium tubes with di erent density polyurethane foam was also brie y examined.?2001Elsevier Science Ltd.All rights reserved.Keywords:Axial compression;Circular tube;Foam;Plastic collapse;Thin-walledtubes0.IntroductionThe behaviour of thin-walledmetal tubes subjectedto axial compression has been stud iedfor many years.Such tubes are frequently usedas impact energy absorbers andReid[1]has pre-sented a general review of deformation mechanisms.Fig.1shows a typical force–displacement curve for quasi-static loading.Generally speaking,the axial load rises until a ÿrst buckle is formedat a characteristic maximum force value,F MAX .This initial buckling behaviour is well ∗Corresponding author.Fax:+61-3-9214-8264.E-mail address:glu@.au (G.Lu).0020-7403/01/$-see front matter ?2001Elsevier Science Ltd.All rights reserved.PII:S 0020-7403(01)00031-52104S.R.Guillow et al./International Journal of Mechanical Sciences43(2001)2103–2123NomenclatureD average diameterF AV average axial forceF MAX maximum axial force forÿrst peakg acceleration due to gravityH half-wavelength of foldL lengthM P full plastic bending moment of tube wall per unit lengthm geometric eccentricity factor—i.e.ratio of outward s foldlength to total foldlength N number of circumferential lobes(or corners)in non-symmetrical bucklingR average radiust wall thickness of tubeV Vickers hardness number(kg=mm2)e e ective crushing distancef density of foam0 ow stress0:20.2%proof stressult ultimate tensile stressFig.1.Typical load–de ection curve for an axially loaded thin-walled metal tube which collapsed by progressive folding.S.R.Guillow et al./International Journal of Mechanical Sciences43(2001)2103–21232105Fig.2.Examples of various collapse modes for thin-walled circular6060-T5aluminium tubes under axial load-ing(more examples shown in Fig.11):(a)axi-symmetric mode(D=97:9mm;t=1:9mm;L=196mm);(b)non-symmetric mode(D=96:5mm;t=0:54mm;L=386mm);(c)mixedmod e(D=97:5mm; t=1:5mm;L=350mm).known and will not be studied in depth here.Thereafter,depending on geometrical parameters such as the ratios of D=t(diameter=thickness)and L=D(length=diameter)and also on material properties,there are a variety of possible modes of collapse.Generally,collapse involves plastic2106S.R.Guillow et al./International Journal of Mechanical Sciences43(2001)2103–2123Fig.3.Schematic axial view of non-symmetric or diamond collapse mode.Two cases are shown,N=3and4 circumferential lobes.buckling andthe formation of progressive fold s(whether axi-symmetric or non-symmetric).The formation of these folds causes the characteristic uctuation in the axial force shown in Fig.1. This plastic collapse behaviour is of primary interest in this paper.Experimentally the following modes of collapse have been observed and Fig.2shows some typical examples:(i)axi-symmetric concertina bellowing,(ii)non-symmetric buckling(also known as diamond or Yoshimura mode),with a variable number of circumferential lobes or corners(refer to Fig.3),(iii)mixed mode(combination of the two previous modes),(iv)Euler or global buckling;and(v)other(simple compression,single fold s,etc.).Research on circular tubes in the past has generally concentratedon annealedaluminium or steel tubes with D=t ratios between10and150.It is common ind ustrial practice to use aluminium alloys in the heat treatedas-receivedcond ition,but little research appears to have addressed this particular case.Moreover,Gupta and Gupta[2]have identiÿed metal temper as one of the signiÿcant factors in determining behaviour.Hence,it was decided to undertake an experimental program to extendthe range of research up to approximately D=t=450andto test aluminium alloy tubes which were in the heat treatedas-receivedcond ition.This work is of potential application in civil,mechanical,marine andaeronautical engineeringÿeld s.1.Review of previous studiesThe following section summarises the available literature on the plastic collapse behaviour of thin-walledcircular metal tubes subject to quasi-static axial load ing.It is arrangedbroad ly in a chronological order.Theÿrst signiÿcant work to address the mechanics underlying the observed behaviour of axially load edthin-walledtubes was by Alexand er[3].He proposeda simple mod el for the axi-symmetric foldpattern(refer to Fig.4)basedon experiments with metal tubes of D=t= 29–89.At a global level,external work done was equated with internal work from bending at three stationary plastic hinges andcircumferential stretching of the metal between the hinges.S.R.Guillow et al./International Journal of Mechanical Sciences 43(2001)2103–21232107Fig.4.Axi-symmetric collapse mechanism assumedby Alexand er [3].Thus the following theoretical equation was obtainedfor average crush force (axi-symmetric folds):F AV =K o t1:5√D;(1)where K is a constant and o is the ow stress.Also,plastic half-wavelength,H (refer to Fig.4)was determined as follows:H =C √Dt;(2)where C is a constant.The experimental results observedby Alexand er were generally in agreement with the above two equations.Although simple,this model seems to re ect the und erlying physical processes involvedandmany subsequent researchers have usedit as a starting point.Pugsley andMacaulay [4]were among the ÿrst researchers to consid er the non-symmetric folding mode,their study being largely empirical.Johnson et al.[5]attempted to develop a theory for the non-symmetric mode based on the actual geometry of folding,with the tube material at the mid-surface being considered inextensional.Hence they were able to develop equations to predict average axial crush force,F AV .However,agreement between their model andtest results for P.V.C.tubes was not particularly good .In 1978Magee andThornton [6]cond ucteda review of previous work by researchers who hadcond uctedaxial crushing tests on circular metal tubes.By consid ering these collectedd ata they d evelopeda number of empirical equations which involvedthe speciÿc ultimate tensile strength of the metal.Andrews et al.[7]conducted a comprehensive series of tests on annealed aluminium alloy tubes covering a wide range of D=t (4–60)and L=D (0:2–8:8).Consequently,they developed a collapse mode classiÿcation chart which predicted the mode of collapse for any given D=t and L=D combination.2108S.R.Guillow et al./International Journal of Mechanical Sciences43(2001)2103–2123Fig.5.Axi-symmetric mod el usedby Abramowicz andJones[8,9].H is the half-wavelength of the fold. Abramowicz andJones[8,9]cond uctedaxial compression tests on a range of thin-walledcir-cular andsquare steel tubes.They analytically consid eredboth axi-symmetric andnon-symmetric modes.Abramowicz introduced the important concept of e ective crushing distance, e(refer to Fig.5),where a foldconsistedof two equal rad ii segments of length H,curvedin opposite d irections andthe material hadÿnite thickness.For axi-symmetric folds,Abramowicz and Jones[9]developed the following equation in1986 (anda similar one in1984[8]):F AV M P =[25:23D=t+15:09][0:86−0:568t=D];(3)where M P= o(t2=4):For non-symmetric fold s,in1984[8]and1986[9]Abramowicz andJones commencedwith two di erent starting relationships.Taking into account e ective crushing distance,material strain rate,etc.,resultedin two d i erent equations for average crush force.The simple relation-ship d evelopedin1984[8]appliedregard less of the number of lobes:F AV M P =86:14Dt0:33:(4)However,thisÿnding appears to have developed from work carried out by Wierzbicki and Abramowicz[10]on rectangular rather than circular tubes.On the other hand,the relationshipS.R.Guillow et al./International Journal of Mechanical Sciences43(2001)2103–21232109Fig.6.Collapse mechanism assumedby Grzebieta[12]for axi-symmetric mod e. Abramowicz andJones d erivedin1986[9]was of the formF AV M P =A N1Dt+A N2;(5)where A N1and A N2are constants which were a function of the number of lobes.For further details the reader is directed to this reference.In Refs.[8,9],Abramowicz andJones observedthat reasonable agreement existedbetween pred ictions of average crush load s basedon the above notedequations andtheir experimental results for steel tubes with D=t=9–65.In a subsequent work,Abramowicz andJones[11] reportedon further tests andsummarisedtheirÿnd ings for both static andd ynamic load ing cases in two failure mode maps,adding to the previous work by Andrews et al.[7].Gupta andGupta[2]performeda series of quasi-static axial compression tests on thin-walled aluminium andmildsteel circular tubes in both the annealedandas-receivedcond itions.They combinedall results andd evelopedempirical equations for the average crushing force in terms of the Vickers hardness and D=t.Grzebieta[12–14]useda strip methodto analyse both axi-symmetric andnon-symmetric folding modes.He equated external work done with internal energy from horizontal,inclined and travelling plastic hinges as well as stretching of the metal,to produce equations for determining the instantaneous forces involved.Unfortunately,these equations do not yield simple expressions for determining the average crush force.Grzebieta’s collapse mechanism model for axi-symmetric mode(refer to Fig.6)was a mod-iÿcation of Alexand er’s.A foldconsistedof three equal lengths,two of which were curves of equal rad ius andthe thirda straight line segment.For the non-symmetric mod e Grzebieta analysedthe fold s as a half-d iamondmechanism.Grzebieta carriedout static andd ynamic tests on steel tubes with D=t=30–300.2110S.R.Guillow et al./International Journal of Mechanical Sciences 43(2001)2103–2123Fig.7.Axi-symmetric mod el usedby Wierzbicki [15]andSingace et al.[16,17].Wierzbicki et al.[15]introduced a new model for the axi-symmetric collapse mechanism (shown simpliÿed in Fig.7)which allows for both inwards and outwards radial displacement.The geometry is governedby an arbitrary geometric eccentricity factor,m ,which is deÿned as the ratio of outwardfoldlength to total foldlength.By consid ering energy rate equations Wierzbicki et al.[15]were able to develop equations for not only determining average crush load but also a representative load–de ection history.The latter helped explain the experi-mental observation that sometimes there are two force peaks during the formation of a single fold.Singace et al.[16,17]extended upon the previous work by Wierzbicki et al..For the axi-symmetric mode,they considered a global energy balance leading to an implicit equation for m ,which when solvedgave a theoretical constant value of m =0:65.In their secondpa-per [17],Singace et al.reportedgoodexperimental agreement with the pred ictedvalue of 0:ter,Singace et al.[18]re-considered the eccentricity factor,m ,for the non-symmetric mode case.From the results of experiments on a small range of circular metal tubes they de-duced that the factor m was (surprisingly)approximately constant at m =0:65for this mode also.The equations developed by Singace et al.[17,18]for calculating average axial crush force are as follows.For axi-symmetric mode:F AV M P =22:27 D t+5:632:(6)For non-symmetric mode:F AV M P =− 3N +2 2N tan 2N D t :(7)One particular problem of interpretation arises with most theoretical equations developed for non-symmetric mode collapse,for example Eq.(7).They require a knowledge of the number of lobes,N ,at a given D=t ratio.We have not foundany publishedequation entirely satisfactory in determining N .S.R.Guillow et al./International Journal of Mechanical Sciences43(2001)2103–21232111Fig.8.Experimental set-up.With regardto energy absorption,it has been suggestedthatÿlling metal tubes with low-density polyurethane foam(to provide wall stability)may be preferable to increasing the wall thickness.Early investigations into the e ectiveness of this foamÿlling methodwere cond ucted by Thornton[19]and Lampinen and Jeryan[20].Reid,Reddy and Gray[21]have conducted experiments on the axial compression of thin-walledrectangular metal tubes which hadbeen ÿlledwith foam.Red d y andWall[22]subsequently testedfoamÿlledcircular aluminium alloy cans.Academic opinion appears to be divided about the relative beneÿts of foamÿlling versus increasing the wall thickness.2.Test procedure and material propertiesA series of approximately70axial compression tests were conducted under quasi-static condi-tions.Tests were carriedout on a SHIMAD ZU universal testing machine which appliedthe axial loadthrough at endplatens(refer to Fig.8).Cross-headspeedwas approximately5mm=min.A LABTECH data-logger recorded the data digitally for later analysis.The tubes tested were made from commercial quality extruded6060aluminium alloy in the as-received,heat treated T5condition.Mechanical properties were determined from tensile testing of coupons cut from several tubes.Fig.9shows a stress–strain curve for a typical tensile test specimen which hada0.2%proof stress, 0:2,of180MPa,an ultimate stress, ult, of212MPa anda Vickers hard ness,V,of73kg=mm2.By averaging results from several tensile tests we were able to determine an empirical relation between the0.2%proof stress and Vickers hardness for this particular type of alloy as follows:Vg= 0:2=3:92,where g=9:81m=s2is the gravitational acceleration.2112S.R.Guillow et al./International Journal of Mechanical Sciences43(2001)2103–2123Fig.9.Typical tensile stress–strain curve for6060-T5aluminium.Fig.10.Stress–strain curves for polyurethane foams of three di erent densities.The variety of commercial tubes available was insu cient to achieve the full range of D=t values we required.To produce tubes with very large D=t ratios,the outside surface of stock tubes was machined to produce the wall thickness desired.Theÿnal thickness,mean diameter and Vickers hardness were measured for each compression testpiece.Vickers hardness read-ings were usedto quantify the mechanical properties of each tube testpiece through the above equation.A representative sample of these tube properties andthe results of our testing may be foundin the append ix.Most tests involvedempty aluminium alloy tubes.However,some tests were carriedout on aluminium alloy tubes which hadbeenÿlledwith polyurethane foam.This polyurethane foam usually comes as a two part mix(base andaccelerator)andwe usedthree d i erent d ensities (35,60and140kg=m3)during testing.Fig.10shows typical compressive stress–strain curvesfor the three di erent density foams,which were obtained from axial compression tests on 96mm diameter cylindrical foam blanks unrestrained laterally.3.Experimental results and discussionOur experimental results are summarisedon the following pages in terms of the collapse mode,average force F AV,force ratio F MAX=F AV,eccentricity factor m andthe e ect of foam ÿlling.3.1.Collapse modeFurther examples of collapse modes are shown in Fig.11,in addition to those shown in Fig.2.Of particular interest was the non-symmetric mode(refer to Fig.2b)which has multiple corners(or lobes).We observedthat for tubes with an increasing D=t ratio,the number ofFig.11.Further examples of collapse modes for axially loaded thin-walled6060-T5aluminium tubes: (a)mixedmod e(D=57:1mm;t=1:15mm;L=628mm);(b)three sided non-symmetric folding (D=57:1mm;t=1:15mm;L=628mm);(c)Euler buckling(D=58mm;t=2:0mm;L=566mm).Fig.12.Schematic axial view of spiralling non-symmetric folding with N=312lobes,from Grzebieta[13].Fig.13.Mode classiÿcation chart for circular6060-T5aluminium tubes. circumferential lobes also increasedfrom2up to5or6.At high values of D=t(¿200),the number of lobes often variedd uring testing(in one case erratically between3,4and5lobes). The number of lobes,N,was not always an integer—for example,in some cases we observed a relatively stable pattern with312lobes in a spiralling arrangement(refer to Fig.12).In other cases the lobes were simply incompletely formed.From our test results for as-received6060-T5aluminium tubes a mod e classiÿcation chart was produced,see Fig.13.This chart is divided up into areas which correspond,approximately, to the di erent modes of collapse.The general shape of our chart is similar to that produced by And rews et al.[7],who testedannealedaluminium tubes.However,there are noticeable di erences in the location of the lines delineating the various areas.For example,consider analuminium tube with D=t=50and L=D=10.From our chart we wouldexpect a mixedmod eFig.14.Plot of non-dimensional experimental average force F AV=M P versus D=t.collapse but from Andrews et al.chart an Euler collapse is indicated.Note that a logarithmic scale is usedfor D=t on our chart in order to cover the wider range of D=t values considered.It may be observed broadly from our chart that non-symmetric mode is present when D=t¿100, while axi-symmetric mode occurs when D=t¡50and L=D¡2.3.2.Average crush forceOne of the most signiÿcant parameters for quantifying the behaviour of axially compressed tubes is the average crush force F AV.This is usually expressednon-d imensionally as a ratio F AV=M P.When calculating the plastic moment,M P,di erent researchers have used various di erent measures for the ow stress, 0.Since our tests involvedonly aluminium we chose to take the value of0.2%proof stress, 0:2,as the ow stress.Thus e ectively:M P= 0:2(t2=4):Fig.14shows our test results for non-dimensionalised average axial force,F AV=M P,plotted logarithmically versus D=t.There is only a relatively small amount of experimental scatter(some points shown represent more than one test result).Note that when calculating the average axial force,F AV,results for the initial peak have been ignored.From Fig.14it can be seen that when plottedlogarithmically,all the results(whether axi-symmetric,non-symmetric or mixed modes)approximately form a straight line.Hence,we obtained the following empirical relation for6060-T5aluminium alloy tubes:F AV M P =72:3Dt0:32:(8)This equation is of similar form to Eq.(4)proposedby Abramowicz andJones in1984[8] for non-symmetric mode but quite di erent from the corresponding equation proposed by Gupta andGupta[2].parison of present experimental results for average crush force with empirical equations of Gupta and Gupta[2].parison of experiment and theory for average forceThe following paragraphs are a subjective comparison between our experimental results for average crush force,F AV,andvarious theories andempirical relationships.Fig.15shows our test results for F AV comparedwith empirical equations by Gupta andGupta [2].They usedVickers hard ness,V,to characterise material properties.These equations were determined from tests on metal tubes with a relatively small range of dimensions(D=t=10–33, L=D=2–3).In view of this,agreement for both axi-symmetric andnon-symmetric mod es is quite goodin the range D=t=10–100.For D=t¿100,their curve for axi-symmetric mode is closer to our experimental test points than their non-symmetric one,even though the actual collapse mode exhibited was non-symmetric.Fig.16shows our test results for average force,comparedwith equations d evelopedby Abramowicz andJones[8].From thisÿgure it may be seen that agreement for both axi-symmetric and non-symmetric modes is fair.Their axi-symmetric equation predicts average forces which are rather low comparedwith our test points.On the other hand,their equation for non-symmetric mode,Eq.(4),predicts average forces which are rather high compared with our test points. Nevertheless,it may be notedfrom Fig.16that the slope of the line representing Eq.(4) (non-symmetric mode)is almost the same as our test points.This is also evident from a comparison of Eqs.(4)and(8).Fig.17shows our test results for average force,F AV,comparedwith the theoretical equations d evelopedby Abramowicz andJones[9].Their axi-symmetric Eq.(3)estimates an average force which is still low comparedwith our test results,but closer to our test points than their 1984prediction.In the case of non-symmetric collapse,Abramowicz and Jones[9]developed Eq.(5),which produces a family of lines,one for each value of N.Thus,we needto know the number of lobes,N,in order to interpret Fig.17.From the appendix it will be noted that formost of the tubes we tested,N falls in the range N=3–4.Agreement between their theory andparison of present experimental results for average force with theory by Abramowicz andJones[8].parison of present experimental results for average force with theory by Abramowicz andJones[9]. our test points is goodin this range.For cases with low D=t values(¡50),where N¡3,their prediction for F AV is rather low.For high values of D=t(¿300),where N¿4,their predicted value for F AV is rather high.Nevertheless,overall it appears that this methodof pred icting F AV is satisfactory.Fig.18shows our test results for average force comparedwith the equations d evelopedby Singace et al.[17,18].Their equation for axi-symmetric mode,Eq.(6),gives values for F AV which are much too low comparedwith our test points.In the case of non-symmetric mod e, their Eq.(7),when plottedon logarithmic axes prod uces a series of very steep lines,one for each number of lobes,N.This makes the process of interpretation even more di cult. Determining the precise number of corners or lobes for each test specimen presents somepractical di culties.As has previously been noted,if D=t¿200we sometimes observedthatparison of present experimental results for average force with theory by Singace et al.papers [16–18].the number of lobes variedd uring the one test.Nevertheless,on Fig.18test points are shown for which we felt conÿdent of the lobe number.It will be noted that the lines representing the Singace et al.Eq.(7)are not inconsistent with our test points although agreement is not close.However,we observedthat when the number of lobes variedd uring testing there was not a corresponding variation in the instantaneous crush force.This observation casts doubt on the validity of Eq.(7),as the large gaps between the lines in Fig.18suggest there should be a large variation in crush force with a change in the number of lobes,N .3.4.Discussion of average forceAt this stage the following observations may be made.In general,the existing theories produce numerical predictions for average force which are reasonable only for a limited range of D=t .Comparison of our test results with these theories has revealedtwo fund amental features which remain inexplicable at present.The ÿrst feature is that all our test points,regardless of mode of collapse (axi-symmetric or non-symmetric),lie on one curve whereas the theories treat these modes quite separately.Further,most theories for non-symmetric mode predict average forces which are a function of the number of lobes but experimentally this does not appear to be the case.The second,more important,feature relates to the functional dependence of average force on D=t .Our experiments clearly show that F AV =M P is empirically dependent on (D=t )0:32.Existing theories for axi-symmetric mode,however,suggest that F AV =M P should be dependent on D=t .In the case of non-symmetric mode,a wide variety of theories have been suggested;typically F AV =M P is seen as being a linear function of D=t as for the Singace et al.Eq.(7).An exception to this is Eq.(4)d evelopedby Abramowicz andJones [9],where F AV =M P was proportional to (D=t )0:33.However,as previously noted,this equation appears to have developed from work by Wierzbicki andAbramowicz [10]on rectangular rather than circular tubes.Thus it seemsFig.19.F MAX=F AV force ratio versus D=t.that for circular tubes a rigorous theoretical explanation of the D=t exponent of13is still to be developed.3.5.Force ratio F MAX=F AVIn a previous paper,Guillow andLu[23]id entiÿedthe force ratio F MAX=F AV as being of some interest.In that paper it was notedthat F MAX=F AV variedas a function of D=t ratio(this has also been notedby other researchers).The variation in force ratio highlights the fact that the mechanics of formation of the initial and subsequent folds is substantially di erent.Fig.19 shows the results of our more recent tests at larger values of D=t.The F MAX=F AV ratio appears to be monotonically increasing up to D=t=450.Variability in the F MAX=F AV ratio increased markedly for D=t¿100.This scatter couldbe d ue to signiÿcant variation in the initial buckling force,F MAX,at large values of D=t.Incidently,the common wisdom attributes the scatter of initial buckling force to imperfection sensitivity of thin-walled shells.However,Calladine[24]has recently provided an alternative explanation basedon post-buckling consid erations.3.6.Eccentricity factor mWhen folds occur during progressive buckling,they form partly on the outside and partly on the inside of the original tube proÿle.As previously noted,Singace et al.[16–18]have investigatedthis phenomenon by consid ering the eccentricity factor,m,(refer to Fig.7for its deÿnition).We were surprised at their claim that the factor m was approximately constant at 0.65.Therefore,we decided to examine our test pieces to see if the Singace et al.ÿndings also applied to6060-T5aluminium alloy tubes.Our test results for axi-symmetric mode folding are shown in Fig.20.They appear to conÿrm that a constant value of approximately0.65alsoapplies in this case.(It is not clear why the m value shouldbe so d i erent at D=t=20.)Fig.20.Eccentricity,m,as a function of D=t,for axi-symmetric mode.Fig.21.E ect of varying density of foamÿlling in6060-T5aluminium tubes.All tubes of length196mm,average diameter97mm and thickness1:0mm.Refer to Fig.10for stress–strain curves of polyurethane foam.3.7.E ect of foamÿllingMost of our tests involvedempty aluminium alloy tubes.However,a few tests were carried out on aluminium alloy tubes which hadbeenÿlledwith polyurethane foam.Fig.21shows some of our test results for foam-ÿlledaluminium tubes andTable1presents the d ata for aver-age axial crush force.Stress–strain curves for foam only were presentedearlier in Fig.10.All of the aluminium alloy tubes usedin this stage of testing were id entical(D=97mm;t=1:0mm and L=196mm).Test results for an identical empty aluminium tube are shown in Fig.1. We expectedto observe an increase in the average crushing force,F AV,for aluminium alloy tubes which hadbeenÿlledwith foam,as comparedwith id entical empty aluminium tubes.In fact,there is a complex interaction between the metal tubes andthe foamÿlling.The foamprovides support for the thin walls of the aluminium tubes leading to an increase in the overall。

等球Packing问题的序列对称换位算法余亮;黄文奇【期刊名称】《计算机应用研究》【年(卷),期】2012(029)005【摘要】为处理等球Packing问题,在基本拟物算法的基础上设计了序列对称换位策略,形成了一个启发式的序列对称换位算法.在球形容器内装填1～50个等球时,此算法改进了其中45项当前记录.特别地,此算法成功将68个半径为1的等球装进半径小于5的球形容器.此结果证否了一个猜想,该猜想认为半径为5的球形容器至多只能装下67个半径为1的等球.其结果的质量说明了序列对称换位算法的有效性.%To deal with the equal sphere Packing problem,this paper designed a serial symmetrical relocation strategy based on the basic quasi physical algorithm to form a serial symmetrical relocation algorithm. When packing up to 50 equal spheres in a spherical container, this algorithm improved 45 current records. Especially, it successfully packed 68 equal spheres of radius 1 into a spherical container whose radius is less than 5. This result proves wrong a conjecture which states the spherical container of radius 5 can at most contain 67 spheres of radius 1. The quality of the results justifies the serial symmetrical relocation algorithm.【总页数】3页(P1695-1697)【作者】余亮;黄文奇【作者单位】华中科技大学计算机科学与技术学院,武汉430074;华中科技大学计算机科学与技术学院,武汉430074【正文语种】中文【中图分类】TP301.6【相关文献】1.输电线路不换位引起的不对称问题及其改进方法 [J], 陶凯;刘明波2.求解等球packing问题的两个策略 [J], 余亮;黄文奇3.不换位输电线路产生的不对称问题及解决方法 [J], 丁洪发;段献忠4.求解一刀切式二维矩形Strip Packing问题的混合搜索算法 [J], 郭超;王磊;尹爱华5.一种求解等圆Packing问题的柔性位置选择算法 [J], 王英聪;张领;肖人彬因版权原因，仅展示原文概要，查看原文内容请购买。

一阶电路first-order circuit三要素法three-element method for analyzingfirst-order circuitss 平面s-plane二端元件two-terminal element二端网络two-terminal network无源网络passive-terminal network有源网络active-terminal networkT 形网络T-networkΓ形网络inverted L-network, Γ-network入射波incidence wave三相three-phase三相电路three-phase circuit三相制three-phase system三相四线制three-phase four-wire system三角形连接delta-connection, △-connection 三角形网络delta-network三端网络three-terminal network端口portπ形网络π- network已调信号modulated signal支路branch支路电流法branch current method支路阻抗矩阵branch impedance matrix支路导纳矩阵branch admittance matrix分压器voltage divider分压比voltage division ratio分贝decibel(dB)分离图separated graph开路open-circuit开路阻抗open-circuit impedance开路阻抗矩阵open-circuit impedance matrix反接inversed connection, connection inopposition反射阻抗reflected impedance反相opposite in phase反向串联inverted series connection反向传输矩阵inverted transmission matrix互感mutual inductance互感应现象mutual induction phenomenon互感耦合mutual-inductance coupling互感耦合电路mutual-inductance coupled circuit 互易性reciprocity 互易定理reciprocity theorem互易网络reciprocity network中线 (零线 )neutral wire中性点 (中点 )neutral point无功功率reactive power无功功率守恒theorem of conservation of reactive 定理power无功伏安reactive Volt-Ampere无功分量reactive component无功因数reactive factor双口网络two-port network, two-port对称双口网络symmetrical two-port network不对称双口网unsymmetrical two-port network 络X 形双口网络lattice network复合双口网络composite two-port networkT 形桥式双口bridge-T two-port network网络双 T 网络double-T network双 T 选频网络double-T frequency selectionnetwork匹配matching方阵square matrix韦伯 (韦)Weber(Wb)乏var辅助分析computer-aided analysis瓦特 (瓦)watt(W)分布电感distributed inductance内部法internal approach分段线性化法piece-wise linear approximation 分布参数电路distributed circuit反射系数reflection coefficient反射波reflected wave匹配match无损耗线lossless line无损耗线的输input impedance of lossless line 入阻抗无畸变distortionless无畸变条件distortionless condition无畸变线distortionless line电路circuit电源source理想电源ideal source1 /15实际电源physical source电位potential电位差potential difference电位升potential rise电位降potential drop电位参考点potential reference point电压voltage电压圆图voltage circle diagram电压源voltage source电压控制电压voltage-controlled voltage source 源电压控制电流voltage-controlled current source 源电压反馈系数voltage feed-back factor线电压line voltage相电压phase voltage电流current电流源current source电流控制电压current-controlled voltage source 源电流控制电流current-controlled current source 源电流放大系数current amplification factor线电流line current相电流phase current电动势electromotiveforce(e.m.f.),electromotance电激流excitation current电阻resistance内电阻internal resistance自电阻self-resistance共电阻 ( 互电mutual resistance阻)电导conductance内电导internal conductance自电导self-conductance共电导 ( 互电mutual conductance导)电感inductance电容capacitance电抗reactance电纳susceptance电信号electric signal 电场能量electric field energy电场强度electric field intensity电磁场electromagnetic field电力网power network电报方程telegraphic equation正弦波sinusoidal wave正弦信号sinusoidal signal正弦函数sinusoidal function正弦响应sinusoidal response正弦交流电路sinusoidal responsealternating current circuit正序positive sequence正相序positive phase sequence正负号函数signup矢量vector节点node节点方程node equation节点电流方程node current equation节点电压法node voltage method节点关联矩阵node incidence matrix节点电导矩阵node conductance matrix广义节点Super-node对称三相电路symmetrical three-phase circuit 对称均匀链形symmetrical uniform chain network 网络对偶原理principle of duality对偶网络dual network对偶元件dual element对应端corresponding terminal对象阻抗image impedance对象参数image parameter对象传输常数image propagation constant平面网络planar network非平面网络non-planar network功率power功率因数power factor功率因数角power factor angle功率三角形power triangle功率守恒定理theorem of conservation of power 平均功率average power有功功率active power无功功率reactive power视在功率apparent power2 /15右手螺旋定则right-handed screw rule外网孔outer mesh失谐状态detuned condition小失谐状态slightly detuned condition四端网络four-terminal network, quadripole 主元pivot element, pivot平衡工作点balanced operating point龙格 -库塔法Runge-Kutta method四阶 R-K 法forth-order R-K method四分之一波长quarter-wave line线史密斯阻抗图Smith Chart网络network网络分析network analysis网络分析法method of network analysis网络方程法network-equation method网络变换法network-transformation method网络拓扑network topology网络模型network-model有源网络active network无源网络passive network线性网络linear network非线性网络nonlinear network网孔mesh网孔电流法mesh-current method网孔矩阵mesh matrix网孔阻抗矩阵mesh-impedance matrix网孔对支路关mesh-to-branch incidence matrix 联矩阵自感 (自感系self-inductance数)并联parallel connection并联谐振parallel resonance有效值effective value有源二端网络equivalent source theorem of active 的等效电源定two-terminal network理有源二端网络equivalent voltage source theorem 的等效电压源of active two-terminal network定理 (戴维南定(Thevenin's theorem)理)有源二端网络equivalent current source theorem 的等效电流源of active two-terminal network定理 (诺顿定(Norton's theorem)理 )同名端dotted terminal同相in phase回路loop回路电阻矩阵loop-resistance matrix回路电流法loop-current method回转器gyrator导纳admittance导纳角admittance angle导纳圆图admittance circle diagram自导纳self-admittance共导纳 (互导mutual admittance纳 )共轭匹配conjugate matching共轭旋转相量conjugate rotating phasor负载load负序negative sequence负相序negative-phase sequence全磁通total magnetic flux全波整流full-wave rectification全通图completely-connected graph 次级线圈secondary coil行row行阵row matrix行子阵row submatrix行矢量row vector列column列阵column matrix列子阵column submatrix列矢量column vector关联incidence关联矩阵incidence matrix正向关联positive incidence负向关联negative incidence似功率quasi-power似功率守恒定theorem of conservation of理quasi-power传递函数transfer function传播常数propagation constant传输矩阵transmission matrix传输效率transmission efficiency米勒定理Miller's theorem3 /15级联cascade connection伏特 (伏 )Volt(V)伏秒Volt-second伏安特性volt-ampere characteristic安培 (安 )Ampere(A)西门子 ( 西)Siemens(S)过渡过程transient state过电压over voltage过电流over current自由分量free component自激振荡self-sustained oscillation自然功率natural power自然频率natural frequency网络的自然频natural frequency of a network率网络变量的自natural frequency of network然频率variables零输入响应的natural frequency of zero-input自然频率response阶跃响应step response冲量响应impulse response冲量响应矩阵impulse response matrix动态电阻dynamic resistance网孔运算阻抗mesh operational impedance matrix矩阵网络函数network function网络函数的极pole-zero diagram of network零点分布图function行波travelling wave正向行波direct wave反向行波returning wave行波功率travelling wave power行波系数travelling wave ratio串联series connection串联谐振series resonance连支link连通图connected graph连续频谱continuous spectrum不连续频谱discrete spectrum初相initial phase初相角initial phase angle初级线圈primary coil角频率angular frequency均方根值root-mean-square value均匀频谱uniform spectrum均匀链形电路uniform chain circuit时变电流time-varying current位移电流displacement current运算放大器operational amplifier两瓦特表法two-wattmeter method亨利 (亨)Henry(H)时域分析time-domain analysis时域位移定理real shifting(translation)theorem 时间常数time constant初始条件initial condition初始状态initial state初值定理initial value theorem张弛振荡relaxtion oscillation阻尼系数damping coefficient均匀传输线uniform transmission line均匀传输线的primary parameters of uniform 原始参数transmission line均匀传输线的differential equations of uniform 微分方程transmission line均匀传输线的propagation constant of uniform 传播常数transmission line均匀传输线的characteristic impedance of uniform 特性阻抗transmission line均匀传输线的attenuation constant of uniform 衰减常数transmission line均匀传输线相phase constant of uniform 移常数transmission line均匀传输线输input impedance of uniform 入阻抗transmission line均匀传输线的lumped equivalent circuit of 集中参数等效uniform transmission line 电路折射波reflected wave状态state状态变量state variable状态矢量state vector状态变量法state variable approach状态方程state equation状态空间state space状态空间法state space approach状态轨迹state trajectory4 /15状态转换矩阵state transition matrix状态变量计算superposition method for computer 机辅助分析的aided analysis of state variables叠加法状态变量计算topological method for computer机辅助分析的aided analysis of state variables拓扑法极限环limit cycle极点pole步长step length延时线time-delay line线性linearity线性电阻linear resistance线性电感linear inductance线性电容linear capacitance线性网络定理linear network theorem线状频谱line spectrum周期period周期信号period signal非周期信号non-periodic signal非线性元件nonperiodic element非正弦周期电non-sinusoidal periodic current流电路circuit单位阵unit matrix单位阶跃函数unit step function单位阶跃电压unit step voltage单位冲量函数unit impluse function单位冲量电流unit impluse current单脉冲信号single pulse signal单口网络one-port network, one-port拓扑图topological graph, graph有向拓扑图oriented graph拓扑结构topology, topological construction 转移transfer转移阻抗transfer impedance转移导纳transfer admittance转移电压比transfer voltage ratio转移电流比transfer current ratio转移函数transfer function转置阵transposed matrix转移函数transfer function转移函数矩阵transfer function matrix空载状态no-load condition 空心变压器air-core transformer参考方向reference direction参考相量reference phasor参考节点reference node受控源controlled source受控源关联矩controlled source incidence matrix 阵图graph子图Sub-graph奇谐波函数odd harmonic function变比transformation ratio环流circulating current直流direct current直流网络direct current network直流分量direct current component阻抗impedance阻抗角impedance angle阻抗逆变器impedance inverter阻抗频率特性impedance-frequency characteristic 自阻抗self-impedance共阻抗mutual impedance内阻抗internal impedance输入阻抗input impedance欧姆 (欧)Ohm's欧姆定律Ohm's law广义欧姆定律generalized Ohm's law欧拉法Euler's method法拉 (法)Farad(F)微法micro-Farad(F)皮法pico-Farad(F)法拉第电磁感Faraday's law of electromagnetic 应定律induction奈培neper(Np)经典法classical method非零状态响应non-zero-state response非强制网络unforced network非线性电路nonlinear circuit非线性电阻nonlinear resistance电流控非线性current-controlled nonlinear电阻resistance电压控非线性voltage-controlled nonlinear电阻resistance范式normal form范式状态方程normal form state equations5 /15放电过程discharge过阻尼放电过Over-damped discharge程欠阻尼放电过Under-damped discharge程非振荡放电过non-oscillatory discharge程振荡放电过程oscillatory discharge临界阻尼放电critically damped discharge过程拉普拉斯Laplace拉普拉斯正变Laplace transformation换拉普拉斯反变inverse Laplace transformation 换拉普拉斯积分Laplace integral拉普拉斯象函Laplace transform数线性组合定理linear combination theorem终值定理final value theorem波长wavelength波阻抗wave impedance波腹loop波节node驻波standing wave驻波系数standing wave ratio规则信号regular signal卷积convolution Integral卷积定理convolution Integral theorem 响应response响应信号response signal相位 (相 )phase相位角phase angle相位差phase difference相位频率特性phase-frequency characteristic 相矢量phasor相矢量分析法phasor analysis相序phasor sequence信号signal信号源signal source总电导total conductance树tree树支tree branch 树余cotree星形 (Y) 连接star-connection, Y-connection星形网络star-connection network复数complex number复数平面complex plane复数阻抗complex impedance复数导纳complex admittance复数功率complex power复数导纳矩阵complex admittance matrix顺接connection in aiding顺序positive sequence独立电源independent source品质因数quality factor逆序negative sequence选择性selectivity选频特性frequency-selection characteristic 恒定分量constant component脉冲pulse脉冲幅度pulse amplitude脉冲高度pulse altitude脉冲宽度pulse width脉冲持续时间pulse duration脉冲重复周期repeating period of pulse指数衰减因子exponential attenuation factor指数矩阵exponential matrix临界电阻critical resistance临界值critical value复频率complex frequency复频率平面complex frequency plane复频谱函数complex frequency spectrumfunction复频域complex frequency domain复频域位移定complex理shifting(translation)theorem复频域等效电complex shifting equivalent circuit 路复频域中广义generalized ohm's law in the欧姆定律complex frequency domain复频域传播常complex frequency domain数propagation constant复频域特性阻complex frequency domain抗characteristic impedance复频域反射系complex frequency domain6 /15数reflection coefficient电容的复频域complex frequency domain阻抗impedance of capacitor电感的复频域complex frequency domain阻抗impedance of inductorRLC 串联电路complex frequency domain的复频域阻抗impedance of RLC series circuit 相移速度phase velocity柏德生法则Peterson's Rule容抗capacitive reactance容纳capacitive susceptance振幅amplitude振幅频谱amplitude spectrum振幅旋转相量amplitude rotating phasor效率efficiency矩阵matrix矩阵分析法matrix analysis特性characteristic特性方程characteristic equation特性阻抗characteristic impedance特性参数characteristic parameter特性损耗characteristic loss特性相移characteristic phase displacement 特勒根定理Tellegen's theorem离散性discreteness离散频谱discrete spectrum高次谐波higher harmonic高斯消去法Gauss elimination method高斯主元消去Gauss elimination with pivoting法T 形阻抗网络bridge-T impedance network浮地电感floating inductance积分电路integrating circuit积分定理integration theorem衰减attenuation衰减系数attenuation constant振荡oscillation阻尼振荡damped oscillation衰减振荡attenuated oscillation减幅振荡attenuated oscillation等幅振荡unattenuated oscillation无阻尼振荡自由振荡高阶电路特征方程特征根 (值 )特征多项式特征方程复频域形式部分分式展开法留数计算法逐步近似法预解矩阵载波调制信号被调制信号换路基本回路基本回路矩阵基本割集基本割集矩阵基本子阵基波基尔霍夫基尔霍夫方程基尔霍夫定律基尔霍夫电流定律基尔霍夫电压定律基尔霍夫电流定律的复频域形式基尔霍夫电压定律的复频域形式偶谐波函数理想元件理想激励源理想电压源理想电流源理想受控源7 /15undamped oscillationfree oscillationhigher order circuitscharacteristic equationcharacteristic root, eigenvaluecharacteristic polynomialcomplex frequency domaincharacteristic equationpartial-fraction expansionevaluation by the residuemethod step-by-stepapproximation resolvent matrixcarriermodulating signalmodulated signalswitchingfundamental loopfundamental loop matrixfundamental cut setfundamental cut set matrixfundamental submatrixfundamental harmonicKirchhoffKirchhoff's equationKirchhoff's lawKirchhoff's current lawKirchhoff's voltage lawKirchhoff's current law in thecomplex frequency domainKirchhoff's voltage law in thecomplex frequency domaineven harmonic functionideal elementideal excitation sourceideal voltage sourceideal current sourceideal controlled source理想变量器ideal transformer理想变压器ideal transformer旋转相矢量rotating phasor混合参数矩阵hybrid parameter matrix累接阻抗iterative impedance接地点ground point谐振resonance谐振状态resonance state谐振电路resonant circuit谐振阻抗resonant impedance谐振频率resonant frequency谐波harmonic谐波分量harmonic component离散化discretization常态树proper tree随机性信号random signal集中参数lumped parameter集中参数元件lumped element集中参数电路lumped circuit等效网络equivalent network等效阻抗equivalent impedance等效导纳equivalent admittance短路short-circuit短路导纳short-circuit admittance短路导纳矩阵short-circuit admittance matrix 超前lead滞后lag惠斯登电桥Wheatstone bridge割集cut set割集电导矩阵cut set conductance matrix 策动点driving point策动点阻抗driving point impedance策动点导纳driving point admittance策动点函数driving point function替代定理substitution theorem链形网络chain network晶体管电路transistor circuit插入功率比insertion power ratio插入衰减insertion loss傅里叶Fourier傅里叶级数Fourier's series 傅里叶积分Fourier's integral傅里叶积分变Fourier's integral transform 换傅里叶系数Fourier coefficient傅里叶正变换positive Fourier transform傅里叶反变换inverse Fourier transform暂态transient state暂态分量transient component强制分量forced component确定性信号regular signal输入input输入电路input circuit输入功率input power输入端口input port输出output输出电路output circuit输出阻抗output impedance输出端口output port感抗inductive reactance感纳inductive susceptance零电位点zero potential point零子阵zero submatrix数值解法numerical analysis数值积分法numerical integration愣次定律Lenz's law幅角argument频率frequency频率特性frequency characteristic频谱frequency spectrum频谱函数frequency spectrum function 频带frequency band频带宽度band width通频带pass-band频域frequency domain频域响应frequency domain response 简谐分量simple harmonic component 微分电路differentiating circuit微分定理differentiation theorem零状态zero state零状态响应zero state response零状态分量zero state component零输入响应zero-input response8 /15零输入分量zero-input component输出方程output equation输入 -输出法input-output approach数值解法numerical solution群速group velocity群时延group time-delay畸变distortion叠加定理superposition theorem磁通magnetic flux磁通链magnetic flux linkage磁耦合magnetic coupling磁场能量magnetic field energy端电压terminal voltage端线terminal wire端口port terminal模modulus缩减矩阵reduced matrix谱线spectrum line稳态steady state稳态响应steady state response赫兹Hertz(Hz)稳态分量steady state component稳定性stability静态电阻static resistance端部法terminal approach截断误差truncation error耦合系数coupling coefficient增广矩阵augmented matrix增广节点导纳augmented node admittance matrix 矩阵额定电压rated voltage额定电流rated current额定功率rated power激励excitation激励信号excitation signal激励源excitation source激励函数excitation function瞬时值instantaneous value瞬时电压instantaneous voltage瞬时电流instantaneous current瞬时功率instantaneous power电压串联电阻 A voltage in series with a resister 电源变换Source transformation 电流并联电阻 A current source in parallel with aresister双边的Bilateral叠加Superposition麻烦的Cumbersome同时发生的Simultaneous术语Terminology二维的Planar安培表Ammeter编造的Fictitious操纵（作）Manipulation相关的Pertinent运算放大器The operational amplifier二极管Diode晶体管Transistor喜好Penchant明智的Judicious求助于Invoke复制品Replica比较器Comparator运动中的电荷Charge in motion定量关系Quantitative relationship绝缘体Insulator电介质材料Dielectric material时变电场Time-varying electric field位移电流Displacement current传导电流Conduction current无源元件Passive element单位是Be measured in图形上Graphically线圈Coiled wire短路Short current跃变Change instantaneously电弧Arcing微分Differential代数的Algebraic功率是消耗能Power is the time rate of对时间的倒数expending energy字母 C Letter C金属板Conductive plate零输入响应Natural response阶跃响应；零Step response状态响应9 /15系数Coefficient一阶电路First-order circuit指数Exponent倒数Reciprocal瞬间响应Transient response稳态响应Steady-state response示波器Oscilloscope类比的Analogous初始电压的指Exponential decay of the initial 衰减voltage减率The rate of decay基本微积分Elementary calculus等幅震荡Oscillation衍生物Derivation特征根Characteristic roots谐振角频率Resonant radian frequency量纲Dimension复频率Complex frequency过阻尼Over damp欠阻尼Under damp临界阻尼Critically damp正弦的Sinusoidal提及的Allude to配线电路Distribution circuit详述Spell out领域Realm间隔时间Interval相互的Reciprocal波幅Amplitude相位角Phase angle平面三角学Trigonometry均方根Rms value直流电压Dc voltage暂态分量Transient component无穷小Infinitesimal丧失Forfeit向量Phasor括号Argument符号Notation向量变换Phasor transform时域Time domain复数域Complex-number domain 黑体字Boldface letter极坐标假设下脚标无意义的术语，命名法无源元件有源元件阻抗电抗瞬时功率有功功率；平功率无功功率视在功率通过A滞后 B120 ° A超前 B120 °相序圆柱体表面定子线圈发电机线电压相电压动态元件滤波器听得见的选频电路衰减图式均衡器低通高通带通带阻滤波器初步通带阻带频率响应曲线幅频特性曲线相频特性曲线截止频率Polar formPostulateSubscriptNonsensical NomenclaturePassive elements Active elements ImpedanceReactance Instantaneous power Average powerReactive power Apparent powerViaA lagB by 120°A lead B by 120°Phase sequence PeripheryStatorWindingGeneratorLine-to-linevoltageLine-to-neutralvoltageReactivecomponentsFilterAudibleFrequency-selective circuitsAttenuateGraphicequalizerLow pass filtershigh pass filtersBand pass filtersBand rejectfiltersPreliminaryPassbandStopbandFrequencyresponse plotMagnitude plotPhase angle plotCutoff frequency 10/ 15Chapter 1 Elements and Laws of Eletrical Circuits电路electrical circuit电路模型circuitmodel电源source负载load导线line开关switch电荷electric charge电流current电压voltage电位potential电位升potential rise电位降potential drop电位差potential difference参考点referencepoint线性电阻linear resistance磁通链magnetic flux linkage功率power能量energy电阻器resistor电阻resistance电动势electromotive force （ e.m.f ）伏安特性u-i characteristicvolt-ampere characteristic电导器conductor电导conductance电感器inductor电感inductance电容器capacitor电容capacitance欧姆定律Ohm’s Law广义欧姆定律generalized Ohm ’s Law参考方向reference direction电压极性voltage polarity正极positive polarity负极negative polarity开路open-circuit短路short-circuit理想独立电压源ideal independent voltage实际电压源physical sourcesource理想独立电流源ideal independent current理想受控源ideal dependent / controlledsource source压控电压源voltage controlled voltage压控电流源voltage controlled currentsource（VCVS ）source（ VCCS ）流控电压源current controlled voltage流控电流源current controlled currentsource（CCVS ）source（ CCCS）节点node支路branch回路loop路径path网孔mesh网络network基尔霍夫电流定律Kirchhoff ’s current law（KCL ）基尔霍夫电压定律Kirchhoff ’s voltage law（KVL ）闭合面closed surface集总参数lumped parameter集总（参数）电路lumped circuit集总（参数）元件lumped element分布参数distributed parameter分布（参数）电路distributed circuit直流direct current （DC）交流alternating current（ AC ）有源元件active element无源元件passive elementChapter 2 Analysis methods to simple resistor circuits端钮terminal串联series connection分压voltage division并联parallel connection分流current division等效变换equivalent transformation等效电阻equivalent resistance入端电阻input resistance最大功率传输定理Maximum power transfer theorem Y- 变换Wye-Delta transformation11/ 15Chapter 3 methods of Analysis节点法node analysis / node voltage method支路电流法branch current method回路电流法loop analysis / loop current method外网孔outer mesh网孔电流法mesh analysis / mesh current method自导纳self admittance互导纳mutual admittance矩阵matrix行row列column参考节点reference node平面电路planar circuit方程equation消去法elimination technique克莱姆法则Cramer’s rule代入法substitution method运算放大器operational amplifier(op amp)同向输入端noninverting input反向输入端inverting input输出端output等效电路模型equivalent circuit model开环放大倍数open-loop gain闭环放大倍数closed-loop gain入端电阻input resistance输出电阻output resistance线性工作区linear region正向饱和区positive saturation反向饱和区negative saturation同向放大器noninverting amplifier反向放大器inverting amplifier加法器summing amplifier / summer积分器integrator微分器differentiator自激振荡self-excited oscillationChapter 4 Circuit Theorems叠加原理superposition theorem齐性原理homogeneity property输入 /激励input / excitation输出 /响应output / response线性电路linear circuit代数和algebraic sum替代定理substitution theorem戴维南定理Thevenin ’s theorem诺顿定理Norton ’s theorem二端网络two-terminal circuit开路电压open-circuit voltage短路电流short-circuit current特勒根定理Tellegen ’s theorem功率平衡定理power-balancing theorem互易定理reciprocal theorem对偶原理principle of duality对偶元件dual element对偶图dual graph对偶电路dual circuitChapter 5 Analysis of Op Amp Circuits非线性电路nonlinear circuit非线性元件nonlinear element压控电阻voltage-controlled resistor流控电阻current-controlled resistor工作点operating point静态电阻static resistance动态电阻dynamic resistance小信号分析small-signal analysis小信号模型small-signal mode分段线性化法piece-wise linear method数值解法numerical analysisChapter 6 First-order Circuit动态电路dynamic circuit一阶电路first-order circuit一阶微分方程first-order differential equation过渡过程transient process/ transient 线性非时变电路linear time-invaried circuit单位阶跃函数unit step function单位冲激函数unit impulse function单位斜坡函数unit ramp function起始条件initial condition起始值initial value换路定则switch law零输入响应zero-input response12/ 15零状态响应zero-state response稳态响应steady-state response 暂态响应transient response时间常数time constant指数函数exponential function冲激响应impulse response阶跃响应step response自由响应natural response自由分量natural component强迫响应forced response强制分量forced component全响应complete response稳态值final value卷积convolution时域延迟time delay换路switching跳变现象jump phenomenon脉冲持续时间pulse duration脉冲重复周期repeating period of pulseChapter 7 Second-order Circuit常系数微分方程constant coefficients differential齐次微分方程homogeneous differential equation equation二阶电路second-order circuit特征方程characteristic equation 特征根characteristic root特征值eigenvalue特征向量eigenvector特解particular solution通解general solution自然频率natural frequency衰减系数damping factor谐振频率resonant frequency过阻尼情况overdamped case欠阻尼情况underdamped case临界情况critically damped case固有频率natural frequency衰减振荡damped oscillation无损lossless正弦响应sinusoidal response波形waveform复数complex衰减attenuationChapter 8-9 Sinusoidal Steady-State Analysis复数complex幅值amplitude / magnitude相位phase相位差phase difference角频率angular frequency周期period频率frequency正弦的sinusoidal初相角initial phase angle瞬时值instantaneous value最大值maximum有效值effective value / root-mean-square value u 领先 i φu leads i byφu 落后 i φu lags i byφ同相in phase反相opposite in phase实部real part虚部imaginary part直角坐标形式rectangular form极坐标形式polar form指数形式exponential form相量phasor参考相量reference phasor旋转相量rotating phasor电压三角形voltage triangle瞬时功率instantaneous power平均功率average power阻抗impedance阻抗角impedance angle阻抗三角形impedance triangle导纳admittance电抗reactance电纳suspectance感性inductive感抗inductive reactance感纳inductive suspectance容性capacitive容抗capacitive reactance容纳capacitive suspectance正弦稳态响应sinusoidal steady-state response时域time-domain相量域phasor-domain瞬时概率instantaneous power视在 /表观功率apparent power功率因数power factor (pf)复功率complex power功率三角形power triangle复共轭complex conjugate有功分量active component有功功率active power无功分量reactive component功率守恒定理theorem of conservation of power无功功率reactive power阻抗匹配impedence matching共轭匹配conjugate matching串联谐振series resonance并联谐振parallel resonance谐振频率resonance frequency品质因数quality factor特性阻抗characteristic impedence频率响应frequency response选择性selectivity选频特性frequency-selection characteristicChapter 10 Magnetically Coupled Circuits耦合couple互感mutual inductance自感self-inductance磁通magnetic flux线圈coil铁心线圈iron core coil匝数turn耦合系数coupling coefficient变压器transformer空心变压器air-core transformer原边primary coils / windings副边secondary coils / windings引入阻抗reflected impendence理想变压器ideal transformer全耦合unity coupling coefficient全耦合变压器perfect coupling transformer变比turns ratio / transformation ratio自耦合变压器auto transformer多绕组变压器multiple-winding transformer激磁电感magnetizing inductance右螺旋定则right-hand screw rule漏感leakage inductance同名端dotted terminalterminals of same magnetic polarityChapter 11 Three-phase Circuits对称三相电路symmetrical three-phase circuit三相电源three-phase sources中线neutral line中性点neutral point三相四线制three-phase four-wire system相电压phase voltage线电压line voltage相序phase sequence正序positive / abc sequence负序negative / acb sequence相电流phase current线电流line currentChapter 12 Steady-State Response of Periodic Excitation信号signal周期函数periodic function周期性非正弦激励nonsinusoidal periodic excitation帕斯瓦尔定理Parseval ’s theorem 指数形式的付里叶级数exponential Fourier series付里叶系数Fourier coefficient基波fundamental harmonic基波频率fundamental frequency 谐波harmonic wave高次谐波higher harmonic频谱frequency spectrum谱线spectrum line线状频谱line spectrum奇次谐波oddharmonic偶次谐波even harmonic奇对称odd symmetry。

2011年技术物理学院08级（激光方向）专业英语翻译重点！！！作者：邵晨宇Electromagnetic电磁的principle原则principal主要的macroscopic宏观的microscopic微观的differential微分vector矢量scalar标量permittivity介电常数photons光子oscillation振动density of states态密度dimensionality维数transverse wave横波dipole moment偶极矩diode 二极管mono-chromatic单色temporal时间的spatial空间的velocity速度wave packet波包be perpendicular to线垂直be nomal to线面垂直isotropic各向同性的anistropic各向异性的vacuum真空assumption假设semiconductor半导体nonmagnetic非磁性的considerable大量的ultraviolet紫外的diamagnetic抗磁的paramagnetic顺磁的antiparamagnetic反铁磁的ferro-magnetic铁磁的negligible可忽略的conductivity电导率intrinsic本征的inequality不等式infrared红外的weakly doped弱掺杂heavily doped重掺杂a second derivative in time对时间二阶导数vanish消失tensor张量refractive index折射率crucial主要的quantum mechanics 量子力学transition probability跃迁几率delve研究infinite无限的relevant相关的thermodynamic equilibrium热力学平衡（动态热平衡）fermions费米子bosons波色子potential barrier势垒standing wave驻波travelling wave行波degeneracy简并converge收敛diverge发散phonons声子singularity奇点（奇异值）vector potential向量式partical-wave dualism波粒二象性homogeneous均匀的elliptic椭圆的reasonable公平的合理的reflector反射器characteristic特性prerequisite必要条件quadratic二次的predominantly最重要的gaussian beams高斯光束azimuth方位角evolve推到spot size光斑尺寸radius of curvature曲率半径convention管理hyperbole双曲线hyperboloid双曲面radii半径asymptote渐近线apex顶点rigorous精确地manifestation体现表明wave diffraction波衍射aperture孔径complex beam radius复光束半径lenslike medium类透镜介质be adjacent to与之相邻confocal beam共焦光束a unity determinant单位行列式waveguide波导illustration说明induction归纳symmetric 对称的steady-state稳态be consistent with与之一致solid curves实线dashed curves虚线be identical to相同eigenvalue本征值noteworthy关注的counteract抵消reinforce加强the modal dispersion模式色散the group velocity dispersion群速度色散channel波段repetition rate重复率overlap重叠intuition直觉material dispersion材料色散information capacity信息量feed into 注入derive from由之产生semi-intuitive半直觉intermode mixing模式混合pulse duration脉宽mechanism原理dissipate损耗designate by命名为to a large extent在很大程度上etalon 标准具archetype圆形interferometer干涉计be attributed to归因于roundtrip一个往返infinite geometric progression无穷几何级数conservation of energy能量守恒free spectral range自由光谱区reflection coefficient（fraction of the intensity reflected）反射系数transmission coefficient（fraction of the intensity transmitted）透射系数optical resonator光学谐振腔unity 归一optical spectrum analyzer光谱分析grequency separations频率间隔scanning interferometer扫描干涉仪sweep移动replica复制品ambiguity不确定simultaneous同步的longitudinal laser mode纵模denominator分母finesse精细度the limiting resolution极限分辨率the width of a transmission bandpass透射带宽collimated beam线性光束noncollimated beam非线性光束transient condition瞬态情况spherical mirror 球面镜locus（loci）轨迹exponential factor指数因子radian弧度configuration不举intercept截断back and forth反复spatical mode空间模式algebra代数in practice在实际中symmetrical对称的a symmetrical conforal resonator对称共焦谐振腔criteria准则concentric同心的biperiodic lens sequence双周期透镜组序列stable solution稳态解equivalent lens等效透镜verge 边缘self-consistent自洽reference plane参考平面off-axis离轴shaded area阴影区clear area空白区perturbation扰动evolution渐变decay减弱unimodual matrix单位矩阵discrepancy相位差longitudinal mode index纵模指数resonance共振quantum electronics量子电子学phenomenon现象exploit利用spontaneous emission自发辐射initial初始的thermodynamic热力学inphase同相位的population inversion粒子数反转transparent透明的threshold阈值predominate over占主导地位的monochromaticity单色性spatical and temporal coherence时空相干性by virtue of利用directionality方向性superposition叠加pump rate泵浦速率shunt分流corona breakdown电晕击穿audacity畅通无阻versatile用途广泛的photoelectric effect光电效应quantum detector 量子探测器quantum efficiency量子效率vacuum photodiode真空光电二极管photoelectric work function光电功函数cathode阴极anode阳极formidable苛刻的恶光的irrespective无关的impinge撞击in turn依次capacitance电容photomultiplier光电信增管photoconductor光敏电阻junction photodiode结型光电二极管avalanche photodiode雪崩二极管shot noise 散粒噪声thermal noise热噪声1.In this chapter we consider Maxwell’s equations and what they reveal about the propagation of light in vacuum and in matter. We introduce the concept of photons and present their density of states.Since the density of states is a rather important property，not only for photons，we approach this quantity in a rather general way. We will use the density of states later also for other(quasi-) particles including systems of reduced dimensionality.In addition,we introduce the occupation probability of these states for various groups of particles.在本章中，我们讨论麦克斯韦方程和他们显示的有关光在真空中传播的问题。

作者简介:王利斌(1982-),男,山西太原人,硕士研究生,工程师,从事机载无线通信设备设计与开发工作,主要研究方向为射频功放设计与无源射频电路设计。

基于ADS 的宽带定向耦合器的设计与仿真Design and Simulation of BroadBand Directional Coupler Based on ADS王利斌(中国西南电子技术研究所,四川成都610036)Wang Li-bin (Southwest China Institute of Electronic Technology,Sichuan Chengdu 610036)摘要：该文简单阐述了定向耦合器的工作原理，通过对比分析微带线耦合器和带状线耦合器。

通过使用Keysight 公司的ADS 仿真软件，设计一款采用LCR 补偿方案可以兼顾平坦度和方向性的带状线双定向耦合器，最后给出该耦合器的实际电路模型和满足设计预期的仿真数据。

关键词:定向耦合器；LCR 补偿方案；带状线中图分类号：TN622文献标识码：A文章编号：1003-0107(2019)09-0038-06Abstract:This paper briefly describes the working principle of directional coupler,and analyzes microstrip-line coupler and stripline coupler.By using Keysight's ADS simulation sofware,a LCR compensation is designed which the scheme can give consideration to both flatness and directional of the stripline bi-directional coupler.Finally,the actual circuit model of the coupler and the simulation result satisfiying the design expectation are given.Key words:directional coupler;LCR compensation;stripline CLC number:TN622Document code:AArticle ID ：1003-0107(2019)09-0038-060引言定向耦合器的基本工作原理同和微带功率分配器一样[1]，同时有四个端口，分别是输入端、耦合端、直通端和隔离端。

Aactive circuit elements 有源电路元件active branch 有源电路alternating current 交流电amplitude （叫变量的）幅值振幅angnlar velocity 角频率 A..C.generator 交流电动机active length 有效长度anti-phase 反向accuracy 精确性准确性精度aperiodic 非周期性的approach 接近途径approximation 接近值arbitrary 任意的algorithm 算法alternative 替换的交替的比较方案a good-quality voltmeter 高质量的电压表Bbio-polar junction transistor双极性晶体管buffer amplifier 缓冲放大器Ccircuit components 电路元件circuit parameters 电路参数conductor 导体conductance 电导circuit diagram 电路图carbon-filament lamp 碳丝电灯circuit branch 支路complex circuit 复杂支路communication circuit 通信电路common base 共基极common collector 共集电极common source 共源极common drain 共栅极channel 信道频道coefficient 系数convergence 收敛conversely 相反的逆的coordinate 坐标criterion 标准规范decaying oscillatory function 衰减震荡函数cascade 串联串级constancy 不变恒定corresponding to 符合于Ddirect-current（D.C）circuit 直流电路displacement current 位移电流double subscript 双下标D.C machine 直流电机definition 定义distribution of B 磁场分布D.Cblocking capacitor 直流耦合电容器 D.C supply 直流供电电源dimension 维数Differentiate 求…的微分Dirichlet 狄里克雷条件discontinuity 心电图心动电流图Dead-hand 死区deem 认为认定diagram 图表简图Diagrammatically 利用图表dead-weight tester 净重测量仪Eelectrical device 电气设备electrical energy 电能energy source 能源energy converter 电能转换器 e.m.f 电动势external characteristic 外特性electrical-sheet stel 电工钢步epoch angle 初相角electrode 电极电焊条emitter 发射器发射机emitter follower 射极跟随器even 偶数的expansion 展开（式）FFrequeney 频率field effect transistor 场效应管foregoing前述的在前的Faithful 可靠的正确的GGenerator 发电机gain增益geometrical 几何学的Geometry 几何学HHeating applicance 电热器heat-treatment 热处理器harmonic current 正弦电流Hybrid-πmodel混合π型模型half-wave symmetry 半波对称harmonical 谐波的Harmonic 谐波hysteresis 滞后hysteresis over 滞后误差IIdeal source 理想电源ideal voltage source 理想电压源ideal current source 理想电流源Internal resistance 内阻instant of time 瞬时instantaneous value of current 电流瞬时值Induction-heading 感应发热initial phase 初相角in quadrature 正交In phase 同相insulator 绝缘体in parallel with 与…并联Isolation 隔离绝缘隔振input resistance 输入电阻identity 恒等式Instant 瞬时瞬间integrand 被积函数integrate 求…的积分Intuitively 直观的直觉的intermittently 间歇的JKLLoad characteristic 负载特性load resistance 负载电阻leakage current 漏电流Lag in phase behind （相位）落后Legendre 勒让德多项式linear 线性的Locus 轨迹linearity 线性度MMagnetic and electric field 直磁场metal-filament lamp 金属丝灯泡mechanical strength 机械强度Modulated by （由…）调制magnetic pole 磁极magnetic induction 磁感应强度Mid-frequency band 中频带main 电源电力网manifestation 表现Minimum 最小是最小化mutually 相互地mapping 映射Momentum 要素magnification 放大放大倍数measurand 被测量Measuring system deemed by expert 由专家认定的测试系统NNon-linear characteristics 非线性特性non-salient pole 隐（非凸）极notation 符号记号Negligible 可忽略的OOhm’s low 欧姆定律over-voltage 过电压output resistance 输出电阻Odd 奇数的单数的ohm 欧姆order 次序阶Origin 原点orthogonal 正交的直角的occasion 时机机会场合Offset 便宜oscilloscope 示波器PPrimary cell 原生电池passive element 无源原件P.D=potential drop 电压降passive circuit elements 无源电路元potential distribution 电位分布period 周期power transmission line 输电线periodic current 周期电流pole-pairs 极对数position reference direction 正（参考）方向peak value （交变量）最大值phase 相位pulsatance 谐振常数角频率phase shift 相位移polarity 极性偏极paralled circuit 并联电路paralled resonance 并联混振paralled series 混联peak 最高的最高峰periodicity 周期perpendicular 垂直的正交的polynomial 多项式的多项式power series 幂级数performance 特性precision 精确度put…away 拿开送走QQuasi-periodic 准周期的Rreceiving end 接收端reference point 参考点remote control 遥控rotor 电机转子radian 弧度rectifier 整流器resistor 电阻器reinforce 加强reproducibility 可再现性resolution 分辨率Ssecondary cell 再生电池self/mutual induction 自/互感storage battery 蓄电池series and parallel equipment circuit 串并联等值电路single-loop network（circuit）单回路网络（电路）symbolized by 用符号表示semiconductor oscillator 半导体振荡器stator 电机定子slip-ring 滑环source follower circuit信号跟随电路steaked up 叠装small signal amplifier 小信号放大器self-bias resistor 偏置电阻slot 槽series 展成级数级数set 集合sinusoidal 正弦的susceptible 敏感的易受影响的symmetry 对称symmetrical 对称的shift operator 移位算子shifting property 筛选特性static friction 静态摩擦sensitivity 灵敏度span 范围tolerance 公差Ttime-invariant 时不变的the dielectric 电介质terminal voltage 端电压term 术语项theorem 定理法则time domain 时域trigonometric 三角法的trigonometric identities 三角恒等式trajectory 轨道truncate 截断截断的Uunidirectional current 单方向电流underlying 基础的在下面的Vvoltage drop 电压降volt-ampere characteristics 伏安特性vector 向量矢量vice versa 反之亦然vicinity 附近Wwire 导线Walsh function 沃尔什函数XYZ。

quasi-experimental shift-share research designsQuasi-experimental shift-share research designs are used to identify the impact of a specific policy or intervention on a particular group or population. These designs are commonly used in social sciences, economics, and public policy research.The shift-share design is widely used to measure the impact of an intervention, policy, or treatment on a specific population by comparing the change observed in the population to that of a comparison or control group. In this design, the population is divided into two groups - those who receive the intervention and those who do not. Using the comparison group, researchers can evaluate the extent to which observed changes can be attributed to the intervention.The quasi-experimental design is similar to the randomized controlled trial, with one key difference. In a randomized controlled trial, participants are randomly assigned to either the treatment or control group. However, in a quasi-experimental design, the researcher does not have control over the assignment of participants to the treatment and control groups. Instead, they must use observational data to create the groups.Despite the potential for selection bias in quasi-experimental shift-share research designs, they are often preferred over randomized controlled trials, especially when the cost of the intervention is high or when ethical concerns make it difficult to allocate certain populations to the control group.There are different types of quasi-experimental shift-share researchdesigns, each with its own strengths and weaknesses. One of the most commonly used designs is the difference-in-differences (DiD) design. This involves comparing the change in the outcome of interest between the treatment and control groups before and after the intervention. The DiD design has the advantage of comparing the change over time between the two groups, making it more robust to time-varying confounders.Another commonly used design is the regression discontinuity design (RDD). This design involves using a cut-off point to assign individuals to the treatment or control group. The cut-off point serves as the threshold for eligibility for the intervention. RDD designs are best suited for situations where the intervention is allocated based on a continuous variable, such as income or test scores.The instrumental variable (IV) design is another commonly used quasi-experimental shift-share design. This involves identifying an exogenous variable that predicts treatment assignment but is not related to the outcome of interest. The IV design is useful when the assignment of the intervention is not random but is instead based on some external factor not related to the outcome.In conclusion, quasi-experimental shift-share research designs are essential tools in evaluating the impact of interventions and policies on populations. Researchers must carefully consider the research design they use, as different designs have different strengths and weaknesses. Despite the potential for selection biasin quasi-experimental designs, they are often preferred overrandomized controlled trials when allocating participants to a control group is not feasible or ethical.。

土木工程专业英语生词整理声明：本文档是笔者结合清华大学俞家欢老师《土木工程专业英语》与同济大学苏小卒老师《土木工程专业英语》上下册整理的一些土木工程领域常用的生词，仅供有需要的朋友学习交流使用。

可能有少量打错的字，请谅解。

barrages 水库canals 运河distributary 引流工程highway 公路expressway 高速公路（美式）levee 码头mitigate floods 减轻洪水construction 建造→施工survey 调查→工程勘察helipad 停机坪truck terminal 铁路站台sewage treatment 污水处理demolish 拆毁central government or local administration中央或地方政府reinvestment 再投资petroleum revenue 石油财政（指迪拜）resort island 度假岛desert country 沙漠地区国家waterfront 滨海区residential apartment 公寓住宅gulf 海湾buttressed design 扶壁设计tripod foundation 三脚架式基础tide and current 潮起潮落traffic congestion 交通拥挤regulate 限制financial crisis 金融危机escalate rent cost 租金持续上涨mega-project 大项目revale 媲美microcosm 缩影tropical cyclone 热带气旋（台风）downstream 产业链下游desalination 海水淡化distillation 蒸馏ubiquitous 无处不在的marine species 海洋生物density 重度（类似密度）gravity 重力→比重toughness 韧性ductility 延性brittleness 脆性creep 徐变，蠕变stiffness 刚度impact strength 冲击强度thermal 热力学特性corrosion resistance 耐腐蚀性acidity 酸性，酸度alkalinity 碱性，碱度sound 声absorption 吸收transmission 传导reflection 反射acoustical 声学特性optical 光学特性physiochemical 生化特性abrasion 磨损indentation 缺口，凹痕machining 蚀刻scratch 切削oxidize 氧化cement-mortar 水泥砂浆quarry 采掘lintel 过梁ballast 压载材料（铁轨下的垫材）brick 砖refractory brick 耐火砖ventilator 通风设备railway coaches 铁路车厢wagon 马车sleeper 枕木masonry construction 砌体结构gravel 砂石，砾石property 性能plastic stage 塑性workability 和易性mix 混合→拌和place 放置→浇筑compacte 压实finish 竣工homogeneity 同质性segregation 离析性coarse aggregate 粗骨料water tightness 水密性bleeding 裂隙pore 孔隙porous 多孔的harshness 粗糙的poorly graded aggregate 骨料级配不良withstand 抵抗moisture variation 潮湿变化freeze and thaw 冻融impermeability 密闭性resistance to wear and tear 耐磨性reinforced cement concrete 钢筋混凝土prestressed cement concrete 预应力混凝土silo 筒仓bunker 煤仓，地堡，掩体ornamental structure 装饰性结构tensile load 抗拉强度slab 板tall chimney 高烟囱aqueduct 高架渠ferro-cement 钢纤维混凝土skeletal steel 钢骨架pre-cast unit 预制单元（构件）vault 拱顶shell 壳结构grid surface 网格表面folded plate 褶皱板partition 隔断ductile 延展性好的susceptible to damage 易损坏harmony express 和谐号动车asbestos cement sheet 石棉水泥板shape memory alloy 形状记忆合金magnetostrictioe material 磁致伸缩材料piezoelectric material 压电材料electrorheological fluid 电流变材料viscosity 黏性deflection 挠度vibration 振动noise mitigation 噪声抑制bridge deck 桥面bridge pier 桥墩slab 板beam 梁grider 大梁、桁架restrained structure 超静定结构differential settlement 不均匀沉降hydrostatic load 静水荷载earth load 土压力earthquake load 地震荷载tile 瓦felt and gravel 毡及卵石层gypsum block 石膏wood stud 木栓texture of the building surface建筑表面形状纹理stiffness of the structure 建筑结构刚度stagnation pressure 风压wind suction 风吸力leeward 背风面的coefficient 系数gust factor 阵风系数essential factor 重要性系数hazardous facility 危险设备seismic load 地震荷载vibration 振型whiplash effect 鞭梢效应a portion of the base shear force底部剪力法storey 楼层hydraulic 水运elevator shaft 电梯井筒folded plate 折板屋顶bearing wall 承重墙shear wall 剪力墙unobstructed surface 无障碍表面erect 建造，建立residential 民用建筑institutional 公共结构serviceability 实用性failure 极限状态rehabilitation 加固verification 验证load transfer mechanism 荷载传递机理flexure 弯曲，屈曲torsion 扭转shear 剪切membrane 拱grid 柱reinforcement bars（rebars）钢筋patent 专利precast concrete 预制混凝土cast concrete 现浇混凝土brick chip 碎砖块cement hydrates 水泥水化物microscopic opaque crystal 微小透明晶体microscopic rigid lattice 微观晶格corrugated 有螺纹的cohesion 黏结力passivate 钝化（钢筋）chloride 氯离子provision 规定，要求moisture 潮湿，水分humidity 湿度，湿热curvature 弯曲，曲度，曲率singly-reinforced beam 单筋梁under-reinforced beam 少筋梁over-reinforced beam 超筋梁balanced-reinforced beam 适筋梁instantaneous 立即，突然material-safety factor 安全系数allowable stress design 许用应力设计flake 剥落mix design 配合比设计penetrate 侵入serviceability failure in limit state design正常使用极限状态破坏bond failure 黏结失效carbonation 碳化作用neutralisation 中和作用（即碳化作用）optimal 最佳选择phenolphthalein indicator 酚酞指示剂admixtures 外加剂rapid set-up 快速初凝mitigate 减轻，缓和capillary 毛细管sound attenuating layer 隔音层slump 坍落度concrete vibrating 振捣steel sire 箍筋iron chain suspension bridge 铁链吊桥rivets connection 铆钉连接wrought iron technology 锻铁技术cast iron 铸铁high-strength bolt 高强度螺栓fabrication 制作technical code 技术规程cold-formed thin-wall steel 冷弯薄壁型钢masonry 砌体材料plasticity 塑性tenacity 韧性isotropic 各项异性ideal elastic-plastic 理想弹塑体proportional limit 比例极限（σp）yield strength 屈服强度tensile strength 抗拉强度fabrication 制作weldability 焊接性能air tightness 气密性press vessel 压力容器heat resistance 耐热性non-refractory 防火性能差fire proof protection 防火保护brittle fracture 脆性断裂large span structure 大跨度结构crane 吊车profiled steel sheet 异型钢板mega-frame structure 组合结构demountable structure 可拆卸结构steel scaffolding 钢脚桁架rupture 破裂buckling 搭扣，屈曲formation of mechanism 形成机构（塑性铰）wind induced oscillation 风致振动provision 规定load-carrying structure 承重结构percentage of elongation 伸长率cold-bending test 冷弯实验single story frame 单层结构bridge crane 桥式起重机residual stress 残余应力sun-dried mud 晒干的泥土shale 页岩lateral load 水平荷载seismic 地震raw material 原材料mortar 砂浆mica 云母filthy 有机杂质odor 气体iron compound 铁化合物mold 模具stirrup 箍筋gravel 砾石compact sand 紧密的砂土trench 沟槽over footing 地梁adherence 黏结性confining column 构造柱minimum covering for concrete最小保护层厚度water cement ratio 水灰比mid-rise segment 中高层建筑glulam beam 胶合木梁dwelling 住宅sport arene 运动场better seismic performance更好的抗震性能interior 内部gypsum 石膏板external cladding 外覆盖层fire-rated assembly 防火组件hybrid construction 混合结构practical 实用的exterior infill wall 外部填充墙energy performance 节能性能renovation 装修flat roof 平屋面extra accommodation 阁楼solid wood panel 实木板freight 运送到up-front invesrment 前期投资mortise 榫眼，榫接tenon 榫erected 直立的flammable 易燃物purlin 檩条spatial construction 空间结构high load-bearing capacity很高的荷载承担能力compaction 密实erection 建造hollow steel tube 中空钢管unfilled tube 中空钢管confinement 约束作用schematic view 示意图favorable stress distribution有利的荷载分布terrain 地形cantilever bridge 悬臂桥arch bridge 拱桥suspension bridge 悬索桥cable-stayed bridge 斜拉桥truss bridge 桁架桥pier 桥墩dissipation 消散（荷载）box girder 箱梁meticulous analysis 精细分析foot bridge 人行桥false work 脚手架counter balance 平衡抵消anchor arm 锚固臂outermost 最外侧pinned joint 铰接节点segment construction 分布施工canyon 峡谷abutment 桥墩（基台）viaduct 高架桥thrust 推力spandrel 拱尖catenary 锁链aforementioned 如前所述的bluff 悬崖pillar 塔架slender 细的parabola 抛物线lattice girder 格构梁drought 干旱flood 洪水cyclone 飓风environmental degradation 环境恶化meteological disaster 气象灾害casualty 伤亡invariably 始终如一的secondary disaster 次生灾害earthquake portent 地震预警landslide 滑坡collapse 崩塌debris flow 泥石流river erosion 河流侵蚀turbid 浑浊fissure 裂缝resilient 弹回，有弹力的sewerage 污水，排水设备snowmelt 融雪水escalation of cast 超过预算time overrun 工期延长pharmaceutical 制药mitigate potential risk 化解潜在风险tenet 宗旨aqueduct 高架渠，渡槽ballistic 弹道学causeway 长堤，堤道channel 沟渠，海峡，槽钢equilibrium 平衡（状态）excavation 挖掘hydraulic 水力的mason 砖瓦石匠obelisk 方尖石塔quarry 采石场sewage 污水reimbursable 可报销的，可补偿的aerated concrete 加气混凝土aggregate 骨料binding agent 粘合剂bitumen 沥青blunt 钝的bolt 螺栓cast 浇筑clamp 夹子corrode 腐蚀course （砖）层，行form 模板grout 薄砂浆，灰浆multistory building 多层建筑rate of contraction 收缩率rate of expansion 膨胀率rivet 铆钉，铆接screw 螺丝钉slab 平板spray 喷射tarlike 沥青thread 螺纹tile 瓦片versatile 多用途的weld 焊接blastfurnace 高炉矿渣asbestos 石棉瓦modulus of rupture 断裂模量hydration 水化作用cohesive 粘性的rapid-hardening 速凝grading 级配dampness 湿度，含水量accelerator 速凝剂inhibitor 抑制剂plasticizer 塑化剂grouting agent 灌浆剂consistency 稠度mobility 流动性compactability 可密实性biaxial 二轴的distortion 扭曲，变形elongate 拉长，延长moment 力矩prismatic 棱柱形的superposition 迭加作用transverse 横向的triaxial 三轴的，空间的vessel 容器bracing 拉条，撑杆conservation of energy 能量守恒conveyor 输送机deviation 偏差flexibility coefficient 柔度系数method of section 截面法pin connection 铰接principle of virtual work 虚功原理redundant force 冗余力sever 断开，分开support reaction 支反力truss 桁架unit-load method 单位荷载法corridor 走廊counteration 退化ductile failure 延性破坏erection 直立建筑物impact factor 冲击系数iterative 重复的，反复的layout 规划，设计图案maintainability 可维护性monorail 单轨铁路quasi-permanent 准永久的sustained 持续不变的tenant 承租人torque 扭矩torsional 扭力，扭转的buggy 手推运料车commentary 注释，条文规范contractor 承包商couple 力偶entrain 加气（给混凝土）fire rating 耐火等级oscillate 摆动，震动rigidity 刚度shoring 支撑anchorage 锚固centroid 形心concrete cover 混凝土保护层eccentricity 偏心距helix 螺旋线的incipient 刚出现的lap splice 搭接longitudinal 纵向的pitch 坡度spall 剥落symmetrical 对称的tie 绑扎（钢筋）curvature 曲率detrimental 有害的flange 翼缘web 腹板render 粉刷，抹灰foundry 铸造厂incombustible 防火的residual 残余的stocky 短粗的vitreous 玻璃的withstand 抵抗，承受gusset 节点板，角板imperfection 缺陷purlin 檩条rafter 椽子slenderness 长细比spandrel 拱肩，托梁stringer 桁条，纵梁sway 晃动，侧接移forge 锻造inspection 检查，弹伤shank 末梢wrench 扳手nut 螺母slag 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Usageof“symmetrical”and“symmetric”What is the appropriate usage of "symmetrical" and "symmetric" (using the geometrical adjectival definition of both terms)? Are they synonymous?Dictionary:Merriam-Webster lists symmetric as being a variant of symmetrical, which is the 'official' dictionary entry:symmetrical, adj : 1 : having or involving symmetry : exhibiting symmetry : exhibiting correspondence in size and shape of parts : BALANCED, REGULAR {the human body is symmetrical} {crystals are often symmetrical} {a symmetrical garden} {a symmetrical grouping} Discussion:Sam Lisi: At least in a mathematical context, I think "symmetric" is far more common. For one thing, there are many technical terms where "symmetric" is the correct choice (e.g. "symmetric space", "symmetric relation", "symmetric group"). I can't think of any technical term including "symmetrical".user16269: "Symmetrical" is a non-technical term, to describe any object that has symmetry; for example, a human face. "Symmetric" means "relating to symmetry", and is also used in a number of technical mathematical contexts (see Sam Lisi's comment under the question).JLG: I don't agree with symmetrical being a nontechnical term. Dorland's Medical Dictionary lists only "symmetrical," and the definition is: "pertaining to or exhibiting symmetry; in chemistry, denoting compounds which contain atoms or groups at equal intervals in the molecule." (Sounds technical to me.)naught101:mitch, because symmetric is defined as "symmetrical" - I assume that's supposed to mean it's a perfect synonym.mitch: naught101: 1) there are no perfect synonyms. Ever. And a crowd sourced definition ain't gonna specify enough to judge. 2) wiktionary is not definitive. Don't take anything it says as gospel or draw logical conclusions from it. Frankly the same could be said for the OED, but wiktionary is not written by people who have spent a long time judging such things.Related:, , ,and the most excellent general discussionasymmetric是不对称，⼀般化合物含义⼿性中⼼，unsymmetrical⾮对称，⼀般化合物不含有⼿性中⼼。

1SSN1672-4305 实 验室科学 第21卷第4期2018年8月CN12-1352/N LABORATORY SCIENCE Vol.21 No.4 Aug.2018PSD法在超精密加工质量评价中的应用闫英，周平，郭晓光，王一奇，白倩，司立坤(大连理工大学精密与特种加工教育部重点实验室，辽宁大连116024)摘要：功率谱密度法（Power Spectral Density, PSD)从物理意义上来讲就是单位频率内的信号能量，用于描述随机过程的功率与频率之间的关系。

P SD法可以用于分析超精密加工表面的形貌特征，也可以分析不同频率在表面形貌中的分布，从而评价加工工艺对超精密加工表面质量的影响。

利用一维P S D的方法，评价了磨削硅片、抛光硅片、抛光铜片表面的质量，通过结果分析可知，与表面粗糙度方法相比，P SD方法可以更全面地评价被加工工件的表面质量。

因此，需要在实验室教学过程中引导学生关注功率谱密度分析方法，建立功率谱密度函数与超精密加工表面质量之间的关系。

关键词：功率谱密度；超精密加工；表面形貌；质量评价中图分类号:TG4506 文献标识码：A doi:10.3969/j.issn.1672-4305.2018.04.004 Application of PSD method in ultra-precision machining quality evaluation YAN Ying，ZHOU Ping，GUO Xiao-guang，WANG Y i-qi，BA1 Qian，S1 Li-kun (Key Laboratory for Precision and Non-traditional Machining Technology o f Ministry o f Education，Dalian University o f Technology，Dalian 116024，China)Abstract：Power Spectral Density (P S D)i s the signal energy per unit o f frequency and widely used t o describe the relationship between the power and frequency in the random process.The P S D method can be used t o analyze the topography characteristics o f ultra-precision machined surfaces and t o analyze the distribution o f different frequencies in surface topography t o evaluate the effect o f machining proces­ses on the surface quality o f ultra-precision machined surfaces.By using the one-dimensional and two -dimensional P S D method，the quality o f the surface o f the ground silicon wafer，the polished silicon wafer and the polished copper surface i s evaluated.According t o the results，the P S D method i s more suitable t o evaluate the machined workpiece than the surface roughness method.1t i s necessary t o lead the students focus on the application o f P S D in the f i e l d o f ultra-precision machining.Key words ：Power Spectral Density(P S D)；ultra-precision machining；surface topography；quality evaluation在工业4.0的时代，超精密加工技术的发展是 制造业的关键，它已经成为一个国家在国际竞争中 取得成功的要素。

A Parallel-Strip Ring Power Divider WithHigh Isolation and ArbitraryPower-Dividing RatioAbstract—In this paper, a new power divider concept, which provides high flexibility of transmission line characteristic impedance and port impedance, is proposed. This power divider is implemented on a parallel-strip line, which is a balanced transmission line. By implementing the advantages and uniqueness ofthe parallel-strip line, the divider outperforms the conventional divider in terms of isolation bandwidths. A swap structure of the two lines of the parallel-strip line is employed in this design, which is critical for the isolation enhancements. A lumped-circuit model of the parallel-strip swap including all parasitic effects has been analyzed. An equal power divider with center frequency of 2 GHz was designed to demonstrate the idea. The experimental results show that the equal power divider has 96.5%—10-dB impedance bandwidth with more than 25-dB isolation and less than 0.7-dB insertion loss. In order to generalize the concept with an arbitrary power ratio, we also realize unequal power dividers with the same isolation characteristics. The impedance bandwidth of the proposed power divider will increase with the dividing ratio, which is opposite to the conventional Wilkinson power divider. Unequal dividers with dividing ratios of 1 : 2 and 1 : 12 are designed and measured. Additionally, a frequency independent 1800 power divider has been realized with less than 20 phase errors.Index Terms—Arbitrary power-dividing ratio, parallel-strip line, ring structure, unequal power divider.I. INTRODUCTIONTHE WIKINSON power divider is one of the conventional and fundamental components in microwave engineering and exists in many microwave circuits. Both distributed and lumped Wilkinson power dividers have been applied in microwave integrated circuits and monolithic microwave integrated circuits [1]. Recently, extensive studies have been made to enhance the performances of the Wilkinson power divider, including size reductions by capacitive loading [2], folded circuitry [3] and resonating structure [4], [5], multiband operation [6], [7], unequal power dividing/combining [8], and active device [9] and waveguide implementations [10]. The power dividers discussed in this paper are focused on the isolation enhancement. The proposed divider is realized in the parallel-strip transmission line. Some parallel-strip circuits were reported with performance enhancement [11], [12]. The parallel-strip line provides more design flexibility than a micro-strip line, especially in realization of a high-impedance line and transitions.Many balanced circuits such as push–pull amplifiers, balanced mixers, frequency multipliers, and antenna arrays employ the Wilkinson power divider because of its simple design with high port-to-port isolation. Isolation is one of the important issuesin the design of the power divider and directional coupler. High isolation implies the minimization of unwanted coupling between active devices, as well as the elimination of unexpected distortions and oscillations. It is because it may provide a positivefeedback path for other frequencies, e.g., in Fig. 1, as unwanted oscillation at f1 may be set up outside of the operation frequency f0. Therefore, a wideband isolation operation is always preferred to suppress the coupling in other frequency bands.Fig. 1. Balanced circuit at frequency f0 and unwanted feedback at f1.The parallel-strip line belongs to a family of balanced transmission line. The conventional printed circuit board (PCB) fabrication technique is able to easily realize parallel-strip lines. It is a simple structure of a dielectric substrate sandwiched between two strip conductors. The signals flowing on the upper and lower strip conductors are always equal in magnitude and 1800out-of-phase. The quasi-TEM mode electric and magnetic fields distributions are closed to the micro-strip line. In this paper, a parallel-strip swap is employed to enhance isolation performance of the power divider. The swap is a passive microwave component. It forms a compact realization of 1800 phase shift by interchanging the connection of two conductors in the balanced transmission line. Various swaps were proposed for performance enhancement in a 1800 hybrid coupler [13]–[15].A new equal power divider, which is realized on a parallel-strip line with a ring-like structure, was first demonstrated in [16]. The four arms and two shunt resistors in the divider provide a high degree of freedom for choosing the circuit parameters. In this paper, the proposed concept is generalized to be arbitrary power dividing without an increase in design complexity. It shows a frequency-independent isolation characteristic, arbitrary power-dividing ratio without an external matching network, avoidance of a very thin strip line for achieving high characteristic impedance, and ease of realizing wideband 1800 dividing. While the conventional Wilkinson powerdivider exhibits limited isolation bandwidth, unequal Wilkinson power dividing relies on an external quarter-wave transformer for realizing unequal power dividing for the same port impedances.High characteristics impedance transmission lines are required for the unequal power divider. The unequal divider has been used with strict restrictions in design and fabrication because it requires a transmission line with very high impedance [8]. On the other hand, the very thin transmission line limits the power handling of the devices. To overcome this limitation in realizing characteristic impedance, the upper and lower strip lines of the parallel-strip line are offset so that it will be easier to highly increase the characteristic impedance. Three power dividers with power-dividing ratios of 1 : 1, 1 : 2, and 1 : 12 were designed, fabricated, and tested.Fig. 2. Schematic diagram of proposed power divider with four arms, a swap, and two shunt resistors.II. THEORETICAL ANALYSISThe structure of the proposed divider is illustrated in Fig. 2.In [13], the equal power divider has been analyzed using even and odd-mode analysis because of symmetry of the divider. For the same reason, the circuit parameters, such as port impedance and line impedances, should be the same as their corresponding parameters Z A=Z C, Z B=Z D, and Z2=Z3. In this paper, we try to generalize the analysis to an unequal power divider with an arbitrary dividing ratio.It consists of an 1800 swap, four quarter-wave-long arms (with characteristic impedances Z A, Z B, Z C, and Z D) and two shunt resistors with resistance . These five parameters determine the input impedances, isolation, and dividing ratio of the divider. In order to determine the arm characteristic impedances and resistor values, several parameters should be known, including port impedances Z1, Z2, and Z3 and power ratio K.Firstly, the impedance matching is considered. To achieve maximum power transfer, all the ports should be matched. The input impedance at port 1 is determined by Z A and Z C and port impedances Z2 and Z3.As illustrated in Fig. 3, it is assumed thata signal is injected to port 1 and will only pass through ports 2 and 3. There is no net current flowing from ports 2 to 3 due to port isolation between ports in the shaded region. Arms B and D with characteristic impedances Z B and Z D , respectively, the two shunt resistors, and the swap can thus be replaced by an open circuit in analysis. The two arms are connected in shunt; the input impedance at port 1 can be expressed as(1)The signal injected to port 2 can be divided into two parts, one flowing to port 1 and the other being absorbed by shunt resistors as shown in Fig. 4. Obviously, there is no net current flowing from arm to arm and port 3 in the shaded region, which can be replaced by an open circuit in analysis. The input impedance at port 2 can be given as(2)Similarly, the input impedance at port 3 can be expressed as(3)For the unequal power dividing and assuming the power ratio of ports 2 and 3 to be K, the power ratio can be determined by the ratio of input impedance of the arms A and C, as shown in Fig. 3, as follows:(4)123221)(-+=C A Z Z Z Z Z 12212)2(-+=B A Z R Z Z Z 12213)2(-+=D C Z R Z Z Z 32222232Z Z Z Z Z Z Z Z k A C A C ==By solving (1), (2), and (4), Z A and Z C are determined and are expressed in (5) and(6), respectively.Solving (4) and (1),(5)Solving (4) and (2),(6)Hence, the ratio of the square of Z B and Z D and shunt resistor can be determined by solving (2), (3), (5), and (6).Solving (5) and (2),(7)Solving (6) and (3),(8)There are four conditions, but five unknown parameters Z A , Z B, Z C , Z D , and R. Therefore, the solutions are singular, which implies there is no unique solution. The 31)1(Z Z k Z C +=21)11(Z Z k Z A +=)11(232kZ R Z D +=)1(222k Z R Z B +=infinite number of solutions provide a high degree of freedom when the divider is designed. For example, the divider can not only be designed for any port impedance without external matching circuits, but also provides unequal power dividing with equal port impedance.Isolation is a very important design issue. The symmetrical structure and the swap provide the possibility of frequency-independent isolation characteristics. Signals flowing through paths A –C and B –D should be equal in magnitude, but 1800 out-of -phase. In order to provide frequency-independent isolation, the phase difference between paths A –C and B –D should be frequency independent at 1800 out-of-phase and with equal amplitude, which is provided by the swap, and the characteristic impedance should be the sameZ A = Z D and Z B = Z C (9)Equation (9) represents the fifth condition for designing a divider with frequency-independent isolation and arbitrary power ratio. After combining the previous conditions, the parameters Z A , Z B, Z C , Z D , and R become unique. The design formulas can be summarized asR=2Z1 (10a)(10b)(10c)31)1(Z Z k Z Z C B +==21)11(Z Z k Z Z D A +==Fig. 5. Geometries of parallel-strip swap and parallel-strip line with equal physical length.III. PARALLEL SWAP AND DISCONTINUITYThe swap is the interchange between the two signal lines in the balance transmission line so that the signal is said to be ―reversed,‖ therefore, it provides 1800 phase shift without the existence of a delay line. It can be easily realized in some of the nonmicrostrip transmission lines such as a coplanar waveguide, coplanar strip line, and parallel-strip line. Fig. 5 shows the geometry of the parallel-strip swap. The upper and lower strip lines are connected by two vertical metical vias. The sections of the swap and parallel-strip line are simulated using Ansoft’s High Frequency Structure Simulator (HFSS). Within the entire simulation band, less than 0.5-dB extra insertion loss is introduced and 1800 phase shift is provided with less than 2 phase error, as shown in Fig. 6. The swap introduces discontinuity for the divider and always degrades the circuit performance. It is necessary to develop proper analysis models. The structure of parallel- strip swap with two shunt resistors used in the proposed divider is shown in Fig. 7. Two resistors are soldered across the two gaps at the upper and lower strip lines. These resistors are used to absorb the signal. They are necessary to provide proper impedance matching and port-to-port isolation, similar to the resistor in the Wilkinson power divider.Extra insertion loss and phase delay are introduced by the vertical via, which can be analyzed by a lumped-circuit model. The lump-circuit model of the swap with two shunt resistors (R S) is illustrated in Fig. 8. The parasitic capacitance (C S) is used to model the edge couplings between strips with different layers. The parasitic capacitance (C C) is used to model the total effect due to edge couplings between strips with the same layers and coupling between the vias. The parasitic inductance (L V) and resistance (R V) are introduced by vertical conductor in via-holes and soldering. Theparasitic components can be extracted from full-wave simulations so that the lumped model of the swap was done.The Z-parameter of the lumped equivalent model of the core in Fig. 8 is given by(11)Fig. 6. Simulated frequency responses of insertion loss and phase difference of a section of parallel-strip swap and line with same physical length.⎪⎪⎭⎫ ⎝⎛+--+=⎪⎪⎭⎫ ⎝⎛212121212221121121Z Z Z Z Z Z Z Z Z Z Z ZFig. 7. 3-D view of parallel-strip swap with two shunt resistors.Fig. 8. Lump equivalent model of parallel-strip line swap.where Z 1= R V + jwL V and Z 2= (1/ R S +1/jwC C )-1 Hence, the S-parameter converted from Z-parameters of the core is determined as follows:(12)(13) ))((020*********Z Z Z Z Z Z Z S S +++==))(()(020********Z Z Z Z Z Z Z S S ++-==The structure shown in Fig. 7 is simulated by the full-wave electromagnetic (EM) simulator HFSS, determining the optimum design of the vias on the substrate dielectric constant of 2.65 and thickness of 1.5 mm where all the gapwidthsFig. 9. Simulated S-parameters of the parallel-strip line swap using lumped model and full-wave EM simulation. (a) Magnitude response. (b) Phase response.are 0.2 mm and the radius of the metallic via is 0.55 mm. Deembedding of the parameters has been performed by utilizing the microwave circuit simulator, Agilent Technologies’s Advanced Design System (ADS). Both EM and circuit simulationsof the parallel-strip swaps with 70.71- terminations are shown in Fig. 9. Good agreement of both the magnitudes and phases responses are achieved within the frequency band of interest. The values of parasitic elements are L V =2.181 nH,C S=0.2939 pF, C C=0.3878 pF, and R V =0.2624Ω. The model circuit is analyzed and, hence, the scattering matrix representing the parallel-strip swap with shunt resistor (R S) is, therefore, obtained, and the entire circuit can thus be easily modeled in the circuit simulation.IV. RESULTS OF SIMULATION AND EXPERIMENTA. Equal Power DividerThe power dividers are fabricated in a conventional printed circuit technique and the dividers designed for demonstration are built on a substrate with a dielectric constant of 2.65 and a thickness of 1.5 mm, as shown in Fig. 10. The derivation in Section II is based on an ideal transmission line model. This analysis provides initial design parameters. Discontinuities or parasitic elements such as T-junctions and steps will be introduced. EM optimization is required to determine all circuit parameters with the best performance.Fig. 10. Implementation of proposed equal power divider on PCB. (a) Upper layer. (b) Bottom layer. are built on a substrate with a dielectric constant of 2.65 and a thickness of 1.5 mm, as shown in Fig. 10. The derivation in Section II is based on an ideal transmission line model. This analysis provides initial design parameters. Discontinuities or parasiticelements such as T-junctions and steps will be introduced. EM optimization isrequired to determine all circuit parameters with the best performance.All the port impedances are designed at 50 , i.e., Z1=Z2=Z3=50Ω The designparameters of an equal power divider are Z A=Z B=Z C= Z D = 70.71Ωand R=100Ω.By removing portion of the ground of a micro-strip line, the parabolic tapered transition between the parallel-strip line and micro-strip line [11] was employed for connecting the coaxial connector for measurement purposes with less than 0.1-dB insertion loss within the entire tested frequency band. However, an approximate 0.5-dB extra insertion loss will be introduced if a subminiature A (SMA) connector is directly connected to the SMA connector. Fig. 11 shows both simulated and measured results of the equal power divider. The EM simulation tool is Ansoft’s HFSS. The measured insertion loss from ports 1 to 2 and 3 are less than 3.7 dB within the operation frequency band, as shown in Fig. 11(a). Some mismatches come from an inaccurate prediction of the vertical structure from the EM simulator and soldering. The mismatches in return losses shown in Fig. 11(b) are due to unexpected errors from soldering between the divider and SMA connectors. The ring-like structure implies similar input and output impedance characteristics, as shown in Fig. 10. The total usable impedance bandwidth is wider than that of the conventional Wilkinson power divider. Due to the imbalances of the two paths, e.g., electrical delay and insertion loss in the swap, the isolation has a finite value. Fortunately, the isolation can still provide great improvement over the conventional divider.The impedance bandwidths of return loss lower than 10 dB of the proposed divider is measured at 96.5%, as observed in Fig. 11(b). In Fig. 11(c), the proposed divider demonstrates more than 25 dB in the entire frequency band in the measurement, while a conventional Wilkinson power divider shows approximately 33% isolation bandwidth of more than 20-dB isolation. Good agreement between experimental and simulated results can be observed.B. Unequal Power DividersApart from the equal power divider, two unequal power dividers with ratios of 1 : 2 and 1 : 12 are realized. The impedance bandwidth is usually reduced with the dividing ratio in the conventional Wilkinson power divider; however, the bandwidth of the proposed divider is increased with a power ratio of . The relation is shown in Fig. 12. Figs. 13 and 14 show the frequency responses of -parameters and the dividing ratio of the 1 : 2 power divider. The design parameters are Z A=Z D=61.24Ω, ZB=ZC= 86.61Ω, and R=100Ω. Measured results agree withEMsimulation.Within the 125% operation bandwidth with lower than 10-dB return loss, more than 26-dB port-to-port isolation is achieved and the average divider ratio is approximately 2.07.Fig. 11. Simulated and measured results of proposed equal power divider.(a) Insertion losses. (b) Return losses. (c) Isolation.A high dividing ratio implies the existence of some high characteristicimpedance transmission lines. The implementation ofhigh characteristic impedance remains challenge because of theFig. 15. Cross section and 3-D view of offset parallel-strip line.Fig. 16. Relationship of characteristics impedance and normalized offset distance with different normalized strip width, where z denotes characteristics impedance, w denotes width of the strip line, d denotes offset distance, and h denotes substrate thickness.technique of extremely thin micro-strip line fabrication. The realization of the unequal power divider may be limited by fabrication of the thin strip line and low power-handling capacity of the divider.In order to easily realize a high-impedance transmission line, a micro-strip defected ground structure was proposed for the 1 : 4 unequal divider [8]. In [17], thecharacteristics impedance parallel- strip line was increased by offsetting the upper and lower strip lines in the finite ground micro-strip line for stopband enhancement. Similarly, the characteristics impedance of a parallel-strip line can be increased by offsetting the strip lines, as shown in Fig. 15. Fig. 16 shows the relationship between characteristics impedances and normalized circuit parameters on the same substrate. It is obvious that the characteristics impedance (z) increases with offset distance (d) without use of very narrow strip lines. A high characteristic impedance parallel-strip line can be realized by offsetting the upper and lower strip lines andit does not need a very narrow line.In the 1 : 12 power divider, two arms with high characteristic impedance are realized by offsetting the parallel-strip line. Figs. 17 and 18 show its -parameters and the dividing ratio varied with frequency. The design parameters are Z A=Z D=50.04Ω, Z B=Z D=180.27Ω, and R=100Ω. Good agreement of both simulated and measured results are obtained. Within the 150% operation bandwidth with lower than 10-dBreturn loss, more than 24-dB port-to-port isolation is achieved and the average divider ratio is approximately 12.68.Fig. 17. Simulated and measured S-parameters of 1 : 12 proposed divider.Fig. 18. Simulated and measured dividing ratio of 1 : 12 proposed divider.C. Frequency-Independent 180 Power DividerConventionally, the symmetric power divider is used for in-phase powerdividing/combining. A power divider with wideband 1800 out-of-phase operation is needed for many balanced circuit such as a push–pull amplifier and balanced mixer. The 1800 hybrid or the power divider with a 1800 delay line is used for such purpose.A 1800 divider can be easily realized by adding an extra section of delay line. However, a delay line limits the bandwidth of phase balances. The conventional 1800 hybrid coupler or Wilkinson power divider with a delay line may not fulfill actual application demands and may degrade system performance. With a similar approach to [12], the frequency-independent 1800 differential phase between ports 2 and 3 is realized by tapering the lower line in port 2 and the upper line in port 3, the parallel-strip line-to-micro-strip line transition, which is used for measurement, is formed as shownin Fig. 19. All circuit parameters are the same as the equal power divider in Section IV. The magnitudes of simulated and measured -parameters are close to that of the equal power divider, as shown in Fig. 11. A frequency-independent 1800 phase difference is observed, as shown in Fig. 20. A small phase error within 2 is introduced due to the thickness of the substrate of the PCB, while it can be minimized by using a thinner substrate with a lower dielectric constant. Similarly, the 1800 unequal power divider with an arbitrary dividing ratio can be realized via the same technique.Fig. 19. Implementation of proposed 1800 equal power divider on PCB. (a) Upper layer. (b) Bottom layer.Fig. 20. Phase response of 1800 equal power divider.V. CONCLUSIONA novel power divider with better isolation than the conventional Wilkinson power divider has been presented. Design formulas for the proposed divider have been proven analytically. The ring-like structure provides design flexibility such as unequal power dividing without extra impedance matching networks. The equal and unequal power dividers were designed and tested with out-performed isolation characteristics. Additionally, a 1800 equal power divider was realized by making use of the balanced structure of the parallel-strip line. Similarly, a 1800unequal power divider can be designed. The proposed design leads to realization of a new geometrical configuration for a high-performance power-divider concept.R EFERENCES[1] L. H. Lu, P. Bhattacharya, L. P. B. Katehi, and G. E. Ponchak, ―X-band and K-band lumped Wilkinson power dividers with a micromachined technology,‖ in IEEE MTT-S Int. Microw. Symp. Dig., 2000, pp. 287–290.[2] K. Hettak, G. A. Morin, and M. G. Stubbs, ―Compact MMIC CPW and asymmetric CPS branch-line couplers and Wilkinson dividers using shunt and seri es stub loading,‖ IEEE Trans. Microw. Theory Tech., vol. 53, no. 5, pp. 1624–1635, May 2005.[3] L. Chiu, T. Y. Yum, Q. Xue, and C. H. Chan, ―The folded hybrid ring and its applications in balance devices,‖ in IEEE Eur. 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2011年技术物理学院08级（激光方向）专业英语翻译重点！！！作者：邵晨宇Electromagnetic电磁的principle原则principal主要的macroscopic宏观的microscopic微观的differential微分vector矢量scalar标量permittivity介电常数photons光子oscillation振动density of states态密度dimensionality维数transverse wave横波dipole moment偶极矩diode 二极管mono-chromatic单色temporal时间的spatial空间的velocity速度wave packet波包be perpendicular to线垂直be nomal to线面垂直isotropic各向同性的anistropic各向异性的vacuum真空assumption假设semiconductor半导体nonmagnetic非磁性的considerable大量的ultraviolet紫外的diamagnetic抗磁的paramagnetic顺磁的antiparamagnetic反铁磁的ferro-magnetic铁磁的negligible可忽略的conductivity电导率intrinsic本征的inequality不等式infrared红外的weakly doped弱掺杂heavily doped重掺杂a second derivative in time对时间二阶导数vanish消失tensor张量refractive index折射率crucial主要的quantum mechanics 量子力学transition probability跃迁几率delve研究infinite无限的relevant相关的thermodynamic equilibrium热力学平衡（动态热平衡）fermions费米子bosons波色子potential barrier势垒standing wave驻波travelling wave行波degeneracy简并converge收敛diverge发散phonons声子singularity奇点（奇异值）vector potential向量式partical-wave dualism波粒二象性homogeneous均匀的elliptic椭圆的reasonable公平的合理的reflector反射器characteristic特性prerequisite必要条件quadratic二次的predominantly最重要的gaussian beams高斯光束azimuth方位角evolve推到spot size光斑尺寸radius of curvature曲率半径convention管理hyperbole双曲线hyperboloid双曲面radii半径asymptote渐近线apex顶点rigorous精确地manifestation体现表明wave diffraction波衍射aperture孔径complex beam radius复光束半径lenslike medium类透镜介质be adjacent to与之相邻confocal beam共焦光束a unity determinant单位行列式waveguide波导illustration说明induction归纳symmetric 对称的steady-state稳态be consistent with与之一致solid curves实线dashed curves虚线be identical to相同eigenvalue本征值noteworthy关注的counteract抵消reinforce加强the modal dispersion模式色散the group velocity dispersion群速度色散channel波段repetition rate重复率overlap重叠intuition直觉material dispersion材料色散information capacity信息量feed into 注入derive from由之产生semi-intuitive半直觉intermode mixing模式混合pulse duration脉宽mechanism原理dissipate损耗designate by命名为to a large extent在很大程度上etalon 标准具archetype圆形interferometer干涉计be attributed to归因于roundtrip一个往返infinite geometric progression无穷几何级数conservation of energy能量守恒free spectral range自由光谱区reflection coefficient（fraction of the intensity reflected）反射系数transmission coefficient（fraction of the intensity transmitted）透射系数optical resonator光学谐振腔unity 归一optical spectrum analyzer光谱分析grequency separations频率间隔scanning interferometer扫描干涉仪sweep移动replica复制品ambiguity不确定simultaneous同步的longitudinal laser mode纵模denominator分母finesse精细度the limiting resolution极限分辨率the width of a transmission bandpass透射带宽collimated beam线性光束noncollimated beam非线性光束transient condition瞬态情况spherical mirror 球面镜locus（loci）轨迹exponential factor指数因子radian弧度configuration不举intercept截断back and forth反复spatical mode空间模式algebra代数in practice在实际中symmetrical对称的a symmetrical conforal resonator对称共焦谐振腔criteria准则concentric同心的biperiodic lens sequence双周期透镜组序列stable solution稳态解equivalent lens等效透镜verge 边缘self-consistent自洽reference plane参考平面off-axis离轴shaded area阴影区clear area空白区perturbation扰动evolution渐变decay减弱unimodual matrix单位矩阵discrepancy相位差longitudinal mode index纵模指数resonance共振quantum electronics量子电子学phenomenon现象exploit利用spontaneous emission自发辐射initial初始的thermodynamic热力学inphase同相位的population inversion粒子数反转transparent透明的threshold阈值predominate over占主导地位的monochromaticity单色性spatical and temporal coherence时空相干性by virtue of利用directionality方向性superposition叠加pump rate泵浦速率shunt分流corona breakdown电晕击穿audacity畅通无阻versatile用途广泛的photoelectric effect光电效应quantum detector 量子探测器quantum efficiency量子效率vacuum photodiode真空光电二极管photoelectric work function光电功函数cathode阴极anode阳极formidable苛刻的恶光的irrespective无关的impinge撞击in turn依次capacitance电容photomultiplier光电信增管photoconductor光敏电阻junction photodiode结型光电二极管avalanche photodiode雪崩二极管shot noise 散粒噪声thermal noise热噪声1.In this chapter we consider Maxwell’s equations and what they reveal about the propagation of light in vacuum and in matter. We introduce the concept of photons and present their density of states.Since the density of states is a rather important property，not only for photons，we approach this quantity in a rather general way. We will use the density of states later also for other(quasi-) particles including systems of reduced dimensionality.In addition,we introduce the occupation probability of these states for various groups of particles.在本章中，我们讨论麦克斯韦方程和他们显示的有关光在真空中传播的问题。