曲型电极在弱导电环境下的电场引发机理研究

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1、曲型电极在弱导电环境下的电场引发机理研究摘要原文对照作为电介质的基本性能，电介质的击穿性能描述了电介质在施加电场的条件下所能保持绝缘正常工作的阈值。绝缘损坏是电力系统出现故障最常见的原因之一在，因此就多数情况来讲，绝缘能否正常工作对电气设备能否正常工作起决定性的作用。近年来高压技术己不限于电力工业的需要，还扩展应用到许多科技领域中，并有很多高场强绝缘的问题。由于这些情况，研究电介质击穿机理、影响因素、不同介质的耐电强度等是十分必要的。本文以血栓作为电介质，在其两端使用曲型电极施加脉冲电场，进行电击穿，对血栓进行溶栓处理。脉冲电场是近年来结合了医学、电学等领域对血栓进行治疗的新方法，但目前对脉冲

2、电场治疗血栓的报道较少；研究对象主要为白血病和结肠癌等，病种较局限。本文以曲型电极组为研究对象，以电极锥头曲率和间隔距离为变量因素，建立了多种不同的电极曲率半径模型的曲型电极组模型，使用Comsol仿真软件，施加脉冲电压，曲型电极锥面、环氧树脂绝缘中的电场强度以及血液、栓塞的电场强度及温度场进行仿真分析，并对其内部的带电粒子进行追踪。结果表明： 本文运用Solid Works软件对曲型电极模型的复杂部分进行了构建，然后使用Livelinks模块将参数化模型导入Comsol,再对其及血栓进行仿真。本文首先分析了电介质的放电击穿理论，为电脉冲击穿血栓提供理论依据，使用Comsol仿真软件分析了电脉

3、冲击穿血栓放电过程的电气参数变化特征，提出了一种新的溶栓方式。关键词脉冲放电；电击穿；溶栓；仿真；Study on Electric Field Initiation Mechanism of Curved Electrode in Weak Conductive EnvironmentAbstractAs the basic performance of dielectrics, the breakdown performance of dielectrics describes thethreshold that dielectrics can maintain the normal op

4、eration of insulation under applied electric银环氧树脂血液血栓(2) 边界条件为了方便用户建模，Comsol Multi-physics软件给予用户可以自设定的边界条件。在使用静电场模块时，程序会根据各种公式和物理理论初始定义了域和边界等等。且会将研究所用到的方程在设置-方程的界面详细的提供给用户。根据设计参数要求，按照如图2-6 (a)和2-6 (b)的数据，在Comsol软件全局定义中设定函数的解析式，通过创建绘图可以绘出所加载的脉冲波形，如图2-6 (c)所示。并通过添加“电流(ec) ”下的“终端”选项，将脉冲波形2.6 (c)加在电极模型上

5、，并将其相反数加在电极的另一端上。置r实例成：g11剧球名称aiist:砧IA200幅值omge200| 角图2-6 (a)电压参数定义设置T解析画绘制煎创建绘图癖： 解析1| |剧函数名称：fv图2-6 (b)电压解析式定义图2-6 (c)电压波形图2-6电极加载电压波形定义3.33设置网格和求解设置(1)设置网格软件内置了手动和自动剖分两种网格剖分模式。自动剖分只需要在模型开发器中单击“网络”在序列类型中选择“物理场控制网格”，选择需要的单元格大小，然后选择“全部构建”，软件就开始自动对网格进行剖分。若对模型的部分区域有其他的剖分要求，软件也提供用户自定义网格参数的功能。使用过细化的网格剖

6、分会大大增加求解时间，而使用过粗化的网格剖分又会对求解的精度造成影响，需要根据设计需要和课题要求，选择合适的剖分单元大小。为减少求解时间并保持仿真的精度，本论文的网格剖分的设置了内置的网格中的“超细化”，其最大单元格尺寸为0.035mm,最小单元尺寸为0.0015mm,最大单元增长率为1.35,曲率因子为0.3,狭窄区域分辨率为0.85,全部区域构建剖分。图2-7网格化的几何模型(2)求解设置Comsol Multi-Physics软件含有稳态、瞬态等各种研究步骤的求解器，将求解器设置为为瞬态求解器，并对求解器时间步等参数进行合理的配置。本次仿真是3.3.4后处理和可视化Comsol Mult

7、i-Physics软件内置了功能完善的后处理功能，它拥有十分便捷的UI界面，方便了用户对仿真结果进行后处理和图形化。在模拟施加脉冲经电极击穿血栓时，为了便于观察电场。可以在模型开发器中单击结果，在设置中更改各种绘图设置，可以自主设置数据采集的时间步、自主定义图形的标题、选择合适的图例颜色、数字格式，来更加清晰的观察电势和电场等的变化情况。后处理和可视化功能可以让我们更直观的分析仿真结果。3.4本章小结本章节介绍了有限元的发展和应用、并介绍了SolidWorks和Comsol两大软件仿真平台，并以曲型电极为例，介绍了SolidWorks和Comsol软件建模的过程。其中包含曲型电极模型的绘制和导

8、入，设置各个域的材料属性，设置边界条件，定义函数、网络剖分和后处理。(1) 模型的儿何参数应该参考实际的参数，不可随意设定。材料参数需要准确设定，否则会严重影响仿真结果的准确程度。(2) 网格剖分时对电极、栓塞进行细分，而对于血液和护套等部分的剖分单元大小可以选择“常规”，这样可以缩短研究时间，提高设计效率。第4章曲型电极的场强仿真及带电粒子追踪本章为了更好地理解介质击穿的机理，以曲型电极-栓塞-曲型电极为研究对象，数值模拟了纳秒脉冲下栓塞的放电过程，仿真了模型的电场、热场以及对带电粒子进行追踪。通过对数值分析，可以更好理解电介质的放电过程，加深对电介质放电机理的理解。4.1曲率对曲型电极在脉

9、冲下电场分布的影响课题的研究目标是使电场高度集中在血栓部分，将血栓作为电介质进行击穿，根据设计要求，选择电场最为集中的电极模型。4.2曲型电极带电粒子追踪4.2.1带电粒子追踪模块简介粒子追踪模块以拉格朗日的形式描述问题，在粒子的释放和传播时，应用牛顿的运动定律，求解常微分方程。这个过程需要定义粒子的属性，其中包括粒子本身所具有的质量和由于粒子自身因素所受到的所有的力。通常情况下粒子的作用力一部分为外因，一部分为内因，外因来自于外场的作用，内因则是由于粒子之间的相互作用。在三位模块中对于每一个粒子都需要对其位置矢量进行常微分方程的求解，三维中的位置矢量有三个分量，就意味着需要进行三次常微分方程

10、的求解。在每一个时间步长中，都能对在外场作用下粒子所在当前的位置所受到的作用力进行计算。如果在模型中考虑粒子间的相互作用力，同样需要在模型中引入，并将它们都加入到总力中。在下一个步长更新粒子所在的位置，重复此过程，直到指定的模拟进行的时间结束。粒子追踪模块应用广泛，可应用于带电粒子、流体中的粒子、稀疏流、稀物质流、分散流、模拟对流和扩散、数学粒子追踪。根据课题需求，对局部放电过程进行模拟，选择了粒子追踪模块去实现该过程，粒子追踪可以用于二维平面模型以及三维空间模型，求解类型为瞬态。其可以用于模拟离子和电子的轨迹，并且模块内已经预置了一些已经定义的电力磁力和弹性碰撞力。当然，也可以用库仑力模拟粒

11、子与粒子之间的相互作用。4.2.2简化模型由于复杂的模型通常会延长计算时间或者出现使结果不收敛的情况，在对模型进行带电粒子追踪分析前，首先对电极和环境模型进行简化，使仿真结果仍能保持准确的情况下，运用简化后的模型如图4-1进行带电粒子追踪。m0.050-0.05图4-1简化后的模型4.2.3网格剖分设置网格剖分的设置了内置的网格中的“极细化”，其最大单元格尺寸为0.0066m,最小单元尺寸为6.6E-5m,最大单元增长率为1.3,曲率因子为0.2,狭窄区域分辨率为1,全部区域构建剖分后如图4-2所示。00.10.20.05o5o300.10.2o5ooSS慧15gTsNr14SS意,一一:!H

12、i潞图4-2间化后的网格几何模型424带电粒子模块参数设置入口特征用来从边界释放粒子，在模型开发器中选择“带电粒子追踪”模块，首先规定整个模块的粒子释放明细为“指定电流”，然后为粒子添加入口，选择入口位置为电极表面。对入口的的初始位置进行设置，“初始位置”设定为“密度”，将“每次释放离子数”设置为1000,如图4-3。初始位置初始位置:密度5位置细化因子:图4-3初始位置设定将初始粒子速度设置为lE6m/s,方向沿着z轴的正方向。然后为模型添加电场，使模型受电场力，规定为内置电场(es/ccn 1) o在“粒子属性”状态中，设置粒子质量为comsol内置参数变量me_const,其意义为电子质

13、量，值为9.10938291e-31 kgo由于研究电子移动轨迹，所以将电荷数设置为-1,如图4-4所示。使用稳态求解器中的“双向耦合粒子追踪”对仿真进行求解，将求解器在(0-3.5e-7) s时间段内的步长设置为1.0e-9o设置呵粒子筐三标签：粒子屈性1I同I|沌粒子袍,粒子mp meconstkg电荷数电荷数:mpme const电荷数电荷数:425带电粒子追踪仿真结果结论xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx宋体小四，夕卜文Times New Roman, 首行缩进两字距，单倍行距，正文文本。参考文献I 费增尧周佩

14、白.高压电极的优化设计D.高压电器,1987.唐耀宗 位志勇.高压电极的优化设计D.高电压技术，1985.3 张守义廖兵.高压电极形状的优化设计D.浙江大学学报(自然科学版),1991.4 张守义廖兵.高压电极形状的计算机辅助设计D.高电压技术，1990.5 万连茂，刘建波.高压电极电场的数值模拟JJ .兵工自动化,2004(06):31-32.6 金彩善.基于NX三维软件电极设计方法J.CAD/CAM与制造业信息化,2013(12):56-60.7 段浩,房建峰，孙天旗，刘兵，刘杰，高忠权,吴筱敏.不同电极结构下电场对甲烷/空气火焰的影响J .西安交通大学学报,2014,48(09):62-

15、67.8 张新国，刘忠乐.电极尺寸对环电极电场的影响分析研究J .水雷战与舰船防护,2012,20(03):7-10.9 李春茂 董磊 彭开晟 魏文赋 高国强吴广宁.电极间隙对介质阻挡放电特性的影响D.西南交通大学学报，2019.10 J.Spielrein:Geometrisches zur elektrischen Festigkeitsrechung HArch.E-lektrotech 5(1917),S,244-254.II (日)正田英介.电磁学M .北京:科学出版社,2001.12 晁立东，件杰，王仲奕.工程电磁场基础M.陕西:西北工业大学出版社,2001.13 严樟侏德恒.高压

16、电绝缘技术M,北京:中国电力出版社,2007:5-6.14 张帆.基于“小桥理论”的变压器油击穿防止措施研究J .中国科学信息,2012,(18):88.15 刘小成.基于SolidWorks二次开发的选煤设备参数化设计研究D.中国矿业大学,2018.15Distance characteristic of electric field waveform andfield peak value caused by micro gap ESD in a pair ofspherical electrodesDistance characteristic of electric field wav

17、eform andfield peak value caused by micro gap ESD in a pair ofspherical electrodesKen KawamataTohoku (iakuin University1-13-1 Chuo Tagajyo,JAPANkawamatamail.lohoku-gakuin.ac.jpShinobu IshigamiIohoku (iakuin University1-13-1 Chuo lagajyo,JAPANshinobu 何 ijcc.lohoku-gakuin.ac.jpShigeki MinegishiTohoku

18、(iakuin University1-13-! ChuoTagajyo,JAPANsminetjcc.tohoku-gakuin.ac.jpOsamu FujiwaraNagoya Institute ofTechnologyGokiso-cho, Showa-ku,Nagoya, JAPANfujiwaranitech.ac.jpAbstract Il is cll knoun that wideband clectroniagncticnoise is caused by ESD (electro-static discharge) events.Especially, the micr

19、o gap ESI) of less than 1 kV products theimpukive electromagnetic noise up to (llz bandwidth. I he ESDnoise is menace to cause malfunction of high-tech electricalequipment and systems. Then, the impulsive electromagneticnoise caused b) (he ESD was examined to clear the radiationmechanism. In this re

20、port, the electric field aeformmeasured using an optical electric field sensor system and thespherical electrode system. As a result. concluded that theelectric field uac form transFurmtd from the static electricfield to (he induction field and Ihe radiation field be caused byincreasing a distance b

21、etween the electrode and the electric fieldsensor. It is provided that the mechanism of electromagneticradiation caused by ESI) in the pair of spherical electrode can beconsidered as the dipole radiation model nith the electroderlcmcnts.Keywords Electrostatic discharge (ESD), Electromagneticradiatio

22、n, Transient electromagnetic field. Optical electric fieldsensor. Static field. Induction field. Radiation fieldI. IntroductionThe troublesome electromagnetic noise is caused by ESD(eleclro-static discharge) events. The ESD produces widebandelectromagnetic noise, and the transient shows very last ri

23、setime. Especially, the micro gap ESD of less than 1 kVproduces the impulsive electromagnetic noise up to GHzbandwidth. The ESD noise is menace lo cause malfunction ofhigh-tech electrical equipment and systems. So far, the greaterparts of studies have been made on electromagnetic noises ofESDs from

24、the view point of electromagnetic compatibility(EMC). The electromagnetic noise characteristics of Ihe ESDsare gradually becoming clearer (I -|7.Ihere are a lot of parameters due to ESD events. Forexample, the charged voltage, ihe transient current, surfacestate of charged body, approach speed of lh

25、e body, anatmosphere around charged body etc., it is complexphenomenon because these are connected with each other.Then, a relationship between the electromagnclic radiationcharacteristics and various parameters of ESD was examined.At first, it was confirmed that an intensity of electromagneticradia

26、tion was proportional to the voltage gradient betweenelectrodes. In addition, il was strongly aftected by the surfaceconditions of eleclnxies 8, 9|. Also, it was clarified that theelectrode approach speed is aftected to the ESD s noise by theprevious study 10, 11. When we investigated about lheappro

27、ach speed, we found that lhe average voltage ofelectromagnetic radiation and the dispersion of the receivedvoltage tended to increase with the approach speed becamefast. Furthermore, we discovered these changes makelogarithmic change by an approximating of lhe least squaresmethod |I2|. The mechanism

28、 of electromagnetic radiationcaused by ESD has gradually been elucidated and organized.In this paper, we examined a distance characteristic ofelectric field waveform caused by the micro gap ESD in a pairof spherical electrodes. The electric field was measured byusing a wideband optica! electric fiel

29、d sensor system.Furthermore peak values of the electric field waveforms wereexamined to verification of the previous research 13, 14.As a result, the electric field waveform was transformed fromthe static electric field to the induction field, and the radiationfield be caused by increasing a distanc

30、e between the electrodeand electric field sensor. It is provided that the radiation modelof electromagnetic wave caused by ESD in lhe sphericaleleclnxie can be considered as the dipole model with electrodeelements.II. EXPERIMENTAL SYSTEMFigure 1 shows the experimental apparatus to measure theradiati

31、on characteristics caused by low voltage ESD in thespherical eleclnxie. This apparatus consists of a pair ofspherical electrode, a high voltage DC. power supply(HAMAMATSU C335O, 0-3 kV), 30 kilo ohms highresistance lines with a 50 kilo ohms lumped resistance, adouble-ridged guide horn antenna (ETS 3

32、115, 1-18 GHz) anda digital oscilloscope (Tektronix DP072004B, 20 GHz, 50GS/s). This apparatus used the pair of spherical electrode withProc, of the 2017 International Symposium on Electromagnetic Compatibility - EMC EUROPE 2017, Angers. France, September 4-8, 2017Digital Osalloacope(Tektronoc: DP07

33、20048. 20 GHz. 50 GS/s)Double Ridged GukteHom Antenna(ETS3156,1-18 GHz)Sphedcal ElectrodesDistanoe(a) Received waveform (positive 一 negative)High resistance(50 kQ)High resistance - *lines (30 kD)H gh Voltage D.C. Power Supply(HAMAMATSU : C3350, (W kV)Fig. I ExpcnmenUil system of dcclromagnetic nidia

34、tion causedby micro gap BSD in a pair of spherical electrodesa diameter of 30 mm. The one of electrode is setting on amovable table and the other is setting on a fixed table. Themovable table is controlled by STAGE CONTROLLER(SIGMA KOK1, Stepping Motor Drive, SHOI-302GS). Inthis experiment, an appli

35、ed voltage for the spherical electrodeswas 500 V and the approach speed of spherical electrodes wasset constant 5.0 mm/s. The surface roughness was finished bythe abrasives liquid cream of 3 micro meters grain size.Figure 2 shows an example waveforms of the receivedvoltage measured by the wideband h

36、orn antenna andoscilloscope. The direction of applied source polarities wereclianged in these figures, the figure (a) is the polarity directionfrom positive polarity to negative polanty, the other figure (b)is the polarity direction from negative polarity to positivepolarity. The received voltage wa

37、veforms were reversed bychanging the direction of applied source polarity. From thistact, it is possible to confirm the existence of the pohrizationplane of the radiated cleclromagnetic wave caused by the ESDFigure 3 shows experimental setup to measure the electricHeld waveform using the optical ele

38、ctric field sensor system(SE1KOH GIKEN: C3-1O55 with CS-1210. 100 kHz 一 1()GHz). In the first place, we measured the frequencycharacteristic as an antenna factor of the optical electric Geldsensor (CS-1210) m shown figure 4. The antenna factor wasmeasured by the standard electric field calibration m

39、ethodusing a TEM cell. The antenna factor was confirmed from 10kHz to 500 MHz. upper frequency was limited by a frequencycharacteristic of the TEM cell. The antenna factor showsgenerally constant about 66 dB in the frequency range from!00 kHz to 500 MHz. Also, the antenna factor was confirmed(b) Rec

40、eived waveftxm (negative - positive)l;ig 2 llie example waveforms ofihe received voltage measuredby the wideband horn antennaby the manufacturer which is about 66 dB in the highfrequency range from 500 MHz to 10GHz.In the exjKnment, a distance characteristic of the ekxtricfield wavetbnn was measured

41、 due to changing a distance fromspark point on the electrode. The measurement point of the E -field sensor was moved Iron) the very near field and near fieldto the iar field. Tlw distance x is changed from 25 mm to 250mm. the electric field sensor arrangements parallel topolarization plane of the ra

42、diation field. The measuredwavetbnn of electric Held was changed caused by the distancesuch as the static field, the induction field, and the radiationfield.111. THE EXPERIMENTAL RESULTSFigure 5 shows experimental results of the electric fieldwave forms measured by the experimental system. In the fi

43、gure5, (a) is distance x = 25 mm, (b) is x = 30 mm. (c) is x = 70mm and (d) is x = 250 mm. Horizontal axis is 400 ps/div,respectively. The voltage value on the vertical axis is asindicated. The antenna factor of lhe optical field sensor used inthis experiment is approximately constant at about 66 dB

44、/m inthe frequency range from 30 kHz to 10 GHz. When theDC Powersupply000VryNMf FWdSpherical EtectrodeFig. 3 Measuremeni setup of eleciric Geld using the opticalE- field sensor.E Field Sensor(SeiKOHGIKEN：C3-1055wtthCS-1210100kHz-10GHz)(a) Distance x = 25 mm (The static E - field)Af IdB/m)om o.iiio t

45、oo loooR*uncy (MHz)0.5 V/div.Distance : 70 mm 400 ps/div.(c) Distance70 mm (The induction E - field)Fig. 5 Ilie electric field wavefbnn measured by lhe opticalcleclnc field sensor system.F ig. 4 An antenna taclor of the oplicai eleclric field sensor (CS-1210) measured by standard electric field cali

46、bration method.measured voltage is converted into the electric Held intensityusing the antenna factor, the peak value of the electric fieldintensity becomes as follows. The peak value of the electricHeld intensity of (a) is about 4.5 kV/m, (b) is similarly 4.5kV/m, (c) is 3.5 kV/m and (d) is about 1

47、.2 kV/m, respectively.The following is distance characteristic of the electric fieldwaveforms. The static electric field component is dominant invery close to the electrode in (a), and a stepwise transientelectric field waveform of about 4.5 kV/m was observed.Furthermore, it can be seen that in clos

48、e range of the electrode(b) which is about 30 mm away from the spaik gap, itgradually changes from the stepwise to an impulse transient ofelectric field waveform. In the figure 5 (c), a single impulsewaveform is observed, which is believed due to lhe dominantinduction field. This impulse waveform is

49、 a diilerentialcomponent of the static electric field waveform of the figure(a), that is, ii represents a current component. Furthermore, inthe figure (d), it can be seen that lhe waveform changeindicates the radiated electric field wavetbmi at a sufficientdistance in the far filed. This radiated fi

50、eld waveform isobtained by further differentiating the current wave form basedon the induction field wavetbrm in lhe figure (c). From theseresults of the distance characteristics in the electric fieldwaveform, lhe radiation mechanism of the impulsiveelectromagnetic field by ESD is considered to be l

51、he radiationfrom the dipole model with electrode elements.Fig. 6 l he relationship between the distance and peak value ofthe electric field.IV. DiscussionFhe following is discussion of the peak value of measuredelectric field waveforms. Figure 6 shows the relationshipbetween distance and the peak va

52、lue of the electric field.Horizontal axis is distance from the pair of sphericalelectrodes, vertical axis is a peak value of the measuredelectric field. In this figure, a solid line is a theoretical value ofradiation electric field in Fujiwaras calculation 13| whichwas used a dipole model with a spa

53、rk resistance law of theRompe - WeizeL A dotted line is the measured peak value ofelectric field with circle mark of measured points. In lhe result,there is a diHerence of about 6 dB between the calculationresult and measurement result. I lowevcr, it can be con finnedthat the measured peak value dec

54、reases according to thereciprocal of the distance (IZv) as the distance characteristic ofradiation field. Furthermore, in the paper, a decompositiondistance at which the radiation Held dominates over theinduction field is defined by the following equation,Dx = ct(I)here, Dx is decomposition distance

55、 from electrode, c=3X 10Km/s, r is time duration of spark discharge. In this paper, thetime duration of spark discharge t was assumed by lhepropagation time of a current path length determined by halfcircumference of the electrode |14|J15. Here, r is 157.3 psin the 30 mm diameter electrode. Then, th

56、e decompositiondistance can be calculated as Dx = 47.2 mm This calculationagreed very well with the distance at which the radiation fieldcharacteristics of the measurement result began to be shown infigure 6. On lhe other hand, veri Heat ion is necessary for levelvalues of electrostatic field and in

57、duction field in future.V. ConclusionThe electric field waveform was measured using theoptical electric field sensor system. As a result, we confirmedthat the electric field wave was transformed from the staticelectric field to the induction electric field, and the radiationelectric tield. Furthermo

58、re, wc discussed the decompositiondistance at which lhe radiation tield dominates over theinduction field. The calculation value agreed very well withthe distance at which the radiation field characteristics of themeasurement result.It was confirmed that lhe mechanism of electromagneticradiation cau

59、sed by ESI) in the pair of spherical electrode canbe considered as a radiation from lhe dipole model withelectrode elements.Acknowlldgmln rThis work was supported by JSPS KAKENHl Grant-in-Aid tor Scienlitk Research (B) Number 26289078.References1. M. Honda,Indirect ESD measuremenl using a shortmonop

60、ole antenna5. 1990 IEI：E IntL Symp. onElectromagn. Compat., pp.641-645, Aug. 1990.2. P.F.Wilson and M.T.Ma/Tield radiated byelectrostatic discharges, IEEE Trans, on EMC, EMC-33, no.l. pp.10-18, Feb. 1991.3. D.Pommcrenke:ESI). transient fields, arc simulationand rise time Journal of ELECIROSI AHCS,vo

61、l.36, pp.31-54, 1995.4. S.Ishigami, R.Gokila, Y.Nishiyama, I.Yokoshima andT.Iwasaki, Measurements of fast transient fields in thevicinity of short gap discharges, 1EICE Trans, onCommun., vol.E78-B, no.2, pp J99-206, Feb. 1995.5. O.Fujiwara/An Analytical Approach to ModelIndirect Eft ecl Causea by El

62、ectrostatic Discharge IEICE Trans, on Common., voI.E-79-B, no.4t April1996.6. R.Zaridze, D.Karkashadze. R.G.Djobava,D.Ponimerenke. and M.Aidam/Numencal Calculationand Measurement of Transient Fields fromElectrostatic Discharge, IIUJ： Trans, on Components,Packaging, and Manuia. Tech., Part C, vol. 19, no.3,July 199677. L.M.MacLeod and K.G.Balmain, “Compact Traveling-Wave Phys