球形载流线圈的场分布与自感1精编版.doc

1、专业：姓名：学号：实验报告日期：地点：课程名称：工程电子场与电磁波指导老师： _熊素铭 _成绩：_实验名称： _球形载流线圈的场分布与自感_实验类型：动手实验及仿真同组学生姓名：一、实验目的和要求（必填）二、实验内容和原理（必填）三、主要仪器设备（必填）四、操作方法和实验步骤五、实验数据记录和处理六、实验结果与分析（必填）七、讨论、心得一、实验目的和要求1、 分析磁通球的典型磁场分布及求解其自感参数；2、 掌握工程上测量磁场的两种基本方法感应电势法和霍尔效应发；3、 在理论分析和实验研究相结合的基础上，力求深化对磁场边值问题，自感参数和磁场测量方法等知识点的理解，熟悉霍尔效应高斯计的应用。二、

2、实验内容1、测量磁通球轴线上磁感应强度B的分布；2、探测磁通球外部磁场的分布；3、磁通球自感系数L的实测值；4、观察电压、电流间的相位关系。实验原理1、球形载流线圈的磁场分析当在 z 方向具有均匀匝数密度分布的球形线圈中通以正弦电流i 时，可以等效看做为流经球表面层的面电流K 的分布，显然，其等效原则在于载流安匝不变，即如设沿球表面线匝密度分布为W ，则在于元长度dz 对应的球面弧元Rd 上，应有N(W Rd )i(dz)i经计算，载流线圈的线匝密度分布 W 正比于 sin ，呈正弦分布。因此，本实验模拟的在球表面上的等效的面电流密度 K 的分布为K N i sin e 2R通过列写边值方程计

3、算的H1m1Nicos er sine3RNi3H 2Rer sinem26R2cosr可得磁通球内部H1 为均匀磁场，其取向与磁通球的对称轴一致，而球外H2 等同于球心处一个磁偶极子的磁场。2、球形载流线圈自感系数L 的分析计算通过上面求得的磁场分布，计算球表面一匝线圈所交链的磁通 ,即0H1 Rsin2经计算可得2N 2 0 RL9在实际测量中，如果外施频率足够高，可以忽略外接电阻，故此时磁通球电压电流相位差约等于90，可以看做纯自感线圈。这是入端电压峰值与电流峰值之比即为感抗wL 的实测值，然后计算可得 L实测值。3、感应电势法测磁感应强度被测处磁感应强度EB2fSN1E 为测试线圈感应

4、电动势有效值；B 为被测处磁感应强度有效值；F 为激励源交变电流的频率；S 为测试线圈的等效截面积4、霍耳效应法测磁感应强度霍耳元件被制备成一块矩形(b l)半导体薄片，如图1-11 所示。当在它的对应侧通以电流置于外磁场B 中时，在其另一对应侧上将呈现霍耳电压Vh，这一物理现象称为霍耳效应。霍耳电压为I ，并VRhlIBfhdbRh 为霍耳常数，取决于半导体材料的特性；d 是半导体薄片的厚度；f( l/b)是霍耳元件的形状系数。、f(l/b)等参数值一定时， Vh B (Bn)。根据这一原理制成的霍耳效应高斯计，通过安在 Rh、d I装在探棒端头上的霍耳片，即可直接测得霍耳片所在位置的磁感应

5、强度的平均值（T 或 Gs， 1T=104 Gs）。本实验采用 5070 型高斯计，它既可测量时变磁场， 也可测量恒定磁场 （该高斯计使用方法简介参阅附录2）。应指出，在正弦交流激励的时变磁场中，霍耳效应高斯计的磁感应强度平均值读数与由感应电势法测量并计算得出的磁感应强度的有效值之间的关系为Bav2 2B 0.9B三、 主要仪器设备磁通球电源测试线圈电阻值0.5 欧姆高斯计示波器四、 操作方法和实验步骤1、测量磁通球轴线方向上磁感应强度的分布1）调整正弦激励源I=1A ， f=5kHz ，沿磁通球轴向方向上下调节测试线圈，从-5cm 到 5cm1cm 由毫伏表测出感应电动势有效值E 一次，并记

6、录，计算相应磁感应强度B；2）激励源依旧为正弦交流1A f=5kHz ，应用 5070 型高斯计探棒探测磁通球表面磁感应强度。直接读出磁通球北极处磁感应强度Bav 。每隔2、探测磁通球外部磁场的分布1）激励源依旧为正弦交流1A f=5kHz ，探测磁通球外部磁场的分布2）激励源改为I=1A ，应用高斯计重复以上探测磁通球外部磁场分布的实测过程，定量读出磁通球北极处的磁感应强度B。3、磁通球自感系数L 的实测值激励源为 I=0.5A ，f=5kHz ，磁通球串联一欧姆电阻，分别测出磁通球电压与电阻电压并记录，计算电感值 L 。五、实验结果与结论（含误差分析）1、画出沿磁通球轴线B（ z）|r=0

7、 的分布曲线S=8.01E-3序号坐标感应电势法z cm测试线圈感应电动势E V计算的B T1-532.00.0009704812-432.00.0009704813-332.00.0009704814-232.50.0009856445-133.00.0010008086033.80.001025077133.50.0010159728233.50.0010159729333.00.00100080810432.10.00097351311529.50.000894662求平均值得 0.00098399 。理论值为 B= Ni/3R=10.98 Gs,实验值较为符合，略小可能误差原因为：1：

8、磁通球边缘效应不可忽略2：外表面电流可能不够1A2、 I=1A ，对比交流直流两种激励情况下进行比较，给出磁感应强度B 实际值与理论值的比较序号坐标霍尔效应法实测值 Bav T磁感应强度 BT B理论值1北极（交流）9.61.052E-31.097E-32北极（直流）9.11.003E-31.02E-33赤道4.14.56E-44.9E-4误差分析：交直流的不同很可能是线圈自身电感造成的，但很难进行定量计算3、计算 L 的实测值，与理论值，并比较正弦激磁电流0.5A5kHz实测电阻电压800mV取样电阻值0.5 欧姆电感电压28.5V实际计算电感5.47E-04 H理论值L=7.55E-4 H

9、实际计算电感比理论值小，可能原因为1：实验设备读数和精度的问题2：取样电阻的电阻值可能与0.5 欧姆有差距导致实验偏差六、实验仿真2.部分仿真图像（ 1）BY 求解图像及其值SBY0.00000.11089E-020.50000E-02 0.11089E-020.10000E-01 0.11090E-020.15000E-01 0.11091E-020.20000E-01 0.11092E-020.25000E-01 0.11093E-020.30000E-01 0.11094E-020.35000E-01 0.11095E-020.40000E-01 0.11095E-020.45000E-

10、01 0.11096E-020.50000E-01 0.11086E-020.55000E-01-0.43121E-030.60000E-01-0.33236E-030.65000E-01-0.26172E-030.70000E-01-0.20972E-030.75000E-01-0.17070E-030.80000E-01-0.14087E-030.85000E-01-0.11757E-030.90000E-01-0.99274E-040.95000E-01-0.84561E-040.10000-0.72666E-04（ 2）Azi 的 156 个离散值及其函数图象SAZ0.00000.57

11、066E-050.88138E-03 0.62508E-050.17628E-02 0.67657E-050.26441E-02 0.72662E-050.35255E-02 0.77567E-050.44069E-02 0.82396E-050.52883E-02 0.87162E-050.61697E-02 0.91875E-050.70510E-02 0.96539E-050.79324E-02 0.10116E-040.88138E-02 0.10573E-040.96952E-02 0.11026E-040.10577E-01 0.11475E-040.11458E-01 0.119

12、20E-040.12339E-01 0.12360E-040.13221E-01 0.12797E-040.14102E-01 0.13228E-040.14983E-01 0.13656E-040.15865E-01 0.14079E-040.16746E-01 0.14497E-040.17628E-01 0.14911E-040.18509E-01 0.15320E-040.19390E-01 0.15725E-040.20272E-01 0.16124E-040.21153E-01 0.16518E-040.22035E-01 0.16907E-040.22916E-01 0.1729

13、1E-040.23797E-01 0.17669E-040.24679E-01 0.18042E-040.25560E-01 0.18409E-040.26441E-01 0.18771E-040.27323E-01 0.19127E-040.28204E-01 0.19477E-040.29086E-01 0.19821E-040.29967E-01 0.20159E-040.30848E-01 0.20490E-040.31730E-01 0.20816E-040.32611E-01 0.21135E-040.33492E-01 0.21447E-040.34374E-01 0.21753

14、E-040.35255E-01 0.22053E-040.47595E-01 0.25497E-040.36137E-01 0.22345E-040.48476E-01 0.25687E-040.37018E-01 0.22631E-040.49357E-01 0.25869E-040.37899E-01 0.22910E-040.50239E-01 0.26043E-040.38781E-01 0.23181E-040.51120E-01 0.26209E-040.39662E-01 0.23446E-040.52001E-01 0.26368E-040.40543E-01 0.23704E

15、-040.52883E-01 0.26518E-040.41425E-01 0.23954E-040.53764E-01 0.26660E-040.42306E-01 0.24197E-040.54646E-01 0.26794E-040.43188E-01 0.24432E-040.55527E-01 0.26919E-040.44069E-01 0.24661E-040.56408E-01 0.27037E-040.44950E-01 0.24881E-040.57290E-01 0.27146E-040.45832E-01 0.25094E-040.58171E-01 0.27247E-

16、040.46713E-01 0.25300E-040.59052E-01 0.27340E-040.59934E-01 0.27424E-040.98715E-01 0.22910E-040.60815E-01 0.27500E-040.99596E-01 0.22631E-040.61697E-01 0.27568E-040.100480.22345E-040.62578E-01 0.27627E-040.101360.22053E-040.63459E-01 0.27678E-040.102240.21753E-040.64341E-01 0.27720E-040.103120.21447

17、E-040.65222E-01 0.27754E-040.104000.21135E-040.66104E-01 0.27779E-040.104880.20816E-040.66985E-01 0.27796E-040.105770.20490E-040.67866E-01 0.27805E-040.106650.20159E-040.68748E-01 0.27805E-040.107530.19821E-040.69629E-01 0.27796E-040.108410.19477E-040.70510E-01 0.27779E-040.109290.19127E-040.71392E-

18、01 0.27754E-040.111050.18409E-040.72273E-01 0.27720E-040.111940.18042E-040.73155E-01 0.27678E-040.112820.17669E-040.74036E-01 0.27627E-040.113700.17291E-040.74917E-01 0.27568E-040.114580.16907E-040.75799E-01 0.27500E-040.115460.16518E-040.76680E-01 0.27424E-040.116340.16124E-040.77561E-01 0.27340E-0

19、40.117220.15725E-040.78443E-01 0.27247E-040.118100.15320E-040.79324E-01 0.27146E-040.118990.14911E-040.80206E-01 0.27037E-040.119870.14497E-040.81087E-01 0.26919E-040.120750.14079E-040.81968E-01 0.26794E-040.121630.13656E-040.82850E-01 0.26660E-040.122510.13228E-040.83731E-01 0.26518E-040.123390.127

20、97E-040.84612E-01 0.26368E-040.124270.12360E-040.85494E-01 0.26209E-040.125160.11920E-040.86375E-01 0.26043E-040.126040.11475E-040.87257E-01 0.25869E-040.126920.11026E-040.88138E-01 0.25687E-040.127800.10573E-040.89019E-01 0.25497E-040.128680.10116E-040.89901E-01 0.25300E-040.129560.96539E-050.90782

21、E-01 0.25094E-040.130440.91875E-050.91664E-01 0.24881E-040.131330.87162E-050.92545E-01 0.24661E-040.132210.82396E-050.93426E-01 0.24432E-040.133090.77567E-050.94308E-01 0.24197E-040.133970.72662E-050.95189E-01 0.23954E-040.134850.67657E-050.96070E-01 0.23704E-040.135730.62508E-050.96952E-01 0.23446E

22、-040.136610.57066E-00.97833E-01 0.23181E-04（ 3）电流密度曲线（ 4）电磁感应强度分布云图全磁场X 向磁场Y 向磁场（ 5）磁感线分布图2.仿真计算值，离散求和结果iAziSIN *(11.5+i)/180Ni2 Aiz*Ni*2 15.71E-060.216440.2529568890.0686767949.91E-0826.25E-060.2334460.2728318150.0740727571.26E-0736.77E-060.2503810.2926236330.0794461581.57E-0747.27E-060.2672390.312

23、3263140.0847953581.92E-0757.76E-060.2840160.3319338580.0901187282.32E-0768.24E-060.3007060.351440290.0954146472.76E-0778.72E-060.3173050.3708396710.1006815023.25E-0789.19E-060.3338080.3901260890.1059176893.80E-0799.65E-060.3502080.4092936710.1111216114.39E-07101.01E-050.3665020.4283365770.1162916855

24、.04E-07111.06E-050.3826840.4472490070.1214263355.74E-07121.10E-050.398750.46602520.1265239976.50E-07131.15E-050.4146940.4846594360.1315831187.32E-07141.19E-050.4305120.503146040.1366021588.19E-07151.24E-050.4461990.521479380.1415795879.13E-07161.28E-050.461750.5396538720.146513891.01E-06171.32E-050.

25、477160.5576639790.1514035621.12E-06181.37E-050.4924250.5755042160.1562471161.23E-06191.41E-050.5075390.5931691470.1610430751.34E-06201.45E-050.52250.6106533930.1657899781.47E-06211.49E-050.5373010.6279516260.170486381.60E-06221.53E-050.5519380.6450585790.175130851.73E-06231.57E-050.5664070.661969040

26、.1797219731.87E-06241.61E-050.5807040.6786778570.1842583512.02E-06251.65E-050.5948240.6951799420.1887386022.17E-06261.69E-050.6087630.7114702670.1931613612.32E-06271.73E-050.6225160.7275438710.197525282.48E-06281.77E-050.6360790.7433958560.2018290322.65E-06291.80E-050.6494490.7590213950.2060713042.8

27、2E-06301.84E-050.6626210.7744157280.2102508043.00E-06311.88E-050.6755910.7895741650.214366263.18E-06321.91E-050.6883560.8044920880.2184164173.36E-06331.95E-050.7009110.8191649550.2224000423.55E-06341.98E-050.7132520.8335882950.2263159223.74E-06352.02E-050.7253760.8477577140.2301628633.93E-06362.05E-

28、050.7372790.8616688980.2339396944.13E-06372.08E-050.7489570.8753176070.2376452654.33E-06382.11E-050.7604070.8886996850.2412784464.53E-06392.14E-050.7716260.9018110550.2448381314.74E-06402.18E-050.7826090.9146477230.2483232364.94E-06412.21E-050.7933550.9272057790.2517326985.15E-06422.23E-050.8038580.

29、9394813990.255065485.35E-06432.26E-050.8141170.9514708410.2583205665.56E-06442.29E-050.8241270.9631704560.2614969655.77E-06452.32E-050.8338870.9745766770.2645937095.98E-06462.34E-050.8433930.9856860320.2676098556.18E-06472.37E-050.8526410.9964951360.2705444846.39E-06482.40E-050.861631.0070006970.273

30、3967026.59E-06492.42E-050.8703571.0171995140.2761656416.80E-06502.44E-050.8788181.027088480.2788504567.00E-06512.47E-050.8870121.0366645840.281450337.20E-06522.49E-050.8949361.0459249090.2839644727.39E-06532.51E-050.9025861.0548666330.2863921147.58E-06542.53E-050.9099621.0634870330.2887325197.77E-06

31、552.55E-050.9170611.0717834830.2909849727.95E-06562.57E-050.9238811.0797534560.2931487888.13E-06572.59E-050.9304191.0873945240.2952233088.30E-06582.60E-050.9366731.094704360.29720798.47E-06592.62E-050.9426421.1016807360.2991019588.64E-06602.64E-050.9483251.1083215280.3009049078.79E-06612.65E-050.953

32、7181.1146247140.3026161978.94E-06622.67E-050.9588211.1205883720.3042353069.09E-06632.68E-050.9636311.1262106860.3057617429.23E-06642.69E-050.9681481.1314899440.307195049.36E-06652.70E-050.9723711.1364245380.3085347639.48E-06662.71E-050.9762971.1410129640.3097805029.60E-06672.72E-050.9799251.14525382

33、50.3109318799.70E-06682.73E-050.9832551.1491458290.3119885439.80E-06692.74E-050.9862861.1526877910.3129501719.89E-06702.75E-050.9890161.1558786310.3138164729.98E-06712.76E-050.9914451.1587173770.314587181.00E-05722.76E-050.9935721.1612031650.3152620621.01E-05732.77E-050.9953971.1633352380.3158409111

34、.02E-05742.77E-050.9969181.1651129460.3163235521.02E-05752.78E-050.9981351.1665357480.3167098371.03E-05762.78E-050.9990481.1676032090.3169996491.03E-05772.78E-050.9996571.1683150060.3171928991.03E-05782.78E-050.9999621.1686709220.3172895281.03E-05792.78E-050.9999621.1686708470.3172895081.03E-05802.7

35、8E-050.9996571.1683147820.3171928381.03E-05812.78E-050.9990481.1676028350.3169995471.03E-05822.78E-050.9981351.1665352230.3167096951.03E-05832.77E-050.9969171.1651122720.3163233691.02E-05842.77E-050.9953961.1633344150.3158406881.02E-05852.76E-050.9935711.1612021930.3152617981.01E-05862.76E-050.99144

36、41.1587162560.3145868761.00E-05872.75E-050.9890151.1558773620.3138161279.98E-06882.74E-050.9862851.1526863740.3129497879.89E-06892.73E-050.9832541.1491442650.3119881189.80E-06902.72E-050.9799241.1452521140.3109314159.70E-06912.71E-050.9762951.1410111060.3097799989.60E-06922.70E-050.9723691.136422534

37、0.3085342199.48E-06932.69E-050.9681471.1314877950.3071944569.36E-06942.68E-050.9636291.1262083920.3057611199.23E-06952.67E-050.9588191.1205859330.3042346449.09E-06962.65E-050.9537161.1146221320.3026154968.94E-06972.64E-050.9483221.1083188040.3009041678.79E-06982.62E-050.942641.101677870.299101188.64

38、E-06992.60E-050.9366711.0947013530.2972070838.47E-061002.59E-050.9304161.0873913770.2952224548.30E-061012.57E-050.9238781.079750170.2931478968.13E-061022.55E-050.9170581.071780060.2909840437.95E-061032.53E-050.9099591.0634834730.2887315527.77E-061042.51E-050.9025831.0548629370.2863911117.58E-061052.

39、49E-050.8949321.0459210780.2839634327.39E-061062.47E-050.8870091.036660620.2814492547.20E-061072.44E-050.8788151.0270843840.2788493447.00E-061082.42E-050.8703531.0171952860.2761644936.80E-061092.40E-050.8616271.0069963390.2733955196.59E-061102.37E-050.8526380.996490650.2705432666.39E-061112.34E-050.

40、8433890.9856814190.2676086036.18E-061122.32E-050.8338830.9745719390.2645924235.98E-061132.29E-050.8241230.9631655930.2614956455.77E-061142.26E-050.8141130.9514658560.2583192135.56E-061152.23E-050.8038540.9394762920.2550640945.35E-061162.21E-050.793350.9272005530.2517312795.15E-061172.18E-050.7826050

41、.9146423780.2483217844.94E-061182.14E-050.7716210.9018055930.2448366484.74E-061192.11E-050.7604030.8886941090.2412769324.53E-061202.08E-050.7489520.8753119180.237643724.33E-061212.05E-050.7372740.8616630970.2339381194.13E-061222.02E-050.7253710.8477518040.2301612583.93E-061231.98E-050.7132470.833582

42、2770.2263142883.74E-061241.95E-050.7009050.8191588310.2223983793.55E-061251.91E-050.6883510.804485860.2184147263.36E-061261.84E-050.6755860.7895678340.2143645413.12E-061271.80E-050.6626160.7744092970.2102490582.94E-061281.77E-050.6494440.7590148660.2060695312.76E-061291.73E-050.6360740.7433892310.20

43、18272332.59E-061301.69E-050.622510.7275371510.1975234562.43E-061311.65E-050.6087570.7114634560.1931595112.27E-061321.61E-050.5948180.695173040.1887367282.12E-061331.57E-050.5806980.6786708670.1842564541.97E-061341.53E-050.5664010.6619619640.1797200521.82E-061351.49E-050.5519320.6450514190.1751289061

44、.68E-061361.45E-050.5372950.6279443850.1704844141.55E-061371.41E-050.5224930.6106460720.1657879911.43E-061381.37E-050.5075330.5931617490.1610410661.30E-061391.32E-050.4924180.5754967430.1562450871.19E-061401.28E-050.4771530.5576564340.1514015141.08E-061411.24E-050.4617430.5396462560.1465118229.77E-0

45、71421.19E-050.4461920.5214716970.1415775018.80E-071431.15E-050.4305050.5031382910.1366000547.89E-071441.10E-050.4146870.4846516240.1315809977.03E-071451.06E-050.3987430.4660173260.1265218596.23E-071461.01E-050.3826770.4472410740.1214241815.49E-071479.65E-060.3664950.4283285880.1162895164.81E-071489.19E-060.3502010.4092856280.1111194284.18E-071498.72E-060.3338010.3901179960.1059154913.60E-071508.24E-060.3172980.3708315280.1006792