球形載流線圈的場分布與自感1.doc

專業(yè)： 姓名： 學(xué)號： 日期： 地點： 實驗報告課程名稱： 工程電子場與電磁波 指導(dǎo)老師：_熊素銘_成績：_實驗名稱：_球形載流線圈的場分布與自感_實驗類型： 動手實驗及仿真 同組學(xué)生姓名： 一、實驗?zāi)康暮鸵螅ū靥睿┒?、實驗?nèi)容和原理（必填）三、主要儀器設(shè)備（必填）四、操作方法和實驗步驟五、實驗數(shù)據(jù)記錄和處理六、實驗結(jié)果與分析（必填）七、討論、心得一、實驗?zāi)康暮鸵?、 分析磁通球的典型磁場分布及求解其自感參數(shù)；2、 掌握工程上測量磁場的兩種基本方法感應(yīng)電勢法和霍爾效應(yīng)發(fā)；3、 在理論分析和實驗研究相結(jié)合的基礎(chǔ)上，力求深化對磁場邊值問題，自感參數(shù)和磁場測量方法等知識點的理解，熟悉霍爾效應(yīng)高斯計的應(yīng)用。二、實驗內(nèi)容1、測量磁通球軸線上磁感應(yīng)強度B的分布；2、探測磁通球外部磁場的分布；3、磁通球自感系數(shù)L的實測值；4、觀察電壓、電流間的相位關(guān)系。實驗原理1、球形載流線圈的磁場分析當(dāng)在z方向具有均勻匝數(shù)密度分布的球形線圈中通以正弦電流i時，可以等效看做為流經(jīng)球表面層的面電流K的分布，顯然，其等效原則在于載流安匝不變，即如設(shè)沿球表面線匝密度分布為W，則在于元長度dz對應(yīng)的球面弧元Rd上，應(yīng)有經(jīng)計算，載流線圈的線匝密度分布W正比于sin，呈正弦分布。因此，本實驗?zāi)M的在球表面上的等效的面電流密度K的分布為通過列寫邊值方程計算的可得磁通球內(nèi)部H1為均勻磁場，其取向與磁通球的對稱軸一致，而球外H2等同于球心處一個磁偶極子的磁場。2、球形載流線圈自感系數(shù)L的分析計算通過上面求得的磁場分布，計算球表面一匝線圈所交鏈的磁通,即經(jīng)計算可得在實際測量中，如果外施頻率足夠高，可以忽略外接電阻，故此時磁通球電壓電流相位差約等于90，可以看做純自感線圈。這是入端電壓峰值與電流峰值之比即為感抗wL的實測值，然后計算可得L實測值。3、感應(yīng)電勢法測磁感應(yīng)強度被測處磁感應(yīng)強度E為測試線圈感應(yīng)電動勢有效值；B為被測處磁感應(yīng)強度有效值；F為激勵源交變電流的頻率；S為測試線圈的等效截面積4、霍耳效應(yīng)法測磁感應(yīng)強度 霍耳元件被制備成一塊矩形(bl)半導(dǎo)體薄片，如圖1-11所示。當(dāng)在它的對應(yīng)側(cè)通以電流I，并置于外磁場B中時，在其另一對應(yīng)側(cè)上將呈現(xiàn)霍耳電壓Vh，這一物理現(xiàn)象稱為霍耳效應(yīng)?；舳妷簽镽h為霍耳常數(shù)，取決于半導(dǎo)體材料的特性；d 是半導(dǎo)體薄片的厚度；f(l/b)是霍耳元件的形狀系數(shù)。在Rh、d、I、f(l/b)等參數(shù)值一定時，Vh B (Bn)。根據(jù)這一原理制成的霍耳效應(yīng)高斯計，通過安裝在探棒端頭上的霍耳片，即可直接測得霍耳片所在位置的磁感應(yīng)強度的平均值（T或Gs，1T=104 Gs）。本實驗采用5070型高斯計，它既可測量時變磁場，也可測量恒定磁場（該高斯計使用方法簡介參閱附錄2）。應(yīng)指出，在正弦交流激勵的時變磁場中，霍耳效應(yīng)高斯計的磁感應(yīng)強度平均值讀數(shù)與由感應(yīng)電勢法測量并計算得出的磁感應(yīng)強度的有效值之間的關(guān)系為三、 主要儀器設(shè)備 磁通球電源測試線圈電阻值0.5歐姆高斯計示波器四、 操作方法和實驗步驟1、測量磁通球軸線方向上磁感應(yīng)強度的分布1）調(diào)整正弦激勵源I=1A，f=5kHz，沿磁通球軸向方向上下調(diào)節(jié)測試線圈，從-5cm到5cm每隔1cm由毫伏表測出感應(yīng)電動勢有效值E一次，并記錄，計算相應(yīng)磁感應(yīng)強度B；2）激勵源依舊為正弦交流1A f=5kHz，應(yīng)用5070型高斯計探棒探測磁通球表面磁感應(yīng)強度。直接讀出磁通球北極處磁感應(yīng)強度Bav。2、探測磁通球外部磁場的分布1）激勵源依舊為正弦交流1A f=5kHz，探測磁通球外部磁場的分布2）激勵源改為I=1A，應(yīng)用高斯計重復(fù)以上探測磁通球外部磁場分布的實測過程，定量讀出磁通球北極處的磁感應(yīng)強度B。3、磁通球自感系數(shù)L的實測值激勵源為I=0.5A，f=5kHz，磁通球串聯(lián)一歐姆電阻，分別測出磁通球電壓與電阻電壓并記錄，計算電感值L。五、實驗結(jié)果與結(jié)論（含誤差分析）1、畫出沿磁通球軸線B（z）|r=0的分布曲線 S=8.01E-3序號坐標(biāo) z cm感應(yīng)電勢法測試線圈感應(yīng)電動勢E V計算的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。理論值為B=Ni/3R=10.98 Gs,實驗值較為符合，略小可能誤差原因為：1：磁通球邊緣效應(yīng)不可忽略2：外表面電流可能不夠1A2、I=1A，對比交流直流兩種激勵情況下進行比較，給出磁感應(yīng)強度B實際值與理論值的比較序號坐標(biāo)霍爾效應(yīng)法實測值Bav T磁感應(yīng)強度B TB理論值1北極（交流）9.61.052E-31.097E-32北極（直流）9.11.003E-31.02E-33赤道4.14.56E-44.9E-4誤差分析：交直流的不同很可能是線圈自身電感造成的，但很難進行定量計算3、計算L的實測值，與理論值，并比較正弦激磁電流實測電阻電壓取樣電阻值電感電壓實際計算電感理論值0.5A 5kHz800mV0.5歐姆28.5V5.47E-04 HL=7.55E-4 H實際計算電感比理論值小，可能原因為1：實驗設(shè)備讀數(shù)和精度的問題2：取樣電阻的電阻值可能與0.5歐姆有差距導(dǎo)致實驗偏差六、實驗仿真 2.部分仿真圖像（1）BY求解圖像及其值 S BY 0.0000 0.11089E-02 0.50000E-02 0.11089E-02 0.10000E-01 0.11090E-02 0.15000E-01 0.11091E-02 0.20000E-01 0.11092E-02 0.25000E-01 0.11093E-02 0.30000E-01 0.11094E-02 0.35000E-01 0.11095E-02 0.40000E-01 0.11095E-02 0.45000E-01 0.11096E-02 0.50000E-01 0.11086E-02 0.55000E-01-0.43121E-03 0.60000E-01-0.33236E-03 0.65000E-01-0.26172E-03 0.70000E-01-0.20972E-03 0.75000E-01-0.17070E-03 0.80000E-01-0.14087E-03 0.85000E-01-0.11757E-03 0.90000E-01-0.99274E-04 0.95000E-01-0.84561E-04 0.10000 -0.72666E-04（2）Azi的156個離散值及其函數(shù)圖象S AZ0.0000 0.57066E-05 0.88138E-03 0.62508E-05 0.17628E-02 0.67657E-05 0.26441E-02 0.72662E-05 0.35255E-02 0.77567E-05 0.44069E-02 0.82396E-05 0.52883E-02 0.87162E-05 0.61697E-02 0.91875E-05 0.70510E-02 0.96539E-05 0.79324E-02 0.10116E-04 0.88138E-02 0.10573E-04 0.96952E-02 0.11026E-04 0.10577E-01 0.11475E-04 0.11458E-01 0.11920E-04 0.12339E-01 0.12360E-04 0.13221E-01 0.12797E-04 0.14102E-01 0.13228E-04 0.14983E-01 0.13656E-04 0.15865E-01 0.14079E-04 0.16746E-01 0.14497E-04 0.17628E-01 0.14911E-04 0.18509E-01 0.15320E-04 0.19390E-01 0.15725E-04 0.20272E-01 0.16124E-04 0.21153E-01 0.16518E-04 0.22035E-01 0.16907E-04 0.22916E-01 0.17291E-04 0.23797E-01 0.17669E-04 0.24679E-01 0.18042E-04 0.25560E-01 0.18409E-04 0.26441E-01 0.18771E-04 0.27323E-01 0.19127E-04 0.28204E-01 0.19477E-04 0.29086E-01 0.19821E-04 0.29967E-01 0.20159E-04 0.30848E-01 0.20490E-04 0.31730E-01 0.20816E-04 0.32611E-01 0.21135E-04 0.33492E-01 0.21447E-04 0.34374E-01 0.21753E-040.35255E-01 0.22053E-04 0.36137E-01 0.22345E-04 0.37018E-01 0.22631E-04 0.37899E-01 0.22910E-04 0.38781E-01 0.23181E-04 0.39662E-01 0.23446E-04 0.40543E-01 0.23704E-04 0.41425E-01 0.23954E-04 0.42306E-01 0.24197E-04 0.43188E-01 0.24432E-04 0.44069E-01 0.24661E-04 0.44950E-01 0.24881E-04 0.45832E-01 0.25094E-04 0.46713E-01 0.25300E-04 0.47595E-01 0.25497E-04 0.48476E-01 0.25687E-04 0.49357E-01 0.25869E-04 0.50239E-01 0.26043E-04 0.51120E-01 0.26209E-04 0.52001E-01 0.26368E-04 0.52883E-01 0.26518E-04 0.53764E-01 0.26660E-04 0.54646E-01 0.26794E-04 0.55527E-01 0.26919E-04 0.56408E-01 0.27037E-04 0.57290E-01 0.27146E-04 0.58171E-01 0.27247E-04 0.59052E-01 0.27340E-04 0.59934E-01 0.27424E-04 0.60815E-01 0.27500E-04 0.61697E-01 0.27568E-04 0.62578E-01 0.27627E-04 0.63459E-01 0.27678E-04 0.64341E-01 0.27720E-04 0.65222E-01 0.27754E-04 0.66104E-01 0.27779E-04 0.66985E-01 0.27796E-04 0.67866E-01 0.27805E-04 0.68748E-01 0.27805E-04 0.69629E-01 0.27796E-04 0.70510E-01 0.27779E-04 0.71392E-01 0.27754E-04 0.72273E-01 0.27720E-04 0.73155E-01 0.27678E-04 0.74036E-01 0.27627E-04 0.74917E-01 0.27568E-04 0.75799E-01 0.27500E-04 0.76680E-01 0.27424E-04 0.77561E-01 0.27340E-04 0.78443E-01 0.27247E-04 0.79324E-01 0.27146E-04 0.80206E-01 0.27037E-04 0.81087E-01 0.26919E-04 0.81968E-01 0.26794E-04 0.82850E-01 0.26660E-04 0.83731E-01 0.26518E-04 0.84612E-01 0.26368E-04 0.85494E-01 0.26209E-04 0.86375E-01 0.26043E-04 0.87257E-01 0.25869E-04 0.88138E-01 0.25687E-04 0.89019E-01 0.25497E-04 0.89901E-01 0.25300E-04 0.90782E-01 0.25094E-04 0.91664E-01 0.24881E-04 0.92545E-01 0.24661E-04 0.93426E-01 0.24432E-04 0.94308E-01 0.24197E-04 0.95189E-01 0.23954E-04 0.96070E-01 0.23704E-04 0.96952E-01 0.23446E-04 0.97833E-01 0.23181E-04 0.98715E-01 0.22910E-04 0.99596E-01 0.22631E-04 0.10048 0.22345E-04 0.10136 0.22053E-04 0.10224 0.21753E-04 0.10312 0.21447E-04 0.10400 0.21135E-04 0.10488 0.20816E-04 0.10577 0.20490E-04 0.10665 0.20159E-04 0.10753 0.19821E-04 0.10841 0.19477E-04 0.10929 0.19127E-04 0.11105 0.18409E-04 0.11194 0.18042E-04 0.11282 0.17669E-04 0.11370 0.17291E-04 0.11458 0.16907E-04 0.11546 0.16518E-04 0.11634 0.16124E-04 0.11722 0.15725E-04 0.11810 0.15320E-04 0.11899 0.14911E-04 0.11987 0.14497E-04 0.12075 0.14079E-04 0.12163 0.13656E-04 0.12251 0.13228E-04 0.12339 0.12797E-04 0.12427 0.12360E-040.12516 0.11920E-04 0.12604 0.11475E-04 0.12692 0.11026E-04 0.12780 0.10573E-04 0.12868 0.10116E-04 0.12956 0.96539E-05 0.13044 0.91875E-05 0.13133 0.87162E-05 0.13221 0.82396E-05 0.13309 0.77567E-05 0.13397 0.72662E-05 0.13485 0.67657E-05 0.13573 0.62508E-05 0.13661 0.57066E-0（3）電流密度曲線（4）電磁感應(yīng)強度分布云圖全磁場 X向磁場 Y向磁場（5）磁感線分布圖2.仿真計算值，離散求和結(jié)果iAziSIN*(11.5+i)/180Ni2Aiz*Ni*215.71E-060.216440.2529568890.0686767949.91E-0826.25E-060.2334460.2728318150.0740727571.26E-0736.77E-060.2503810.2926236330.0794461581.57E-0747.27E-060.2672390.3123263140.0847953581.92E-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-050.3665020.4283365770.1162916855.04E-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-050.477160.5576639790.1514035621.12E-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-050.5664070.661969040.1797219731.87E-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-050.6494490.7590213950.2060713042.82E-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-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-050.8038580.9394813990.255065485.35E-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-050.861631.0070006970.2733967026.59E-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-06552.55E-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-050.9537181.1146247140.3026161978.94E-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-050.9799251.1452538250.3109318799.70E-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-050.9953971.1633352380.3158409111.02E-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-05802.78E-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-050.9914441.1587162560.3145868761.00E-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-050.9723691.1364225340.3085342199.48E-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-050.942641.101677870.299101188.64E-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-061052.49E-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-050.8433890.9856814190.2676086036.18E-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-050.7826050.9146423780.2483217844.94E-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-050.7132470.8335822770.2263142883.74E-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-050.6360740.7433892310.2018272332.59E-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-050.5519320.6450514190.1751289061.68E-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-071421.19E-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-060.3172980.3708315280.1006792923.08E-071517.76E-060.3006990.3514321020.0954124242.60E-071527.27E-060.2840090.3319256250.0901164932.17E-071536.77E-060.2672320.3123180410.0847931111.79E-071546.25E-060.2503730.292615320.0794439011.45E-071555.71E-060.2334390.2728234660.0740704911.15E-07自動求和值： =M=7.55E-04 =1A L=7.55E-04 H3.MATLAB函數(shù)調(diào)用計算（1）計算編程r1=0.05;r2=0.051;r=(r1+r2)/2;pi=2*asin(1);ds=pi*(r2*r2-r1*r1)/360mm=0;k=1;while(k=156) mm=mm+sin(pi*(11.5+k)/180)*ds; k=k+1;end;i=1;M=0;while(i=156) p=r*sin(pi*(11.5+i)/180); Ni=131*sin(pi*(i+11.5)/180)/(mm*ds); A=1.136*10(-18)*i5 + 8.887*10(-14)*i4 - 2.763*10(-11)*i3 - 9.775*10(-10)*i2 + 4.836*10(-7)*i + 5.829*10(-6) M=M+2*pi*p*A*Ni; i=i+1;end;（2）關(guān)于以i為自變量對Azi進行函數(shù)擬合圖像離散點圖像5次函數(shù)擬合表達式 5次函數(shù)擬合后的圖像4.ANSYS仿真命令流文件finish/clear! 定義參數(shù)，單位均采用國際制單位r0=0.5 ! 場域外邊界所對應(yīng)的半徑r1=0.05 ! 球形載流線圈內(nèi)半徑r2=0.051 ! 球形載流線圈外半徑dcita=1.0 ! 每個小線圈截面所占的角度pi=2*asin(1) !