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  • 星-三角变换

    http://www.amobbs.com/forum.php?mod=viewthread&tid=3661385&page=3#pid3803226

    对R13 R16 R17做星-三角变换:
    RAB = R13 + R17 + R13 * R17 / R16 = 4.63K
    RBC = R16 + R17 + R16 * R17 / R13 = 14.03K
    RCA = R13 + R16 + R13 * R16 / R17 = 46.3K
    变换后RAB固定接于5V和地之间,可忽略。

    Vpwm变化范围0-5V,根据虚短原理,C点电压变化范围也是0-5V。
    现在问题变成:A = 5V,B = 0V,C = 0-5V,求Vout范围。

    先求各臂电流关系:
    Ir15 = (Vc - Vout) / R15
    Irca = (5 - Vc) / RCA
    Irbc = Vc / RBC

    根据基尔霍夫电流定律:
    Ir15 + Irca + Irbc = 0
    (Vc - Vout) / R15 + (5 - Vc) / RCA + Vc / RBC = 0

    最后得出:
    Vout = Vpwm + [(5 - Vpwm) / RCA + Vpwm / RBC] * R15

    代入Vpwm = 0-5V计算得出Vout范围约-1.08-8.56V。

     这样考虑更简单:
    1. 5V,R13,R17可等效为电动势和内阻:

    电动势 : 5V*(1/(1+3.3))=1.162790V 

    内阻 : 1*3.3/(1+3.3)=0.76744K


    2. 设:U5A输入阻抗无穷,则流过R15和上述内阻的电流相同。

    (y-x)/10 = (x-1.162790)/(0.76744+10) = 0.0928726 x - 0.107991
    化简:
    y = 1.928726 x - 1.07991 
    验算:
    x = 5, y = 8.56372

    Y = Vout

    X = Vpwm

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  • 原文地址:https://www.cnblogs.com/shangdawei/p/3286381.html
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