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RMS and average current triangle

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  1. Mar 26, 2015 #1
    I would like to know how to find RMS and average current of a triangle???
    i searched the web. but it focus from 0. which i know.
    but my waveform is different from the internet. i have attached the waveform..
    Maximum = 2.5 , Minimum = 1.8

    i need to find out the RMS and average current
     

    Attached Files:

  2. jcsd
  3. Mar 26, 2015 #2

    donpacino

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    Gold Member

    Last edited: Mar 26, 2015
  4. Mar 30, 2015 #3
    Following the definition:

    "The RMS over all time of a periodic function is equal to the RMS of one period of the function."

    And :

    frms=sqrt[integral(f(t)^2/T]

    f(t)up=yo+(y1-yo)/(x1-xo)*(x-xo) integrated for x=x1 and x=xo

    f(t)down=y1-(y1-yo)/(x1-xo)*(x-x1) for x=2*x1 and x=x1

    where T=0.05 xo=0;x1=T/2;yo=1.8;y1=2.5

    frms=sqrt{[integral(f(t)up^2+integral(f(t)down^2]/T}

    integral(f(t)up^2=aup*x+bup*x^2/2+cup*x^3/3 x=x1 and x=xo

    integral(f(t)down^2=adown*x+bdown*x^2/2+cdown*x^3/3 x=2*x1 and x=x1

    Let's put k= (y1-yo)/(x1-xo).Then:

    aup=yo^2-2*k*yo*xo+k^2*xo^2

    bup=2*yo*k-2*xo*k^2

    cup=k^2

    adown=y1^2+2*y1*k*x1+k^2*x1^2

    bdown=-2*y1*k-2*k^2*x1

    cdown=k^2

    frms=2.16[approx.]
    upload_2015-3-30_8-20-57.png
     
  5. Mar 30, 2015 #4

    NascentOxygen

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    Staff: Mentor

    What have you calculated as its average value?
     
  6. Mar 31, 2015 #5
    Following:

    http://en.wikipedia.org/wiki/Average

    AM=1/n*Sum[y(i)]|y(1)=yo to y(n)=y1

    Let's take n number of equal distanced points on upright part of the triangle.The number of intervals

    will be n-1.Each y[y(i)] value will be y(i)=yo+(i-1)*(yn-yo)/(n-1)

    Sum[y(i)]|y(1)=yo to y(n)=y1=n*yo+ (y1-yo)/(n-1)*Sum(1+2+3+..n-1)

    Sum(1+2+3+..n-1)=n*(n-1)/2. Then:

    Sum[y(i)]|y(1)=yo to y(n)=y1=n*yo+n*(n-1)/2*(y1-yo)/(n-1)=n*yo+n/2*(y1-yo)

    AM=1/n*Sum=yo+(y1-yo)/2=(y1+yo)/2

    AM=(1.8+2.5)/2=2.15
     
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