Transformer - Flux density

Discussion in 'Physics' started by Skeebopstop, Mar 19, 2009.

  1. Skeebopstop

    Thread Starter Active Member

    Jan 9, 2009
    358
    3
    Hi all,

    I am working through the physics of transformer design, and on the attached slide, hit an inquiry of where the divide by 2 factor came from?

    Any insight? I understand the rest.

    Regards,
     
  2. thatoneguy

    AAC Fanatic!

    Feb 19, 2009
    6,357
    718
    Most calculations involve the angular velocity of the AC waveform - ω - radians/second.

    ω=2 π FHz

    An easier to understand explanation is below, from This site, towards bottom of page

     
  3. studiot

    AAC Fanatic!

    Nov 9, 2007
    5,005
    513
    The direct answer to your question is that your extract specifically states "the positive peak". You need to double this to get the negative peak as well.

    You should observe that the frequency of the power waveform is twice that of the voltage, current or flux waveform.

    I will use sinusoids.

    If \Phi is the maximum value of the flux and f the frequency then the flux changes from +\Phi to -\Phi in half a cycle i.e. 1/2f seconds.

    So the average rate of change of flux is 2\Phi /0.5f = 4f\Phi

    Note the 2\Phi is the distance between positive and negative peaks.

    But the average rate of change of flux = average emf induced.

    Thus induced emf = 4f\Phi volts per turn

    Multiply this by the form factor (1.11 for sinusoids) to get the RMS value and we have the well known equation

    EMF induced per turn = 4.44Nf\Phi where N is number of turns.

    --------------------------------------------------------------------

    A calculus method is as follows; If \phi is the instantaneous flux then

    \phi = \Phisin2π ft

    Instantaneous induced voltage per turn is

    -d\phi/dt volts

    = -\Phi x cos2πft volts (note the minus sign)

    = 2πf\Phi x sin(2πft -π/2)

    Thus the max value occurs when the sin term is 1 and equals 2πf\Phi volts per turn.

    Thus the RMS value = √2 x 2πf\Phi volts per turn = 4.44f\Phi as before.

    This is a shortened version of thatoneguys's link.
     
  4. Skeebopstop

    Thread Starter Active Member

    Jan 9, 2009
    358
    3
    Thanks guys
     
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