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UC3845A: Primary inductance of Flyback Transformer

Atul Bhakay1
Prodigy 160 points
Part Number: UC3845A

Hi there,

In various application notes I come across 2 formulae to calculate the primary inductance of a flyback transformer.. These 2 formula are given below :-

a) Lp = (Vin min² x Dmax² x effeciency) /  (2 x Freq x Po).  where Vin min = min input DC voltage, Dmax = max duty cycle, Po = output power, Freq = freq of operation.

b) Lp = Lsec (Np/Ns)², where

    Lsec = (Vo+Vf)(1-Dmax) / (ΔIsec x Freq).   where Vo = output voltage, Vf = voltage drop of output diode, 

where ΔIsec = (Io x 0.3) / (1-Dmax),   where Io is output current

Np/Ns = (Dmax) / (1-Dmax)  x  (Vin min) / (Vo = Vf)

My question is that if i apply formula given in first equation , i get a particular value of Lp and when I derive the Lp using the second set of equations i get a VASTLY different value for Lp (much higher that Lp derived from 1st equation)

This has left me confused

Kindly advise correct equation to derive Lp for a flyback transformer

Regards

Atul Bhakay

  • 0
    TI__Genius 13660 points

    Hi Atul,

    There two equation are all derived from the basic operation method.

    But in where ΔIsec = (Io x 0.3) / (1-Dmax),   where Io is output current,  I think (1-Dmax) is unreasonable, it is not required.

    Regards,

    Teng

  • 0 in reply to Teng Feng
    Prodigy 160 points

    Hi Teng,

    Thanks for your reply. Let me take a small example to show what I mean.

    Let us calculate the primary inductance of a flyback transformer with following details :-

    Input voltage range = 50VDC to 80VDC.    Required output = 12V at 6 amperes. Hence Output power = 12 x 6 = 72 watts

    Assume a freq of 50KHz and efficiency of 75%.  Considering UC3845A, the max duty cycle = 0.45

    a) Using formula, Lp = (Vin min² x Dmax² x effeciency) /  (2 x Freq x Po)

    Lp = 50² x 0.45² x 0.75 / (2 x 50 x 10³ x 72)  = 52.7uH = 0.0527 mH   .......... Eq 1

    b) Using the second set of formulae and taking your advise

    ΔIsec = (Io x 0.3). = 6 x 0.3 = 1.8

    Lsec = (Vo+Vf)(1-Dmax) / (ΔIsec x Freq) = 12.7 x 0.55 / 1.8 x 50 x 10³) = 0.077 mH

    Np/Ns = (Dmax) / (1-Dmax)  x  (Vin min) / (Vo + Vf) = (0.45/0.55) x (50/12.7) = 3.22

    Lsec (Np/Ns)² = 0.077 x 3.22² = 0.798mH = 798uH  .........Eq 2

    KINDLY NOTE THE VAST DIFFERENCE IN Lp IN THESE 2 EQUATIONS

    So we come back to my basic question --- Which formulae to use to calculate Lp (Primary inductance of a flyback transformer) ?

    Kindly advise

  • 0 in reply to Atul Bhakay1
    Prodigy 160 points

    Hi Teng or anybody else,

    Awaiting your reply

    Regards

    Atul Bhakay

  • 0 in reply to Atul Bhakay1
    Prodigy 160 points

    Hi,

    Why isnt any body replying ?

    Teng - awaiting your reply

    Regards

    Atul Bhakay

  • 0 in reply to Atul Bhakay1
    TI__Genius 13660 points

    Hi Atul,

    I am sure Calculator 1 is right for CCM fly-back inductance calculation.

    But I didn't find the the Calculator 2 you mentioned.  Below picture shows how to calculation secondary side current.

    Thank you.

     

  • 0 in reply to Teng Feng
    Prodigy 160 points

    Hi Teng,

    Thanks for sharing these equations.

    Similarly, can you share equations for Discontinuous conduction mode (DCM) ?

    Regards

    Atul

  • 0 in reply to Atul Bhakay1
    TI__Genius 13660 points

    Hi Atul,

    For your reference, thank you.

    www.ti.com/.../slyu036