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TPS546C23: Output ripple current of individual output cap calculation

Wenhao Wu
Genius 9046 points
Part Number: TPS546C23

Hi Team,

My customer is asking how to calculate ripple current of an individual output cap. For example, they use 2*47uF ceramics and 2*470uF/2.5mOhm MLCC. The inductor current is 600kHz, 15A pk-pk. They want to know what is the RMS current in an individual MLCC so that they can know lifetime of that cap in advance.

Any ideas or consideration for this?

Thank you very much!

-Wenhao

  • 0
    TI__Mastermind 48180 points

     

    The ripple current in the output capacitors will be divided among the output capacitors inversely to their impedance at the switching frequency.

    Check the capacitor impedance at 600kHz 

    470uF / 2.5mOhms has 0.564mOhms (Capacitive) and 2.5mOhms (Resistive) for a total impedance of about 3mOhms

    47uF / 2mOhm has 5.64mOhms (Capacitive) and 2mOhms (Resistive) for a total impedance of about 7.64mOhms.

    The 470uF capacitor will carry about 2.54x as much current as the 47uF capacitors.  That puts 71.6% of the ripple current on the 470uF capacitors or 5.37A pk-pk.

    The RMS current in a triangle waveform is 1 / (2 x Sqrt(3) ) x pk-pk so that comes to 1.55Arms in the 470uF and 0.610Arms in the 47uF. 

  • 0 in reply to Peter James Miller
    TI__Genius 9046 points

    Hi Peter,

    Since the current is triangle shape, can i use Flourier to divide it, calculate how much those elements can go to 470uF cap and then convolute them together? I think this could be very complex, or can i just use base element, that is 600kHz sine wave?

    -Wenhao

  • 0 in reply to Wenhao Wu
    TI__Mastermind 48180 points

    Hi  

    Yes, you could perform a Fourier transform on the asymmetric triangle waveform, understanding that it will vary depending on the duty-cycle, and then evaluate the impedance divider at each harmonic of the switching frequency if you needed a more accurate estimate of the RMS current in the capacitors, but for these estimates, which will slightly over-estimate the current in the 470uF capacitor, are generally close enough for heating and life-time estimates.

    Looking at the ratio of impedances, based on the above estimates of ESR (2.5mOhms for the 470uF and 2mOhms for the 47uF)  at harmonics above fundamental, so 1.2MHz and higher, the impedances are very similar, so it would be a reasonable estimate that the 470uF capacitors will each carry 35% of the ripple current at the fundamental frequency and then 25% of the current for each of the harmonics.  That would be a little more accurate than what I did above, which assumes the ripple is a sine-wave at 600kHz, but the error would be pretty small.

    In a 50% duty cycle triangle waveform, the fundamental frequency contains about 90% of the energy, so estimating 35% of instead of 25% of the higher harmonics is introducing less than 5% error to the estimation, and greatly simplifies the math.