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Energy and power in a boost converter

Discussion in 'Electronic Design' started by Paul E. Schoen, Mar 2, 2007.

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  1. I posted this at the end of the gaps thread, but that turned into a
    cussfest, so here's another shot at trying to understand the energy and
    power transfer in a simple boost converter I have built.

    Basically, I can predict the maximum current in the inductor, and hence the
    energy stored, vs frequency. Using LTspice with a 61 ohm load, I found that
    at 200 kHz and 70% duty cycle the maximum inductor current with 12 VDC at
    10 uH is 4.4A (Energy = 97 uW-sec * 0.2 = 19.4 W), and I get 40 volts (26.2
    W). At 100 kHz, I can get 48 volts (37.7W) with a maximum inductor current
    of 8 A (32 W). The actual inductor current in the first case, which is
    running in continuous mode, includes a DC component of 650 mA from the 12
    volt source. Adding that gives a power contribution from the battery of 7.8
    watts in the first case and 9.4 watts in the second.

    The maximum output will be generated when the inductor starts charging
    again after its energy has been discharged into the output capacitor, so
    there will be no "dead time". With 12 volts, the inductor charges to 8.4 A
    in 7 uSec, and it takes 3 uSec to charge the output capacitor, for 70% duty
    cycle. The output is about 48 VDC into 61 ohms, or 38 watts. I calculate
    the average input power to be about 70% of sqrt(8.4*8.4/2) * 12 V = 35.3
    watts, plus the 780mA * 12V = 9.4W from the battery, or 44.7. I'm guessing
    at this, but the simulator measured input watts to be 43, so I'm close.
    This is 82% efficiency.

    I'm running simulations in LTspice, and I think they are pretty much
    correct, but I am still a little puzzled. In the continuous mode operation
    at 200 kHz, I can see the DC component through the inductor as a 388 mA
    minimum current. I get input power of 28.77 W and output of 25.77 W or
    89.5% efficiency. In the discontinuous mode at 100 kHz, I get 38.7 watts
    out, 43.1 watts in, and 89.8% efficiency. However, I have a hard time
    grasping how it can output 38.7 watts when there is almost no inductor
    current (It's actually negative) 10% of the time, and peak energy of 320
    uW-Sec at 100 kHz or 32 watts. Maybe I'm simplifying the calculation too
    much. The true power is probably the integral of the peak energy
    (0.5*I^2*L) over the entire waveform, times frequency. OK, when I do that,
    I get an average of about 98 uJ, but a peak of 316 uJ = 31.6 W.

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