P

#### Paul E. Schoen

- Jan 1, 1970

- 0

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.

Paul