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Hi all,
I’m looking through Lloyd Dixon’s Control Loop Design paper at http://focus.ti.com/lit/ml/slup098/slup098.pdf, and I have a few questions:
1. On page 7-4, I don’t fully get the equation for Gp. There is a –j in the numerator that seems to come out of nowhere. I think I see where it comes from, and here’s what I’ve got:
-The calculation for vCA makes sense to me, d*Vs.
-vi, on the other hand, confuses me. It should be a voltage corresponding to the inductor current.
-Rt is in series with L, so iRt = iL. vi =iL * Rt > vi / Rt = iL
-The inductor can be represented by vL = jwL * iL. Rearrange to iL = vL / jwL
-Plug the above into the one above that, and you get vi / Rt = vL / jwL, which goes to vi = (vL * Rt) / jwL
-The inductor always has Vout across it, Q on or Q off. When Q is on, the inductor also has Vin – Vout across it. So, Vin * d is the voltage across the inductor.
-Substitute the above into the equation before it, and you get vi = Vin * d * (Rt / jwL)
-vi / vCA then is (Vin / Vs) * (Rt / jwL)
-Plug in the real numbers, and I get 159Vin / (j * fs), or –j159Vin / fs. This is the equation shown in the paper.
I hope that’s clear. Ultimately, I believe the equation for vi, right above the equation for Gp, might need a j in the denominator to be correct. This also affects the intermediate step of calculating Gp which also needs a j in the denominator. As it is, it seems to me there’s a –j in the numerator without an explanation when the j should be present in the proceeding calculations.
2. The last paragraph on page 7-4 mentions the closed loop gain is flat until it rolls off at fci (16.7kHz). Looking at Fig 4, isn’t the rolloff actually at fci/2, or 8kHz?
3. Figure 5, on page 7-5, shows Vca leaving 7.0V at 20us. The gain of the CA is 15 above fci, where Cfi isn't having any effect, and the gain increases at lower frequencies. I can understand that the difference between the inputs multiplied by the gain will be the output voltage of the CA. And where the CA output is pegged high, it's equivalent to the loop being open, and Lloyd wrote. But if Cfi is storing extra charge and holding high, why does Vca leave 7.0V before IL*Rt crosses Vset? I'm sure there's something simple I'm just missing, so if anyone could add to the description of Figure 5 and point out where I'm confused, that would be great.
Thanks for any help! Evan
