Am I correct in believing that since my PWM duty cycle is limited at 50%, I do not need any slope compensation?
Ah yes... this most awful of oft-repeated falsehoods.
But, let this be a lesson on the quality of appnotes. Even some academic articles and books repeat it, sadly!
The error is this: note what condition 50% relates to. In almost all setups, the turns and voltage ratios are such that CCM occurs at 50% duty. This is the least stressful case for FET, diode and inductor, so it's the most common setup.
CCM is actually what's important. Every single time they say "50% duty", they mean "CCM".
If you're using a different turns/voltage ratio, this point will fall somewhere else. You can indeed get period doubling at, like, 10% say -- doesn't matter, it can be arbitrarily low, if the voltage ratio is weird enough. Consider startup conditions, where the output voltage is very low and the inductor doesn't discharge quickly: duty can be quite low in this condition and still be deep into CCM.
You need slope comp to avoid chaos -- literally. In fact, fascinatingly enough, the peak current mode control, for given peak current reference, is an implementation of the
logistic map function, a chaotic system.
Generating the bifurcation diagram is not exactly trivial unfortunately, so it's not a beauty you're going to see pop up on your oscilloscope; but in short, if the inductor retains some current from the previous cycle (it's nominally in CCM), that initial offset adds to the next pulse, making it shorter than expected. The difference builds up until one pulse crosses into DCM (setting the inductor's state), and the cycle repeats.
For higher current setpoints, it bifurcates again, into 4, then 8, etc. discrete pulse widths before resetting. Pretty quickly thereafter, it explodes into myriad states, which might not be easily counted, or indeed cannot be counted due to errors in the circuit (resulting in randomness instead).
The bifurcation diagram is plotting the %duty (x, rescaled) for each pulse in the cycle, versus current setpoint (r, also rescaled). You can see there are regions of stability here and there, in the right side regions, including a three-state loop (and then 6, etc.). Pretty crazy.
I won't go into further detail about the effects -- there are excellent papers (maybe even videos, I'm not sure?) out there, now that you have some keywords to search on -- just suffice it to say, for control purposes, we want smooth and consistent control without unexpected behavior, and therefore need to operate low on the curve (r < 3). Which means we must stay in DCM.
What slope compensation does, is skew the system, so that it can remain stable up to higher current setpoints, that is, less than 100% ripple fraction (RF being ΔIpk / Idc, as seen by the inductor). Roughly speaking, the maximum stable ripple fraction equals the fraction of Isense coming from the switch.
If it's pure current mode (switch current only, no slope), it's not stable in CCM, but switch current is perfectly controlled (peak never above setpoint, at least for very long).
If it were pure voltage mode (slope only, no switch current sensed), it would be stable at any current -- but we wouldn't know what current is flowing through the switch and it's easily blown up. No good.
This is a continuous case between extremes, so we must choose a compromise between losing accuracy of switch current (which raises switch losses at extreme conditions i.e. high Vin, high Iout, low Vout), and lowering ripple fraction (which reduces inductor losses). Typically 50 to 30% ripple fraction is as low as you want to go with peak current mode control -- which worsens peak switch current control by 2-3x, which is usually tolerable.
Tim
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