As the posters above explained, LLC is a setting that counters absolute Vdroop. The rest of what Vdroop does or is allowed is a complex subject.
Vdroop is a phenomenon governed by the laws of physics. The reason that engineers allow Vdroop is because there is a level of safety associated with transient response. If the LLC is set too close to the user applied voltage, the voltage can experience excursions beyond the set voltage. This occurs within fractions of a second and cannot be monitored without a suitable oscilloscope.
On top of that, the ability of a power circuit to react to load changes quickly depends on a number of factors; capacitance, switching frequency, inductance, loop gain to name a few. These things are not trivial enough for a simple forum post. But what we can say is that a certain amount of Vdroop compliments the power supply, helps to prevent excessive overshoot of voltages beyond the set voltage and helps the components to last longer (including the CPU).
Vdroop itself DOES NOT make the system "unstable". There are situations in which Vdroop actually helps stability because there is enough of a buffer zone for the power supply to react to the load change in time. Most of the time, any instability a user blames on Vdroop is actually the result of not setting a sufficient voltage to ensure the correct load voltage. It is not because Vdroop "makes things unstable".
Maybe it would help to think of Vdroop in another context:
Imagine someone is throwing heavy books from a height for you to catch. Due to the laws of gravity, when you catch the books, there will be a reactionary downwards movement in your arms. The heavier the books and the faster they are thrown down, the more movement there will be before you recover and are stable. The tension in your arms to receive the books can be viewed as LLC. You can increase the tension in your arms to counter the downwards movement, at the expense of perhaps having a trickier/riskier recovery time. If you tense up a lot, then there is a chance you will have a hard time stabilizing the weight quickly.
By asking the voltage circuit to recover from heavy loads quicker we are asking it to do something similar - catch the load and settle quickly. By manipulating the level of LLC we are playing with the recovery time and the excursion of voltage past the set target. Of course, there are some side-effects to doing so as the current (the weight of the books) increases. It becomes more difficult for the circuit to keep the voltage closer to the defined level, and there are more voltage spikes with a longer duration above and below the defined level. These are the factors that may negatively impact system stability (tho less often seen these days with VRM solutions being so good) and component lifespan.
The better a VRM circuit as a whole, the less Vdroop one can get away with without affecting performance to a noticeable degree for the end user. Sadly, what has happened in the marketplace over the years with the LLC levels on offer on all vendor boards is the result of engineering having to bend in the direction of unwitting user-demands for LLC levels that appear to be rock stable. Most of the time, such LLC levels are not complimentary to the circuit they have to be applied to in order to keep the masses happy.
Each VRM circuit has a comfortable LLC level that compliments the amount of stored charge in the inductors and the circuits intrinsic error recovery capabilities. By applying a level of LLC that appears to keep voltage stable, we may be breaching that comfort zone. The result is by no means catastrophic (we'd see a lot of VRM failures if that were the case), but its not really ideal either. I suppose this last point is testament to how good the VRM components on boards are these days - to be able to counter non-ideal usage scenarios at least for the duration of the product's immediate lifespan so it's acceptable to continue.
Crude explanation and certainly not complete, but if we think about the pitfalls of this situation, it should help us understand the laws and intricacies of action and reaction.
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