Three stage LDO design

In a three-stage LDO (i.e. two stages of error amp and one stage of pass transistor), there are at least 3 poles exist. One is at the LDO’s output, the other two are at the output of each stage of error amp. Assuming that the output cap is very small, which may be true since you said about capless LDO, we can say that the three poles location is quite near. In order to achieve stability, you need to:
1. push one of the pole to lower freq and push the others to higher freq, or
2. in addition to step 1, add LHP zero to increase the stability even more.

There are many techniques to push the pole to lower frequency. The most famous one is by using Miller compensation, which is based on pole splitting technique. The problem with this technique is the existence of RHP zero, which is unwanted. To eliminate this RHP zero, many method has been proposed, e.g. using nulling resistor, feedforward stage, voltage buffer, current buffer, current mirror, cascode compensation (enhanced method of current buffer). Some of these technique even can introduce LHP zero.

One of the problem in LDO is due to its changing load resistance. In conventional LDO, people create a dominant pole using this changing load resistance and a very big output cap. The problem occurs when RL is very small (due to the heavy load current). At this time, the dominant pole shifts to higher frequency, causing the non-dominant poles to be located inside the UGF. Thus, ESR zero was used to compensate the LDO. However, this technique requires a very big cap and specific range of ESR, which makes this compensation a bit troubelsome and not suitable for SoC.

Nowadays, people very seldomly make use of the output pole as the dominant one. They usually create a dominant pole by using the enhanced Miller compensation, which has been discussed earlier. To compensate the changing pole, some people try to lower the UGF and use a constant zero to compensate it when it comes near the UGF. Other researchers proposed to use a dynamic zero, which is able to change its location according to the load current. The problem with this technique is that, it cannot accurately track the load pole, because it is only able to track the load current, but not the load capacitance. However, it is still much better than just a constant zero.