Small singal of CMOS hysteresis comparator using coss-coupled (cross-gate)

hi all,

As I know, there are 3 types of CMOS comparators:
1. Opamp-based (low speed)
2. Latch-based (high speed but also this type is discrete-time comparator and need clock signal for tracking and latching phases).
3. Hysteresis type (as shown in the attached figure below)

Currently, I am designing comparator used in buck converter. However, I can not explain in details about 2 things below:

1. The mechanism of this circuit, especially, the "positive feedback" mechanism in this circuit.
2. The small signal to analyze and calculate the propagation delay time

(The analysis for opamp-based and latch-based are deeply analyzed in Allen and Martin's book, however, I can not find down some material for the hysteresis comparator using cross-gate)

Do you have any opinions about this. Always appreciate the supports from community.

Thank you

The long-tail pair operates in a manner that is not obvious. M1 influences M2 and vice-versa. This happens because M5 is installed. If something causes current to increase in M1, then current decreases in M2. This behavior creates the differential amplifier.

As for the cross-coupling, it creates snap action. M1 is On when M2 is Off, and vice-versa. Changing input voltages reaches a condition where M1 & M2 change state suddenly. This is the principle of the RS flip-flop.

By adding hysteresis you give the flip-flop stability. It is not clear from the schematic how much range of hysteresis it has. A simulation should give an idea. If I were doing it I would apply sinewaves to the inputs, and watch what combinations cause M1 & M2 to change state.

That comparator is not necessarily hysteretic. This depends
on the ratio-ing of the cross-coupled loads. People use this
topology in op-amps too, with mirror ratios <= 1. Too much
current gain and you become hysteretic and then small
signal is inappropriate as analysis. You can get a DC solution
that puts you on the tip of decision, and you can get one
that snaps to either side, or you can just get convergence
failure (roll the dice, take what you get).