I blieve that offset voltage of the comparator should be concerned, right ? which means a comparator with auto zero should be used ?
the second thing I see some people use simple two stage comparator, other use clocked comparator, some other used comparator with hysteresis, which one should be the best to use ?
The clocked comparators fit well into a SAR because the SAR is a clocked system. Since you are looking at using the SAR for calibration, you are not really aiming at speed and I guess you can afford to add autozeroing to your clocked comparator.
I have also read that clocked (also called it latched or degenerated comparator) use less power, and his dynamic performance is fast,
I have seen many articles about auto zero open-loop comparator, but not auto zero clocked comparator, could you please direct me to some resources so I can work on it. Without Auto zero, I think the clocked comparator is worst among other types
Regenerative comparators are known for high offset that also depends on input common mode and even imbalanced capacitive loading. To do autozeroing you need to have some kind of preamplifier. Maybe this paper can help, I haven't read it myself
I. Mehr and D. Dalton, "A 500-MSample/s, 6-bit Nyquist-rate ADC for disk-drive readchannel
applications," IEEE J. Solid-State Circuits, pp. 912-920, July 1999.
If the offset voltage is a problem in the latched (or named clocked or regenerative comparator), what the things attract us to use it when it is also possible to use continuous-time open-loop comparator?
You can't beat regenerative comparators in terms of speed. They are the fastest. Also, usually they are dynamic, so no DC power consumption. When you build high-end ADCs they are the best choice of a comparator to use. Offset you can deal with in different ways.
It means if the speed is not the limit, like the case of the digital offset calibrationusing SAR, it can be implemented with the normal open loop comparator
Also I understand from you, that if I would use the open loop comparator for high speed application, this requires to supply the comparator with high biasing current to improve the settling time
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By the way, it is also possible to increase the speed of open loop comparator by using an inverter at the output as shown below
Using inverters is more for shaping the output and yes, it improves the slew rate when driving capacitive loads. Even here in the circuit you are showing you have some sort of positive feedback by the bottom NMOS transistors which speeds up the process.
In general you can use slower comparators for a slower binary search used in calibration.