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During the real operation of comparator, the input baseline is lower than the threshold voltage. How do we justify small signal analysis of comparator while we know that the biasing condition for the input devices are different? am I forgetting some basic theoretical understanding here?

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    \$\begingroup\$ Why would you want to justify it? \$\endgroup\$
    – Andy aka
    Jan 8 at 21:29
  • \$\begingroup\$ @Andyaka because, as I understand it, small signal is valid only around the biasing point. In the comparator case, the input devices are biased at different point. \$\endgroup\$ Jan 8 at 21:34
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    \$\begingroup\$ Small signal analysis is only valid when the circuit behaves linearly. A comparator does that only when the input voltage (difference) is near zero. I would generally not care about that behavior as it is not a state in which the comparator spends much of its time. A comparator spends most of its time in its non-linear state. Also the time response behavior (speed) of a comparator is mainly determined by slew-rate which is a large signal behavior. \$\endgroup\$ Jan 8 at 21:45
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    \$\begingroup\$ It's true that large signal slew rate is a factor, but decision (switching) and settling time is a function of resistance and capacitance. The resistance is defined by the small signal gm (inverse). So fast transitions are dependent on this value. Mismatch is function of area (large L*W => better matching). So large gm faster, but that also requires low L. There's tradeoffs here. These design choices are governed around the small signal analysis and center of the decision threshold point. Your thoughts seem ok on that. \$\endgroup\$
    – pat
    Jan 8 at 22:06
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    \$\begingroup\$ 2nd pole is usually best pushed out far from 1st You want to avoid too much ringing and problems associated with non-dominant poles occurring before gbw. I would simulate step response and optimize around speed and settling characteristics. Slew Rate is an issue, but the assumption is you have enough not to affect linear settling characteristics. \$\endgroup\$
    – pat
    Jan 8 at 22:20
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The comparator isn't 'active' when the inputs are more than a few mV different in voltage, it's saturated to one rail or the other. The important parameters, propagation delay and input offset, are a function of how the comparator amplifier behaves when in the linear region.

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When any amplifier saturates the gain is zero.

When analyzing the small-signal performance of a comparator, we assume it is not saturated and thus operates in the linear region, which is rather difficult as it is not unity gain compensated to do so but may perform well in an open loop with low offset.

This means comparators are not designed for linear operations and linear Op Amps are not designed to be good high-speed comparators. We like to call comparators "slicers" or "limiters".

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