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these inverters should be different size, and become the bigger step by step in order to drive big mosfet by the bigger current, because of the parasitical capacitor.It is an aim to run the higher frequency.
using the equal ratio inverter chain can decrease the delay, so it can make mosfet turn on fully fast in order to save the power dissipation.
this is a basic skill to drive large loading.
If the driver is analog signal, you may be not use the inveter, thus, the analog buffer is the best selection.
In fact, there is an optimum number of stage which is used to driver large capacitor. Many digital books have the equation and derivation.
opamp output is analog, and inverter output is digital. this question is not right. for example, if the opamp output is not at rail, the inverter right after with opamp may draw hugh amount of current. if the opamp out is at rail, you are using an opamp as a comparator, then why not just use a comparator?