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miller capacitance is the increase in the value of a capacitor connected between the output and input due to the gain of the system.... this leads to shorting of input and output at high frequency leading to reduction in gain at high frequencies
miller capacitance appears both as unwanted effect that degrades preformance of amplifiers and as means in circuit design to achieve a particular frequency characteristic. When designing e. g. operational amplifiers frequency compensation, you can create a dominant pole by artificially increasing an already existing miller capacitance, simultaneously eliminating additional higher oder poles.
The very well known inverting MILLER integrator is equivalent to a simple RC low pass with a capacitance which is increased by a factor Ao (opamp open loop gain).
This increase is due to the MILLER effect.