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Let's say I have a common source amplifier with parasitic capacitances Cgs and Cgd (it can be any amplifier but I gave this concrete example to simplify my question). In order to approximate the 3db frequency (which can be certainly done by calculating the entire transfer function of the amplifier), I would like to use Miller's theorem. After calculating the gain from the gate to the drain, I reflect the augmented impedance into the drain and the gate. My question is, what would be a better estimate of the 3db frequency ? Taking the two reflected capacitances into account in the open-circuit method or just take the dominant pole which is normally the input capacitance. This leads me to a more general question , how does the original circuit differ from the Miller's equivalent circuit ?

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Have a look at slides on the Miller effect.

Since the source is grounded in the CS amplifier, \$C_{gs}\$ is not modified by the Miller's effect and has no sizable influence on the 3dB frequency. For hand calculation, you can ignore it.

The gate drain capacitance, \$C_{gd}\$ is multiplied by the gain of the amplifier and reduces the 3dB bandwidth of the amplifier. Look at eq 2.5 from the slides.

Use a simulator for exact location of the poles.

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