Every six months or so, human enhancement
I encounter the Miller effect and can never remember what it is. Every six months or so, page
I open my copy of Sedra and Smith to look up the Miller effect only to forget it over the upcoming six months, hopefully this short write-up will help store it in long term memory. The idea is this, the differential voltage (Vo-Vi) across the impedance Z is dependant on the input voltage and the gain, so for the same change in voltage (per change in time) on the input, different gains can create almost any voltage at the output. This dependence on the gain can lower the effective impedance as the gain goes up for the same input signal. Most amplifier stages have some sort of capacitance and this Miller effect tends to increase the effective capacitance by a factor of 1-G. How much of this effect is seen in real amplifiers really depends on the configuration, especially on the feedback network and the resulting output impedance. In resonant circuits, the Miller effect can be understood, as it linearly depends on the circuit gain, and can sometimes be exploited to get away with using smaller capacitors. On the other hand, filter topologies, such as Sallen-Key, can be used as their pass-band gain is unity and therefore they do not exhibit the Miller effect.
On a side note, there is also the Miller theorem, which allows one to break Z apart into Zi and Zo, which are connected from Vi and Vo respectively to ground. This is the method that is often employed when calculating the input impedance of an amplifier, usually at open loop gain.