Miller Effect - Derivation

Derivation

Consider an ideal inverting voltage amplifier of gain with an impedance connected between its input and output nodes. The output voltage is therefore . Assuming that the amplifier input draws no current, all of the input current flows through, and is therefore given by

.

The input impedance of the circuit is

If Z represents a capacitor with impedance, the resulting input impedance is

Thus the effective or Miller capacitance C_M is the physical C multiplied by the factor .