Miller effect

The Miller effect is the apparent multiplication of a capacitor's value that occurs in inverting amplifiers when that capacitor bridges the input and output terminals. A small coupling capacitance between input and output becomes a much larger impedance burden on the input, degrading the amplifier's high-frequency response. The effect appears because the gain of the stage magnifies the voltage swing across the capacitor, forcing more current in or out of the input node than the physical capacitance would suggest.

Consider a common-source or common-emitter amplifier with gain A. If capacitance C exists between gate (or base) and drain (or collector), the input impedance contribution from Miller effect is approximately C times (1 + A). With typical gains of 10 to 100 or more, a 1 picofarad feedback capacitor can appear as 10 to 100 picofarads at the input. This directly reduces the input impedance and kills bandwidth by forming a low-pass filter with the source resistance.

The effect is most severe in voltage amplifiers with high gain and high impedance inputs. In practical circuits, Miller effect is the dominant parasitic limitation of the input stage in many transistor amplifiers operating above 100 MHz. The effect appears in BJTs, MOSFETs, and vacuum tubes equally. Cascode configurations and other topologies are used specifically to minimize Miller capacitance by isolating the input stage from the high-impedance output node.

The term 'Miller effect' traces to 1919 and the work of John Milton Miller on vacuum tube circuits, but the phenomenon applies to any inverting amplifier stage. Designers combat it by reducing the feedback capacitance itself (using smaller component layouts, shielding, isolation), reducing the gain (through emitter or source degeneration), or isolating the input from the output (through buffering or cascode). In high-frequency work, the Miller effect often determines whether a design meets its bandwidth specification.