Miller effect

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In electronics, the Miller effect describes the fact that a capacitance between input and output of an amplifier is multiplied by a factor of (1 + A_v), where A_v is the voltage gain of the amplifier.

Since, intuitively, a gain represents a voltage multiplication between points, any capacitor across these points will charge and discharge with a current which is multiplied by (1 + A_v).

[edit] Derivation

Consider an inverting amplifier with the voltage gain A_v, thus V₂ = − A_vV₁. The amplifier is assumed to have a high input impedance. An impedance Z₃ added between the input and output of the amplifier will exhibit the Miller effect. The input current is given by

and the input impedance is

.

Using Z₃ = (jωC) ^{− 1}, the resulting input impedance is

.

This means that the capacitance is effectively multiplied by the factor (1 + A_v).

[edit] Note

As most amplifiers are inverting amplifiers (i.e. A_v < 0) the effective capacitance at the input is larger. For noninverting amplifiers, the Miller effect results in a negative capacitor at the input of the amplifier (compare Negative impedance converter).

Naturally, this increased capacitance can wreak havoc with high frequency response. For example, the tiny junction and stray capacitances in a Darlington transistor drastically reduce the high frequency response through the Miller effect and the Darlington's high gain.

The Miller effect applies to any impedance, not just a capacitance. A pure resistance or pure inductance will be divided by 1 + A_v. In addition if the amplifier is non-inverting then a negative resistance or inductance can be created using the miller effect.

It is also important to note that the "Miller Capacitor" is the capacitance seen looking into the input. If looking for all of the RC time constants (poles) it is important to include the capacitance seen by the output. The capacitance on the output is often neglected since it sees and amplifier outputs are typically low impedance. However if the amplifier has a high impedance output, such as if a gain stage is also the output stage, then this RC can have a significant impact on the performance of the amplifier. This is when pole splitting techniques are used.

The impact of the Miller effect is often reduced by using a cascode or cascade amplifier rather than a common emitter. For feedback amplifiers the miller effect can actually be very beneficial since stabilizing the amplifier may require a capacitor too large to practically include in the circuit, typically a concern for an integrated circuit where capacitors consume significant area.

[edit] References

• Miller effect on carcino.gen.nz
• John M. Miller, an American, described this effect in 1919 in the Scientific Papers of the Bureau of Standards, v.15 [1].