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 − Av), where Av 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 − Av).
[edit] Derivation
Consider an amplifier with the voltage gain Av, thus V2 = AvV1. 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 − Av).
Example: A 10 pF capacitor placed across an amplifier with a gain Av = − 10 would appear to be (1 − ( − 10))10 pF, or 110 pF.
[edit] Note
As most amplifiers are inverting amplifiers (i.e. Av < 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.
[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].
