Miller effect
In electronics, the Miller effect (named after its discoverer John Milton Miller) accounts for the increase in the equivalent input capacitance of an inverting voltage amplifier due to amplification of the effect of capacitance between the amplifier's input and output terminals, and is given by where
Although the term Miller effect normally refers to capacitance, any impedance connected between the input and another node exhibiting gain can modify the amplifier input impedance via this effect.
The Miller capacitance due to undesired parasitic capacitance between the output and input of active devices like transistors and vacuum tubes is a major factor limiting their gain at high frequencies.
The same analysis applies to modern devices such as bipolar junction and field-effect transistors.
Consider a circuit of an ideal inverting voltage amplifier of gain
, then the circuit's resulting input impedance will be equivalent to that of a larger capacitance
This can reduce the bandwidth of the amplifier, restricting its range of operation to lower frequencies.
The tiny junction and stray capacitances between the base and collector terminals of a Darlington transistor, for example, may be drastically increased by the Miller effects due to its high gain, lowering the high frequency response of the device.
If looking for all of the RC time constants (poles) it is important to include as well the capacitance seen by the output.
The Miller effect may also be exploited to synthesize larger capacitors from smaller ones.
One such example is in the stabilization of feedback amplifiers, where the required capacitance may be too large to practically include in the circuit.
This may be particularly important in the design of integrated circuits, where capacitors can consume significant area, increasing costs.
The Miller effect may be undesired in many cases, and approaches may be sought to lower its impact.
A current buffer stage may be added at the output to lower the gain
This will typically reduce the Miller effect and increase the bandwidth of the amplifier.
This can be achieved by feeding back an additional signal that is in phase opposition to that which is present at the stage output.
By feeding back such a signal via a suitable capacitor, the Miller effect can, at least in theory, be eliminated entirely.
In practice, variations in the capacitance of individual amplifying devices coupled with other stray capacitances, makes it difficult to design a circuit such that total cancellation occurs.
Historically, it was not unknown for the neutralising capacitor to be selected on test to match the amplifying device, particularly with early transistors that had very poor bandwidths.
The derivation of the phase inverted signal usually requires an inductive component such as a choke or an inter-stage transformer.
This had the effect of screening the anode from the grid and substantially reducing the capacitance between them.
(The load is irrelevant to this discussion: it just provides a path for the current to leave the circuit.)
The coupling capacitor is replaced on the input side of the circuit by the Miller capacitance
In this example, this transformation is equivalent to setting the currents equal, that is or, rearranging this equation This result is the same as
, upon the frequency response of this circuit, and is typical of the impact of the Miller effect (see, for example, common source).
is not zero, Figure 2B shows the large Miller capacitance appears at the input of the circuit.
In analog amplifiers this curtailment of frequency response is a major implication of the Miller effect.
The effect of CM upon the amplifier bandwidth is greatly reduced for low impedance drivers (CM RA is small if RA is small).
[3] Ordinarily these effects show up only at frequencies much higher than the roll-off due to the Miller capacitance, so the analysis presented here is adequate to determine the useful frequency range of an amplifier dominated by the Miller effect.
Determination of CM using Av at low frequencies is the so-called Miller approximation.
