# Miller Effect  Written by

The Miller effect is usually used to describe a situation where the capacitance between the input and output of an amplifier appears as a larger capacitance (sometimes much larger) at the input. This effect can be applied more generally to any impedance as we shall see. The effect was first described by John M Miller in a paper written in 1920 in relation to vacuum tubes; “Thus the apparent input capacity can become a number of times greater than the actual capacities between the tube electrodes…”

Before we get into the theory let’s look at an example where we can get an intuitive sense of the Miller effect. Figure 1 shows a standard common-emitter amplifier (sans bias components) with the transistor’s parasitic capacitances shown. It’s easy to see that CBE appears as a capacitance to ground on the input of the amplifier and CCE appears as a capacitance to ground at the output. But what about CCB?

Consider a small positive voltage excursion at the transistor’s base. Since the common-emitter amplifier is an inverting amplifier, this will result in a negative excursion at the collector which bigger than that at the input by the gain of the amplifier. The voltage across CCB is therefore (1 + K) VBE, where K is the amplifier gain. The current flowing through CCB will also therefore be higher by the same factor.

This is effectively equivalent to a capacitor with a value of (1 + K) CCB in parallel with CBE. The parasitic capacitances are usually only a few picofarads, but as the gain of the stage increases the effect can become significant.

Figure 2 shows a more generalised treatment. Here an ideal amplifier with gain K has an impedance Zf connectedfrom input to output. The input current is given by:

so, we can find the input impedance:

We can see that the input impedance is a factor of 1+K smaller than the feedback impedance. This is the same answer that we got in the intuitive example, recalling that a lower impedance corresponds to a larger capacitance.

Now we know this we can look at what we could do to mitigate the problem for the circuit of Figure 1. The simplest approach might be to look at what’s driving the common-emitter amplifier – if the output impedance of the source is low enough, the Miller capacitance might not matter. If you are stuck with a medium or high-impedance source, you might be able to add a low output impedance buffer ahead of the amplifier.

Alternately, you could use a differential pair as shown in Figure 3A. There is no resistor in the collector of Q1, so its collector voltage is fixed and so the Miller effect does not occur. There is no Miller effect in Q2 since its base is grounded (which is about the lowest source impedance you can get). Figure 3B shows an alternative using a neat cascode circuit. Q2 has a fixed base voltage (bias components not shown) and therefore an emitter voltage one VBE drop below that. Now Q1’s collector is at a fixed voltage, so no Miller effect can occur. Q1’s collector current passes through Q2 and the load resistor as before.

The Miller effect is not confined to discrete circuits – it will appear any time a resistor, capacitor or inductor is connected across an amplifier – which, given the ubiquity of parasitics, means nearly all the time. You need to be aware of this important effect and decide if it is going to be important for your circuit.

References

“Miller Effect.” In Wikipedia, January 25, 2022. https://en.wikipedia.org/w/index.php?title=Miller_effect&oldid=1067766321.

Lundberg, Kent H. “Origin of the Miller Effect,” n.d., 22. http://web.mit.edu/klund/www/papers/jmiller.pdf

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