# Miller Effect For Non-Inverting Amplifiers

#### cake4all

Joined Oct 19, 2018
6
Hello, currently I am trying to understand the miller effect. Somehow I have two questions for which I am having trouble to find the answer via Google.

1) According to "Art Of Electronics" and Wikipedia, the Miller Effect is only relevant for inverting amplifiers. For inverting amplifiers with gain $$A < 0$$, the capacitance between input and output $$C_{m}$$ is transformed into a capacitance of $$C_{m} \cdot (1 - A)$$ between input and ground.

But what happens if $$A >> 0$$? What if I have a non-inverting amplifier? As far as i understand the derivations of the miller effect, the formula above should still be valid. The capacitance between input and ground has in this case a negative sign. But what does that mean? Does it still work as a low-pass filter with the source resistance? Or is it a high-pass because negative capacitance is something like inductivity?

2) In the high-frequency model of the BJT from "Art Of Electronics" (see Attachment), it seems as if there is a capacitor missing between collector and emitter. Why was it omitted? Is the capacitor already in $$C_L$$ included?

Cheers

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#### MrAl

Joined Jun 17, 2014
7,591
Hello there,

First, the capacitance itself is never multiplied it is the effect that is multiplied so a given circuit behaves as it would if a different circuit was used with a bigger capacitor. Note that there are other ways of showing an apparent multiplication of capacitance but they are not related to the Miller Effect.

This implies a couple things. First, that we have a circuit with low capacitance that works in a certain way, and second that we have a second circuit that behaves in a similar manner but because of added parts or different arrangement of parts the capacitor we use makes the first circuit look like it has a bigger cap value.
In both cases though there is a good reason for both circuits and that's why we bother to do the second circuit.
Also, just because we see an apparent increase in capacitance that does not mean it is the Miller Effect.

Now in a given amplifier design we can show that the effect of the capacitor is multiplied by the gain when it has negative feedback, and in the same design with positive feedback we can show that the effect is multiplied by the gain minus 1, which means if we set the gain high enough we still see a larger effect. The problem though in this particular design is that the positive feedback causes the amplifier output to saturate so it is effectively worthless.

So we can say for sure that the effect of the capacitance is multiplied, but we can not say that it does us any good unless we can find an application that benefits from the circuit but we cant really call it the Miller Effect because the Miller Effect is still different to some degree and is defined for negative feedback.

Can we call it the Positive Feedback Miller Effect? Well, we might, but if you want to call it that then you should be able to find or produce one example where this effect does us any real life good in some application.
Maybe it would show promise in an oscillator of some kind or maybe with the right value of gain we might get some benefit.

So see if you can find or produce one example that benefits mankind and then we can go from there to name it.
You could also go back and read the original Miller paper and see if he mentions anything about positive feedback.

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