The Miller Effect and Pole Splitting(By Thomas Lee)

STMicro

The Miller Effect and Pole Splitting(By Thomas Lee)

Introduction:

Engineers frequently design systems to be dominated by a single pole. Aside from being
easily analyzed (certainly an extremely attractive property in its own right), such systems
also have the highly valuable attribute of being able to tolerate large amounts of negative
feedback without stability problems.1 While it is impossible in practice to build a system
that is truly single pole, it is not hard to approximate single pole behavior over a broad
enough frequency range to be useful. Consider, for example, the Miller effect: it can
increase dramatically the time constant associated with a capacitance that feeds back
around an inverting gain stage. Usually, this effect is considered undesirable (because it
degrades bandwidth), and we therefore often expend a great deal of design effort to avoid
it (through cascoding, for example). However, the Miller effect can also be useful; it can
be exploited to make a system’s open-loop transfer function approximate simple firstorder
dynamics over a wide range by creating a dominant pole.
To be confident that the pole created is indeed dominant, though, we must have some way
of determining or estimating the location of the next pole. As with open-circuit time constants,
we will avoid traditional, rigorous paths to an exact answer. Instead, we’ll content
ourselves with approximations that convey an intuitive appreciation of the dynamics of a
particular two-pole system that recurs with surprising frequency in analog circuit design.
It is this intuition that we will emphasize in what follows.
Among the more important insights is that the Miller effect generally makes one pole
more dominant while simultaneously making the other one less so. That is, as one pole
moves down in frequency, the other moves up in frequency. When this contrary motion
(known as pole splitting) is an intended consequence, the Miller effect is often renamed
Miller compensation. It is a powerful way to force the resulting transfer function to appear
first-order over an exceptionally large frequency range2.
Even if one is uninterested in shaping the frequency response of an amplifier, an understanding
of pole splitting is essential to extending to the second order many important
insights developed during our study of first-order systems.

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zhujun134

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