POLESPLIT

# POLESPLIT - T.H Lee EE214 The Miller Effect and Pole...

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T.H. Lee EE214 The Miller Effect and Pole Splitting©2000 Thomas H. Lee, rev. October 17, 2004; All rights reserved Page 1 of 6 The Miller Effect and Pole Splitting 1.0 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 first- order 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 con- stants, 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 range 2 . Even if one is uninterested in shaping the frequency response of an amplifier, an under- standing of pole splitting is essential to extending to the second order many important insights developed during our study of first-order systems. 2.0 Two-pole Amplifier Figure 1 is a model of the system we’ll consider. It is a quite general representation of any unilateral two-port linear amplifier with capacitive feedback. For example, this model 1. You may recall that a truly first-order system is unconditionally stable for any amount of purely scalar negative feedback.

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## This note was uploaded on 04/17/2008 for the course EE 214 taught by Professor Murmann,b during the Fall '04 term at Stanford.

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POLESPLIT - T.H Lee EE214 The Miller Effect and Pole...

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