[095] Current-Model History and Loose Ends Part IV – Infinite Gain Model

Papers from MIT and others indicate a current loop gain of infinity under all conditions, clearly an impossibility according to Nyquist.

Introduction

In this article, Dr. Ridley shows how a third way of defining average current leads to an infinite gain of the modulator gain for current-mode systems. Another simple derivation produces a fourth expression for the modulator gain, thus completing the set of gains to be found in the literature.

Different Current-Mode Modulator Models

In the first part of this series on current-mode control, it was mentioned that several researchers considered the inductor to be a current source since its peak value was directly set by the control voltage into the modulator. This is an implicit assumption of infinite gain in the current loop, otherwise the current source would not be ideal.

Other researchers, including Drs. Middlebrook and Lee, did not regard the gain around the current loop as infinite, recognizing quite correctly that the controller set the peak value of the current exactly, but not the average level. In the last two parts of this series, we showed how the average value could be defined in two different ways, and these definitions of average current give rise to the modulator gains that were found by Middlebrook and Lee in their work.

Figure 1 below shows a table of the different analysis approaches and the equivalent gains of the modulator. So far we have three different expressions for the modulator gain. In this part of the series, we will show how a third definition of average current leads to the infinite value of modulator gain, thus vindicating the current-source models.

Figure 1: Different Models for the Modulator Gain