Current-Mode History and Loose Ends Part V – The Correct Modulator Gain
The correct modulator gain is confirmed by experiment. Different analysis results are completely resolved when choosing the right modulator gain.
In the last part of this series, Dr. Ridley shows that only one of the modulator gains found in the literature can be confirmed with measurements. Furthermore, it is shown that the discrepancies in all the models are easily resolved by proper sampling of the system.
Different Current-Mode Modulator Models
In the previous parts of this series on current-mode control, it was shown that four very different modulator gains were derived by various researchers in the past. The source of the differences was caused by different definitions of what was meant by the “average” current in the system. These same definitions continue to be used, resulting in great confusion in our industry.
Figure 1 below shows the four different modulator gains, and the researchers that used these gains in their papers.
Figure 1: Modulator Gains from Different Researchers, With and Without Ramp Added
Current Loop Gain Plots
The effect of each of these modulator gains on the current loop gain of the system is shown in Figure 2. Notice that there is a wide disparity in the results. The simplest model, corresponding to the reciprocal of the ramp height, predicts a crossover frequency at about 1/3 of the switching frequency. This is the only model to show that the current loop will cross over below half the switching frequency. Middlebrook’s model crosses over at 2/3 the switching frequency. Lee’s model, and the infinite gain model, cross over at much higher values.
Middlebrook’s model is widely cited in the literature, since his was one of the earliest to analyze current-mode control, but we know from modern sampling theory that this cannot be correct. And yet, the analyses all looked good, so the result was accepted by university researchers and industry.
Figure 2: Plot of Current Feedback Loop Gains
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