# [018] Boost Converter with Current-Mode Control

### Introduction

testing  In this article, Dr. Ridley presents a summary of current-mode control for the boost converter. A free piece of analysis software, the fourth in a series of six, is provided to readers of this column to aid with the analysis of their current-mode boost converters.

### Modeling Power Supplies with Current-Mode Control

In the last article, the complications of modeling power circuits were discussed in some detail for a boost converter with voltage-mode control. The boost converter was shown to have the complication of a right-half-plane zero which makes control with voltage-mode very difficult in some cases.

The problem is made much easier with current-mode control. This is always the preferred approach for the boost converter, implemented as shown in Figure 1.

Figure 1: Boost converter with current-mode control. The green components show the current feedback; without these, the control is voltage-mode.

As with the buck converter, a whole new world of mathematical complexity arises when current-mode control is used for a power supply. The full analysis of current-mode control is completed, and you can download the complete book on the topic from www.ridleyengineering.com.

The dynamic analysis of current mode involves advanced techniques, including discrete-time and sampled-data modeling. This is essential to arrive at a model which explains all of the phenomena seen with your converter, and which accurately predicts the measured control-to-output response and loop gain of the current-mode converter.

There are several important points to learn from the full analysis of the current-mode boost converter:

The power stage has a dominant-pole response at low frequencies, determined mainly by the time constant of the output capacitor and load resistor values.

The power stage has an additional pair of complex poles at half the switching frequency which, under certain conditions, will create instability in the current feedback loop. The damping of these complex poles is controlled by the addition of a compensating ramp.

The resulting transfer function of the power stage is third-order, even though there are only two state variables in the converter. (This apparent anomaly, for control theorists, is caused by the fact that the switching power converter is a nonlinear, time-varying system.)

The second-order double poles at half the switching frequency cannot be ignored, even though they may be well beyond the predicted loop crossover frequency.

The capacitor ESR zero is unchanged by the presence of the current loop feedback.

Finally, and most importantly, the current-mode boost converter retains the exact same RHP zero as the voltage-mode converter. However, since the current feedback has eliminated the double poles of the filter resonance, it is not difficult to control this RHP zero effectively.

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