# [016] Buck Converter with Current-Mode Control

### Introduction

In this article, Dr. Ridley presents a summary of current-mode control for the buck converter. A free piece of analysis software, the second in a series of six, is provided to readers of this column to aid with the analysis of their current-mode buck 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 buck converter with voltage-mode control. Even for that simple configuration, the analysis can have different levels of complexity. This will depend on how many parasitic components are included in the analysis, and any assumptions made about their relative values.

We don’t usually use voltage-mode control for rugged converter design. Current-mode control is the preferred approach, implemented as shown in Figure 1.

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

A whole new world of mathematical complexity arises when current-mode control is used for a power supply. Fortunately, the full analysis of current-mode control is completed, and you can download the complete book on the topic from http://www.ridleyengineering.com/freesoftware.html.

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 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 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.

As explained in reference [1], current-mode control has many advantages. These include elimination of the resonant filter frequency, the ability to current share with multiple power stages, simplified compensation design, and inherent peak current limiting.

### Designing with Current-Mode Control

While the analysis of current-mode control is quite complex to read and understand, the design process is quite simple. Much simpler, in fact, than voltage-mode control, and this is one of the reasons that current-mode control is so popular today.

Figure 1 shows the current-mode feedback system. The inductor current, or switch current, is sensed and compared to a voltage reference to set the duty cycle of the converter. A sawtooth ramp may also be added to the signal to stabilize the current  loop.

## AVAILABLE WORLDWIDE

Our worldwide HQ
601 E Daily Drive
Suite 112
Camarillo, CA 93010 USA

Phone US: +1 805 504 2212
Phone UK: + 44 (0)1509 276 245
Fax +1 888 339 6419
Email: info@ridleyengineering.com