Buck-Converter Design Demystified

Jun 1, 2006 12:00 PM
By Donald Schelle and Jorge Castorena, Technical Staff, Maxim Integrated Products, Sunnyvale, Calif.

An LIR of 0.3 represents a good tradeoff between efficiency and load-transient response. Increasing the LIR constant — allowing more inductor ripple current — quickens the load-transient response, and decreasing the LIR constant — thereby reducing the inductor ripple current — slows the load-transient response. Fig. 2 depicts transient response and inductor current for a given load current, for LIR constants ranging from 0.2 to 0.5.

Peak current through the inductor determines the inductor's required saturation-current rating, which in turn dictates the approximate size of the inductor. Saturating the inductor core decreases the converter efficiency, while increasing the temperatures of the inductor, the MOSFET and the diode. You can calculate the inductor's peak operating current as follows:

For the values listed in Fig. 1, these equations yield a calculated inductance of 2.91 µH (LIR = 0.3). Select an available value that is close to the calculated value, such as a 2.8 µH, and make sure that its saturation-current rating is higher than the calculated peak current (I_PEAK = 8.09 A).

Choose a saturation-current rating that's large enough (10 A in this case) to compensate for circuit tolerances and the difference between actual and calculated component values. An acceptable margin for this purpose, while limiting the inductor's physical size, is 20% above the calculated rating.

Inductors of this size and current rating typically have a maximum dc resistance range (DCR) of 5 mΩ to 8 mΩ. To minimize power loss, choose an inductor with the lowest possible DCR. Although data sheet specifications vary among vendors, always use the maximum DCR specification for design purposes rather than the typical value, because the maximum is a guaranteed worst-case component specification.

Output Capacitor Selection

Output capacitance is required to minimize the voltage overshoot and ripple present at the output of a stepdown converter. Large overshoots are caused by insufficient output capacitance, and large voltage ripple is caused by insufficient capacitance as well as a high equivalent-series resistance (ESR) in the output capacitor. The maximum allowed output-voltage overshoot and ripple are usually specified at the time of design. Thus, to meet the ripple specification for a stepdown converter circuit, you must include an output capacitor with ample capacitance and low ESR.

The problem of overshoot, in which the output-voltage overshoots its regulated value when a full load is suddenly removed from the output, requires that the output capacitor be large enough to prevent stored inductor energy from launching the output above the specified maximum output voltage. Output-voltage overshoot can be calculated using the following equation:

Rearranging Eq. 2 yields:

where C_O equals output capacitance and ΔV equals maximum output-voltage overshoot.

Setting the maximum output-voltage overshoot to 100 mV and solving Eq. 3 yields a calculated output capacitance of 442 µF. Adding the typical capacitor-value tolerance (20%) gives a practical value for output capacitance of approximately 530 µF. The closest standard value is 560 µF. Output ripple due to the capacitance alone is given by:

ESR of the output capacitor dominates the output-voltage ripple. The amount can be calculated as follows:

Be aware that choosing a capacitor with very low ESR may cause the power converter to be unstable. The factors that affect stability vary from IC to IC, so when choosing an output capacitor, be sure to read the data sheet and pay special attention to sections dealing with converter stability.