Inductor Current Rating for a Buck-Boost Converter

May 1, 2004 12:00 PM
By Ron Lenk, Tyco Electronics Corp., Menlo Park, Calif.

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Buck-boost converters produce a regulated output voltage either less than or greater than the input voltage. When the input voltage is higher than the output, the converter acts as a buck. When the input is lower than the output, the converter boosts. Two simple formulae determine the current rating of the inductor. The rating is either the dc saturation current rating associated with buck-converter operation or the energy-storage rating associated with operation of a nonisolated flyback. ^[1]

Here, “buck-boost” refers to a chip-controlled type that can switch between configurations and modes as required. A buck-boost converter operates in three different configurations. When input voltage is higher than output voltage, it operates as a conventional buck converter. In the figure, Q1 is pulse-width modulated, with Q2 acting as the synchronous rectifier of the buck. Q4 is on 100% of the time, and Q3 is always off, so the inductor current flows directly to the output.

In the second configuration, the input voltage is lower than the output, and the buck-boost acts as a nonisolated flyback. The red lines show that this time, Q1 is on 100% of the time, and Q2 is always off. Q3 acts as the boost transistor, and Q4 is the synchronous rectifier. In this configuration, the converter can be either in continuous (CCM) or discontinuous conduction mode (DCM).

In the third configuration, the input voltage is equal to the output voltage, and in the approximation in which the transistors have no resistance, both Q1 and Q4 are on 100% of the time, and Q2 and Q3 are always off, so that the input and output are directly connected, as expected.

With this description, it's easy to calculate the maximum current the inductor must carry in the three configurations and two modes. When operating as a buck, the current carried by the inductor is equal to the output current, I₀. ^[2] This value represents the large inductance approximation and is accurate to the extent that ripple current can be ignored. This approximation is also true in the third mode because input and output are directly connected.

When the converter is operated as a flyback, the inductor current depends on whether it's operated in CCM or DCM. In DCM, output power (P) depends on input voltage (V_IN), duty cycle (DC), inductance (L) and frequency (f) according to the following formula, which ignores efficiency

We also know that the peak current (I_pk) is

Substituting from the first equation, we have

It is in DCM, so this formula is valid only so long as half the peak-to-peak current is less than the output current, which can be expressed as

The maximum occurs when the equality is fulfilled, yielding

In CCM, again using the zero-ripple approximation, the inductor current is again just equal to the output current.

Thus, for all configurations and modes of operation of the buck-boost converter, the maximum current the inductor must carry will be either I₀ or V_o/Lf, whichever is greater. So, selecting an inductor that won't saturate is easy. Just use one of the two formulae shown above that gives the greatest current value, and then add some safety margin.

Choosing the inductance value can be done on the basis of limiting ripple current in the buck configuration, and deciding where the transition between DCM and CCM modes occurs in boost configuration. Results may be extended to the case where there's significant voltage drop across the transistors, particularly where Q2 and Q4 are diodes. The resulting analysis is a simple exercise in algebra.

1. Ron Lenk, “Practical Design of Power Supplies,” IEEE Press/McGraw Hill, 1998.

2. This approximation is true for all practical buck-boost converters with which the author is familiar.

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