[031] Choosing the Inductor for a Buck Converter

How to select the size of the inductor for a buck converter. 

Introduction

In this article, Dr. Ridley examines how the value of a buck inductor should be selected. A supposedly simple process can turn out to be much more complicated than expected, and the range of allowable inductors is found to be quite large.

Design Rules for Choosing the Inductor

Five or six times a year, I teach a class in power supply design to 30 working engineers. One of the design examples involves a buck converter, and the design starts with the choice of the inductor value. I always ask the students what value inductor should be used, or how much ripple current should be in the inductor. (Ripple current ratio is usually defined as the peak-to-peak value of the inductor current at high line, divided by the maximum load). Their answers typically vary, from a value of 10% up to perhaps 30%.

A traditional value of inductor current ripple is 10%, and you will find this in several books. Reference [1] uses this value as a starting point for design, but does suggest at the end of the article that the value can be changed depending on the desired output ripple. Further examination of literature shows a huge range of recommendations. References [1] to [13] suggest ranges from 2.5% to 50%.

References [14,15] select the inductor according to the minimum load, with the intent of keeping the converter always in continuous-conduction mode (CCM). This can lead to a very large inductor if the light load is very small.

Which one of these is the correct value? As is often the case in designing power supplies, there is no one correct answer, and it will always depend on the very specific converter that you are working on at the moment.

Where do the Rules come from?

We usually find in power electronics that design “rules-of-thumb” arise from some practical basis in reality. There are several different factors that drive the choice of inductor value.

1. Output Ripple Voltage – older output capacitor types tend to drive inductor values to a higher number. Modern innovations in capacitor design have driven the ESR down to very low values, and rarely is the output ripple the driving factor in choosing the inductor.  

2. Inductor Loss – Higher ripple current leads to higher RMS current in the inductor, plus greater AC currents and higher proximity losses. Core losses will also increase with larger ripple current. A higher value of inductor, with low ripple, has higher dc conduction loss.

3. Switch Conduction Loss – the RMS current in the switch climbs with inductor current ripple.

4. Rectifier Conduction Loss – the RMS current in the rectifier climbs with inductor current ripple. This is an important factor when using a synchronous rectifier, but less important when using a diode.

5. CCM operation – References [14,15] choose the inductor to give a ripple which is twice the minimum load. This is to avoid DCM operation at light load. In the early days of power supply design, this was an important factor to keep good transient performance under all conditions. With a modern power supply, using current-mode control, there is no reason at all to keep the converter in CCM operation.

Buck Converter Design Example

Searching deeper into the literature than the short list included with this article will not lead you to any conclusions regarding the right value of inductance. For every converter design that you do, the proper answer will depend upon your very specific set of circumstances. And for each specific case, a detailed design must be completed and tested before coming to any conclusions about the right value.

For example, Figure 1 shows a specific design case. The switching frequency of the buck converter is 200 kHz, and the output specification is 5A at 12 V from a 18-36 V input. The output capacitor is preselected at 1000 µF with a 10 mΩ ESR. The choice of the output capacitor can be as wide ranging as the choice of the inductor value, and is not discussed in more detail in this article due to space constraints.

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Figure 1: Buck Converter with Parameter Values

The ripple current in the converter is maximum at high line, and the value of the ripple is shown in figure 2 for an inductance of 160 µH which gives a current ripple ratio of 10%.

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Figure 2: Inductor Current Waveforms 10% Ripple

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