DC-DC Converter Design and Magnetics--Introdction

This section, “DC-DC Converter Design and Magnetics”, contains the following discussions:

• DC Transfer Functions
• The DC Level and the “Swing” of the Inductor Current Waveform
• Defining the AC, DC, and Peak Currents
• Understanding the AC, DC and Peak Currents
• Defining the “Worst-case” Input Voltage
• The Current Ripple Ratio ‘r’
• Relating r to the Inductance
• The Optimum Value of "r"
• Do We Mean Inductor? Or Inductance?
• How Inductance and Inductor Size Depend on Frequency
• How Inductance and Inductor Size Depend on Load Current
• How Vendors Specify the Current Rating of an Off-the-shelf Inductor and How to Select It
• What Is the Inductor Current Rating We Need to Consider for a Given Application?
• The Spread and Tolerance of the Current Limit
• Worked Example (1)
• Worked Examples (2, 3, and 4)
• Worked Example (5) — When Not to Increase the Number of Turns
• Worked Example (6) — Characterizing an Off-the-shelf Inductor in a Specific Application
• Calculating the “Other” Worst-case Stresses

The reader is strongly advised to read Section 1 before attempting this section.

The magnetic components of any switching power supply are an integral part of its topology.

The design and/or selection of the magnetics can affect the selection and cost of all the other associated power components, besides dictating the overall performance and size of the converter itself. Therefore, we really should not try to design a converter, without looking closely at its magnetics, and vice versa. With that in mind, in this section, we will be introducing the basic concepts of magnetics -- in parallel with a formal dc-dc converter design procedure.

Note that in the area of dc-dc converters, we have only a single magnetic component to consider - its inductor. Further, in this particular area of power conversion, it’s customary to just pick an off-the-shelf inductor for most applications. Of course there cannot possibly be enough "standard" inductors going around to cover all possible application scenarios. But the good news is that, given a certain inductor, and knowing its performance under a stated set of conditions, we can easily calculate how it will perform under our specific application conditions. And thereby, we can either validate or invalidate our initial selection. It may take more than one iteration or attempt, but moving in this direction, we can almost always find a standard inductor that fits our application.

In the next section we will take up "off-line" power supply design. Such converters usually work off an ac (mains) input that ranges from 90 to 270 Volts. To protect users from the high voltage, these converters almost invariably use an isolating transformer - in addition to or in place of the inductor. But though these topologies are really just derivatives of standard dc-dc topologies, in terms of their magnetics, they are quite different. For example, we encounter significant (non-negligible) high-frequency effects within the transformer - like skin depth and proximity effects - the analysis of which can be quite challenging.

In addition, we find that there are definitely not enough general-purpose (off-the-shelf) parts going around, that can meet all possible permutations and combinations of requirements, as can arise in off-line applications. So in these applications, we usually always end up having to custom-design the magnetics. And as mentioned, this is not a mean task. But by trying to first understand dc-dc converter design, and the selection of off-the-shelf inductors, we are in a much better position to tackle off-line power supplies. We can thereby build up basic concepts and skills, while garnering a much-needed "feel" for magnetics.

Off-line converters and dc-dc converters are also relatively quite different in terms of some rather implicit (often completely unstated) differences in basic design strategy - like the issue relating to the size of the magnetics vis-à-vis the current limit of the converter, as we will soon learn. With regard to their similarities, we should remember that both can have a wide-input voltage range, not a single-value input voltage, as is often assumed in related literature. Having a wide-input raises the following question - what voltage point within the prescribed input range is the "worst-case" (or maximum) for a given stress parameter? Note that in selecting a power component we often need to consider the worst-case stress it’s going to endure in our application. And then, provided that that particular stress parameter happens to be a relevant and decisive factor in its selection, we usually add an additional amount of safety margin, for the sake of reliability. However, the problem is that different stress parameters don’t attain their worst-case values at the same input voltage point. We therefore realize that the design of a wide-input converter is necessarily going to be "tricky." For sure, designing a functional switching converter may be considered "easy," but designing it well certainly isn't.

Toward the end of this section, we will finally present the detailed dc-dc converter design procedure. But to account for a wide-input range, we will proceed in two distinct steps:

++ A "general inductor design procedure," for choosing and validating an off-the-shelf inductor for our application. We will see that depending on the topology at hand, this is to be carried out at a certain, specified voltage end - one that we will identify as being the "worst-case" from the viewpoint of the inductor.

++ Then we will consider the other power components. We will point out which particular stress parameters are important in each case, and also the input voltage at which they reach their maximum, and how to ultimately select the component.

Note that, although the design procedure may be seen to specifically address only the buck topology, the accompanying annotations clearly indicate how a particular step or equation may need to change if the procedure were being carried out for a boost or a buck-boost topology.

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Tbl. 1: Derivation of dc transfer functions of the three topologies

Applying Voltseconds Law and D = tON/(tON + tOFF)

Steps VON × tON = VOFF × tOFF

Therefore,

D = VOFF

VON + VOFF (duty cycle equation for all topologies)

Buck Boost -- Buck-Boost

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