The Buck Regulator – Power Supply Design Tutorial Part 2-1

In Part 2-1 of our Power Supply Design Tutorial we’re going to start a deep-dive into the buck converter and select one very important part, the output inductor. Then, we’ll begin with the design philosophy for the input capacitors.

Section 2-1 Agenda

  • Synchronous and non-synchronous implementation of buck converters
  • Selection of external components:
    • Output inductor
  • Design philosophy for external components:
    • Input capacitor – types (bulk or MLCC)
    • Input impedance and damping

There are far fewer topics in this session than in the previous two, introductory sessions. The reason is because the level of detail.

The output inductor, or the buck inductor, is the key piece of this and nearly every other switching regulator. Then, the input capacitors, often overlooked, are crucial not only for proper operation of the converter but also for electromagnetic compatibility or EMC. We’ll look at different capacitor technologies and then discuss the phenomenon called power supply interaction that can arise if the input filter isn’t designed properly. The background discussed in this section will be used in the next section to actually select input capacitors, but it will also be reused for just about every other switching converter topology as well.

How are Power Supply Engineers like Chickens?

Okay. I didn’t write this cheesy joke, but a little humor can go a long way. If you work with complex digital systems, especially FPGAs, then you probably have a 12-volt rail and a 5-volt rail and you have a whole lot of buck regulators. Every now and then, you might get lucky and have to create a negative output or maybe boost up a voltage for some reason. Mostly, you buck, buck, buck, buck, and buck. That’s why power supply engineers are just like chickens. 

Definition of Key Terms

  • Nominal input voltage, VIN, ex. 13.8V for passenger vehicles
    • Maximum input voltage, VIN-MAX, ex. 42V for a clamped load dump
    • Minimum input voltage, VIN-MIN, ex. 4.5V for start-stop
  • Maximum output current / maximum load, IO-MAX / RO-MIN
  • Nominal Duty Cycle, DNOM, when input voltage is nominal
    • Maximum duty cycle, DMAX, when input voltage is at a minimum
    • Minimum duty cycle, DMIN, when input voltage is at a maximum
  • Multi-layer ceramic capacitors, MLCCs
  • DC resistance, DCR, of inductors
  • Equivalent series resistance, ESR, of capacitors
  • Converter or regulator: switching IC with at least one internal power MOSFET
  • Controller: switching IC with external power MOSFET(s)
  • Module: switching control, power switches, inductor and passives in one package

Don’t worry, I’m not going to read you this list. There are other, more effective, sleep aids available out there. No, this is for you to come back in case I talk about a variable and you don’t know what it is.

Schematic for Generic Non-Synchronous Buck Regulator

In sections 1-1 and 1-2, I showed a buck with ideal switches and then a buck with practical switches. Now before you is an even more practical buck. Look closely at the input capacitors and the output capacitors. Notice that I drew one polarized and one non-polarized symbol for each rail. One of the keys to good switching power supply design is to make sure that your voltage rails are low impedance as possible over as wide a frequency range as possible. Different sizes and different types of capacitors provide that low impedance over the wide frequency range.

I’m sure you noticed how L IN, the input inductor snuck in there too. That might not be a discrete device, but it’s always there. That’s because all cables, and PCB traces, and any other real conductor that carries current has inductance. The trick is to make it work for you, not against you.

Duty Cycle Equations, Non-Sync

This is the first time I’m showing a range of duty cycles based upon the variation of the input voltage, V IN. I’m assuming, of course, that V OUT is fixed. That’s not a given either, but it is true for many switchers. Engineering in general is about designing systems that can handle the worst case plus some margin. We need to know the extremes of input voltage, duty cycle, output current, switching frequency, and temperature just to name the basic ones in order to make a good design for our switching converter.

Find the Electrically Quiet Side

This is a good time to talk about measurement techniques. There’s a theory from quantum physics stating that the very act of measuring something changes that thing. It’s one thing to say that watching a planet changes the planet, but measuring currents and voltages definitely influences those quantities. In most cases, there are good places to place a current probe and bad places. 

Most switching regulator storage inductors have a quiet side (voltage-wise) and a noisy side

This is the long-suffering synchronous buck regulator I’ve used for most of the buck topology experiments in this seminar. I’ve only boned-it up twice. That’s how I know it’s robust. In any case, in the buck, the “switching node” is where the two power FETs for synchronous bucks like this one or the FET in the diode, that would be for non-synchronous bucks, connect to one side of the inductor. This node is very electrically noisy.

The other side of the inductor is nice and quit. That’s the output voltage with its nice mix of different capacitors to make it low-noise over a wide range of frequency.

Inductor: Noisy Side vs. Quiet Side

This scope capture says it all. The switching node bounces up and down by 20 volts with plenty of noise and harmonics at both the switching frequency and the reading frequency. See those transient spikes? Then, there’s the other side of the inductor, which only moves about two volts peak-to-peak. Actually less, because some of that noise isn’t real. It’s induced by the common ground shared by the two voltage probes.

Put Wire Loop in Series with Quiet Side

Right now, it’s not voltage probes we’re worried about, it’s where to put our current probes. These active current probes have pretty large heads, although they are the clip-around type. They’re for about 30 amps max. You need to insert a loop of wire around 15 milometers by 15 milometers to clip them on. That loop should always go in series with the electrically quiet side of the inductor. Adding this loop of wire adds inductance, but adding inductance in series with inductor is usually no problem. It does change the circuit operation slightly, but if we add 100 nanohenries in series with ten microhenry inductor, the effect is negligible.

Now, here’s something to ponder. What happens if you put 100 nanohenries in series with a filter capacitor while switching MOSFET? Stick around to find out.

The Output Inductor

The buck conductor stores energy and filters the raw square wave voltage into a smooth voltage, or, at least, a smoother voltage. Once this part of the converter has been properly selected, the remaining components selection is pretty straightforward. 

  • The magnetic (inductors and/or transformers) are the heart of all switching converters
  • Switching frequency has a large influence on physical size

It might not be immediately obvious, but this scope shot was taken in free-running trigger mode. Notice that the falling edges of the switched node voltage are nice and sharp. By sharp, I mean free of jitter. A clean wave voltage at the switching node, free of falling and jitter, and a clean triangle with current through the inductor are the first two things I look at when checking the health of a switching regulator.

One of the key design compromises that every switching power supply designer must make is selecting the switching frequency itself. Lower frequency is generally more efficient, but higher frequency leads to smaller, cheaper, and lighter magnetics. You’ve probably heard or will hear that lower frequency is better for EMC too, but I’m not convinced of that. I do look carefully at the conducted EMC standards before picking my frequency, but that’s to avoid sensitive frequency bands or to purposefully put the fundamental of my noise source in a range with a high EMI limit.

I generally pick the largest inductor that will fit when I have control over the switching frequency. Or, to put it another way, I pick the lowest switching frequency that allows me to fit the inductor on the board or inside the enclosure of my power supply.

Average Current in the Buck Inductor

Average output current and average inductor current are equal

One of the practical aspects of a converter with an average inductor current that’s equal to the average output current is that the control IC selection is nice and easy especially for devices with internal power switches and fixe current limits. When you read, for example, “5 amp buck regulator” it usually means that the power switches can handle the power dissipated when 5 amps flows to the output. The buck is the only topology that works in this way. For plenty of detail, be sure to view boost SEPIC or Flyback sections of this seminar.

Output Inductor Design Equations

These equations for selecting the inductance are based upon CCM operation. Remember, this is when inductor current stays above zero for the whole switching cycle. Keep in mind that all non-synchronous buck regulators will enter DCM when the load drops low enough. DCM is not a problem in and of itself.

This is the first time in this seminar that we’re seeing the concept of component selection to maintain a given ratio of ripple or the AC component to the average or the DC component of a wave form. We’ll see this concept over and over again. It’s one of the basic tenets of switching-regulator design.

Inductor Peak and RMS Currents

Whenever you see RMS, think heat. If you exceed the RMS rating of a device, the device heats up. Not necessarily too much, that depends on many factors. When you see peak or “Sat” that’s saturation. When the core can’t handle anymore magnetic flux density.

The scope capture shown at the bottom here is the response of the buck regulator to an output short circuit. One of the big challenges in inductor design is to decide whether or not to pick a saturation current high enough to tolerate the peak current limit of the system. Most peak current limits are about 50 percent above the maximum average current to give margin for the ripple current and for load transience.

Now, a saturated magnetic element doesn’t explode or anything like that, nor does it suffer any permanent damage, but you can get very high peak currents in saturation and that often happens during output short circuits. That, in turn, leads to high RMS currents. High RMS currents make everything heat up. On the other hand, high-peak current ratings make the inductors larger, heavier, and more expensive.

Ferrite Core vs. Powdered Iron Core

That’s where the trade-off comes in. Ferrite and powdered iron are pretty much the only two choices for magnetic cores of off-the-shelf catalog inductors. There are lots of cases where both can work, but, in general, ferrite devices provide higher inductance at lower peak currents so they’re more common in circuits with higher output voltage but lower output currents. Powered iron devices tend to have lower inductance but much higher saturation currents.

Just take a look at the two-wheel devices I’ve picked for this slide. Both handle 12 amps RMS, but the powered iron part can handle twice the current before it saturates. For that reason, powered core parts are more common in low output voltage, high output current bucks.

The Input Capacitors

Overlooked and under-appreciated

One thing that seemed strange to me when I started writing datasheets and application notes was that the output capacitors got lots of attention, and the equations were all similar, whereas each author had a different approach for the input capacitors. Some design guides didn’t give any equations at all, or were very vague.

My goal in the next nine slides to is to convince you, my viewers, that the input capacitors in buck regulators are absolutely crucial.

Only the simplest, smallest, and most cost-sensitive buck regulators have only a single input capacitor. In such cases, the EMI filtering is done in a previous stage. Now, to take this scope shot shown here, I purposefully removed all but one of the input capacitors of a small buck regulator. That’s why I show that empty spot between B IN and C IN-1 in the schematic.  Then I put a small sense resistor in series with C IN-1, which was a multi-layer ceramic capacitor abbreviated as MLCC.

Here we can see the trapezoid wave current being drawn when the switch node is high meaning that the control FET is on. Trapezoid waves have high RMS values, which cause lots of heating and high harmonic content, which causes lots of EMI. Now, see the quasi-sinusoidal shape at the input current that’s IN-DC? Our goal is to make that current as close to DC as possible. 

I promised that we would see the concept of AC control as a percentage of the DC value again and again. All of the same elements present in this equation from minimum input capacitance were present in the equation for minimum output inductance. But notice, instead of 20% to 40% as the recommended ratio, it’s 1% to 5%. The main reason for that is that voltage ripple and input current ripple are directly proportional. Input current ripple must be very, very low to meet most conducted EMI requirements.

To give you an idea of how that is in the time domain, input current ripple usually must be less than one milliamp peak to peak. When you’re calculations for C IN Min come out to less than 10 microfarads more of less, consider using all multi-layer ceramic caps or MLCCs. These are those brown or gray rectangular capacitors. They used to be used only for high-frequency filtering, but, in the 15 years that I’ve been designing power supplies, the range of voltage in capacitance has increased so much that now they can be used in place of tantalum, aluminum, and other capacitors that previous were the only choices for capacitance greater than around 10 microfarads.

MLCC Capacitance Loss with DC Bias

MLCCs are about as close to ideal as you can get with real life capacitors in many aspects. For example, there equivalent series resistance or ESR is often less than 5 milliohms. Some tantalum or aluminum capacitors have ohms worth of ESR. The equivalent series inductance, or ESL, of MLCCs is also very low because of their small size and geometry. These are the things that make ceramic caps great for high-frequency filtering.

But, nothing is perfect. One key drawback to MLCCs is that they lose capacitance when you use them with DC voltages. In general, the smaller the cap, the lower the voltage rating, and the higher the nominal capacitance the worse this effect is. As the graphs here show, MLCCs can lose well over half of their capacitance if you use them at their full rated DC voltage. For capacitors over one microfarad, I always use X5R or X7R dielectrics. Those are great for temperature stability. I typically pick devices with graded voltages that are twice the working voltage. So, for example, a 12 volt rail would use these 25-volt rated MLCCs.

Bulk Cap vs. Frequency: Al-Electrolytic

Let’s look at some typical technologies for so-called bulk capacitors. When I say “bulk” I mean a device that provides a lot of capacitance. How much capacitance? You ask. Well, as always, that depends. Generally, use the so=called bulk capacitors when you need more capacitance than MLCCs can provide. Of course, you can always parallel lots of MLCCs. That’s what the serious core rails from microprocessors and FPGAs do. But lots of times you don’t have the budget or the PCB area. If one aluminum electrolytic capacitor will do the job, then fine.

The big text box and arrow make the principle drawback of this aluminum capacitor evident. It’s simply not a capacitor past around 20 kilohertz or so. That’s the ESL, that parasitic inductance that cause the impedance to increase past a certain frequency. Surface-mount aluminum electrolytic are generally better because their leads are shorter. Remember that inductance is a function of length among other things.

Before you start to think that this capacitor is worthless for a DC to DC switching converter, for example at one megahertz, remember that plenty of events such as load-transience occur at much lower frequency. Don’t discount the noble aluminum capacitor just yet.

Bulk Cap vs. Frequency: Polymer Al

This polymer aluminum device has a solid electrolyte. One big advantage is that, under the same temperature and the same thermal stress, this capacitor would last longer than the standard aluminum electrolytic, which has a liquid electrolyte that evaporates over time. The polymer aluminum would also be a better candidate for the core of a digital processor. By that I mean a highly dynamic load that requests lots of current very rapidly and then drops to nearly nothing just as quickly. That’s because this capacitor has much lower ESR and also keeps that ESR fairly low even at cold temperature.

Cold is where standard electrolytic also have big problems because their electrolyte can freeze. That makes the ESR go so high that it effectively open-circuits the capacitor. So far, polymer aluminum caps haven’t reached much beyond 25 volts, so they’re mostly used at the outputs of step-down regulators.

Bulk Cap vs. Frequency: Solid Tantalum

Solid tantalum sometimes also known as dry tantalum is one of the few alternatives to aluminum electrolytic technology for a few years in cases where fairly large amounts of capacitance were needed at voltages up to around 50 volts. I still remember my co-worker having a laugh at my expense the first time I applied too much voltage to one of these caps. No one was hurt, and the cherry-red flame as the tantalum cap burnt to a crisp was pretty. Those problems are mostly gone, but tantalum is still a fairly expensive technology.

As far as ESR and ESL go, this type of capacitor is better than aluminum electrolytic but not as good as MLCC. For low voltages, my feeling in general is that polymer aluminum and polymer tantalum are more popular these days.

Bulk Cap vs. Frequency: Polymer Ta

Polymer tantalum and polymer aluminum capacitors are quite similar in many ways. They have similar voltage ranges, rarely above 25 volts maximum, similar capacitance ranges, usually up to around 1000 microfarad or so, and similar ESR values, typically from below 10 milliohms to up to around 50 milliohms or so. They also look quite similar. In fact, they look like surface mount tantalum capacitors and are also footprint compatible.

Like the polymer aluminums, polymer tantalum caps can handle a lot of ripple current thanks to their low ESR, and they stand up well to low temperatures. Also, here we’re talking about input capacitors, but the fairly low-rated voltages mean that these devices are most commonly found at the outputs of bucks, generally for use at 5 volts DC and below.

Capacitance of MLCC vs. Frequency

Last, but most certainly not least, is the MLCC. This plot is for a 1206-sized device, nominally 10 microfarad and rated to 25 volts DC. It’s capacitance out to nearly an order of magnitude higher than any other capacitor type we’ve seen. This plot shows us the reason that series digital cores are surrounded by MLCCs. Nothing else can stay capacitive at the frequencies and slew rates that microprocessors, FPGAs, series microcontrollers demand.

Besides have an ESR that’s around 3 milliohms, the MLCC has far lower ESL. Remember that that means parasitic inductance and that’s lower than all the other capacitor types. That’s the real reason that MLCCs are king in terms of capacitance at high frequency. Finally, that low ESR and the solid temperature-resistant material, ceramic, makes MLCCs capable of handling way more ripple current per unit volume than any other capacitor type. In short, they are nearly ideal for use as input capacitors for buck regulators.

The Input Capacitors, Part 2

  • More and more bucks use 100% MLCC input caps
  • Low ESR is good, BUT:
  • The input line/leads have a parasitic inductance, LIN
  • Or, an input inductor is added on purpose
  • This L-C filter has a low damping factor and can:
    • Cause an overshoot at VIN upon startup
    • Ring in steady state

I just stated that multi-layer ceramic capacitors or MLCCs are nearly ideal for use as input capacitors to buck regulators. They have low ESR, low ESL. They can handle more ripple current per unit volume than any other technology, but, strangely enough, being nearly ideal isn’t always ideal. Now that MLCCs are available in voltages up to 100 volts, which covers the vast majority of DC to DC converters, and MLCCs are available with capacitance over 10 microfarad, sometimes well over 10 microfarad, that will satisfy the need for capacitance for many circuits. You could, in theory, use only ceramics at the inputs of many buck converters.

In practice, if you only have MLCCs input capacitors and their long, inductive input leads, then a second order LC input filter is formed. Sounds good right? The trouble is that this filter has a very high Q value. Another way to state this is that an input filter made of input leads and MLCCs has very, very little damping. Any small transient will make it oscillate or ring. The same thing can happen if your buck regulator has an actual discrete input filter inductor. As the circuit diagram shows, you will need to be careful about having an input filter with a higher impedance, Z S, than the input impedance to the switching regulator, negative Z IN.

What is Negative Input Impedance?

This might be the first time that you hear the term “negative impedance” so let’s dig a little deeper. Switching power supplies that are properly designed maintain high efficiency over a range of input voltages. For a buck, that’s usually over 90%. Imagine a circuit that has a 5-volt output, delivers one amp of output current, and has a 10-volt input. If the efficiency is 90% for example, then the input current as given by this formula is around .55 amps. Now, if VIN rose to 20 volts, but the output voltage, output current, and power efficiency all stay the same, then the input current would drop to 0.27 amps. That’s conservation of power. If the current drawn by a load drops as the voltage applied goes up, then, from a mathematical perspective, that load has a negative input impedance.

Filter Impedance and Converter Impedance

Now, the reason we care about that negative input impedance is due to the input oscillation or ringing or the power supply interaction that I talked about. If the output impedance of the input filter Z S is equal to the absolute value of the converter’s input impedance then, in theory, the system will ring to infinity volts. In one of my favorite movies, Ghostbusters, the character Egon says, “It would be bad.” In practice, whenever the filter output impedance is higher than ZN, the input impedance of the switcher, the system is likely to oscillate. That’s why I give a calculation for ZN MIN, so we know the worse case. By the way, for switching converters, the worst case is usually with a maximum load and with a minimum input voltage. More on that in a boost SEPIC, inverter, and Flyback sessions later on in the seminar.

Input Filter Damping (for MLCCs)

In the previous section, section 2-1, I said that the aluminum electrolytic capacitor wasn’t dead yet. It turns out that aluminum electrolytic capacitors, with their high capacitance per unit volume, high ESR, and low cost are perfect for damping LC filters. A large-lossy aluminum in parallel with the MLCCs works wonders for input oscillation. Note that the 4 X capacitance for damping was initially proposed by Dr. Middlebrook, one of the great names in power electronics.

Whenever I layout a PCB for a circuit that I know will have long, inductive input leads, I often place a footprint for a resistor in series with the damping capacitor. That way if, for any reason, an electrolytic cap that’s otherwise perfect doesn’t have enough ESR, I can just add in however much I want.

Input Filter Damping Factor

In this equation for damping a factor delta, RS is the resistance of the input leads and RDN is any discrete resistor placed in series with the damping capacitor.

A few more tips for input filter damping, if you’re designing a power supply for very high-temperature environments and you’re worried that even good-quality electrolytics will dry out, you can also use polymer aluminum, polymer tantalum or even a big bank of parallel MLCCs with a discrete series resistor. I don’t recommend dry tantalum because they can be sensitive to inrush currents. By sensitive, I mean they can blow up.

You could actually damp an LC filter by placing a branch in parallel with the inductor with four or five times the inductance of the main inductor and a discrete resistor, but that’s expensive and bulky. I only do that for specific input filters on some very special AC to DC applications.

You probably won’t see any difference in the peak-to-peak input voltage ripple after adding the damping cap because it’s usually not very capacitive at the switching frequency, but you will see a nice improvement in the input voltage drop during load transience.

Next Up: Section 2-2 – Buck Converters

  • More Input capacitor design philosophy
    • Selecting input capacitance
    • RMS (ripple) current in input caps
    • Combining MLCC and bulk capacitors
  • Design philosophy and selection of output capacitors
  • Design philosophy and selection of the control MOSFET (the high side switch) when it is external

The next session will provide equations for picking capacitance, calculating the maximum ESR and RMS ripple current for input capacitors to a buck converter, and how to combine bulk and ceramic capacitors for low impedance and a long service lifetime. Then we’ll talk about the output capacitors, and the final part of section 2-2 will be selection of the thermal fin for the high side switch when it’s a discrete MOSFET.

That concludes part 2-1, and I hope you have learned something and that you come back to see the next session and future ones as well. In part 2-2, we’ll stick with the buck converter and first we’ll actually pick some input capacitors. Then, we’ll move on toward a comprehensive design guide for all the other external parts and components. I’d like to thank Power Electronics News for giving me the opportunity to present this series, and I look forward to seeing everyone, at least virtually, for part 2-2.

Link to next section: 2-2 Buck Converters, Part 2

Link to previous section:  1-2 Topologies and Fundamentals, Part 2


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