The DC-DC Boost Converter – Power Supply Design Tutorial Section 5-1

The boost is the second most common non-isolated typology, in terms of units sold and functioning, and a lot of that is thanks to LED drivers, especially mobile devices. The boost is a logical next step to analyze after the buck, and it’s the second of the three most basic DC to DC typology. 

Section 5-1 Agenda

  • Explanation of the boost as a “backwards buck”
  • Non-synchronous vs. synchronous boosts
  • Duty cycle equations
  • Design and selection of the boost inductor
  • Design and selection of the input capacitors

To be clear, the other common use of the boost converter is for AC to DC power supplies for power factor correction and that requires a complete and separate treatment. When I say DC to DC, I mean converters with an input voltage that is positive and does not move up and down quickly.

Now, boost is nothing more than a backwards buck. In fact, while testing experimental bucks, I’ve sometimes seen them boost their own input voltage accidentally. This section starts with a non-synchronous boost schematic, gives equations for the duty cycle over the range of DC input voltage, and then contrasts that circuit with a synchronous boost. Something that has become more and more common as LED drivers, DC to AC inverters, and systems powered by solar panels, and other harvested energy sources gain in popularity.

After those basics, we’ll look in depth at equations for selecting the boost inductor calculating its peak in our mass currents and how to select actual catalog parts. The conclusion to part 5-1, first of three for the boost deals with input capacitors on how to calculate and pick the optimum devices.

Schematic for a Generic Boost Converter

In most any power supply schematic, the inputs are on the left and power flow is towards the load on the right. A boost is a little more than a backwards buck, though, so for a moment, let’s imagine that V-in and V-out in this schematic were reversed. Now, it would change D1 and Q1. The boost is a buck going backwards.

Let’s come back to the normal boost schematic. Clearly, the biggest difference is that this circuit only increases the output voltage with respect to the input but there’s another important practical detail. The controls were at Q1 is ground referenced and MOSFEDs are very easy to drive when their source is connective ground. So, the only possible competition for that NfeD is a PSP bipolar transistor found in some monolithic parts. When the low-sides switch is external, it’s pretty much always an end-fit.

Another great thing about controllers for low-side NfeD and regulators with internal ground reference power switches is that you can use them for lots of other topologies too.

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

I try my best to be consistent and to use the same terms throughout this webinar series but there aren’t any set names for many features and power supplies. This list is for you to refer to in case I mention something, and you’re not sure what it is.

Duty Cycle Equations, Non-Sync

Converter topologies that can increase the upward voltage are far more likely to run into maximum duty cycle limits and there are always practical limits. Whereas the buck regulator has a few calculations where the worst cases at the maximum input voltage for the boost is pretty much always the minimum input voltage that sets the worst case. At V in-min, you have the maximum duty cycle, the highest peak in our mass current and all the power path components and therefore, the greatest thermal stress for everything.

In some cases, the diode forward voltage won’t make much difference, but it becomes more and more important if V-in and V-out are fairly low. If you’re boosting from 2.5 V up to 5 V, for example, then the added 0.5 V drop of a diode would be very important. 

Basic Synchronous Boost Converter

For circuits with a high output current generally starting above three amps and especially five amps or more, replacing the output diode with a MOSFED makes a lot of sense, both for efficiency and for heating. These are the same levels that I recommend for switching from a non-synchronous buck to a synchronous buck.

There are some big shocky diodes and power packages that can be bolted on the heat syncs, but given the trend of miniaturization of pretty much all electronics, diodes and TO-247 with bulky heat syncs aren’t very attractive.

This is a good time to talk about a big drawback to the boost regulator be it synchronous or none. Input over voltages and output short circuits are both unstoppable. Short the output of this circuit and the source will start pumping all the current it can through the conductor which quickly saturates and becomes a short circuit.

You can’t flip the MOSFET on the vertical axis but the upward voltage would forward bias the body diode and try to source current back to the input. The same is true with input voltages that exceed the output voltage. The inductor quickly becomes a little more than a DC resistance. The output diode or body diode forward biases, and the upward voltage ends up equal to the input voltage minus a diode drop.

Typical Sync Boost Schematic

This realistic schematic for a synchronous boost converter shows the practical needs for the floating upward MOSFED if this is an N type. P-MOSFEDs would need this charge pump or bootstrap which is comprised of D1 and C9. In this case, my circuit used two lithium-ion batteries in series and the application was an LED driver for reproduction light save. It was maximum efficiency I was looking for since you wouldn’t want to be defending the galaxy and run out of juice halfway through a battle with the dark side.

Duty Cycle Equations, Sync Boost

It’s time for me to confess something. I left several practical elements out of the equation for the non-synchronous boost converter duty cycle over the range of input voltage. To be really, truly precise, I should have included the voltage drop across the control which went on, the voltage drop across the inductor, the voltage drops across all the circuit traces, the cabling. So if you’re thinking that it gets a bit ridiculous, well, you’re right. There’s no practical value in estimating all of those voltage drops. Most of them are insignificant compared to V-in and V-out and the body diode drop, Vd.

For synchronous bucks, the voltage drop across the control MOSFED and the upward MOSFED rarely exceed 100 millivolts. And what I prefer to do is estimate the power efficiency and then divide the ideal duty cycle equation by that efficiency. You might be thinking how can he know the efficiency before building the converter. Well, I don’t but I draw upon previous circuits, demo-boards, and experience to estimate it.

Prepping a PCB for Test

A little solder now saves a lot of time later

If you’ve already watched the previous four sections of the webinar series talking about prepping PCBs for test, then please, feel free to skip these next slides.

I have no illusions about current probes. I know they’re very expensive and that many of my viewers simply cannot afford one. It is my honest opinion that power supply engineering requires an active current probe, one that can measure DC as well as AC currents, but I’m sure many of my viewers are not dedicated power-supply engineers but systems engineers with managers that don’t see the benefit of spending several thousand euros on lab equipment.

If you do have a current probe, you want to measure the inductor current and this should be done by inserting a loop of insolated wire at the quiet side of the inductor. That will be where the boost inductor connects to the input voltage. If you put that loop of wire on the other side of the inductor where it connects to the switch node, you’ve just created a nice look antenna that will radiate more EMI.

For voltages, I suggest placing text fixtures made of 2.54 mm pitch female break-away headers in three or four section pieces. Cut of the central pins and solder the outer pins from the switch node to ground as well as right across the input and output capacitors.

The Inductor

Proper design of the inductor is the cornerstone of a good boost design as well as any other switching power supply. When the inductor has the proper inductance and can handle the peak and RMS currents over the full range of V-in and V-out, especially taking into account the frequency of the circuit, then everything else tends to fall into place.

That nearly perfect triangle wave inductor current is a good indicator that this boost converter, actually an LED driver boost converter is working properly. I included the upward current waveform to make it clear that for boost converters, the average inductor current is always higher than the average output current. In fact, for boosts, average input current is the same as the average inductor current.

Without a doubt, the most important decision to be made is the switching frequency. With that compromise at higher frequency reduces component size and cost not just for the inductor but for the power capacitors as well. But, higher frequency increases several different types of loss penalizing the power efficiency. 

Average Current in the Boost Inductor

Of these two expressions for estimating the average input current, again, being the same value as the average conductor current, I prefer the one on the right because you always know the input voltage, the output voltage, and the output current. If your customers like to change their minds halfway through the design, well, that’s normal. You’ll just have to recalculate.

I showed all these values as nominal but you remember that we usually look for the worst case and design to it, then the upper current should always be the maximum load current expected and the input voltage should be the minimum value. In fact, the equation on the right makes it easy to see why V-in min is the worst case. The smaller it is, the higher the average currents in the input and at the inductor.

Inductance Selection Equations

Inductance and the boost converter is selected in the same way as in most hard switch DC to DC converters and is based upon setting a certain ratio between the average current and the peak to peak ripple current. In general, a peak to peak ripple that’s between 20 and 40% of the maximum input current gives a good compromise between the size of the inductor, that’s proportional to weight and cost, and the RMS currents throughout the converter.

It took me a while personally to really understand why RMS currents are such a big deal. The main reason is for heating. The higher the ripple in any given waveform, the higher the RMS value even if the average value stays the same. So, for example, nothing would stop you from designing a boost or any other switcher with an enormous inductor that emitted ripple to only 5% peak to peak of the average value. But your purchasing manager will probably have some sharp words since big inductors cost big money. Similarly, you could put a very low-value inductor and have 100% peak to peak ripple, but be prepared for hot MOSDEFs, toasty diodes, and steaming capacitors.

Discontinuous Conduction Mode (DCM)

Keep in mind also that DCM is usually when the output power is low so there isn’t much energy in the DCM ringing. DCM is, in fact, a case where the inductor ripple current is 200% of the average since it falls all the way to zero. Really low power boosts are sometimes designed to run in DCM on purpose since you can really lower the inductance and that makes for tiny and cheap inductors. But the general trend is to stay in CCM and run at high frequency when a small size is necessary.

That second inductance equation from two slides ago is more useful as shown here, rearranged to indicate at what point the converter will undo DCM. Even synchronous boosts usually turn off the output FED if the current tries to reverse direction, so they, too, will enter DCM at light load. This expression is useful if your load toggles back and forth between two known states.

For example, a modern microcontroller might have an active mode where it draws around one amp and then a so-called sleep mode where the current drops to 100 milliamp. Digital loads are known to slow quickly from low current to high current and back again. And as we’ll see later on, these transitions happen faster if the converter stays in CCM. So, in such a case, you might want to go back to equation L-min-2 and use a higher induction to do this.

There always comes a point where trying to keep your boost and CCM at very light loads makes no sense and that’s shown here on this graph. The curve is exponential and at currents below 10 milliamp you’d need inductors so big that they would be, as we often joked back at National Semiconductor, like boat anchors.

Current Ratings for the Inductor

Having balanced the needs for a CCM or DCM with the requirements of ripple current, we now know how much inductance is needed. It’s time to calculate the currents. First, rearrange equation L-min-1 and that will give you the actual peak to peak ripple current. As an interesting aside, the ripple current is actually a higher peak to peak at the maximum input voltage. But since our goal is the maximum peak current, we calculate this at Vin-min.

Peak (Saturation) Current Ratings

Most of the time you’ll be selecting an inductor from existing catalog parts. There must be hundreds of power magnetics manufacturers and there are about 10 that I consider to be world class. One of the things that distinguishes a true high-quality inductor or a transformer manufacturer is their documentation. I want to see separate specifications for both saturation current sometimes called peak current, and RMS current sometimes called average current.

When sorting through a perimetric tables online, I usually start with the peak or saturation current. The inductor core is saturated when the magnetic flux density, B, stops increasing even though the magnetic field strength, H, increases. When this happens, induction starts to fall. A good data sheet will tell you by what percentage the induction falls for a given current. For a truly robust design, pick a part whose saturation current rating is higher than the peak current limit of your boost converter. Sometimes that’s a fixed value usually with monolithic parts and sometimes it’s adjustable which is normally the case with external control MOSFETs. 

RMS (Self-Heating) Current Ratings

Once I filtered my parametric search results for all the parts that fit my peak current needs, I look at the RMS current ratings. Since RMS is a calculation based upon how much heating occurs, it makes sense that RMS limits are specified based upon temperature rise. No standards exist to say what that temperature rise is nor how it’s tested. Once again, good manufacturers have lots of footnotes as you can see here have explained those limits.

If you pick an inductor with an RMS grading greater than the maximum input current, then you can expect the temperature rise to be less or equal to the specified value in the majority of cases.

The Input Capacitors

In sections 2-1 and 2-2 of this series, you heard me dedicate quite a lot of time to the input capacitors for buck converters. For boosts, input capacitance is less important because the boost inductor is always connected to the input and it reduces the capacitance needed while greatly reducing the RMS currents in the input capacitors.

This plot was taken with a low inductance, 0612, 10 milliohm resistor placed in series with the two MLCC input caps but it still upset the operation of the converter. I was hoping that the boost converter would behave a little bit better than the buck when I tried this, but it didn’t. You can clearly see the subharmonic isolation in all three waveforms. In just a few slides, I’ll explain why this happens. It’s a phenomenon known as “power supply interaction”.

Simulate Input Currents

If you want to check the currents and the input capacitors or the output capacitors or the power switches, I suggest doing so with a simulation so that the converter actually works properly. But it is an important catch to be aware of with simulations. This one in LTspice is a good example. By default, voltage sources in LTspice have an output impedance of nearly zero so they can source infinite current at infinite frequency. I sure wish these existed in real life.

In all seriousness, I suggest adding some inductance and resistance, perhaps 100 nH and 10 to 15 milliohm so that the source is more realistic and so those input capacitors actually do some work. Remember that their job is to source as much of the AC current as possible.

Input Capacitor Design Equations

The minimum input capacitance is calculated based on the maximum input voltage ripple. The inductor insures that this ripple is much lower than it would be for a buck, buck boost or fly-backs. All these are topologies with discontinuous input currents.

One note here. The factor of eight in the denominator is due to the triangle wave shape as opposed to two Pi which would be for a sinusoid.

MLCC Capacitance Loss with DC Bias

More and more DC to DC power supplies are using banks of purely multi-layer ceramic capacitors or MLCCs. Low ESR and low ESL coupled with high RMS current tolerance makes MLCCs nearly ideal but they do have a notable drawback. The loss of capacitance with DC bias. 7.2 volts is the nominal input voltage for light-save driver and I could have used 10 volt or 16 volt rated MLCCs, but I chose a 10 micro-FED part rated at 25 volts and then the 12-10 case size, because higher voltage ratings and bigger physical size are both inversely proportional to the capacitance loss versus voltage.

Oscillograph of Input Ripple Current and Voltage

At first glance, this high-frequency ringing also known as spikes or technically as PARD noise looks really bad on the delta VN trace in yellow. But that’s only 200 millivolts per vertical division whereas the switch node is bouncing up and down by 34 volts. If the input capacitors were perfect and ideal, then the input current in pink would be purely DC. Now that isn’t practical for real circuits. Input filters are needed to get the I-in ripple low enough to meet EMI standards such as CISPR 25 used for automotive applications and that’s precisely where an LED driver with an 12 volt input is likely to be found.

Input Capacitors / Input Filter Damping

If you’ve already seen section 2-1 of this webinar series, feel free to skip this slide and actually the next three. Otherwise, in practice, if you only have MLCCs and their long input inductive 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 osculate or ring. The same thing can happen if your boost regulator has an actual discreet input filter inductor.

As the second diagram shows, you need to be careful about having an input filter with a higher output impedance ZS and the input impedance to the switching regulator, negative Zin.

Filter Impedance and Converter Impedance

The reason we care about that negative input impedance is due to the input osculation or ringing or what I call power supply interaction. That’s what you saw in the slide “The Input Capacitors”.

If the output impedance or the input filters ES is equal to the absolute value of the converters input impedance than in theory the system could ring to infinity volts. In practice, whenever the filter output impedance is higher than Zin, the system is likely to osculate. That’s why I give a calculation for Zin-min so we know the worst case.

Not surprisingly, the worst case is when VIN is at a minimum and upper power is at a maximum. The series resistor added when I took the scope capture for slide 21 had enough resistance and inductance to increase the output impedance ES and that pushed the system into oscillation. 

Input Filter Damping (for MLCCs)

In section 2-1 of this webinar series where I looked at various capacitor technologies, 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 and parallel with the MLCCs at the input works wonders for input osculation. Note that the 4X capacitance for damping was first proposed by Dr. Middlebrook, one of the great names in power electronics.

When I lead a PCB for a circuit that I know have long 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, it doesn’t have enough ESR, I can just add in discreetly however much more I want. 

Input Filter Damping Factor

In this equation for damping factor delta, RS is the resistance of the input leads and RDN is any discreet resistor placed in series with the damping capacitor. A few more tips for input filter damping.

  1. If you’re designing a supply for a very high-temperature environment and you’re worried that even good quality electrolytic will try out, you can also use polymer aluminum, polymer tantalum, or even a big bank of paralleled MLCC with a discreet series resistor. I don’t recommend dry tantalum because they can be sensitive to inverse currents and explode.
  2. You can actually dampen an LC filter by placing a branching in parallel with the inductor with four to five times the inductance and a discrete resistor but that tends to be both expensive and bulky. I usually only do that for specific input filters on some AC to DC applications.
  3. You probably won’t see any difference in the peak to peak input volt ripple after adding the damping cap because it’s not very capacitive at the switching frequency but you will see a nice improvement in the input voltage drop due to low transients.

Input Capacitor Types

For a DC to DC converters, the two types of capacitors used at the input are MLCCs which reduce the peak to peak ripple at the switching frequency and bulk types. That’s pretty much everything else and those are used for damping of the input and for response to lower frequency events.
Please look at section 2-1 of this series for an in-depth discussion of the various types of bulk capacitors. 

Grouping Capacitor Types

This is also a repeat from part two, the buck webinar, so skip ahead if you’ve already seen it. If not, I like to simplify my analysis of capacitor banks using a mix of bulk and MLCC capacitors by first grouping all the bulk caps into one device. That’s assuming there’s more than one bulk cap in parallel. Then I do the same thing for the MLCCs.

I don’t bother including the small or low-value MLCCs, those 100 nF or 1 uF devices since they rarely contribute anything to the total capacitance.

Input Capacitor RMS Currents

Calculating and calculating the split of RMS input current in boost, SEPIC, or choke converters is mostly an exercise in being thorough. That’s because all these topologies have an inductor at their input that prevents higher MS current from cooking their input capacitors.

Just by looking at the equation for our MS current, you can see that it will be quite low. The square root of 12 is around 3.5. So take the already controlled conductor current ripple and reduce it by 3.5 times. In any case, I still recommend always calculating the RMS currents in every power capacitor, especially aluminum, polymer, and tantalum capacitors, because these are almost always the shortest-lived components in the system, the weakest link in the chain. 

Simulation Still Best for Current Split:

I’ve gone back to a simplified simulation to check the ripple current split between my bulk and my ceramic input caps. Keep in mind that the actual current split will send less current to the bulk caps because their capacitors at the switching frequency has usually dropped off quite a bit.

This example is a 600-kilohertz front end to my light saver and no bulk cap that I know of is very capacitive at that frequency. LTspice lets you program in capacitive loss versus frequency but that’s a time-consuming process requiring and LCR meter which many labs do not have access to. Instead, I look at the LTspice plot with the ideal capacitors and if the current split keeps the bulk capacitors armors current nice and low, again, here it is, then I’m happy. I know I have a good engineering margin.

 Next up:  Section 5-2:  The DC-DC Boost Converter, Part 2

Section 5-2 continues the discussion of the power-train components for a lose converter starting with plenty of detail for the output capacitors. We’ll look at equations based upon steady-stage voltage ripple and then equations based upon the response to lower transients. Then the RMS current calculations are discussed in detail since these elements suffer lots of RMS abuse. Section 5-2 then continues on to the control MOSFET and that’s various types of loss. Finally, the last part on the power-train, the output diode is examined exploring packaging options and power loss.

Link to next section: Part 5-2 The DC-DC Boost Converter, Part 2

Link to previous section:  4-2 Switching Edge Control for EMC





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