Power Supply Design Tutorial (Part 1-2) – Topologies and Fundamentals, continued

Welcome to part 1-2 of the Power Induced Design Power Supply Design seminar, brought to you by Power Electronics News. In this session we’ll look at the three basic DC to DC converter topologies in more detail. We’ll also examine the flyback converter, and some of the compound switching converters.

Seminar Section 1-2 Agenda

  • The buck, the boost and the inverting buck-boost in detail: duty cycles, volt-second balance
  • Negative buck and negative-to-positive buck-boost topologies
  • Compound topologies: four-switch buck-boost and SEPIC
  • The flyback regulator
  • Packaging and integration of power ICs

In store for this session is detail on the basic topologies. Some talk about practical switches. Duty cycles. And then topologies that are derived from the three basic switchers. Finally, I’m going to do just a tiny bit of marketing. And talk in general terms about the elements of a switching converter that can now be found inside the package of the control IC. As well as those components that still live outside the package.

Buck Converter

Here is a Buck Converter in a more practical circuit diagram. Up until now, the switches were represented as ideal devices. But it’s time to replace those with practical devices. I’ve drawn the control switch, or High Side Switch as an internal MOSFET, because that’s the most common type of controlled switch used in modern switching regulators. But it could also be a PMOSFET or even an NPN Bipolar Transistor.

The uncontrolled switch or Low-Side Switch, is called that because it connects the system ground. And I’ve drawn it as a schottky diode. It could also be a PN diode for voltages above 200 volts, where schottky usually aren’t available. Or it could be an NMOSFET. More on the pros and cons of schottky, PN diodes, and MOSFET’s later on in this seminar.

The classic analysis about switching converter, consists of drawing the circuit in its two switching states and assigning a consistent polarity to the voltage across the inductor. That’s VL. To be more complete we would also draw the currents with their polarities in the input and output capacitors. But for now lets stick to the inductor voltage.

In session one-one I talked about the “Volt Second Balance” across the inductor, and that’s what we’ll use to analyze this buck converter. With a control switch, the MOSFET is on, the voltage across the inductor is V in minus V out. When it’s off, we have negative V out. Now again, that voltage is not negative with respect to system ground, it’s only negative with respect to the polarity that we assign to the inductor. By the way, all the math would turn out the same if you assign the opposite polarity to the inductor voltage. The key here is to be consistent across both switching states.

Buck Converter Duty Cycle

Using the principal of Volt Second Balance, and running through some math, now I know we all love math, but I’m gonna skip that part. We get to the converters transfer function and duty cycle equation, for an ideal buck that’s simply V out divided by V in. Now we can see mathematically why the buck can only decrease the output voltage with respect to the input. At a duty cycle of 100 V out equal’s V in. No more.

Now I’m afraid that I’ll have to take you out of that perfect ideal world and look at the practical side of things. When current flows through MOSFET’s and diode’s, there’s an associated voltage drop that’s definitely greater than zero. The practical result of this is that for a given set of conditions, actual convertor duty cycle is higher than the ideal duty cycle. For example, if V in was 10 volts exactly and V out was 5 volts exactly, in real converting the duty cycle would actually be greater than 50%. Another way to think about this is the higher the efficiency, the closer the practical duty cycle is to the ideal.

Before I dig into some more topologies, I wanted to say a few words about Continuous Conduction Mode, CCM. And Discontinuous Conduction Mode, DCM. Any switching converter with a fixed switching period, that would be a PWM control device. Or a fixed on time. Or a fixed off time. These are PFM, or Pulse Frequency Modulation devices. They can go into discontinuous mode if they use a diode as the uncontrolled switch. This happens at light loads, and it means that the inductor current falls to zero before the end of the switching cycle.

There’s an LC tank oscillation, which can be seen on the right, in the switch node voltage. As long as you understand that DCM is perfectly natural and not an indication of a problem with the converter, there’s no need to worry. If you’re thinking that the LC oscillation could be a source of electromagnetic interference, or EMI, well in theory, yes it is. But in practice you only see this oscillation at light loads. And when only a small amount of current is flowing, the energy in that EMI source is quite low. Now if you stick around for the advanced session on control loops, we’ll look at why DCM is rarely, if ever, a problem from a small single perspective either.

The Negative Buck Converter

Each of the three basic DC to DC topologies has a negative alter ego. But they’re not evil, and some are actually quite helpful. These topologies arise by putting the controlled switch where the uncontrolled switch was, and naturally, putting that uncontrolled switch where the controlled switch used to be. This circuit is great for stepping negative 12 volts down to negative five volts. Except that this situation isn’t very common.

This topology finds far more use when connected to a positive input voltage. And then it gets a bunch of new names. Because each semiconductor company that designs an IC has a marketing department. Floating Buck and V in Reference Buck are two common names. And both indicate that the output voltage is not referenced to ground.

That limits the usefulness for DC to DC voltage regulators, and makes this a very popular circuit for LED driving. Where output current is the one being controlled. One very, very useful feature when you connect the circuit to a positive V in, is that the controlled switch is the low side switch. That means that the drive circuit is ground referenced. And that makes it way easier to drive the NMOSFET.

Okay, great, the NMOSFET, you might be thinking, why do I care? The answer is that NMOSFET’s almost always provide the best combination of performance and cost. Not to mention selection and availability.

Here’s the Boost Converter in detail. And like I said in session one-one, it’s a little more than a backwards block. Before we analyze it further though, lets look at one highly important detail. The Boost converter can’t protect the output form two classic dangers that every power supply designer fears.

One, an input over voltage. If this happens the inductor saturates, then its reduced to nothing more than it’s DC resistance. And the output diode, being an uncontrolled switch, forward biases and drops only a few hundred millivolts.

Two, an output short circuit. Again, the inductor would quickly saturate, the diode drops maybe half a volt, insulators are fused at the input. The source pumps current until something melts. It’s usually the poor diode that melts. Despite these drawbacks, Boost are still very popular at applications like LED driving, battery charging, and actually an AC to DC use as well.

During the first portion of the switching cycle, with the controlled MOSFET on, the inductor voltage equaled to V in. During the second portion, the voltage equaled to V in minus V out. Remember that Boosts can only increase V out, so the voltage during the second portion of the switching cycle is always negative with respect to the assigned polarity.

Boost Converter Duty Cycle

Here are the results of more math that I skipped. But there are plenty of resources that describe how to arrive at these equations if you would like. In this first expression, we can see two important things. One, even for a duty cycle of zero, V out is equal to at least V in. In practice, V in minus a diode drop.

Two, in theory V out can go to infinity. Sounds great, right? Hopefully though, you’re not too surprised or disappointed to hear that in practice, this isn’t possible. I would say that step up ratios of one to 10 are about the practical limit. That means that if V in is five volts don’t expect to get much more than about 50 volts out.

Inverting Buck-boost in Practice

Alright, you’ve seen the Buck. You’ve seen the Boost. Now we’ll talk about the topology that my professor at university always seemed to love the best. He always called it the Buck-booost. one thing that isn’t immediately obviously, but is quite important, is that the Buck-Boost never connects the input directly to the output.

I say directly, and what I really mean to say is through the inductor. But there is an important difference. The buck and the boost are always more efficient at the same power level than the Buck-boost. Because the Buck-boost has to stuff all the energy needed for each cycle into the magnetic field of the inductor in the first part of the cycle. Then it has to pull that energy back out during the second part of the cycle. That means higher currents. Higher voltage drops. And more losses.

Inverting Buckboost Converter Duty Cycle

The first important thing to note on this slide is that whenever you see V out, that’s an absolute value. The math won’t come out right if you treat V out as a negative voltage. As with the boost converter this converter can output infinity volts in theory. But in practice it’s even more limited than the boost. My recommendation is not to exceed a step up ratio of more than about one to seven.

The next thing I want to draw attention to is the ideal duty cycle equation. We’re going to see this equation time and time again. Since nearly all the compound topologies are also Buck-boost. And all of them have the same ideal duty expression. As a final note. Even though the inverting Buck-boost is less efficient than the Buck or the Boost, it is the most efficient of the Buck-boost topologies, because it has the lowest number of elements in the power path.

The Negative-to-Positive Buck-boost

Remember that negative Buck? Well the alter ego of the inverting Buck-boost is the circuit shown here. If used with the negative input voltage it generates a positive output voltage with respect to ground. Now in 15 years of power supply design I’ve only done that twice. It was used on a very high power LED driver, that used the negative Buck topology but also needed a positive voltage for interfacing to the PWM dimming control circuits. And I also did one designed for a customer in Vermont.

This circuit is quite popular as an LED driver also. Especially when connected to a positive input voltage. In that case, all the same benefits of having a low side NMOSFET come into play. And the LED current returns back to the positive node of the input. All you have to do is sense current and voltage differentially to make it work.

By the way, the reason the Buck-boost converters are so popular for LED driving, is that when both the input voltage and the output voltage change, and that’s true in most LED circuits, and especially over wide ranges, the chances that they overlap become quite high.

Four-Switch Buck-boost and SEPIC

Next up are some of the compound topologies formed by putting two of the basic DC to DC topologies in series, or cascading them. The main goal is to achieve Buck-boost operation without averting the polarity. And also, to have an output voltage reference to the same ground as the input voltage.

The naming of this converter is pretty obviously. And it has the distinction of being the most efficient of the ground referenced, non inverting Buck-boost’s. When you combine the back half of a Buck and the front half of a Boost, you can eliminate the capacitor in the middle and combine the two inductors into one device.

Now me, I love inductors. But I know that they’re a hated and feared component in many cases. I know plenty of engineers, not to mention Purchasing Managers, who stick to the philosophy “The fewer inductors, the better.”

The Four-Switch Buck-boost in Practice

The duty cycle control boxes represented by the D, turn on the two MOSFET simultaneously during the first part of the switching cycle. And then the FEETS turn off and the two diodes carry the current.

Notice that the voltage is applied across the inductor are exactly the same as with the inverting Buck-boost. Or the negative to positive Buck-boost for that matter. In fact for most of the Buck-boost circuits that we’re going to see. Like the two Buck-boost’s that we have seen so far, this converter never connects the input voltage to the output voltage directly. Now that’s bad for efficiency, but actually good for problems like input over voltage. Or output short circuit.

Remember that those events usually destroy a Boost converter and or it’s load. But the force which Buck-boost can at least protect the load.

4-Switch Buck-Boost Converter Duty Cycle

It’s the practical analysis that sheds some light on the lower efficiency of a four switch Buck-boost converter compared to an inverting Buck-boost. That factor of two is the key.

Of course, the force which Buck-boost generates a positive output with respect to ground, and that’s key to many applications. One way to boost the efficiency of this type of converter is with smart control. A good control IC will operate as a Buck, only when V in is greater than V out. Operate as a Boost, only when V in is less than V out. And only drive both MOSFET’s, or actually both MOSFET’s and both diodes, or in some cases, four MOSFET. When V in and V out are more or less equal.

A second way to boost the efficiency of this converter in fact, just about any switching converter, is to replace the diode or diodes with MOSFET’s. This is called synchronous operation. We’ll dive into detail in the sessions that come examining each topology in detail.

To Make a SEPIC…

Here we have one of my favorite topologies of all, the SEPIC. Now SEPIC stands for “Single-Ended Primary-Inductor Converter” now you’ll hear that acronym listed again and it won’t matter. In any case take the front half of a Boost regulator and the back half of an inverting Buck-boost regulator, saw them in half, and this time, since we don’t have an inductor in the middle, we’ll use a capacitor to couple them together. You’ll often hear this capacitor referred to as a coupling cap or a SEPIC cap.

Now while we’re at it, well flip the output diode around to get a positive output voltage. This converter has a fancy name, but in reality, it’s just another non inverting ground referenced, positive output Buckboost.

I remember the SEPIC converter as a homework example from that Introduction to Power Electronics class that made such a big impression on me. After analyzing the Buck and the Boost, and yes, the inverting Buck-boost too, I figured this one would be easy. But that SEPIC capacitor stumped me.

Now the voltages across the input cap and the output cap are pretty obvious, but it took me a while, and actually some help from a friend, to figure out that the average voltage across the SEPIC capacitor is equal to V in. That’s what the funny little hat sitting over the V is. A symbol implying average value.

Another helpful hint is that for all of these converters with two inductors, or two windings, the voltage across those two windings must be equal for proper operation. So the SEPIC looks complicated and intimidating, but actually the voltages across those two inductors are exactly the same as the voltage across the single inductor, and the other Buck-boost’s.

SEPIC Duty Cycle

I’m probably starting to sound like a broken record player here, but once again, note that the duty cycle equation for the SEPIC is the same as it is for all the other Buck-boost topologies when it’s ideal.

To be more specific, all of the Buckboost topologies that use simple inductors or one to one coupled inductors, have the same ideal transfer function. The SEPIC suffers from somewhat lower efficiency because of the higher currents in the two switches equal to the input plus the output current when the switch is on. And also the fact that the current has to pass through the DCR of the two windings of the inductor. Or the DCR of the two inductors.

Flyback Regulators

If any switching regulator could dethrone the Buck as the most common switcher, it would be the Flyback. This is by far the most common topology for AC to DC regulators or off line regulators. So called because they connect off the line. Remember when those [wall warts 00:14:12] were actually heavy? That was because they had 50 or 60 Hertz transformers inside, and then a linear regulator.

Now think about the charger for your cellphone. And the charger for your tablet. And the power supply for your internet router. And your cable box. And your PlayStation. You own a lot of flyback regulators. You just didn’t know it.

A flyback is a Buck-boost from the perspective that it can increase or decrease the output voltage with respect to the input voltage. But a Flyback does a lot more than that. It can also invert the polarity if you want, and most importantly the Flyback can provide galvanic isolation from the input to the output.

One important thing about Flyback converters, the magnetic component is also called a transformer. But that device does more than just transform the levels of voltage and current. It also stores energy. In the strictest sense, it’s really a coupled inductor. For more detail, and I mean lots more detail, there’s a session dedicated to the Flyback converter later in this seminar.

The Flyback in CCM, in Practice

Here on this slide I’ve simplified some things. I only showed the voltage across the winding that’s carrying the current and there is of course a voltage across the primary when the secondary conducts. A big voltage in fact. And there’s a voltage across the secondary winding when the primary conducts.

But really the only difference between this circuit and the other Buck-boost we’ve seen, is that the turns ratio lets us do all kinds of interesting things to the device. For example, an output of thousands of volts from an input of only 12 volts. Your spark plugs, if you drive a gasoline powered car, do that thousands of times per minute.

Flyback currents in CMM

I couldn’t resist the urge to show some actual wave forms here. Even though I haven’t done so so far for the other topologies. Because I want to make it clear that continuous conduction mode, CCM, is really about the continuity of the magnetic field. As soon as the primary current in pink begins to fall, the secondary current in green begins to rise.

If we had an oscilloscope probe, for magnetic fields, we would see two things. One, even though the currents change abruptly, the magnetic field cannot change abruptly. And two, the magnetic field never falls to zero. If it did, this would be a Discontinuous Conduction Mode Converter, or DCM. As a final note, look at these trapezoid waves. They’re very common in switching converters and they’ll be very important later for analysis of RMS voltages, and RMS currents.

Flyback Duty Cycle in CCM

After some math, and taking into account the voltage across either the primary, during both parts of the switching cycle. Or the voltage across the secondary during both parts. You get the equations on the top of the screen. See my notes about the voltage stresses on the primary MOSFET and across the secondary diode? Those are the voltages that make Flyback’s less efficient than Buck-boosts. But of course, the Flyback can isolate and it can perform voltage ratios that other Buck-boosts can’t.

Flyback Currents in DCM

See how the current waveform here in DCM are triangles instead of trapezoids? That’s a clear indicator of a circuit in DCM. Also check out the LC residence during T3. That’s the primary induction resonating with the parasitic capacitance of everything else. But mostly the primary MOSFET. You might be wondering why the resonance is barely noticeable in the secondary. That’s because the secondary has a lot less turns and a lot less inductions.

Flyback Duty Cycle in DCM

The reason I haven’t discussed DCM much at all up until the Flyback, is that Flyback’s up to about 10 watts of max output power often run in DCM on purpose. Not too many Bucks do that. The interesting thing about DCM is that the low current influences the duty cycle. That square root in the denominator is energy.

DCM converters transfer all the energy they had stored in their magnetic elements to the output during each cycle. And that’s a big different between DCM and CCM. Remember that if there’s current in the magnetics, there’s a magnetic field. With energy in it.

Packaging and Integration

This last part of section one-two is as close as I’m going to get to marketing. If I had a nickel, or more appropriately, a five Euro cent piece for every time I heard a semiconductor CEO or Distributor CEO say something about increasing integration or power density I’d already have my mansion in Majorca. But I’m still designing power supplies for fun. Take note you application engineers, marketing is like the dark side of the force, once you start down that path, there’s no return.


This nomenclator isn’t universal, but it is quite common. Controllers are still my favorite way to design component level power supplies, because you have control over the layout of each part of the power path. As well as control of the gates or bases of the power switches. They are however the most challenging to design because of all that freedom.

“Regulators” Have Internal Power FETs

Moving one or both power switches inside, together with the control slogan is great for lower power, lower voltage applications. Though I have to say that internal power switches for so called regulators are available for higher and higher voltages and higher and higher occurrence every day.

“Modules” Have Internal Power Inductors

The module is the latest darling of many a marketing department. And they’re perfect for the highest density applications. They’re also great for engineers who don’t have the desire or the time to design with regulators or controllers. Curiously enough, at least to me, is how little the marketing departments talk about the excellent radiated EMI characteristics of a module. This will become more obvious when we talk about PCB layout later on in this seminar.

The Ham Converter

This converter was invented by me. And it’s a tribute to two of my favorite things in life, power supplies and cured Spanish ham. You can see that the acorn, which draws from earth naturally, provides the flavor for Jamon lberico de Bellota, the finest of Spanish hams. The amount of acorns that the pigs eat is controlled by the pig rancher, who goes around knocking the acorns off of the Hammock trees. The delicate earth tones are stored in the Iberian Black footed Hog. And then my friend Carlos turns the pig into meat. The final product is a plate of finely shaved ham. Few things in life are better.

Link zu next section: 2-1 Buck Converters

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



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