Welcome

A transformer turns one AC voltage into another almost for free - no meaningful loss, just iron and copper. So here is a fair question: why can't we do the same for DC?

The honest answer is that there is no such thing as a DC transformer. You cannot put 100 V DC in and get 50 V DC out by winding wire around a core, because a transformer only responds to changing current. A steady DC current produces no changing magnetic field, so nothing is induced on the other side.

The buck converter is the workaround. It is the most common circuit in all of electronics for turning a higher DC voltage into a lower one efficiently - and "efficiently" is the whole point. You could always drop voltage with a resistor, but a resistor turns the difference into heat. A buck converter does the same job at 95 % to 98 % efficiency, wasting almost nothing.

A place you'll meet it: solar charge control

Here is a use case worth keeping in mind the whole way through. A solar panel does not produce a fixed, convenient voltage - it produces a higher voltage that wanders with sunlight and temperature, while the battery you want to charge sits at a lower, fairly fixed voltage. Something has to bridge that gap: take the panel's variable, higher voltage and step it down to exactly what the battery needs, while wasting as little of your hard-won sunlight as possible.

That something is a buck converter. It is the heart of a solar MPPT charge controller - the box between the panels and the battery in almost every off-grid or hybrid solar system.

One thing up front, so nobody feels they are missing background: solar and MPPT are not topics of this course. We only borrow the solar charge controller as a concrete picture to hang the numbers on. If the words "solar" or "MPPT" mean nothing to you, that is completely fine - read them as "the thing the buck is plugged into" and you will lose nothing. Everything you actually need is about the buck itself.

The buck's job in one picture: take the panel's higher, variable DC and step it down to the lower, controlled voltage the battery wants. The buck converter lives inside the MPPT charge controller.

We will use one realistic charge-controller operating point as the running example throughout the book - roughly a 1 kW unit charging a 48 V battery bank from a solar string. You do not need to know anything about solar to follow along; it is just a concrete place for the numbers to live.

Who this is for

This guide is for anyone who wants to understand how a buck converter works and how you control it. You need a little comfort with basic maths and some basic electronics - what voltage and current are, and roughly what a resistor, capacitor, and inductor do. That is it. Whether you come from power systems, embedded software, hardware design, or you are simply curious, you have what you need. Every time a formula appears, it is followed by a plain sentence telling you what it means.

How this course is organised

• Chapters 1-2 - How it works. Why we step DC down, the switch-and-store idea, and how the inductor and capacitor behave.
• Chapter 3 - Designing the filter. How to choose the inductor and capacitor from the ripple you will accept.
• Chapter 4 - Where the energy goes. Why a real buck is not perfect, and the shape of its efficiency curve.
• Chapters 5-8 - How you control it. Why the circuit needs feedback, how PWM turns a duty cycle into switching, a voltage controller (PI with feed-forward), and the cascade of voltage and current loops that real converters use. You write each one as a few lines of C in the simulator.

A few recurring boxes will help you navigate:

The converter we'll come back to

Throughout this book we use one specific buck converter, shown in Figure 1, drawn as a half-bridge: two switches, $Q_1$ on top and $Q_2$ on the bottom, stacked between the input and ground, with the inductor and capacitor forming the output filter.

If you have seen a buck converter before, you have probably seen it drawn a little differently: with a single switch on top and a diode on the bottom. That diode version is the more common textbook picture, and the two work almost exactly the same way. We use the two-switch (half-bridge) drawing here because it makes the core idea easier to see - both switches are the same kind of device, and it is obvious how the switch node is pulled up or down. We will meet the diode version properly in Chapter 4.

Figure 1 The half-bridge (synchronous) buck converter used throughout this guide.

The numbers we will use everywhere are collected below - a realistic operating point for a ~1 kW solar charge controller. Don't try to absorb them now; just know that whenever a worked example appears, these are the values behind it.

Why step down DC?

The job, in one sentence

A buck converter takes a DC voltage in and produces a lower DC voltage out, while wasting as little energy as possible. In our running example it takes the roughly 100 V from a solar string and delivers the 50 V a 48 V battery wants while charging. Wherever a circuit needs a lower DC voltage than the supply provides, there is almost certainly a buck converter doing the conversion.

Why not just use a resistor?

If all you want is a lower voltage, the simplest idea is to put a resistor in series with the load and let it soak up the extra voltage (Figure 2). It works, and for tiny signal-level jobs it is fine. But it is hopeless for power, and it is worth seeing exactly why, because the reason is what motivates the whole buck converter.

Figure 2 Dropping voltage with a series resistor. Whatever voltage you remove, $V_{drop}$, is burned as heat in $R_{drop}$.

Take our solar numbers: 100 V in, and we want 50 V at the 20 A the battery is drawing. To drop the voltage with a series resistor, that resistor must carry the full 20 A while 50 V appears across it. The power it burns is

The battery receives 50 V × 20 A = 1000 W. So you would throw away a full kilowatt as heat to deliver a kilowatt - half of your hard-won solar power, gone, and the resistor glowing. And the deeper you step down, the worse it gets.

The trick: chop, don't drop

Look at the point labelled $v_m$ in Figure 3 (our converter again, repeated here so you don't have to flip back) - the node sitting between the two switches. This node is the whole secret of the buck converter, so let us watch what happens to its voltage as the switches operate.

Figure 3 The same half-bridge buck. The switch node $v_m$ is driven by the gate signals $S$ (top switch) and $\overline{S}$ (bottom switch).

The two switches always do the opposite of each other: when one is closed, the other is open. (They must never be closed at the same time - that would connect $V_{in}$ straight to ground through both switches, a dead short.) So at any instant there are only two possible states. Let us call the state of the top switch $S$: $S = 1$ when $Q_1$ is closed, and $S = 0$ when $Q_1$ is open.

State $S = 1$ - top switch closed. A closed (ideal) switch is just a piece of wire. So $Q_1$ becomes a wire connecting $V_{in}$ directly to $v_m$. A wire between two points forces them to the same voltage:

State $S = 0$ - top switch open, bottom switch closed. Now $Q_1$ is an open gap and $Q_2$ is the wire. $Q_2$ connects $v_m$ directly to ground, so

So the switch node is never held at some in-between voltage - it is yanked all the way up to $V_{in}$ or all the way down to 0, depending only on which switch is closed. We can write both cases in one line. Since $v_m = V_{in}$ when $S = 1$ and $v_m = 0$ when $S = 0$,

It helps to see each state as its own circuit (below). In each one, the conducting path is drawn solid and carries the green current arrows; whatever is not part of the active circuit is greyed out and crossed off. When the top switch is closed (left), it acts as a plain wire pulling $v_m$ up to $V_{in}$, while the bottom switch is open and out of the picture. When the top switch is open (right), the input is disconnected entirely (so $V_{in}$ itself is crossed off - it no longer has a complete path), and the current instead free-wheels up through the bottom switch, which holds $v_m$ at 0.

The two switch states. Left ($S=1$): the top switch is a closed wire, $v_m = V_{in}$. Right ($S=0$): the top switch and the input are disconnected, and the current free-wheels through the bottom switch, $v_m = 0$.

Figure 4 shows this happening. The top trace is the gate signal $S$ that drives the top switch - on, off, on, off. The bottom trace is the switch node $v_m$ it produces: every time the gate goes on, $v_m$ leaps up to $V_{in}$; every time it goes off, $v_m$ falls to 0. The switch node is just the gate signal scaled up to $V_{in}$ - exactly what $v_m = S\,V_{in}$ says.

Figure 4 The gate signal $S$ (top) and the switch node $v_m$ it produces (bottom), at $D = 0.5$. The dashed line marks the average of $v_m$, which is the output voltage. Open in simulator ↗

The beautiful part is that this chopping wastes almost no energy. A closed ideal switch has no voltage across it (it is a wire), and an open switch carries no current - and power is voltage times current, so either way the switch itself burns essentially nothing. Unlike the resistor, which had to sit there dissipating $V_{drop} \times I$ the whole time, the switches pay almost no toll. That is the heart of it: a buck converter trades a lossy voltage drop for a lossless voltage chop.

From a square wave to a steady output

A square wave jumping between 0 and $V_{in}$ is not what the battery wants - it wants a calm, steady $V_{out}$. That is the job of the inductor $L$ and the capacitor $C$. Together they form a low-pass filter: they iron out the fast switching ripple and pass through only the slow average of whatever they are fed. (Chapters 2 and 3 open this up in detail.)

Because the filter passes the average, the output voltage is simply the average value of the switch-node square wave:

The "average of $S$" is just the fraction of each cycle that the top switch is closed - and that fraction has a name: the duty cycle, $D$. Putting it together gives the single most important equation in this whole book:

Figure 5 shows why $D$ is the control knob. In each panel the blue trace is $v_m$ and the dashed line is its average - the voltage the battery actually feels. Keep the top switch on for only a quarter of the time ($D = 0.25$) and the average sits low; keep it on for three-quarters ($D = 0.75$) and the average rides high. Sliding $D$ between 0 and 1 slides $V_{out}$ anywhere between 0 and $V_{in}$ - exactly the lever a controller (or the MPPT brain) pulls to set the charging voltage.

Figure 5 The same switch node at two different duty cycles. More on-time means a higher average, so a higher output: $V_{out} = D\,V_{in}$. Open in simulator ↗

The averaged model: a voltage source of $D\,V_{in}$

This last point is worth turning into a picture, because it makes a lot of what follows much easier. We have just seen that, on average, the chopped switch node behaves like a steady voltage of $D\,V_{in}$. So whenever we care about the slow behaviour - how the output settles, how it reacts to a load step, how the controller behaves - we can simply forget the chopping and replace the whole switching stage with a single voltage source equal to $D\,V_{in}$. The buck then collapses into the simple circuit below: a DC source of $D\,V_{in}$ feeding the inductor and capacitor.

The averaged model. For anything slower than the switching, the chopping half-bridge is just a voltage source of value $D\,V_{in}$ driving the L-C filter.

This is called the averaged model, and it is the mental picture behind the rest of the book. It also shows, at a glance, why $D$ is such a clean control knob: turning $D$ turns the source voltage $D\,V_{in}$ directly, and the output follows. We will use this picture whenever we stop caring about the individual switching cycles and start caring about the converter as a whole.

The bottom switch we have drawn as a transistor $Q_2$, but it is often a plain diode instead (Figure 6). The diode is less clever, but it happens to conduct automatically at exactly the moments $Q_2$ would have been closed - so it produces the same $v_m = 0$ state on its own, with no control signal. That cheaper, more famous version is the asynchronous (or diode) buck; our two-switch version is the synchronous buck. We compare them properly in Chapter 4.

Figure 6 The asynchronous (diode) buck: the bottom switch is replaced by a freewheeling diode $D$. It conducts on its own when the top switch opens, recreating the $v_m=0$ state with no gate signal.