DC-DC Converters

Your phone battery puts out 3.7 V, but the processor inside needs 1.2 V and the screen backlight needs 12 V. A USB port gives you 5 V, but your Raspberry Pi wants 3.3 V. How do you get one DC voltage from a different DC voltage — efficiently?

That is exactly what a DC-DC converter does. It uses a fast electronic switch (a MOSFET) that flicks on and off thousands of times per second, plus a few passive components to smooth the result.

First — What is Duty Cycle?

Every DC-DC converter relies on a switch that turns on and off repeatedly. The duty cycle (D) is simply the fraction of time the switch stays on:

D = \frac{\text{ON time}}{\text{total period}} \quad (\text{ranges from 0 to 1})

Figure 1. PWM signal with D = 60% — the switch is ON for 60% of each cycle

$D = 1.0$ → switch is always on (100% of the time)
$D = 0.5$ → switch is on half the time
$D = 0$ → switch is always off

By adjusting D, we control how much energy reaches the output — and therefore the output voltage.

1. The Buck Converter (Step-Down)

The buck converter produces an output voltage lower than its input. Think of it like a water valve that opens and closes rapidly — the average flow is less than the full supply.

Why does it need an inductor?

In an AC rectifier, the input is already a smooth sine wave — diodes select half-cycles and a capacitor fills the gaps. Here, the MOSFET chops steady DC into a harsh square wave (full voltage, then zero, thousands of times per second). Connecting that directly to a capacitor and load would cause massive current spikes and a noisy output.

The inductor acts like a flywheel — it resists sudden current changes, slowly ramping up when the switch is on and slowly ramping down when it's off. Together with the capacitor, it forms an LC low-pass filter that blocks the high-frequency switching and passes only smooth, steady DC to the load.

How it works — step by step

Switch ON: The MOSFET connects $V_{in}$ to the inductor. Current flows through the inductor, charging it like a spring, and powers the load.

Switch OFF: The MOSFET disconnects. The inductor doesn't like sudden current changes — it keeps pushing current through the freewheeling diode $D_1$ , slowly releasing its stored energy.

The Schottky diode (D₁) is essential — without it, the inductor's current has nowhere to go when the switch opens, creating a destructive voltage spike. A Schottky type is chosen over a regular diode because its lower voltage drop (~0.3 V vs ~0.7 V) wastes less power, and its fast switching keeps up with 100+ kHz operation.

The capacitor smooths out the ripple, giving the load a nearly steady DC voltage.

Figure 2. Buck converter — MOSFET switch, freewheeling diode, LC filter, and load

The key formula

V_{out} = D \times V_{in}

The output is simply the duty cycle times the input. Since D is always between 0 and 1, the output is always ≤ the input.

Worked example — 12 V battery → 5 V for a microcontroller

Given: $V_{in} = 12\,\text{V}$ , we need $V_{out} = 5\,\text{V}$ .

D = \frac{V_{out}}{V_{in}} = \frac{5}{12} = 0.417 \quad (41.7\%)

The controller keeps the switch on for 41.7% of each cycle. If the switching frequency is 100 kHz (period = 10 µs), the switch is on for 4.17 µs and off for 5.83 µs.

\Delta I_L = \frac{(V_{in} - V_{out}) \cdot D}{f_{sw} \cdot L}

The inductor current ripple $\Delta I_L$ depends on switching frequency and inductance — higher frequency or larger inductor means smoother current.

2. The Boost Converter (Step-Up)

The boost converter produces an output voltage higher than its input. It's like pumping up a bicycle tire — the inductor stores energy in short bursts, then releases it at a higher pressure (voltage).

How it works — step by step

Switch ON: The MOSFET shorts the inductor's right end to ground. Current builds up in the inductor, storing energy in its magnetic field. The load is temporarily powered by the capacitor alone.

Switch OFF: The MOSFET opens. The inductor's stored energy has to go somewhere — it adds its voltage on top of $V_{in}$ , pushing current through the diode into the capacitor and load at a higher voltage.

Figure 3. Boost converter — inductor first, MOSFET to ground, diode to output

The key formula

V_{out} = \frac{V_{in}}{1 - D}

Worked example — 3.7 V lithium cell → 12 V for an LED strip

Given: $V_{in} = 3.7\,\text{V}$ , we need $V_{out} = 12\,\text{V}$ .

D = 1 - \frac{V_{in}}{V_{out}} = 1 - \frac{3.7}{12} = 0.692 \quad (69.2\%)

The switch stays on ~69% of each cycle, giving the inductor plenty of time to store energy before releasing it at a higher voltage.

As $D \to 1$ , the formula says $V_{out} \to \infty$ . In practice, component losses limit the boost ratio to about 4–5× before efficiency drops too low.

3. The Buck-Boost Converter

The buck-boost can step up or step down — but with a catch: it inverts the output polarity. If the input is +12 V, the output is negative (e.g., −5 V or −15 V).

How it works — step by step

Switch ON: The MOSFET connects $V_{in}$ across the inductor, charging it. The diode is reverse-biased, so the load is powered only by the capacitor.

Switch OFF: The inductor's collapsing field drives current through the diode into the capacitor — but in the opposite direction, creating an inverted output voltage.

Figure 4. Buck-boost converter — inverted output polarity

The key formula

|V_{out}| = \frac{V_{in} \cdot D}{1 - D}

Worked example — duty cycle controls buck vs boost

With $V_{in} = 12\,\text{V}$ :

$D = 0.3$ : $|V_{out}| = \frac{12 \times 0.3}{0.7} = 5.14\,\text{V}$ → bucks (steps down)
$D = 0.5$ : $|V_{out}| = \frac{12 \times 0.5}{0.5} = 12\,\text{V}$ → unity (same magnitude)
$D = 0.7$ : $|V_{out}| = \frac{12 \times 0.7}{0.3} = 28\,\text{V}$ → boosts (steps up)

All outputs are negative polarity.

Inductor Current in CCM

In all three converters, the inductor current ramps up when energy is being stored and ramps down when energy is being released. As long as the current never drops to zero, the converter is in continuous conduction mode (CCM).

Figure 5. Triangular inductor current waveform — continuous conduction mode

The green triangle shows current rising (switch ON) and falling (switch OFF)
The dashed blue line is the average current — this is what the load "sees"
$\Delta I_L$ is the ripple — smaller ripple means smoother output

Topology	Output range	Polarity	Typical use
Buck	0 to V_in	Same	5 V rail from 12 V battery
Boost	V_in to ∞ (ideal)	Same	LED driver from 3.7 V cell
Buck-Boost	0 to ∞ (ideal)	Inverted	Negative rail for op-amps