Buck Converter Working Principle and Design Equations

The circuit

Download diagram (WebP)

A buck converter has four power components:

• Switch S, usually a MOSFET, turned on and off by a pulse width modulation (PWM) controller.
• Diode D (or a second MOSFET in a synchronous converter), which carries the inductor current when the switch is off.
• Inductor L, which stores energy and smooths the current.
• Output capacitor C, which smooths the output voltage.

How a buck converter works

1. Switch on (time D × T). The input is connected to the inductor. The voltage across the inductor is Vin − Vout, so its current rises linearly. The inductor stores energy, and current flows to the capacitor and load.
2. Switch off (time (1 − D) × T). The inductor keeps its current flowing, so the switch node falls until the diode conducts. The inductor now has −Vout across it, and its current falls linearly as it releases stored energy to the load.

In steady state the inductor current must return to the same value at the end of each period. Its average voltage over a period must therefore be zero, which is called volt-second balance:

$$(V_{in} - V_{out})\,D\,T = V_{out}\,(1 - D)\,T \quad\Rightarrow\quad V_{out} = D\,V_{in}$$

This ideal result ignores losses. In a real converter the controller adjusts D slightly upwards to make up for voltage drops in the switch, diode and inductor.

Design equations

Inductor ripple current. During the on time, the inductor current rises by:

$$\Delta I_L = \frac{(V_{in} - V_{out})\,D}{L\,f_{sw}} = \frac{V_{out}\,(1 - D)}{L\,f_{sw}}$$

where fsw is the switching frequency. A common starting point is to choose L so that ΔIL is about 20 to 40 percent of the maximum output current.

Peak inductor and switch current. IL(peak) = Iout + ΔIL / 2. The inductor’s saturation current rating must exceed this value with margin.

Output voltage ripple. If the capacitor’s resistance is negligible, the ripple voltage is approximately:

$$\Delta V_{out} \approx \frac{\Delta I_L}{8\,f_{sw}\,C}$$

The capacitor’s equivalent series resistance (ESR) adds a further ripple of about ΔIL × ESR, which often dominates with electrolytic capacitors. Ceramic capacitors have very low ESR.

Losses and efficiency

The main losses in a buck converter are:

• Conduction loss in the MOSFET: I² × RDS(on) during the on time.
• Switching loss: energy lost in each transition, which rises with switching frequency and input voltage.
• Diode loss: forward voltage × current during the off time. At low output voltages this is large, which is why synchronous rectification is used.
• Inductor loss: resistance of the winding (DCR) and core loss.
• Capacitor loss: ripple current flowing through ESR.

Higher switching frequency allows smaller inductors and capacitors but increases switching loss, so the frequency is a trade-off between size and efficiency.

Choosing the components

• Controller or converter IC: many designs use an integrated buck regulator that contains the MOSFETs, control loop and protection. Choose one whose input voltage range, output current and switching frequency suit the application.
• MOSFET: if discrete, select drain-source voltage rating with margin above the maximum input voltage, low RDS(on) for conduction loss, and low gate charge for switching loss.
• Diode: a Schottky diode with a reverse rating above Vin and a current rating above the output current, or a synchronous MOSFET instead.
• Inductor: inductance from the ripple calculation, saturation current above the peak current with margin, RMS current rating above the output current, and low DC resistance.
• Input capacitor: must handle a large RMS ripple current, which is close to half the output current when D is about 0.5. Low-ESR ceramic capacitors placed close to the switch are the usual choice.
• Output capacitor: sized for ripple and for load transient response, with its effective capacitance checked at the operating voltage.

Layout tips

The switching current in the input loop, made of the input capacitor, the switch and the diode or low-side MOSFET, changes very quickly. Keep this loop as small as possible, place the input capacitor right at the switch, and use a solid ground plane. Keep the feedback trace short and away from the switch node, which carries a fast square wave that can couple noise into sensitive circuits.

Continuous and discontinuous conduction

In continuous conduction mode (CCM), the inductor current never reaches zero, and Vout = D × Vin. When the load current falls below half the ripple current, the inductor current drops to zero before the end of each cycle. This discontinuous conduction mode (DCM) changes the voltage relationship, and the controller must adjust D further to hold the output.

Protection features

Practical buck regulators include protection that the basic circuit lacks: cycle-by-cycle current limiting to protect the switch and inductor, soft start to limit inrush current into the output capacitor, undervoltage lockout so the converter does not run from too low an input, and thermal shutdown.

Applications

• Point-of-load supplies that step 12 V or 5 V down to the core voltages of processors and FPGAs.
• Battery-powered devices, where efficiency directly extends run time.
• Automotive electronics, converting the vehicle battery voltage to 5 V and 3.3 V rails.
• LED drivers, where the converter regulates current instead of voltage.

Related reading

• PCB Design Basics: Layers, Traces and Design Rules
• Logic Gates: Types and Truth Tables Explained