How do I calculate the duty cycle of a buck converter?

For an ideal buck converter the duty cycle is simply the output voltage divided by the input voltage. Stepping 12 V down to 5 V needs a duty cycle of 5 divided by 12, about 0.417 or 41.7 percent. Real converters run a slightly higher duty to make up for switch and inductor losses, but the ideal ratio is the right starting point.

How do I size the inductor for a buck converter?

Pick the inductor from the ripple current you want. The inductor ripple current equals the output voltage times the input minus output voltage, divided by the input voltage times the switching frequency times the inductance. Designers usually target a ripple of 20 to 40 percent of the maximum load current, then choose the nearest standard inductor value.

What sets the output voltage ripple?

For a buck converter the output ripple voltage is the inductor ripple current divided by eight times the switching frequency times the output capacitance, ignoring capacitor resistance. A larger output capacitor or a higher switching frequency lowers the ripple. In real designs the capacitor's equivalent series resistance often dominates the ripple.

Buck Converter Calculator

This buck converter calculator works out the key operating figures for a step-down switching regulator: the duty cycle, the ripple current swinging through the inductor, the ripple voltage left on the output, and the switch on-time per cycle. Enter the input voltage, the target output voltage, the switching frequency, the inductor value and the output capacitor value, and the calculator returns all four so you can check a design before you build it. A buck converter chops the input with a switch, then an inductor and capacitor smooth the result down to a steady lower voltage, with the duty cycle, the fraction of each cycle the switch is on, setting the ratio. For an ideal converter that duty cycle is just the output divided by the input. The inductor ripple current follows from the volt seconds applied to the inductor each cycle, and the output ripple voltage from how much of that ripple the capacitor absorbs. The defaults step 12 V down to 5 V at 100 kHz through a 47 microhenry inductor and a 100 microfarad output capacitor, a common small point of load design. Designers usually aim for an inductor ripple of roughly 20 to 40 percent of the full load current, so use the ripple figure to check your inductor choice, and raise the capacitance or frequency if the output ripple is too high for your load.

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Input voltage (Vin)

Output voltage (Vout)

Switching frequency

kHz

Inductor

µH

Output capacitor

µF

Ideal continuous-conduction model. Real ripple is usually higher because of capacitor resistance and switch losses.

41.67%

duty cycle (switch on fraction)

Inductor ripple current620.6 mA

Output ripple voltage7.76 mV

Switch on-time4.17 µs

Ideal buck equations assuming continuous conduction and no losses. Capacitor equivalent series resistance, diode or switch drops and layout will raise the real ripple. Estimate only.

How it works

The duty cycle is the output voltage divided by the input voltage. The switch on-time is that duty cycle divided by the switching frequency. During the on-time the inductor sees the input minus output voltage, and during the off-time it sees the output voltage, so the inductor ripple current is the output voltage times the input minus output, divided by the input times the frequency times the inductance. The output capacitor soaks up the triangular ripple current, and the resulting output voltage ripple is the inductor ripple current divided by eight times the frequency times the capacitance.

Worked example

Stepping 12 V down to 5 V at 100 kHz through a 47 microhenry inductor and a 100 microfarad capacitor, the duty cycle is 5 divided by 12, which is 41.67 percent. The switch on-time is 0.4167 divided by 100000, about 4.17 microseconds. The inductor ripple current is 5 times 7, divided by (12 times 100000 times 0.000047), about 620.6 milliamps. The output ripple voltage is 0.6206 divided by (8 times 100000 times 0.0001), about 7.76 millivolts.

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Capacitor Energy Calculator: output capacitor energy.
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LED Resistor Calculator: current-limiting resistors.

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