Buck Converter - Duty Cycle and Inductor Sizing

A buck converter calculator solves the steady-state design equations for a step-down DC-DC switching converter. A buck converter takes a higher DC input voltage and produces a lower DC output voltage by storing energy in an inductor while the switch is closed and releasing that energy into the output capacitor and load while the switch is open. This calculator works in continuous conduction mode (CCM) and returns the duty cycle, output voltage, average currents, inductor value, and output capacitor from your input voltage, target output, switching frequency, and load.

• • Step a 12 V rail down to 5 V logic: The buck converter calculator picks L and C values to convert a 12 V bus into a regulated 5 V rail for microcontrollers and USB peripherals.
• • Verify a switching regulator design: Use the buck converter calculator to confirm the duty cycle and ripple targets a textbook problem needs before picking a controller IC and inductor.
• • Teach continuous conduction mode: Walk students through Vout = Vin * D and the ripple budgets used in power-electronics courses.
• • Compare buck and boost topologies: Estimate the inductor current and ripple when stepping a supply down to a lower rail for an LED string with the calculator.

A buck converter is one of three basic PWM DC-DC switching topologies along with the boost (step-up) and buck-boost converters. Because the output is always below the input, the inductor current equals the load current on average. The calculator treats the converter as lossless, with switch on-resistance, diode forward drop, and inductor DCR neglected.

When the load instead requires a higher rail than the supply, Boost Converter handles the step-up side of the same DC-DC design family.

The calculator applies volt-second balance to the buck inductor and charge balance to the output capacitor, both over one switching period.

• Vin: DC supply voltage feeding the buck converter input.
• Vout: Average DC output voltage at the load.
• D: Switch duty cycle, the fraction of each switching period that the transistor is on.
• f: Switching frequency in hertz, set by the controller IC.
• Pout: Output power delivered to the load in watts.

Once the duty cycle is known, the load current Iout = Pout / Vout and the load resistance R = Vout / Iout follow directly. In continuous conduction mode the inductor carries Iout on average, the switch only conducts during the on-time so the period-averaged switch current is D * Iout, and the diode only conducts during the off-time so the period-averaged diode current is (1 - D) * Iout. The required inductance L = (Vin - Vout) * D / (f * dIL) and the required output capacitance C = dIL / (8 * f * dVout) keep the ripple inside the budget.

According to Texas Instruments application note SLVA477, applying volt-second balance to the buck inductor in continuous conduction mode gives the steady-state transfer function Vout/Vin = D.

To convert the load power into the load resistance used by the buck converter calculator, Ohm's Law Calculator handles the V = IR relationship directly.

Four concepts describe how the calculator handles a switching converter and what each one means inside a design.

If the inductor current touches zero the converter enters discontinuous conduction mode (DCM), and the simple transfer function no longer holds. The calculator stays in CCM because that is where the closed-form formulas come from. If your load is so light that DCM becomes likely, lower the inductor ripple fraction or raise the switching frequency so the average inductor current stays above half of its peak-to-peak ripple.

A buck converter and a resistive divider both scale a voltage down, so Voltage Divider Calculator is a useful companion when you explain why a switching converter beats a linear regulator for efficiency.

Six numbered steps walk through a typical design pass. The example uses 12 V in, 3.3 V out, 250 kHz, and 3.3 W.

1. 1 Enter the input voltage: Type the DC supply voltage. A 12 V lead-acid rail is 12 V, a USB-C PD rail can be 5 V, 9 V, or 15 V, and a 24 V industrial bus is 24 V.
2. 2 Enter the target output voltage: Type the DC voltage the load needs. The calculator returns D = Vout / Vin once Vout is lower than Vin.
3. 3 Enter the switching frequency: Pick the frequency from the controller datasheet. Most buck controllers run between 100 kHz and 1 MHz; faster switching shrinks the inductor but raises switching losses.
4. 4 Enter the load power: Type the output power the load draws in watts. The calculator converts this into load current and load resistance internally.
5. 5 Set the ripple fractions: Choose the inductor ripple fraction (0.2 to 0.4 is common) and the output ripple fraction (0.01 to 0.05 for analog rails).
6. 6 Read the required inductance and capacitance: Use the calculated L and C as a starting point. Real designs pick the next standard E-series value above the calculated minimum.

For a 12 V supply that must power a 3.3 V, 3.3 W microcontroller rail at 250 kHz with 30 percent inductor ripple and 2 percent output ripple, the buck converter calculator returns D = 27.5 percent, L = 32 uH, and C = 2.27 uF. A real board would pick a 33 uH inductor and a 4.7 uF X7R ceramic.

Five reasons students, hobbyists, and practising engineers prefer the buck converter calculator over solving the equations by hand each time.

• • Saves design time: The buck converter calculator returns duty cycle, inductor value, and output capacitor value in one pass so you move from spec to bill of materials quickly.
• • Catches invalid designs early: Flags requested Vout at or above Vin, switching frequencies at zero, and ripple fractions of zero that would force infinite L or C.
• • Connects theory to numbers: The transfer function taught in class becomes a concrete L and C value for a specific Vin, Vout, and load.
• • Makes ripple budgets visible: Entering inductor and output ripple fractions turns an abstract specification into a pair of concrete component values.
• • Supports homework and lab prep: Students confirm their hand calculations before building a circuit, which makes troubleshooting easier when measurements disagree.

Treat the output as a starting point rather than a final answer. Real converters also need to budget for switch on-resistance, diode forward drop, inductor DCR, output capacitor ESR, and the controller current limit. Once the basic design is in place, fine-tune the inductor and capacitor on the bench with an oscilloscope to confirm the ripple stays inside the agreed limits.

Five factors drive the design numbers returned by the calculator. The first three are inputs it accepts; the last two are real-world caveats.

• • The calculator assumes continuous conduction mode (CCM). At light load the converter may slip into discontinuous conduction mode (DCM), where the Vout = Vin * D relation no longer holds.
• • The calculator uses an ideal lossless model. Switch on-resistance, diode forward drop, inductor DCR, output capacitor ESR, and switching losses are not modelled, so reserve headroom on the duty cycle and on the input current limit of the chosen controller.

If the calculator returns a duty cycle above about 80 percent, the converter is close to the passthrough limit and any drop in Vin or rise in Iout can push Vout out of regulation. Below 10 percent the step-down ratio is large and the inductor ripple becomes a larger fraction of the load current, so revisit the topology.

According to Texas Instruments application note SLVSA14 (Understanding Buck Power Stages in Switchmode Power Supplies), the output capacitance required for a target peak-to-peak ripple voltage dVout in continuous conduction mode is C = dIL / (8 * f * dVout).

According to MIT OpenCourseWare 6.622 Power Electronics, the buck converter only stays in continuous conduction mode while the average inductor current is above half the peak-to-peak ripple current.

To size the input bulk capacitor against the supply impedance, Capacitor Charge Time Calculator applies the same RC time constant analysis to a different stage of the converter.