How Does a Boost Converter Work? Step-Up Duty Cycle Math

To convert 5V DC to 12V DC using a boost converter, the required steady-state duty cycle (D) is exactly 58.3%. The governing ideal formula is V_out = V_in / (1 - D). Substituting our target values: 12V = 5V / (1 - D), which solves to D = 1 - (5/12) = 0.5833. This means the internal MOSFET switch must be ON for 58.3% of each switching cycle and OFF for 41.7% to maintain 12V at the output, assuming Continuous Conduction Mode (CCM) and ideal components.

The Core Assumptions Fixing This Conversion

The 58.3% duty cycle is a mathematical ideal. On your workbench, three physical assumptions fix or break this answer:

• Continuous Conduction Mode (CCM): The formula assumes the inductor current never drops to zero during the switch OFF time. If your load is too light or your inductor is too small, the converter enters Discontinuous Conduction Mode (DCM), and the output voltage will spike above 12V unless the controller implements pulse-skipping.
• Ideal Diode (0V Drop): The formula ignores the Schottky diode's forward voltage drop (V_f). In reality, a standard 1N5819 diode drops about 0.4V at 1A. To get 12V at the load, the switch node must actually pump up to 12.4V. This shifts the real-world required duty cycle closer to 61.2%.
• Zero Parasitic Resistance: The math assumes the MOSFET R_DS(on), the inductor's DC resistance (DCR), and PCB trace resistances are zero.

Neighboring Conversion Values (±20% Input Range)

Battery-powered projects rarely sit at a perfect 5.0V. A single-cell Li-ion battery sags from 4.2V down to 3.2V, while a USB power bank might fluctuate between 4.8V and 5.2V under transient loads. Here is how the required duty cycle shifts across a ±20% input voltage range to maintain a strict 12V output:

Note: As the input voltage drops, the duty cycle must increase. If your controller has a maximum duty cycle limit of 90%, a 4.0V input is still well within the safe operating area for a 12V output.

Sizing the Inductor for Continuous Conduction

Knowing the duty cycle is only half the battle; you must select an inductor that prevents the current from hitting zero. The inductor ripple current (ΔI_L) is calculated as:

ΔI_L = (V_in × D) / (f_s × L)

Let's use a Texas Instruments SLVA372 reference design approach. If your switching frequency (f_s) is 100 kHz and you want to limit ripple to 30% of your 1A maximum load current (0.3A ripple):

L = (5V × 0.583) / (100,000 Hz × 0.3A) = 97 µH

In practice, you would select a standard 100µH shielded power inductor with a saturation current rating at least 20% higher than your peak switch current. If you use an unshielded inductor (like the tiny drum cores found on $1 eBay boost modules), the magnetic field will couple into nearby analog traces, injecting switching noise into your microcontroller's ADC readings.

When the DC-DC Conversion Becomes Meaningless

The ideal boost formula is a powerful tool, but it becomes physically meaningless under two specific conditions:

1. The 120V vs 230V vs 3-Phase AC Mains Mismatch

Readers frequently ask how this step-up math shifts for 120V vs 230V vs 3-phase power. It doesn't, because a boost converter is strictly a DC-DC topology. If you apply 120V AC RMS directly to the input of a DC boost converter, the negative half-cycles will instantly avalanche and destroy the input capacitor and switching MOSFET.

If your goal is to step 120V AC up to 230V AC, you need a traditional iron-core step-up transformer or an AC-DC-AC matrix converter. However, there is one exception: Active Power Factor Correction (PFC). In a PFC front-end, 120V AC is first rectified to ~170V pulsating DC. A boost converter is then used to step that 170V DC up to a stable 230V or 400V DC bus. In that specific rectified scenario, the duty cycle dynamically shifts from roughly 26% (at the 170V peak) up to near 100% (as the rectified sine wave approaches zero crossing) to maintain the 230V bus.

2. The Duty Cycle > 90% Parasitic Wall

The conversion formula is meaningless when you attempt extreme step-up ratios, such as boosting 3.3V to 33V (which demands D = 90%). At duty cycles above 90%, the MOSFET is ON almost constantly. The inductor's DCR and the MOSFET's R_DS(on) create a parasitic voltage divider. According to the TI Boost Converter Topology Overview, these parasitic resistances physically cap the maximum achievable output voltage. No matter what the ideal math says, you will never reach 33V; the converter will simply max out around 20V-25V while the MOSFET overheats. For ratios exceeding 1:4, you must switch to a coupled-inductor (flyback) or transformer-isolated topology.