DC to DC Boost Converter: Voltage, Current, and Duty Cycle Conversion

Designing a step-up switching power supply requires more than just matching input and output voltages. The actual component stress, inductor sizing, and input trace width depend entirely on the duty cycle and the efficiency of the conversion stage. Below is the complete breakdown of the math, real-world IC limitations, and the edge cases where standard textbook formulas fall apart on the bench.

The Core Conversion Formulas and Assumptions

The calculations above are fixed by two primary assumptions: Continuous Conduction Mode (CCM) and a fixed efficiency ($\eta$) of 85%. In CCM, the inductor current never drops to zero during the switching cycle, which locks the output voltage strictly to the duty cycle regardless of the load current.

1. Duty Cycle ($D$):
The ideal formula for a boost converter in CCM is $V_{out} = V_{in} / (1 - D)$. Rearranging for $D$:
$D = 1 - (V_{in} / V_{out})$
Substituted: $D = 1 - (3.7 / 12) = 1 - 0.3083 = 0.6917 \text{ (or 69.2\%)}$

2. Input Current ($I_{in}$):
Assuming conservation of energy, $P_{in} = P_{out} / \eta$. Therefore, $V_{in} \times I_{in} = (V_{out} \times I_{out}) / \eta$.
$I_{in} = (V_{out} \times I_{out}) / (V_{in} \times \eta)$
Substituted: $I_{in} = (12 \times 1) / (3.7 \times 0.85) = 12 / 3.145 = 3.815\text{A}$

Note that the input current is nearly four times higher than the output current. This is the most common point of failure for hobbyists: sizing the input traces or battery leads for the 1A output, only to melt them when the converter pulls 3.8A from the source.

Real-World Boost Converter IC Specifications

Theoretical math assumes an ideal switch and diode. In reality, you must select a controller or integrated module capable of handling the peak switch current ($I_{sw}$), which is always higher than the average input current due to inductor ripple. Below is a data-dense comparison of common boost ICs used in 2026 for step-up designs.

Source: Manufacturer datasheets and TI Boost Converter Topology Overview.

Input Voltage Variance: The ±20% Discharge Curve

A 3.7V Li-ion cell does not stay at 3.7V. It starts at 4.2V fully charged and drops to roughly 3.0V before the BMS cuts it off. Because input current and duty cycle are inversely proportional to $V_{in}$, the lowest input voltage dictates your worst-case thermal and current stress. Here is how the requirements shift across a ±20% variance (the typical discharge curve).

If you are using a generic MT3608 module with a 2A internal switch limit, it will immediately trip its internal overcurrent protection or sag the output voltage when the battery drops below 3.5V, because the required average input current (plus ripple) exceeds 2A. Always size your inductor and IC switch limit based on the minimum expected $V_{in}$, not the nominal.

When Standard Conversions Become Meaningless

Unlike AC-DC power supplies where stepping from 120V single-phase to 230V or 3-phase shifts input current calculations via power factor (PF) and $\sqrt{3}$ multipliers, DC to DC boost conversions have no power factor, phase shift, or RMS derivations. The input is pure DC. Attempting to apply AC power factor math to a DC switching node is fundamentally incorrect.

However, the standard CCM formulas above become meaningless under two specific bench conditions:

1. Assuming 100% Efficiency: If you calculate $I_{in}$ assuming $\eta = 1.0$, you will undersize your input power supply. Real-world losses include the MOSFET $R_{DS(on)}$ conduction loss, the Schottky diode forward voltage drop ($V_f$), and the inductor's DC resistance (DCR). At high step-up ratios (e.g., 3.3V to 24V), efficiency can plummet below 70%, drastically spiking input current.
2. Discontinuous Conduction Mode (DCM): If your load drops significantly (e.g., the 1A load drops to 50mA) and you are using a standard PWM controller without pulse-skipping, the inductor current will fall to zero before the next switching cycle begins. In DCM, the output voltage is no longer fixed strictly by the duty cycle; it becomes highly dependent on the load current and inductor value. The $V_{out} = V_{in} / (1 - D)$ formula completely fails in DCM, and the converter will over-voltage if not regulated by a feedback loop.