How to calculate the inductance of a BUCK step-down converter

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How to calculate the inductance of a BUCK step-down converter [Copy link]

Introduction

The inductor design in the buck circuit is very critical, which is closely related to the system efficiency, output voltage ripple (VOUT), and loop stability.

This article will use MPQ2314 as an example to explain how to calculate the inductance of a buck converter, as well as other key parameters such as inductor temperature rise current, saturation current DC resistance, operating frequency, and magnetic loss. Working principle of buck topology In the buck topology, the working state of the upper tube (Q1) is divided into two processes: inductor charging mode and inductor discharging mode (see Figure 1).

In the inductor charging mode, Q1 is turned on, the inductor current (IL) increases, the inductor stores energy, and the output capacitor is charged; in the inductor discharging mode, Q1 is turned off, IL decreases, and the inductor releases energy.

Figure 1: Inductor charging mode and inductor discharging mode

The inductance (L) can be calculated based on the relationship between the voltage and current across the inductor, as shown in formula (1): $$V = L \times dl / dt$$ Wherein, the voltage across the inductor is VIN - VOUT, dI is the peak-to-peak value IL (IL) (usually 10% to 60% of the maximum output current IOUT), and dt is the on-time of Q1, which can be calculated by formula (2): $$dt = D \times t_{sw}$$ Formula (1) can be used to analyze the energy storage state of the inductor when Q1 is turned on.

Figure 2 shows how to calculate the duty cycle, inductor current change, and inductance.

Figure 2: Calculating duty cycle, inductor current change, and inductance

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