Power Supply Unit Design Fundamentals: Inductor Behaviour in a Switching Power Supply

Introduction

In this introductory article, we’re going to talk about the action of an inductor in a switch mode power supply. If you’re new to power supply design and you’re wondering why a diode seems to be forward-biased while it looks like it shouldn’t be, then in all likelihood, that is because of the inductor. This article is for you.

Understanding Inductors

Initially, we studied inductors at university, both in AC and DC circuits. In an AC circuit, we give the inductor a sinusoidal input and observe changes in amplitude and phase. In a DC circuit, we provide a unit step input and study the resulting changes in current or voltage across the inductor.

However, the behavior of an inductor in a switch mode power supply differs significantly from the simple AC or DC circuits studied in university.

Basic Inductor Principles

An inductor always tries to maintain the current flowing through it. It opposes any change in current by creating a back EMF. For instance, if there is 1A flowing through an inductor and a change is attempted, the inductor generates a back EMF to oppose this change. This principle can be likened to pushing a heavy car from rest—it resists movement initially, and once in motion, it resists stopping.

Inductor in a DC Circuit

Consider a simple DC circuit with a 1V battery, a switch, a 1-ohm resistor, and an inductor. Initially, there is no current flowing through the inductor. When the switch is closed, 1V is applied, and the current starts to flow. The inductor opposes the change from 0A to 1A by generating a back EMF equal to the applied voltage (1V). This creates a logarithmic rise in current through the inductor over time.

An inductor in a Switching Power Supply

In a power supply, the resistance is nearly zero ohms, and the current does not follow the same logarithmic curve. Instead, it rises in a straight line, forming a triangular current waveform. The switching on and off of the current results in this triangular shape, which simplifies the analysis using the equation for a straight line (y = mx + c).

Example Circuit Analysis

Let’s consider a circuit with a 1V source, a switch, a 1-ohm resistor, an inductor, and an additional 2-ohm resistor controlled by another switch. When the initial switch is closed, the current rises to 1A. If this switch is opened and the second switch is closed simultaneously, the inductor forces the current to flow through the new path with 3 ohms of resistance, creating a back EMF of 3V to maintain the 1A current flow.

Mechanical vs. Semiconductor Switches

Mechanical switches can open instantaneously, creating a high back EMF that can ionize air and cause sparks. This is why the AC voltage rating of a switch is higher than the DC rating. Semiconductor switches, however, take a finite time to open and close, affecting the inductor’s behavior. The standard equation for the inductor’s back EMF is E = -L (di/dt), derived from Faraday’s and Lenz’s laws.

Inductor Behaviour in Practical Power Supplies

In practical power supplies, the rapid switching of MOSFETs can create large voltage spikes due to high di/dt values. For example, switching from 10A to 0A in 10 nanoseconds generates a massive back EMF, manifesting as noise and spikes.

Conclusion

In this article, we discussed the behavior of inductors in DC-DC switch mode power supplies, the triangular current shape, the direction of back EMF, and the impact of high di/dt on voltage spikes.

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