# In-depth analysis of inductive current

## Introduction

In the design of switching power supply, the design of inductance brings many challenges to engineers.The engineer should not only choose the value of inductance, but also consider the current that inductance can withstand, winding resistance, mechanical size and so on.This paper focuses on explaining the DC current effect on inductors.This will also provide the necessary information to select the right inductor.

## Understand the function of inductance

Inductance is often understood as the L (C is the output capacitance) in the LC filter circuit at the output end of the switching power supply.While this understanding is correct, to understand the design of the inductor you must understand the behavior of the inductor in greater depth.

In the step-down conversion (typical of Fairchild's switching controllers), the inductor side is connected to the DC output voltage.The other end is connected to the input voltage or GND by switching the frequency switch.

In state 1, the inductor is connected to the input voltage via (high-side "high-side") MOSFET.

In state 2, the inductor is connected to GND.

With this type of controller, inductive grounding can be achieved in two ways: by diode grounding or by (low-side "low-side") MOSFET grounding.

If this is the latter method, the converter is called a "synchronus" method.

Now consider how the current flowing through the inductor varies in these two states.

In state 1, one end of the inductor is connected to the input voltage and the other to the output voltage.For a step-down converter, the input voltage must be higher than the output voltage, thus creating a forward voltage drop on the inductor.

In state 2, by contrast, the inductor end of the input voltage is connected to the ground.For a step-down converter, the output voltage must be positive, thus creating a negative voltage drop on the inductor.

We use the formula of voltage calculation on inductance:

V = L (dI/dt)

Thus, when the voltage on the inductor is positive (state 1), the current on the inductor increases;When the voltage on the inductor is negative (state 2), the current on the inductor decreases.The current through the inductance is shown in figure 2:

From the figure above, we can see that the maximum current flowing through the inductor is half of the peak current of the DC current plus the peak current of the switch.The figure above is also called ripple current.According to the above formula, we can calculate the peak current:

Where, ton is the time of state 1, T is the switching period (inverse of the switching frequency), and DC is the duty ratio of state 1.

Warning: the calculation above assumes that the voltage drop on each component (the on-off voltage drop on MOSFET, the on-off voltage drop on inductor, or the forward voltage drop on schottky diode in asynchronous circuit) is negligible compared to the input and output voltage.

If the decline of the device is not negligible, the following formula should be used for accurate calculation:

Synchronous switching circuit:

Asynchronous conversion circuit:

Where Rs is the resistance of inductive resistance plus inductance winding resistance.Vf is the forward voltage drop of schottky diode.R is Rs plus MOSFET conducting resistance, R=Rs+Rm.

## All-inductor core saturation

By calculating the inductance peak current, we can find out what is generated on the inductance.It is easy to see that as the current flowing through the inductor increases, its inductance decreases.

This is due to the core material physical characteristics determined.How much the inductance is reduced is important: if the inductance is reduced much, the converter will not work properly.

When the current passing through the inductor is large enough to be ineffective, the current is called the saturation current.This is also the basic parameter of inductance.

In fact, the switching power inductor in the conversion circuit always has a "soft" saturation.To understand this concept, look at the actual measured inductance vs. DC current curve:

When the current increases to a certain level, the inductance does not drop sharply, which is called the "soft" saturation characteristic.If the current increases further, the inductance will be damaged.

Note: inductance drop occurs in many types of inductors.Examples are toroids, gapped e-cores, etc.But rod core's inductance doesn't change that way.

With this soft saturation property, we can see why the minimum inductance at the DC output current is specified in all converters.Moreover, the ripple current does not affect the inductance seriously.

In all applications, the ripple current is expected to be as small as possible, because it will affect the ripple of the output voltage.This is why people always care about the inductance of DC output current and ignore the inductance of ripple current in Spec.