How to choose the inductor of DCDC step-down switching power supply

Choosing the appropriate inductor is one of the keys to switching power supply circuit design. This article will help you understand the relationship between inductor value and circuit performance.

A buck converter, also called a step-down converter, is a switch-mode voltage regulator that efficiently converts a higher DC input voltage to a lower DC output voltage. We will use LTspice to study the electrical behavior of switch mode voltage converters. This article begins by exploring the design tasks and trade-offs associated with circuit inductance.

The LTspice schematic shown in Figure 1 will allow us to simulate the power stage of a buck converter. To become a complete converter we need to add a feedback control loop to regulate the voltage.

Buck Converter Inductor Formula

from Texas Instruments Application Notes The following equation is provided to calculate the inductor size:

The meanings of each formula are as follows:

• VOUT: is the output voltage. The voltage can be higher or lower than the output.

• VIN: Again, we usually expect a switching regulator to tolerate a range of input voltages, so if your VIN is not fixed, you can choose a value somewhere in the middle of the range.

• fS (switching frequency): Before calculating the inductor value, you must consider the switching frequency. Somewhere between 200 kHz and 2 MHz is a reasonable starting point.

• ΔIL: This represents the inductor current ripple, that is, the up and down changes in the inductor current caused by the on-off action of the switching element, as shown in Figure 2.

In response to the on/off action of the switching elements, the inductor current in a buck converter fluctuates up and down, above and below the load current (i.e., the average value of the inductor current). The magnitude of these deviations is represented by the inductor current ripple (ΔIL).

If we express current ripple (CR/current ripple) as a percentage of expected load current, the recommended CR specification is 30%. This means that the maximum inductor current is 15% higher than the expected load current and the minimum inductor current is 15% lower than the expected load current.

You may see terms like "maximum load current" or "full load current" instead of "expected load current." We do not consider unusually high transient currents when setting the ΔIL target.

Calculate the inductor value of a buck regulator circuit

Let's use a concrete example to illustrate how to calculate inductance. We're going to change various parameters in the LTspice circuit so that we can actually do something new.

Let's say our goal is to accept a fairly high system voltage and generate a power rail suitable for a low-power mixed-signal embedded system. Let's assume our nominal input voltage is 24 V, the desired output voltage is 3.3 V, and the expected load current is 70 mA.

For this type of application, switching regulators are preferred because such large voltage differences can cause linear regulators to overheat.

Because we will be powering some analog circuitry, therefore, we want to reduce the ripple in the output voltage. Additionally, we will choose a higher switching frequency - say 1.5 MHz - since higher switching frequency helps reduce output ripple.

We also need to choose an initial duty cycle. To do this, we can use the maximum duty cycle required by the circuit at the specified input and output voltages and calculate the maximum duty cycle as follows:

Assuming 90% efficiency, so our maximum duty cycle is about 15%:

In Figure 3, the schematic has been updated with switching frequency and duty cycle.

I'm using 1µF as the default value for capacitor C1.

Also, please note that I have replaced the load resistor with a current source ILOAD. This ensures that the load current will remain 70mA regardless of the output voltage.

We calculate the inductance like this:

Here is the updated schematic:

Buck Regulator Power Stage Simulation

Figure 5 shows the inductor current, load current and output voltage of our new buck converter:

These results look good, but there are a lot of details to check. We will discuss this in a future article.

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