Consumer applications are the main driver of demand for modern DC/DC converters. In these applications, power inductors are primarily used in battery-powered equipment, embedded computing, and high-power, high-frequency DC/DC converters. Understanding the electrical properties of inductors is critical to designing compact, cost-effective, high-efficiency systems with excellent thermal performance.

An inductor is a relatively simple component consisting of insulated wire wrapped in a coil. But the complexity increases when the individual components are combined to create an inductor with the appropriate size, weight, temperature, frequency, and voltage while still meeting the target application.

When selecting an inductor, it is important to understand the electrical characteristics stated in the inductor data sheet. This article provides guidance on selecting the right inductor for your solution and explains how to predict inductor performance when designing new DC/DC converters.

An inductor is a circuit element that stores energy in its own magnetic field. Inductors convert electrical energy into magnetic energy by storing it, then providing energy to the circuit to regulate the current flow. As the current increases, the magnetic field increases. Figure 1 shows the inductor model.

**Figure 1: Electrical model of an inductor**

An inductor is a circuit element that stores energy in its own magnetic field. Inductors convert electrical energy into magnetic energy by storing it, then providing energy to the circuit to regulate the current flow. As the current increases, the magnetic field increases. Figure 1 shows the inductor model.

**Figure 2: Inductor parameters**

Table 1 shows how to calculate inductance (L).

**Table 1: Calculation of inductance (L)**

Below, we describe common inductor parameters in detail.

Magnetic permeability is the ability of a material to respond to magnetic flux and also indicates how much magnetic flux can pass through an inductor in an applied electromagnetic field. Table 2 shows the enhancement of magnetic permeability to magnetic flux density (B).

**Table 2: Calculated magnetic flux density (B)**

As can be seen from Table 2, the concentration of magnetic flux depends on the magnetic permeability and size of the magnetic core.

Figure 3 shows a coil without a core.

**Figure 3: Air core coil**

The magnetic permeability of an air-core coil is a constant value (µr air), approximately equal to 1.

Figure 4 shows an inductor with a magnetic core. Of course, with a magnetic core, the magnetic field is enhanced.

**Figure 4: Inductor with magnetic core**

Different core materials have different typical magnetic permeabilities. Table 3 lists the magnetic permeability of three different core materials.

**Table 3: Magnetic core permeability**

**Inductance value (L)**

The ability of an inductor to store induced electrical energy as magnetic energy is reflected by its inductance value. While the switching input voltage drives the inductor, the inductor must provide a constant DC current to the output load.

Table 4 shows the relationship between current and inductor voltage. It can be seen that the voltage across the inductor is proportional to the change in current over time.

**Table 4: Calculation of inductor voltage drop**

First, determine the inductance range required for the design. It is important to note that the inductance value is not constant over the entire operating condition and will change as frequency increases. Therefore, applications with higher switching frequencies require special considerations. Inductor manufacturers typically test inductors at frequencies from 100kHz to 500kHz because most DC/DC converters operate in this range.

The inductor's current resistance causes heat dissipation, which affects efficiency. The total copper loss includes RDC loss and RAC loss. RDC is independent of frequency and is always constant; RAC depends on frequency. Table 5 shows the method for calculating RDC.

**Table 5: Calculating copper wire RDC**

The only way to reduce copper loss is to increase the wire area, that is, switch to thicker wires, or use flat wires. Using flat wire allows the winding window to be fully utilized, resulting in lower RDC. Table 6 shows a comparison of the cross-sectional areas of round wires and flat wires.

**Table 6: Comparison of cross-sectional areas of circular and flat wires**

Table 7 compares the characteristics of round wire and flat wire.

**Table 7: Comparison of characteristics between round wire and flat wire**

The inductor DC copper loss (RDC) can be estimated using Equation (1):

(PAC) Copper loss depends on PAC, which is caused by frequency-driven proximity effect and skin effect. The higher the frequency, the higher the PAC copper loss.

Normally, ferromagnetic materials can meet the required magnetic properties of core inductors. Depending on the core material, the relative permeability of the inductor ranges from 50 to 20,000.

The material's magnetic domain structure reacts when a magnetic field is applied; without a magnetic field, the direction of the magnetic moments is random. When magnetic energy changes, core losses occur. Magnetic domains orient their magnetic moments in the direction of the magnetic field. As the magnetic domains expand and shrink, some of them get stuck in the crystal structure. Once the stuck magnetic domains are able to rotate, the energy is dissipated in the form of heat.

Ripple current (ΔIL) is the change in current during a switching cycle.

Inductors may not function properly outside their peak current range. The inductor's ripple current is typically designed to be within 30% to 40% of IRMS.

Figure 5 shows the waveform of the inductor current.

**Figure 5: Inductor current waveform**

Rated current is the DC current required to raise the inductor temperature by a specified amount. Temperature rise (ΔT) is not a standard value, but is typically between 20K and 40K.

Rated current measured at ambient temperature. Its value is usually provided in the inductor data sheet and is the expected current value for the end application. For applications with higher ambient temperatures, designers should choose inductors with higher self-heating temperatures.

Figure 6 shows the relationship between temperature rise and rated current. This curve can be used to determine the current value corresponding to any temperature rise.

**Figure 6: Rated current curve of inductor**

In an application, the operating temperature (TOP) is determined by the ambient temperature (TAMB) and the self-heating value of the inductor (ΔT). TOP can be estimated by formula (2):

A given rated current is the best way to estimate the inductor temperature rise. Temperature rise is also affected by circuit design, PCB layout, proximity to other components, and trace size and thickness. Excessive AC losses in the inductor core and windings can also cause additional heat.

If lower self-heating is required, an inductor with a larger package size needs to be used.

The saturation current rating is the DC current that an inductor can support before the nominal inductance drops by a specified percentage.

The reference percentage inductance drop value is unique for each inductor. Typically, manufacturers set this value between 20% and 35%, which can make inductor comparisons difficult. But the data sheet usually provides a curve showing how the inductance changes with DC current. This curve can be used to measure the entire range of inductance and how it responds to DC current.

DC saturation current depends on temperature and the inductive magnetic material and its core structure. Different structures and cores will affect the ISAT value.

Ferrite cores are the most common and are characterized by a hard saturation curve (see Figure 7). It is critical to ensure that the inductor does not operate beyond the drop-off point; beyond this point, the inductance drops off sharply and functionality decreases.

The synthetic plastic inductor has a stable decrease in inductance when the temperature changes and has soft saturation characteristics. Because its sensitivity gradually decreases, it provides designers with greater flexibility and a wider working range.

Figure 7 shows two saturation curves. The blue curve is a typical example of soft saturation of synthetic plastic inductors; the red curve is a typical example of hard saturation of NiZn/MnZn drum core inductors.

**Figure 7: Inductor saturation current curve**

Inductors with small inductance (or large package size) can handle higher saturation currents.

The self-resonant frequency (fR) of an inductor is the lowest frequency at which the inductor resonates with its self-capacitance. Below the resonant frequency, the impedance is at its maximum peak and the effective inductance is zero. Figure 8 shows the circuit model of the inductor.

**Figure 8: Inductor circuit model**

An inductor has inductive properties up to the resonant frequency (fR) (shown as the blue curve in Figure 9) because as frequency increases, the impedance increases. At the resonant frequency, the negative capacitive reactance (XC) is equal to the positive inductive reactance (XL), whose value can be estimated by equation (3):

Beyond the resonant frequency (shown as the red curve in Figure 9), the inductor exhibits capacitive behavior with reduced impedance. Beyond this point, the inductor will not work as expected.

Figure 9 shows the relationship between sense magnitude and frequency.

**Figure 9: Relationship between sense quantity and frequency**

By understanding the basic meaning of each parameter in the inductor data sheet, you can easily select an adequate inductor. But if you understand the details hidden in each parameter, you can select the optimal inductor for your DC/DC converter application and predict system performance under different conditions.

There are many types of inductors on the market for different applications, and choosing the most suitable inductor is not an easy task. For example, larger inductors reduce DC losses and increase efficiency, but they are physically larger and run hotter. No inductor is perfect, and it is important to understand the parameters of each inductor and the relationship between different parameters to help designers determine whether an inductor is suitable for a specific DC/DC application.

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