In high-frequency DC-DC converters, an inductor filters the ripple current superimposed on the DC output. Whether the converter is a buck, boost, or buck-boost topology, the inductor smooths the ripple to provide a stable DC output. An inductor's efficiency is highest when the combined iron and copper losses are at their minimum. To achieve the highest efficiency—that is, the lowest loss—by selecting a good component to smooth the ripple current, it is crucial to ensure that the inductor's core does not saturate and its winding does not overheat when the operating current passes through. This article introduces how to evaluate inductor losses and presents methods for designing and quickly selecting high-efficiency inductors.

1. Inductor Loss Evaluation

Evaluating an inductor's core and copper losses is quite complex. Core loss typically depends on several factors, such as the ripple current value, switching frequency, core material, core parameters, and the air gaps in the core. The circuit's ripple current and switching frequency are application-dependent, while the core material, parameters, and air gaps are inductor-dependent.

The most common equation for evaluating core loss is the Steinmetz equation:

Where:

Pvc = Power loss per unit volume of the core

K, x, y = Core material constants

f = Switching frequency

B = Magnetic flux density

This equation shows that core loss (iron loss) depends on frequency (f) and magnetic flux density (B). Since magnetic flux density depends on the ripple current, both are application-dependent variables. Core loss is also related to the inductor itself, as the core material determines the constants K, x, and y. Furthermore, the magnetic flux density is jointly determined by the effective core area (Ae) and the number of turns (N). Therefore, core loss depends on both the application and the inductor's specific design.

In contrast, calculating DC copper loss is relatively straightforward:

Where:

Pdc = DC power loss (W)

Idc_rms = RMS current of the inductor (A)

DCR = DC resistance of the inductor winding (Ω)

Evaluating AC copper loss is more complex, as it increases due to the higher AC resistance caused by the skin effect and proximity effect at high frequencies. An ESR (Equivalent Series Resistance) or ACR (AC Resistance) curve may show some increase in resistance at higher frequencies. However, these curves are typically measured at very low current levels and thus do not include the iron losses resulting from the ripple current, which is a common point of misunderstanding.

For example, consider the ESR vs. Frequency curve shown in Figure 1.

Figure 1. ESR vs. Frequency

According to this graph, the ESR is very high above 1 MHz. Using this inductor above this frequency would seem to result in very high copper loss, making it an unsuitable choice. In a real-world application, however, the inductor's actual loss is much lower than what this curve suggests.

Consider the following example:

Assume a converter has an output of 5V at 0.4A (2.0W) and a switching frequency of 200 kHz. A 10µH Codaca inductor is selected, with its typical ESR vs. Frequency relationship shown in Figure 1. At the 200 kHz operating frequency, the ESR is approximately 0.8Ω.

For a buck converter, the average inductor current is equal to the load current of 0.4 A. We can calculate the loss in the inductor as:

6.0% = 0.128W / (2.0W + 0.128W) (The inductor would consume 6% of the input power)

However, if we operate the same converter at 4 MHz, we can see from the ESR curve that R is around 11Ω. The power loss in the inductor would then be:

46.8% = 1.76W / (2.0W + 1.76W) (The inductor would consume 46.8% of the input power)

Based on this calculation, it would seem that this inductor should not be used at or above this frequency.

In practice, the converter's efficiency is much better than what is calculated from the ESR-frequency curve. Here’s why:

Figure 2 shows a simplified current waveform for a buck converter in continuous conduction mode with a small ripple current.

Figure 2. Simplified Buck Converter Current Waveform

Assuming the Ip-p (peak-to-peak ripple current) is about 10% of the average current:

I_dc = 0.4 A

I_p-p = 0.04 A

To accurately evaluate the inductor's loss, it must be divided into low-frequency loss (DC loss) and high-frequency loss.

The low-frequency resistance (which is effectively the DCR) is approximately 0.7Ω from the graph. The current is the RMS value of the load current plus the ripple current. Since the ripple current is small, the effective current is approximately equal to the DC load current.

For the high-frequency loss,That is , R is ESR (200kHz), Where I is merely the root mean square (rms) value of the ripple current:

At 200 kHz, the AC loss is:

Therefore, at 200 kHz, the total predicted inductor loss is 0.112 W + 0.000106 W = 0.112106 W. 

The predicted loss at 200 kHz is only slightly higher (less than 1%) than the DCR-predicted loss.

Now, let's calculate the loss at 4 MHz. The low-frequency loss remains the same at 0.112 W. 

The AC loss calculation must use the ESR at 4 MHz, which we previously estimated to be 11Ω:

Therefore, the total inductor loss at 4 MHz is 0.112 W + 0.00147 W = 0.11347 W.

This is much more telling. The predicted loss is only about 1.3% higher than the DCR loss, which is far below the previously predicted 1.76 W. Furthermore, one would not use the same inductance value at 4 MHz as at 200 kHz; a smaller inductance value would be used, and the DCR of that smaller inductor would also be lower.

2. High-Efficiency Inductor Design

For continuous current mode converters where the ripple current is small relative to the load current, a reasonable loss calculation must be performed using a combination of DCR and ESR. Additionally, the loss calculated from the ESR curve does not include iron loss. An inductor's efficiency is determined by the sum of its copper and iron losses. Codaca optimizes inductor efficiency by selecting low-loss materials and designing inductors for minimum total loss. Using flat wire windings provides the lowest DCR within a given size, reducing copper loss. Improved core materials reduce core loss at high frequencies, thereby increasing the inductor's overall efficiency.

For example, Codaca's CSEG series of molded power inductors is optimized for high-frequency, high-peak-current applications. These inductors feature soft saturation characteristics while offering the lowest AC loss and a lower DCR at frequencies of 200 kHz and above.

Figure 3 shows the inductance vs. current characteristics for 3.8/3.3 µH inductors from the CSBX, CSEC, and CSEB series. The CSBX, CSEC, and CSEB series are clearly the best choices for maintaining inductance at currents of 12A or higher.

Table 1. Comparison of DCR and Isat for CSBX, CSEC, and CSEB.

When comparing the AC loss and total loss of the inductors at 200KHz, the CSEB series, with its innovative structure that surpasses all previous designs, achieves the lowest DC and AC losses. This makes the CSEB series the optimal choice for high-frequency power converter applications that must withstand high peak currents while requiring the lowest possible DC and AC losses.

Figure 3. Comparison of Saturation Current and Temperature Rise Current Curves for 3.8/3.3μH Inductors in the CSBX, CSEC, and CSEB Series.

Figure 4. Comparison of AC Loss and Total Loss at 200KHz for CSBX, CSEC, and CSEB Series.

3. Inductor Quick Selection Tool

To accelerate the inductor selection process for engineers, Codaca has developed selection tools that can calculate losses based on measured core and winding data for every possible application condition. The results from these tools include current-dependent and frequency-dependent core and winding losses, eliminating the need to request proprietary inductor design information (like core material, Ae, and number of turns) or to perform manual calculations.

The Codaca selection tools calculate the required inductance value based on operating conditions such as input/output voltage, switching frequency, average current, and ripple current. By inputting this information into our Power Inductor Finder, you can filter for inductors that meet these requirements, with each inductor's inductance, DCR, saturation current, temperature rise current, operating temperature, and other information listed.

If you already know the required inductance and current for your application, you can input this information directly into the Power Inductor Finder. The results will display the core and winding losses and the saturation current rating for each inductor, allowing you to verify whether the inductor will remain close to its design specifications under the application's peak current conditions.

The tools can also be used to plot inductance versus current behavior to compare the differences and advantages of various inductor types. You can start by sorting the results by total loss. Placing all inductor information (up to four types) on a single chart and sorting them helps with this analysis, enabling you to select the most efficient inductor.

Calculating total loss can be complex, but these calculations are built into Codaca's selection tools, making the selection, comparison, and analysis as simple as possible, so you can more efficiently choose a high-efficiency power inductor.

【References】:

Codaca Website: DC/DC Converter Inductor Selection -Shenzhen Codaca Electronics Co., Ltd. (codaca.com)

Codaca Website: Power Inductor Finder-Shenzhen Codaca Electronics Co., Ltd. (codaca.com)

Codaca Website: Power Inductor Loss Comparison-Shenzhen Codaca Electronics Co., Ltd. (codaca.com)