## The Importance of Estimating Power Losses in Consumer Power Supply Magnetic Components

*Examining an LED lighting string application to discover it’s not worth it to be in the dark on inductor performance at high switching frequencies.*

Using inductors can significantly diminish power losses in consumer electronics at high switching frequencies. Yet relatively little information exists on inductor performance in these circumstances. The mystery exists despite abundant tools to help engineers design and simulate power supplies. For instance, one important data point that may not be readily available about inductors is the accurate AC resistance of a particular magnetic component. Another area where it’s important to shed some light involves the role core losses play in surface mount power inductors. Yes, core losses are small compared to AC losses in many surface mount power inductors, but this article will show that it is nevertheless a critical evaluation point. That is why it is a recommended design step to estimate power losses before selecting an inductor for a particular power supply.

Estimating Power Losses

There are multiple factors to consider when estimating power losses. A main component to evaluate is the forward converter, which is the industry-standard name for an isolated buck converter. The elements to consider in the design phase are the input and output voltages, the transformer and the switch current, which are shown in Figure 1. The block diagram illustrates the basic elements of the open loop section of a single-switch forward converter:

Figure 1. Basic Block Diagram of Forward Converter Power Stage |

Using an LED lighting string application as an example, Table 1 lists the typical design requirements for a power supply. For simplicity, the control circuit and feedback loop are omitted in the example.

Table 1. |

- Based on the block diagram in Figure 1, the peak voltage at D1 is calculated as

VD1 = 8*v*+0.5*v*+0.1^{diode}*v*(*pcb conduction loss*)*D*= 13.23 V. - The voltage measured across the inductor ΔV during the first interval is, therefore, 5.23 V.
- The subsequent inductance value is: L = ΔVxDx (1

However, since 21.58 µH is not a standard inductor value, the LED lighting power supply example would need to select a 22 µH inductor, which is the closest standard inductor available.

Based on the requirements for this application, designers might select a shielded power inductor in a surface mount package that has a resistance of 62 mΩ and a RMS current of 2.3 A. An educated first look would indicate that the calculated losses are due to the DC resistance of the winding and the DC current of 2 A. This calculation gives a power loss of 0.248 W. The typical information provided on this sample power inductor’s datasheet shows that it can conduct up to 2.3 Arms giving a total power dissipation of 0.327 W, and may have a temperature rise of 40 °C at full load. If the ambient temperature is 40 °C, then the inductor is expected to rise in temperature to less than 80 °C at the required current of 2 A. These calculations would take a designer in one direction, but to find the optimal power inductor solution, however, requires taking the following additional factors into account.

Thermal: Copper has a very high temperature coefficient. The resistance at 43 °C ambient will increase to 67 mΩ. The DC loss in the winding will, therefore, be 0.268 W at a current of 2 A.

AC Resistance: The distribution of current in each layer of a multi-layered wound inductive component will be unevenly distributed depending on the frequency of the current. The magnetic fields generated by the multiple layers are responsible for this effect, which is also known as “proximity.” There is a one-dimensional solution to the complex differential equations describing the ratio of the AC resistance to the DC resistance, which is called the Dowell equation. This equation enables us to calculate losses in the inductive component due to proximity.

Using Dowell’s equation, the AC resistance plot against frequency of the sample power inductor used previously is shown in Figure 2.

Figure 2. Dowell Equation Applied to Sample Power Inductor |

The AC current in the inductor is a saw tooth waveform, and can be written as Irms = *I*1/3. For this device, the RMS values are calculated at 0.22 A given that the current in the inductor is 0.75 A peak to peak.

Taking the AC resistance at the switching frequency is 2.4 Ω from Figure 2 would generate a loss due to proximity of 0.112 W in the inductor.

Core Losses: The ferrite core also generates some losses due to the eddy currents generated by the swings in flux as current rises and falls in the coils of the inductor. These are known as core losses where Faradays Law is used to calculate the flux density “B” in the wound core.

B = 1*NA***edt*: Faraday’s Law

Using this calculation, the peak flux in this application is 26 mT. By convention, the change in flux density or ΔB is taken as one half the peak flux or 13 mT. By checking the core data, it is known that the loss at 210 KHz at a ΔB of 13 mT is 50 mW.

The total dissipation in the inductor is now determined to be 0.438 W (0.268 W + 0.12 W+0.05 W), which is far different than the original calculation 0.248 W proved now to be erroneous. The updated measurement indicates that the device is actually above the rated full power of the inductor at 0.325 W.

This information can significantly save designers’ time in the component selection process. It is very important when selecting the right magnetic component to calculate AC resistance curves along with the understanding that AC losses are more significant than core losses.

Figure 3: AC Resistance of Bourns® Model SRR1260-220M at 40 °C |

**Determining the Optimal Inductor Solution**

Taking into consideration the series power loss estimates provided, the optimal solution for this particular application is for designers is to select an inductor that has the same dimensions as the example component but with a lower DC resistance. The most optimal inductor for the LED lighting application would be one that has the same core as well as the exact footprint (12.5x 12.5 x 6 mm) with the identical number of winding layers, which means that the ratio of AC to DC resistance is unchanged. Applying Dowell’s equation to determine AC resistance on a different power inductor device such as one that is shielded with a current range of 1.70 A to 9.8 A is shown in Figure 3. Using this inductor at 210 KHz, the AC resistance is 1.7 Ohms, giving a total power loss, including core losses, of 0.3 W (0.170 W + 0.082 W + 0.05 W), which is well below the rated maximum DC power of 0.688 W for this particular device.

**Designing for Improved Power Supply Reliability**

To achieve the highest power supply operational reliability, it is crucial to avoid selecting an inductor purely based on the rated DC current as written in the datasheet. The selection process must also include evaluating data to help prevent power losses that can lead to other complications, such as overheating and premature failures in the field. While core losses are often mentioned as being a problematic source, AC resistance can be much more detrimental to the application and is frequently overlooked. If AC resistance information is not available, designers are typically forced to “over-specify” the inductor as to allow enough margin to accommodate any additional losses. The curve charts are a great resource for design engineers in estimating power losses to determine the optimal inductor for their next power supply design.

*Cathal Sheehan is Market Manager of the Consumer Market Segment at Bourns, Inc. He has held several roles in Bourns in product management and application engineering. Sheehan holds a Masters Degree in Electronic Engineering from University College Cork and a Masters in Business Administration from Open University.*