Embedded Inductors with Laser Machined Gap
Energy efficiency is a major driver in the evolution of electronics and electronics packaging. To manage power consumption, portable appliances such as smartphones, tablets, e-readers, etc., often use multiple supply voltages and DC/DC converters. Most are based on switch mode power conversion (SMPC). In a power converter, inductors and transformers are used to temporarily store energy during switching cycles. They also have the function of filtering noise. The power magnetics are often the largest and most expensive devices in the circuit. Integrating the magnetics into either a power converter module or system board can significantly reduce size and cost of the power converter function.
Embedded magnetics offer a means for integrating the magnetic functions into a PCB substrate. Ferromagnetic cores are embedded into a PCB substrate, and the inductive windings are implemented using photolithography and standard PCB processes. Rather than building one-at-a-time, devices are arrayed on a PCB panel and fabricated using automated and batch process. In most instances, the embedded core will be a ring shaped (toroid), since this is the most efficient shape in terms of delivering high inductance per turn and containing the induced magnetic flux. Additionally, toroids are a relatively easy shape to manufacture and generally inexpensive compared to other core shapes. Common materials are pressed ceramic ferrites and tape-wound amorphous metals.
Figure 1: Embedded magnetic construction.
As indicated above, inductors and transformers are used in power converters to temporarily store energy during a switching event. A key metric of magnetic materials is their ability to store magnetic flux energy. When current is driven through a conductor wound around a magnetic core material, it produces a magnetic field (H) which induces a magnetic flux (B) in the underlying core material. The current energy is temporarily converted to magnetic flux and stored within the magnetic core. The flux, B, is essentially the field density within the core. B has units of Tesla (T) (or Gauss, G; 10,000 G = 1 T) and H is the measure of magnetizing field strength and has the units of Oersteds (Oe; 1 A/m = 4 x 10-3 Oe). B and H are closely related to voltage and current, where the flux density is proportional to the applied voltage and the magnetizing force, H, is proportional to current. The relationship between the field and flux is tied by the materials permeability, μ.
(1) B = μ H
Flux density may also be expressed in terms of inductance and drive current, as characterized through the relationship:
(2) B = LI/NAc
where L is the inductance, I is the drive current, N is the number of windings and Ac is the cross section area of the core.
Designers often use the B-H curve to analyze the relationship between the drive voltage and drive current. Figure 2 identifies that magnetic materials have a flux saturation level, BSAT, which is the state where the magnetic core has reached peak flux density. At that point, the core cannot store more energy, regardless of the amplitude of drive voltage. For ferrite materials, saturation occurs in the range of 0.350 to 0.550 T (Tesla is a unit of magnetic flux density.), depending on the composition. Cores with high permeability will saturate with modest currents. To allow higher drive currents, a gap is often introduced into the magnetic flux path. This effectively reduces the permeability of the core material and results in a reduction of the inductance of the windings. As depicted in Figure 2, gapping the core flattens out the B-H curve. Reducing the inductance allows the core to store energy from higher drive currents.
Figure 2: Typical B-H graph for an ungapped and gapped ferrite core.
A gap is produced by placing a small cut through the core. Gapping is a common method for reducing the inductance and enabling the core to be driven at higher currents before reaching saturation. It also serves to stabilize the performance of a core over different operating temperatures and drive currents. Basically, gapping the core reduces the effective permeability. The relative permeability for a gapped core can be calculated by the equation:
(3) μr' = μr / (1 +( g x μr /le)
where g is the gap distance and le is the path length of the flux around the circumference of the core. In many instances, the reduction in permeability by gapping will exceed 10x. It may seem counterproductive to create materials and core structures with high permeability and then diminish them with a gap. However, this is necessary to add stability and allow higher drive currents. There is always the option of using powdered iron core materials, which are often described as having a distributed gap. These materials generally have permeability’s less than 100 and are generally more expensive due to the precious metals used in their construction and limited number of suppliers. With conventional ferrites, we can apply a gap to achieve permeability values between 100 and 1000, which reduces the number of windings required to achieve a specific inductance. Reducing the number of windings is beneficial in reducing resistance loss in the windings. Also powdered iron materials generally exhibit higher core loss which can also impact the power converters efficiency. Core losses are a result of an alternating magnetic field in a core material. The core losses are due to hysteresis, eddy current and residual losses in the core material and is dissipated as heat.
Figure 3: Example of a gapped toroid.
Figure 4 shows a typical graph of permeability vs. temperature for a 2000 permeability manganese zinc (MnZn) material, which is typically used for power applications. Here, we see wide variations over temperature. Gapping the core reduces the permeability to about 350 and flattens out the characteristics over the full temperature range. This is important for applications that need to perform to at temperatures below 0°C.
This brings us to a design methodology. Once the designer determines the inductance required for an application, it is then a matter of over designing for much higher inductance, in anticipation that the inductance will be diminished after the core has been gapped.
Figure 4: Ferrite permeability vs. temperature (1500 permeability @ 25°C).
For power converters, embedded magnetics are useful in applications ranging up to 60 W. The power capability is primarily dictated by core sizes that are suitable for embedding into a PCB substrate. The PCB construction is limited by the PCB thickness and height (thickness) of the core. Practical applications include power to a microprocessor, battery chargers and LED lighting. There are many semiconductor SMPC controllers on the market tailored specifically for these applications. Most of these devices operate with switching speeds ranging from 500 kHz to 2 MHz. At these switching speeds, inductors in the range of 1 µH to 10 µH are commonly used. For this investigation, a test coupon was designed with indictors ranging from 2.2 µH to 10 µH. The 10 µH configuration is the focus of this paper. Generally, for power applications, it is best to select MnZn ferrite materials with permeability in the range of 2K to 3K, due to their core loss properties. In this gapping experiment, however, cores with 5K permeability were selected simply because this value was available in the author’s inventory. This difference in permeability is not significant in this particular experiment. Once the gap is applied, the core’s inductance per turn is dominated by the gap with. The differences in the initial permeability only accounts for minor difference in the final inductance.
The 5K permeability core has the following mechanical dimensions; 6.35mm OD x 3.81 mm ID and x 2.54 mm height. To calculate the inductance, one first needs to know the cores inductance factor, AL. The AL value is generally provided by the ferrite manufactures, yet can also be calculated by the relation:
(4) AL = μ0 μr Ac / le
From Equation 4, the inductance factor is directly proportional to the relative permeability, μr. In the case of the 5K permeability 6.35 mm OD core, the AL value is 1.6 µH/N2, where N is the number of windings applier to the core. From the manufacturer specifications, the core has a cross section area Ac of 3.2 mm2 and a path length le of 15.9 mm. To calculate the AL value for the gapped core, we need to return to Equation 3. We have all the details to calculate the gapped AL value, except the gap width, g. Selecting the gap size requires trial and error. Inductors with larger gaps will have more stability, yet AL values decrease with wider gaps. Cores with larger gaps require more windings to achieve a specific inductance.
For this experiment, the objective is to cut a 0.15 mm gap into the 6.35 mm OD cores. Large cores are often gapped using diamond wheel cutters and other milling techniques. A typical gap from a diamond wheel is ≥0.25 mm. For small diameter cores (< 10mm OD), the handling and required fixtures for diamond wheel cutting can be challenging. With the embedded magnetic structure, we have the advantage of the cores being embedded and arrayed in an FR-4 substrate. This greatly facilitates the handling during the gapping procedure. Rather than holding each core individually, panel arrays can be placed on and X-Y stepping table and each core can be laser machined with a high degree of precision and efficiency. Gap widths can be narrower than what is practical with diamond wheel cutting. Also, the laser gapping process time is in the range of 3 to 10 s per core, which is much faster than what can be achieved with mechanical gapping, where one has to fixture and handle each core. For the core machined with a 0.15 mm slit, the new AL' value is calculated as follows:
μr' = 5000 / (1 + (0.15mm x 5000/15.9mm)) = 103
AL =(12.57)(119)(3.2mm2) / (15.9mm) = 260 nH/N2
Inductance can now be calculated by multiplying the AL value by the square of the turns:
(5) L = AL N2
With desired inductance of 10 µH, the required number of windings are calculated to be 6 turns. To test the gapping of the embedded cores, a test panel was designed with different winding configurations. Embedded magnetic inductors were designed with 8, 10 and 12 windings. A 3 mm thick panel of FR-4 sheet stock was milled with cavities to accommodate the cores. The cavities were milled to 2.8 mm depth and the ferrite cores were inserted and encapsulated with low shrink epoxy. Around 1 oz Cu foil was applied to the top and bottom surfaces using two layers of 1080 pre-preg. Vias were drilled and plated to interconnect the top and bottom layers. Inductive windings were then applied through photolithography. Figure 5 shows the layer stack-up for the PCB.
Figure 5: Test coupon cross section.
For laser cutting, there are two basic systems that are commonly used in industrial machining; CO2, and YAG. The CO2 has the larger beam width of 10 µm while the YAG beam width is 1.06 µm. Either system can be used for gapping the embedded cores. CO2 is good for cutting organics while YAG is often preferred for cutting metals and ceramics. In the cutting region, the bulk of the PCB cross section is filled with the ceramic ferrite material. So, for this experiment, the narrow beam YAG laser was selected with the objective of producing a 0.13 mm (130 µm) gap. To optimize the laser cutting, the key parameters include beam power, beam aperture, feed rate, pulse rate, and focus depth. Experimental cuts were made using different power settings, focus levels. Additionally, different focus depths and multiple passes were investigated. After some experimentation, we settled on one pass focused 1 mm below the top surface of the panel and a feed rate of 1.3 mm/s. The cutting distance is 1.78 mm, so the actual cutting time was within 3 s. Forced argon gas was used to cool the cutting surface and blow out slag.
Figure 6: Laser gapped embedded inductors, 10 winding configuration.
Two test panels were fabricated with three different windings configurations; 8, 10 and 12 windings. For each configuration, two rows of 10 units were implemented for each winding implementation. Here, the results are reported for the 10 turn configuration. The first panel was used to experiment with laser settings. Once the settings were established, they were used to run the second panel. Figure 6 shows some of the 10 winding devices. While the objective was to cut a 0.15 mm gap, during the experimentation phase, the gaps were inspected under a microscope and it was noticed that some debris and particulate remained in the gap after laser cutting. Also, inductance was measured after each test cut. Better consistency was achieved by widening the gap to about 0.2 mm. This allowed much of the debris to be blown out of the gap by the laser and forces argon gas. With the wider gap, it was still possible to achieve 10 µH of inductance when using the 10 winding configuration. Table 1 summarizes the laser parameters that were used to cut gaps in the second panel. The inductance data for 20 units of the 10 winding configuration is summarized for each row in Table 2. Before gapping, the cores exhibited an AL value of 1.6 µH/N2. After laser gapping, the AL value diminished to 0.10 µH/N2. This is much lower than the calculated value and is attributed to the wider gap width. For the top row, the average inductance was 11.4 µH, 14% above the design target of 10 µH. For the second row, the nominal value was within 4% of 10 µH. The data in the second row is partly skewed due to the low inductance value of the 10th unit in that row. The laser settings were by no means optimized and further refinement of the gapping process can narrow the data distribution and tolerance.
Table 1: Summary of laser parameters used in the experiment.
In addition to inductance, the winding resistance is another key performance parameter. For power conversion, the winding resistance contributes to power loss and impacts the system efficiency. Table 3 summarizes the winding resistance for the 10 µH inductors. Average resistance is 0.065Ω, which is acceptable for most power converter applications. However, resistance can be reduced further by using heavier Cu foils on the top and bottom layers, and by plating the vias thicker. The vias in this experiment were plated to IPC standard 25 µm. Further resistance reductions can be achieved by plating the vias to 35–50 µm and capping the via barrels with copper.
Table 2: Inductance data.
Table 3: Winding resistance.
As described earlier, gapping reduces the cores sensitivity to DC currents. Figure 7 shows the inductance versus DC current for a typical 5K permeability core and the gapped samples. Prior to gapping, the embedded 10 turn inductors exhibited inductances in the range of 140 to 170 µH. To demonstrate the response of the un-gapped core, a 10 turns inductor with 158 µH at 0 DC bias current was tested. As DC current is applied, the inductance diminished quickly. At 40 mA of DC current, the inductance of the un-gapped core diminishes to half of the starting value. In comparison, the second plot shows the performance for 5 gapped inductors when a DC bias current is applied. Degradation over the range of 0 to 0.5A is about 20% to 25%.
Figure 7: Inductance vs DC current for un-gapped and gapped ferrite cores.
Additionally, devices were tested over temperature. Figure 8 shows the characteristics for the un-gapped and gapped core from 0°C to 100°C. The ungapped core exhibits variation exceeding 20% over the temperature range while the gapped devices exhibit very little variation over the temperature range and remain within 10% of their value at ambient temperature.
Figure 8: Inductance vs. temperature for un-gapped and gapped ferrite cores.
Finally, a few of the inductors were cross sectioned to inspect the laser cut. Figure 9 shows a photo of a cross sectioned part. The direction of the laser cut was from top to bottom. The laser cut has a width in the 0.20 mm to 0.25 mm range.
Figure 9: Cross section view.
This paper demonstrates the viability for laser gapping embedded transformers and inductors. The PCB structure of the embedded magnetics brings efficiency to the gapping process. A design example was presented for a 10 µH inductor. After gapping, the device exhibited good stability under varying temperatures and DC bias current. Such device would be suitable for SMPC power converters operating in the 500 kHz to 2 MHz range. The embedded toroid structure is useful for reducing the circuit footprint and cost and is suitable for implementation in either a power conversion module or directly in the system board.
The original objective was to produce a 10 µH inductor using a 6 winding configuration and 0.15 mm wide gap. After experimentation, a 0.2 mm gap was implemented. The larger gap allowed debris to be blow out of the gap during the laser process and provided more consistency between inductance of the gapped devices. The caveat is that the larger gap requires designing the inductor to have a higher initial value. A 10 µH inductor was realized using a 10 turn configuration that had a pre-gapped inductance in the range of 140 µH to 170 µH. Design equations and methodology were presented as a guide for designers who want to pursue this technology.
1. Ferroxcube Product Selection Guide 2009.
2. Sanjaya ManikTala, Switching Power Supplies A to Z, 2006 Elsevier Inc., Burlington, MA.
This paper was first presented at the 2018 IPC Apex Expo Technical Conference and published in the 2018 Technical Conference Proceedings.
Jim Quilici is a design consultant at Radial Electronics. You may reach Jim at email@example.com.