Embedded Inductors with Laser Machined Gap

Estimated reading time: 14 minutes

(4)        A_L = μ₀ μ_r A_c / l_e

From Equation 4, the inductance factor is directly proportional to the relative permeability, μ_r. In the case of the 5K permeability 6.35 mm OD core, the A_L 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 A_c of 3.2 mm² and a path length l_e of 15.9 mm. To calculate the A_L value for the gapped core, we need to return to Equation 3. We have all the details to calculate the gapped A_L value, except the gap width, g. Selecting the gap size requires trial and error. Inductors with larger gaps will have more stability, yet A_L 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 A_L' value is calculated as follows:

μ_r' = 5000 / (1 + (0.15mm x 5000/15.9mm)) = 103

A_L =(12.57)(119)(3.2mm²) / (15.9mm)  = 260 nH/N²  

Inductance can now be calculated by multiplying the A_L value by the square of the turns: 

(5)        L = A_L 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 A_L value of 1.6 µH/N². After laser gapping, the A_L 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.

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