Embedded Inductors with Laser Machined Gap

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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.

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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.

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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.

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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.

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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.



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