Magnetics Business & Technology - Spring 2014 - (Page 12)

FEATURE ARTICLE Optimizing Magnetic Core Gapping for Low-Loss Sine-Wave Inductors By Kenneth Pagenkopf, Principal Engineer * Acme Electric Improving Energy Efficiency Redesigning inductors to reduce their losses is a requirement for high-efficiency power conversion. Starting with a basic understanding of the construction and applications of these components and moving to a critical analysis of the mechanisms and theory behind the magnetic field fringing that occurs will lead to a methodology of predicting gap sizes and inductance that minimizes losses and improves performance. A few simple formulas can help find design limits and a more comprehensive approach can help the designer establish optimal positions, quantities and sizes for gaps within inductor cores. There are additional benefits that can be realized from this approach, which allow for smaller size and lower costs. A broad-thinking design approach based in solid magnetic equations can help optimize magnetic core gapping for low-loss sine-wave inductors. Figure 1. Core Construction Inductor Applications Three-phase sine-wave inductors are used in many types of equipment that convert energy using pulse-width modulation (PWM) techniques. These include motor drives, inverters for alternative energy and regenerative systems. The PWM developed needs to be made into a clean, smooth, sine-wave for power drive and energy supply applications. Even though there are electronic means of accomplishing this, it is still primarily done by passive filtering with inductors and capacitors. Traditional construction of the three-phase inductors can be done by combining three single-phase components or by the use of a single three-phase inductor. Then, these can be constructed by using powdered cores, wound amorphous cores or laminated silicon steel cores. This discussion will be directed toward the construction of three-phase laminated silicon steel core sine-wave inductors. Steel Core Construction Standard steel-core construction involves three legs and two yokes of laminated material having a consistent width (lamination) and depth (stack) as shown in Figure 1. The structure is clamped together and is usually glued for audible noise reduction. Each leg of the core is surrounded by a wound coil and there is at least one gap in each of the core legs. The gaps serve to allow the adjustment of inductance and control flux density in design. The quantity, size and placement of these gaps can have a large impact on the power losses of the assembly and the inductance balance between legs. Understanding how they work and how to predict their effects is the key to optimizing efficiency in inductor design. Gapping Theory Air gaps affect inductance through reluctance and flux. When magnetic flux goes around a magnetic circuit, it is much like current in a resistive circuit and the inductance of the inductor is most simply calculated by the circuit shown in Figure 2. With multiple gaps, the reluctance is summed linearly. Yet, the magnetic field in an air gap is not as tightly constrained to the core's cross-sectional area as it is in the core. The field fringes outward around the gap and the amount of fringing is affected by what magnetic structures and fields are around it. When fringing occurs outside the coils, the core structure bends it and when within the coils, the coils constrain it. Much like skin effect in conductors, in operating inductors, the coils create opposing forces that push back on the fringing and reduce its effects. A simple way to see the effects of fringing is to envision it creating a larger effective cross-sectional area (Ae) as it goes through the gap as shown in Figure 3. This will make the inductance look larger. Basic formulas shown in Figure 4 show that the reluctance of the core can usually be neglected. This is because the air gap reluctance is significantly larger when air gaps and steel permeability are reasonably large. It is also seen that inductance is directly proportional to Ae. Inductance Prediction Considering that fringing affects the perception of the size of Ae, it is natural to see that inductance is affected by fringing. The common way to show this is by adding a fringing factor (FF) to the basic inductor equation as shown in Figure 5. This FF has been a sub- 12 Magnetics Business & Technology * Spring 2014 Figure 2. Reluctance Calculation Figure 3. Gap Fringing Refinement Figure 4. Inductance Calculation

Table of Contents for the Digital Edition of Magnetics Business & Technology - Spring 2014

Editor's Choice
Magnetic Design and Applications Using Halbach Theory
Test & Measurement
Optimizing Magnetic Core Gapping for Low-Loss Sine-Wave Inductors
White Paper: Toroidal Line Power Transformers
Magnetics, Materials & Assemblies
Research & Development
Software & Design
Industry News
Marketplace / Advertising Index
Spontaneous Thoughts: NdFeB: It's About the Cerium

Magnetics Business & Technology - Spring 2014