Core Shapes

The variety of shapes and combinations provide designers with many different options to achieve the best performance in their required footprint. Choosing the most appropriate shape is influenced by a variety of factors including the allowable mounting footprint and volume, the application, radiation limits, size of windings, operating and maximum temperature, and the mounting configuration.  Some of the most popular core shapes are toroid, rods, E-cores and blocks. Many more complex shapes, and even custom designs are possible.  Micrometals has vast experience in designing and manufacturing custom shapes and even creating custom material formulations that can provide unique performance attributes for challenging applications.
In addition, an inductor's magnetic core can be created from multiple piece stacks or assembled together. Multi piece cores made of the same magnetic material may be required for extremely complex shapes
or larger inductors.  Micrometals can even fabricate cores into mounting plates, rings or other
composite configurations.

Cores should be chosen with an understanding of how windings will be installed. Sometimes, windings are wound directly around the core. Other times, the windings may be wound on a sleeve, or bobbin, which is commonly slipped over a protruding part of the core. Wire used for inductors are usually insulated to prevent adjacent turns from shorting out. 

 

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Inductor Design Basics – One Approach

After a basic approach to a core shape is determined based upon footprint and desired performance a series of calculations is carried out to determine how much wire and possible orientation is required to provide the desired electrical effects.  Below is one approach to designing an inductor: 

1. Determine required specifications including Peak Inductor Current (A), Vin RMS min, Vin RMS max ,
    
2. Vout DC, f (Hz) – Switching, f (Hz) – Fundamental
    
3. Select a core based upon size, material and targeted inductance per turn. These factors work together to determine the flux density and core loss.  
    
4. Next, calculate inductance and turns based on Al.
    
5. Calculate copper loss.
    
6. Calculate flux density and core loss. 
    
7. Calculate temperature rise.
    
8. Reiterate as required to get the turns to layer nicely on the core for good coupling and low leakage inductance.

Experienced engineers can quickly move through many of these steps as their experience has provided them with a deeper insight into the relationships and trade-off between different design approaches.  Below are of those insights to consider:

 

Design Considerations

• A design dominated by core loss is not a prudent thing to do regardless of core material.  
   
• As a starting point, consider a 50-50 split between core and copper loss.
   
• A better design is on the order of 20-80 split between core and copper loss.
   
• Core loss is expressed in mW/cm³ of volume.
   
• Copper loss is expressed as I² x Resistance.
   
• The higher the ripple current in a specific design the lower the energy storage capability is for a given size core.
   
• As the % of Ripple Current increases, the greater the core loss will become. A larger core, lower permeability or a completely different core material may be necessary to assure longevity.
   
• Reduce the core loss at the expense of the copper loss.

 

Thermal Considerations

• Assuming a +55°C ambient, a good design practice to follow is +40°C temperature rise or less.
   
• This rule will keep UL and Product Safety people very happy.
   
• The design will have a built in safety margin which will tolerate abnormal overloads.
   
• A 25°C reduction in temperature will improve the life expectancy of the core by one order of magnitude.
   
• Most applications for Iron Powder cores have a maximum ambient temperature of +55°C or less.
   
• Some designs are safe in a +70°C ambient provided Thermal Aging is considered and the life expectancy meets end of life goal for the product.
   
• Temperature Rise of the Magnetic component will set the maximum safe ambient temperature.
   
• It is much easier to remove heat from the copper winding than from the core material.
   
• Good thermal data is not always easy to obtain.
   
• The placement of thermocouples and connections is critical for reliable and repeatable data.
   
• Static Air means just that, no air flow at all. A closed box may take 3 - 5 hours in order to reach temperature equilibrium.
   
• Do not be fooled by adding Forced Air to solve an overheated Magnetic Component problem.
   
• Variable speed fans can be Deadly for a design that is dominated by core loss. Even at reduced power, a PFC choke still has constant core loss and heat.
   
• Thermal Conductivity of a given core material may mask an internal core temperature that is +5°C to +30°C hotter on the inside Vs measured on the outside surface.
   
• Iron Powder Cores allow for easy placement of a thermocouple inside the core. A small diameter hole is drilled into the core. The thermocouple is installed into the hole and glued in position.
   
• Improperly designed and not adequately tested Magnetics can lead to Thermal Runaway of the core material.
   
• Thermal Aging is generally not a problem at frequencies below 10 KHz.
   
• Eddy current losses become increasingly significant at higher frequencies. Thermal Aging increases the eddy current loss of the core.
   
• Hysteresis loss is the major loss at low frequencies but is not effected by Thermal Aging.
   
• The Volume of the core is directly related to how quickly a material will age - Larger cores age at a faster rate than smaller cores.

 

Mechanical Mounting Precautions

• Iron Powder cores have a distributed air gap structure.
   
• The placement of ferrous materials around or under E-cores, U-cores and HS-cores will short the gap structure and dramatically increase the core loss.
   
• Cores can be secured by the following
   

      •     Phosphor bronze or nonmagnetic stainless steel banding materia

      •     Brass hardware

      •     Various electrical tapes

      •     Cable tie wraps

      •     Filled epoxy or filled super glue. 
 

• Pay close attention to the upper thermal limits of these materials.

 

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Inductor losses - Core & Copper

The quality of an inductor is defined as the dimensionless factor Q, which is a ratio of the inductance reactance at a given frequency divided by the combined losses in the inductor.  Lower losses equal higher quality inductors.  Losses present themselves in several forms.

Core losses are a result of an alternating magnetic field in a core material. The loss generated for a given material is a function of operating frequency and total flux swing (∆B).  The core losses are due to hysteresis, eddy current and residual losses in the core material.  These circulating currents produce losses that are proportional to the square of the inducing frequency.

Hysteresis is represented by the enclosed area within a BH curve and results from the energy required to reverse the magnetic domains in the core material. These core losses increase in direct proportion to frequency, since each cycle traverses the hysteresis loop.

DC Resistance also known as DCR or copper loss consists strictly of the DC winding resistance and is determined by the wire size and total length of wire required as well as the specific resistivity of copper. 
Skin Effect increases the wire resistance above approximately 50 kHz because the current tends to travel on the surface of a conductor rather than through the cross section. This reduces the current-carrying cross sectional area.

In applications where the total losses are dominated by core loss rather than copper loss, an overall improvement in performance can be achieved by using a lower permeability core material.  This is typically the case in high frequency resonant inductors.

By utilizing a lower permeability core material additional turns will be needed to achieve the required inductance. While additional turns will increase the winding losses, it will reduce the operating Ac flux density which will result in lower core loss.

Winding strategies to reduce loss
The winding around an inductor care has resistance determined by the length and cross sectional area of the conductors within the winding and the resistivity of the conductor material.  Current flowing through the winding introduces resistive losses. Alternating current flow through the winding causes eddy currents in the conductors and reduces a portion of the conductor cross section, thereby reducing the effective current carrying area which increases the resistance of the winding.

To reduce these eddy current effects Litz wires are typically used.   A Litz wire is a bundle of many thin insulated strands, with a diameter much less than the skin depth. In the Litz bundle, each strand is cyclically transposed from the center to the surface and back to the center so that each strand is periodically located along every place in the cross section of the bundle. This stranding and cyclic transposing reduces the skin and proximity effect and makes the current density more uniform across the cross section, minimizing winding resistance.  One should note that the dc resistance of a Litz wire is higher compared to a solid conductor with equivalent total cross-section.