Power Electronics

One Powerful Decade: Keep Core Geometry in Mind When Designing Transformers

One Powerful Decade: Core geometry affects transformer performance, so the designer must be aware of the characteristics of the typical types: E cores, round center leg E cores, toroids and pot cores.

Design engineers are constantly faced with the challenge of specifying a transformer that will meet design specifications as well as cost constraints. The designer who draws up the circuit specification is seldom expected to design the transformer. However, the designer is expected to know the basic differences various core shapes offer, if not the techniques used in designing with them.

If core shape is not specified, the task of designing the transformer is left to the transformer vendor. Each vendor has a specialty, or niche product. Previous proven designs dictate the way custom products will be developed. When broadly specified transformers arrive, they are guided into one niche or standard process. In this way, the component is more efficiently and economically produced because the manufacturing process is addressed during the design phase. The end product will be a reliable transformer, but it may be optimized for production, rather than for circuit performance. This physical separation between the circuit designer and the transformer designer often leads to cost effective designs, but sometimes does not address overall system needs.

By comparing and contrasting various ferrite cores, evaluating design equations, looking at manufacturing techniques, and stepping through the design process, a basic understanding of component design should be achieved. Ferrite cores were chosen because they offer a wide range of shape choices, are available as standard product by most vendors, and their performance is well documented by ferrite manufacturers.


When ferrite material was introduced, it became possible to make magnetic circuits of conventional shapes, as well as custom shapes. Excluding toroids, most ferrite transformer cores consist of two like pieces assembled together by proper grinding and polishing techniques so the resultant air gap between the mating surface is virtually eliminated. Although a discrete air gap may need to be introduced into the magnetic structure to allow the core to support higher dc bias levels that would otherwise drive the non-gapped core into saturation. This gap is commonly ground into the center post, or leg, of the core by the ferrite core manufacturer, but placing non-magnetic shims and spacers between the core halves is sometimes used by the transformer manufacturer.

Ferrite transformer cores are made in a variety of different shapes. Each shape has optimum proportions to obtain specific desired characteristics. For example, the pot core is designed for a high degree of magnetic shielding, while ER cores are designed for their low profile. Even with this optimization, it must be remembered that practical considerations must be met. Typically, the termination requirement, land pattern, EMI concerns, and profile height all lead to the proper choice of core shape. The geometric arrangement of the terminals must usually be compatible with the printed circuit grid or land pattern. These considerations lead to the use of a specific coil former having a specified number of terminal pins or pads arranged in a particular pattern. The core selection must often be designed around the termination requirement. In today's industry, height restrictions and EMI shielding are becoming an issue. Therefore, low profile designs and pot cores may need to be considered.


The pot core (Figure 1) is a closed cylinder containing an upright round center post on which a bobbin is placed. Pot cores, when assembled, nearly surround the wound bobbin. This aids in shielding the coil from picking up external EMI sources. Good electromagnetic coupling is readily obtainable with this core configuration. The pot core dimensions typically follow IEC standards so that there is interchangeability between manufacturers. Both plain and printed circuit bobbins are available, as are mounting and assembly hardware.

Mounting on a p. c. board tends to be very straightforward. The main disadvantage of the pot core is that the lead out slots are not wide enough to accommodate a coil former having a large number of fixed terminal pins. Because of its design, the pot core is a more expensive core than other shapes of comparable size. Pot cores for high power applications are not readily available and the bobbin windings have limited exposure to air circulation.


The first ferrite transformer cores were made in the form of double E cores to match the standard scrapless lamination shapes that had long been in use for 50/60 Hz transformers. Lamination size E shapes (Figure 2) are available to fit commercially available bobbins. E cores are less expensive than pot cores, and have the advantages of simple bobbin winding plus easy assembly. Gang winding is possible for the bobbins used with these cores. E cores can also be pressed to a different thickness, providing a broad selection of cross sectional areas. Consideration should be given to those core sizes where bobbins are readily available from several bobbin suppliers. E cores can be mounted horizontally or vertically, depending upon whether above board height or board real estate area is most important. Printed circuit bobbins are available for low profile mounting. Figure 3 shows various mounting styles used at API Delevan for E core transformers, including horizontal, vertical and surface mount arrangements. E cores are popular shapes due to lower cost, ease of assembly, ease of winding and ready availability of a variety of hardware. The shielding on E cores is not nearly as effective as the shielding on pot cores.

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The double E core, while matching the standardization of the industry, also carries with it the inherent restriction that the core center leg is rectangular. It was soon realized that pressed ferrite cores need not be restricted by a square center leg. Therefore, E cores with round center legs were developed (Figure 4). These cores have the advantage of easier winding on a cylindrical coil, and better control in production over the leakage inductance and self-capacitance. These shapes offer a cross between E core and pot cores. Like E cores, they provide a wide opening on each side. This gives adequate space for the large size wires required forlow output voltage switchmode power supplies. It also allows air flow that keeps the assembly cooler. One of the advantages of the round center post is that the winding has a shorter path length around it than the wire around a square center post with equal area. This reduces the losses of the windings by approximately 13% and enables the core to handle a higher output power. The round center post also eliminates the sharp bend in the wire that occurs when winding on a square center post.


Toroids (Figure 5) are the least costly of all comparable core shapes. While no bobbin is required, accessory and assembly costs vary widely. The simplest method of mounting is the self-leaded style where the magnet wire extends beyond the core winding to provide the device leads for insertion into the circuit board. There are a limited assortment of bases available from several sources for surface mount applications. Assembly costs associated with them also vary.

Figure 6 shows several different mounting styles API Delevan uses for toroids. Windings are placed on the cores by either a manual process, whereby a predetermined length of wire is cut to length and then the wire is thread through the center of the core one turn at a time, or by using a toroid winding machine. The machine is required to load, or prewind, a fixed length of wire unto a shuttle prior to start of the winding. Each method has its advantages, typically the hand wind is used for heavier wire and fewer number of turns. As produced, the toroid core has sharp edges and must be tumbled in its manufacture to prevent magnet wire insulation from being cut through during the winding process.

To provide higher voltage insulation between the windings toroid cores typically will be insulated by use of parylene or epoxy coatings. A few suppliers can grind a small gap in the core to provide an air gap for applications that require a dc bias that would otherwise saturate the core. A more common method of attaining higher saturation levels is to use materials other than ferrite, such as molypermalloy or Kool-Mµ. These materials are only available in a toroid configuration, although the Kool-Mµ has just recently been introduced in an E-coreshape. The toroid shape provides excellent shielding.


To illustrate an example of each of these core types; a widely-used power transformer will be designed. The transformer has a push-pull primary and a center-tapped secondary. Also assume a 1.0 V diode drop (Vd) on the output. Its specs are:

Input Voltage, Vin= 25 V

Output Voltage, Vo= 25 V

Output Current, Io= 1.375 A

Frequency, f = 21 kHz

Efficiency, η= 0.9875

Temperature Rise = 25°C

Flux Density, Bm= 0.2 T

Core configuration constants given in McLyman's book[1] can guide selection of the proper core geometry. This process is simply a guideline for proper core selection. By modifying parameters after this initial core determination, further optimization can be achieved.

Table 1

lists the constants for E cores (EE as well as round center leg E cores, Pot cores, and toroids.

Using the allowable core loss calculations, a suitable ferrite material can be selected from a vendor catalog. The transformer designer is faced with a set of constraints that must be observed in the design of any transformer. As described above, some of these constraints are output power (Po), minimum efficiency (η), and permissible temperature rise. Others are pad layout, profile height, and EMI concerns. The transformer engineer's problem is only partially indicated by the variety of materials whose mechanical, electrical, magnetic, dielectric, thermal, and environmental characteristics he must know.

Transformer designers have used various approaches to use all these parameters to arrive at a satisfactory design. The engineer would like to produce the final design by the direct application of general principles to the specifications before him, but in practice the design procedure is often influenced by previous proven designs.

When a designer is faced with specifications not indicating core preferences, the final design is typically guided into the easiest to manufacture. These designs have a history of performance and the manufacturing process has been designed around them. Thus, the design process may involve some cut and try of an existing design in which iterative calculations yield a satisfactory solution.

Depending on the application, certain geometric constraints will dominate. Some factors affecting these constraints can then be modified as necessary to achieve the more practical designs. It is not possible to optimize all the parameters in a design because of their interaction and interdependence. For example, if lower volume and weight are important, reductions in both can often be achieved by operating the transformer at a higher frequency but the cost will be lower efficiency. When the frequency cannot be increased, weight and volume reductions may still be possible by selecting a more efficient core material, but at increased cost. By knowing the application and design history, a cost-effective transformer can be produced.

Table 3

from the Magnetics' ferrites catalog shows the relative merits of the four core types discussed.

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  1. W. T. McLyman, Transformer and Inductor Design Handbook, 2nd ed. New York; Marcel Dekker, 1988.

  2. E. C. Snelling, Soft Ferrites Properties and Applications, 2nd ed. London,U.K.:Butterworths,1988.

  3. Magnetics Ferrites 2000 Catalog.

  4. N. R. Grossner, Transformers forElectronic Circuits, New York; McGraw Hill, 1967.

  5. R. Lee, Electronic Transformers and Circuits, 3rd ed., New York; John Wiley & Sons, 1988.

  6. J. K. Watson, Applications of Magnetism, Gainesville, FL, Published by the author, 1985.

  7. W. M. Flanagan, Handbook of Transformer Design & Applications, 2nd ed., New York, McGraw Hill, 1993.

  8. A. I. Pressman, Switching and Linear Power Supply, Power Converter Design, Rochelle Park, Hayden Book Company, 1977.


Output power
Po = (Vo + Vd)Io
35.75W 35.75W 35.75W 35.75W
Total power
Pt= Po[(20.5/η) + 20.5]
101.8W 101.8W 101.8W 101.8W
Area product
Ap= [(Pt×104)/(KfBmfKuKj)]x
K= Waveform coefficient
Kf= 4 for square waves, = 4.44 for sine waves
Ku= Window utilization factor, or the fraction of available space occupied by the winding.
Typical values:
Ku= 0.25 for toroids, otherwise = 0.4
0.283 cm4 0.366 cm4 0.560 cm4 0.366 cm4
From catalog choose core with closest Ap to calculated value 0.392 cm4 0.421 cm4 0.707 cm4 0.421 cm4
From vendor information, choose appropriate bobbin or coil form (if necessary) and read the actual Mean Length Turn (MLT) 3.76 cm 4.54 cm 2.58 cm 4.09 cm
Actual core area, Ac. Also available from vendor information 0.931 cm2 0.401 cm2 0.374 cm2 0.401 cm2
Actual window area, Wa. Also available from vendor information 0.421 cm2 1.05 cm2 1.89 cm2 1.05 cm2
Actual weight of core, Wtfe. Also available from vendor information 20 grams 15 grams 11.6 grams 15 grams
Approximate transformer surface area
At= KsAp0.5
21 cm2 27 cm2 21 cm2 27 cm2
Number of primary turns
Np = (Vin ×104)/(KfBmfAc)
16 37 40 37
Primary, input current
Ip= Po/(Vinη)
1.45A 1.45A 1.45A 1.45A
Current density allowed for 25°C rise
J = KjApy
536 A/cm2 413 A/cm2 432 A/cm2 413 A/cm2
Primary wire area
Aw= (0.707Ip)/J
(In center tap configuration, Ip is multiplied by 0.707)
0.0019 cm2 0.0025 cm2 0.0024 cm2 0.0025 cm2
Primary wire size from wire table #24 AWG #22 AWG #23 AWG #22 AWG
Primary Winding Resistance
Rp = (MTL)(Np)(µΩ/cm)×10-6
0.0506Ω 0.0895Ω 0.0684Ω 0.0806Ω
Primary copper losses
Pp= Ip2Rp
0.106W 0.188W 0.143W 0.169W
Number of secondary turns
Ns= (NpVs)/Vp
16 37 40 37
Secondary wire area using output current and allowable
current density
0.0018 cm2 0.0024 cm2 0.0023 cm2 0.0025 cm2
Secondary wire size (from wire table) #24 #22 #23 #22
Secondary winding resistance
Rs= (MTL)(Ns)(µΩ/cm)×10-6
0.0506W 0.0895W 0.0684W 0.0806W
Secondary copper losses
Ps= Is2Rs
0.096W 0.169W 0.129W 0.152W
Total copper loss
Pcu= Pp+Ps
0.202W 0.357W 0.272W 0.321W
Allowable core lossPfe= (Po/η-Po)-Pcu 0.251W 0.096W 0.180W 0.131W
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