Why a Toroid? Notes on Toroidal Transformers

Why a Toroid? Notes on Toroidal Transformers

Ralph Livingstone

Toroidal (“donut shaped”) transformers are a popular choice for the most demanding applications – where size and weight are at a premium in the end-use system. The shape of the toroidal transformer core results in several advantages to the transformer design – as well as several disadvantages. It is in the best interest of the system designer to consider how each factor may affect his application when selecting a transformer.

Size and weight

Moving dead weight around is costly. Studies of commercial and military aircraft fuel economy report differing results – but it is generally agreed that a single pound of weight on an aircraft will cost tens of thousands of dollars in fuel costs over the service life of the aircraft. It therefore has become a primary objective of the aircraft system or component designer to minimize weight as far as practicable. In a transformer this means minimizing the masses of both the core and winding materials used. Although the optimum transformer design is always a balancing act between core cross section and copper winding area, it can be argued that copper loss is the one variable that determines the ultimate size and weight of a transformer.

In order for a conventional transformer to effectively transfer energy from the primary winding to the secondary, it is necessary to operate the magnetic core within the region well below the point of saturation flux density. Operating above that limit will result in high peak input currents, harmonic currents imposed on the input source, and distortion or droop of the secondary voltage waveform. In the equation to calculate maximum flux density, both the transformer core cross-sectional area and the number of primary turns are in the denominator. This means that the core size can be reduced by the same ratio that the number of primary turns is increased, without affecting flux density.

In practice, in order to fit more primary turns into a given core winding area, the wire diameter must be reduced. The simultaneous reduction of wire diameter and increase in winding conductor length (with increased turns) will result in an increase in resistive winding losses. Increasing the available winding area, and decreasing the length of wire needed to complete each turn are two effective ways to mitigate the increased copper losses caused by an increase in turns.

Increasing the winding area may be achieved by increasing either the depth or the width of the winding – but increasing depth alone can result in greater difficulty shedding waste heat from the winding structure. It therefore becomes apparent that a core that allows the placement of wire over the full length of its structure will assure the optimum use of available winding area. A rod-shaped core fits this criterion – but its open magnetic structure would result in high magnetizing current and undesirable stray magnetic field influence. Joining the ends of a rod-shaped core to close the magnetic path would result in a core that was toroidal in shape. In theory, a round core cross section represents the optimum shape for reduction of winding turn length per unit of volume – as a circle is the shape that encloses the greatest area per unit length of perimeter. In practice though, it is often possible to take better advantage of actual available volume using a toroid core with a square or rectangular cross-section.

The windings on a toroidal transformer are exposed over the entire surface of the transformer – affording optimum transfer of waste heat from the copper windings. This often will allow the designer to use somewhat smaller gauge wire than would otherwise be prudent – without exceeding the specified temperature rise limit – if load regulation and efficiency considerations allow.

The resulting decreases in the core and copper volumes therefore work together to make the toroidal configuration the ideal choice when reduction of size and weight are primary considerations.


The closed-structure of the toroidal core – with no natural air gap in its magnetic path – greatly reduces stray magnetic field leakage, compared with conventional core shapes. The placement of the transformer windings over the entire core surface results in optimized coupling of magnetic core flux to the windings. This placement has the effect of limiting the influence of magnetic H-field leakage from the core upon external circuitry; and toroidal transformers in most applications require no additional magnetic shielding. The addition of an external magnetic shield can of course still be used if necessary to limit the effects of external H-field radiation upon the transformer windings. The shape of the toroidal coil makes the addition of an external electrostatic shield a simple matter – limiting the influence of E-field radiation on or from the outer transformer windings.

The other shoe – disadvantages of toroids

For all the advantages they offer, toroidal transformers do have several drawbacks when compared to conventional core or shell type transformer geometries. The first of these and most apparent is the labor cost associated with the winding of a toroidal transformer coil. In a conventional bobbin or tube-wound coil, each winding can be continuously fed at high speed onto the coil form directly from the roll of magnet wire. The core structure – whether a stack of laminations, a cut core, or pressed ferrite shape etc. – is then added onto the prepared coil structure. Using a toroidal core, the entire remaining length of wire for the complete winding must be passed through the core aperture every time a single turn of wire is added to the coil. This means that in a bobbin-wound transformer with 3300 turns on its primary, each turn is wrapped around the bobbin a single time. In a similar transformer that is wound on a toroidal core, the entire length of wire for the coil must first be loaded through the core aperture onto a shuttle. Each turn of wire must then pass again through the aperture between 1 and 3300 times – depending on where it falls within the winding. The increased labor time required to perform this repetitive motion is somewhat mitigated, since in the toroidal construction no core stacking or assembly is required. The final effect though, is usually a net increase in total labor time.

Another disadvantage of the toroidal core is one that occasionally causes problems either during testing or in the field during actual operation. This is the problem of inrush current. When a transformer is in operation, its core is magnetized alternately from +BMAX to – BMAX, in accordance with induced primary magnetizing current. If voltage applied to the primary winding is instantaneously interrupted, as when opening a switch, the core will remain magnetized to some extent in the same polarity as it was at the moment when the input was removed. This state is referred to as residual magnetism. When power is reapplied to the primary winding, if the polarity of the applied sinusoidal voltage is such that its increasing amplitude reinforces the flux in the already magnetized transformer core, it is not uncommon for the core flux to approach or even exceed the core saturation limit for a few cycles – resulting in a surge in input current which may greatly exceed the normal full-load input current. This irritating phenomenon, referred to as inrush current, is practically independent of output load. If uncontrolled, this may result in nuisance-tripping of system fuses or circuit breakers. In a conventional transformer core, the assembly of the lamination stack or core set results in a natural air gap on the order of a few ten thousandths of an inch in the magnetic path. The low permeability of this air gap in series with the core permeability tends to help limit inrush current. In a toroidal core however, this air gap does not exist. It is therefore prudent for the end user to be aware of this issue – and to specify maximum inrush current if it may become a problem on the system level. The designer should control and test inrush of each new transformer design – especially when using a toroidal core.

One additional difficulty which should be mentioned when discussing toroids is the matter of adding electrostatic shielding between windings. In the conventional transformer construction, the addition of a shield is a fairly simple matter of adding a layer (or several layers) of insulated conductive foil between windings, taking care to terminate properly and of course avoid shorting the shield ends together. In a toroidal coil, the shape makes installing this style of shield very labor-intensive. For that reason, many transformer manufacturers construct shields for toroidal transformers by wrapping between winding layers with overlapping turns of insulated copper or aluminum foil tape. In order to conform to the toroidal coil neatly, this often means using many turns of narrow tape. Unfortunately, the turns of foil tape passed through the core aperture may have significant self-inductance – which will be in series with the drain path – greatly limiting the effectiveness of the shield. Adding an effective electrostatic shield to a toroidal transformer is therefore somewhat of a tradeoff between economy of labor and shield performance.

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