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Toroidal Transformer Basics


A toroid is a doughnut-shaped object whose surface is a torus. Its annular shape is generated by revolving a circle around an axis external to the circle.

A coil of insulated wire in a doughnut shape (usually with a core of iron or similar metal) is an example of a toroidal object. These are used as inductors in circuits such as low frequency transmitters and receivers because they possess higher inductance and carry greater current than similarly constructed solenoids. They are also used as transformers in main power supplies. Toroidal coils reduce resistance, due to the larger diameter and smaller number of windings. The magnetic flux in a toroid is confined to the core, preventing its energy from being absorbed by nearby objects.

In the geometry of torus-shaped magnetic fields, the poloidal flux direction threads the "donut hole" in the center of the torus, while the toroidal flux direction is parallel the core of the torus.


Advantages of Toroidal Power Transformers
The Toroidal Core
Stray Magnetic Fields
Duty Cycle
Size Considerations
Temperature Considerations
Custom Toroidal Power Transformers

Advantages of Toroidal Power TransformersToroidal Power Transformer

Toroidal transformers offer many advantages over standard laminated power transformers. Toroidals provide quiet, efficient operation with very low stray magnetic fields. Their small size and weight support a package that is easy to design into any application.

The Toroidal Core

At the heart of the toroidal is a highly efficient donut shaped core. To construct the core, grain-oriented silicon-iron is slit to form a ribbon of steel which is then wound, like a very tight clock spring. The result is a core in which all of the molecules are aligned with the direction of flux. Molecules not aligned with the flux direction increase a core's reluctance (the capacity for opposing magnetic induction), degrading performance to the level of common steel when the molecules are 90 degrees out of phase. EI laminated cores, which are stamped from grain-oriented Si-Fe, may have as much as 40% of the total core area perpendicular to the ideal grain direction, with another 40% acting only as a return flux path. This more efficient use of the core material in a toroidal can result in a size and weight reduction of up to 50% (depending on power rating), allowing the design engineer to innovate by exploiting the toroidal's small size, low weight, ease of mounting, and flexible dimensions.


Since toroidal cores are constructed of a continuously wound ribbon, there is virtually no air gap. The windings are evenly wrapped over the entire core allowing the transformer to operate at a higher flux density than in standard transformers. Toroidal transformers can operate at 1.6 to 1.8 Tesla (16,000 to 18,000 Gauss) while EI cores are limited to 1.2 to 1.4 Tesla (12,000 to 14,000 Gauss). The magnetic flux of the windings is oriented in the same direction as the grain-oriented core, thus achieving very high electrical efficiencies. Efficiency is a measure of a transformer's ability to deliver the input power to the load. Efficiency is expressed as a percent by:

% = ( PO / PI ) x 100

where; PO = Output power, PI = Input power, % = Efficiency

Also, standby losses are greatly reduced under no-load operation due to the lower magnetizing currents required by the toroidal core.

Stray Magnetic Fields

The primary cause of leakage flux from any transformer is the air gap. Ideally, a magnetic circuit should have no air gap. In traditional transformers with EI laminations stacked to form the core, the air gap at the junction of the I and the E is the source of most of the leakage flux. This flux strays into the surroundings due to the high reluctance of the air and the concentration of flux in the laminations. For the same reasons, mounting holes and grooves in the laminations also cause a small amount of leakage flux. The tape wound cut-C core is an improvement; but there is still an large air gap causing unwanted stray flux. Since toroidal cores are wound from a continuous ribbon of steel, stray fields from air gaps are eliminated.

In addition, the windings of the toroidal transformer uniformly encase the core in copper. This results in a natural magnetic screening effect which, in combination with the elimination of the air gap, results in an 8:1 reduction of radiated magnetic field over an equivalent rated EI transformer. The windings covering the solid ring core also help reduce magnetostriction -- the main source of acoustic "hum" in standard transformers. Audible noise can be reduced even further by varnish impregnating the toroidal core and/or the copper windings.

Duty Cycle

Significant reductions in transformer size and weight may be realized in many cases where the transformer is loaded intermittently. In such cases, the load is on (tON) for only a small portion of the total period (tCYCLE). The period is much shorter than the thermal time constant of the transformer. To calculate the nominal power rating (VA) of the transformer use the following equation:


where; tCYCLE = tON + tOFF


The regulation (percentage of voltage drop) may be expressed with the following equation:

% Regulation = [( VNL - VFL ) / VFL ] x 100

VNL = Open circuit, no load voltage

VFL = Full load voltage

Common values for regulation are around 5%. However, regulation can be adjusted to conform to most requirements. Regulation is inversely proportional to efficiency, physical size, and cost, and is directly proportional to temperature rise. All these factors should be taken into consideration when the regulation spec is determined.

Size Considerations

While the cross-sectional area of the toroidal core must be held constant, the height and diameter may be varied to meet package constraints. The functional optimum ratio of diameter to height is 2:1. A 3:1 ratio may be used in applications where a very low profile is required. And if a minimum footprint is required an aspect ratio of 1.5:1 could be considered. The only physical restrictions on the size of a toroidal transformer are the limitations of the winding machinery. A minimum center hole must be maintained in order to permit the insertion of the winding magazine, for application of the wire and insulation.

Temperature Considerations

Operating temperature is an important safety factor which must be considered. It is common to see a 60C to 70C rise above ambient at rated power. Heat generated by the power transformer is due to the sum of the copper and, to a lesser extent, the core losses. Since copper has a positive temperature coefficient, its resistance increases with temperature. As the temperature of the coil rises, the DC resistance of the windings also increases, resulting in a self heating cycle. Temperature rise can be reduced by increasing both the diameter of the winding wire and the size of the transformer. However this is at the expense of increased costs. Tabtronics transformers utilize UL recognized insulation systems for Class B (130C) operation. Temperature rise will also depend on where and how the transformer is mounted and how well it is cooled. When higher temperature ratings are needed, we offer UL recognized systems to Class F (155C) and Class H(180C).

Custom Toroidal Power Transformers

At Tabtronics, Inc., we provide custom solutions to all your electromagnetic requirements. We know that you need more than a prepackaged transformer for your unique application. That is why we are committed to providing individualized attention to your needs. Call our experienced technical sales department to discuss all the options available in toroidal mounting, leads, terminations, and safety protection and recognition.

While there is no prepackaged solution to your individual requirement, we do recognize the need for general design guidelines to aid the engineer in the early stages of product development. The chart below shows theoretical size, weight, and no load losses for toroidal transformers from 15VA to 1900VA. Remember, your application requires a unique solution, so please call the factory to consult with the experts.

Theoretical Size, Weight, and No-load Losses for Toroidal Power Transformers 
Nominal Power (VA)1
Copper Losses (W)2
Core Losses (W)
O.D. (in)
Height (in)
Weight (lb)
15 (18) 3.0 0.20 2.5 1.3 0.7
30 (36) 5.8 0.25 3.0 1.5 1.1
50 (60) 8.6 0.45 3.2 1.4 1.6
80 (95) 12.0 0.60 3.9 1.5 2.2
120 (145) 16.0 0.90 3.9 1.9 3.0
160 (190) 19.0 1.20 4.5 1.7 3.8
225 (270) 20.0 1.40 4.5 2.0 4.9
300 (360) 22.0 1.70 4.6 2.6 5.7
400 (480) 27.0 2.00 5.4 2.0 6.5
500 (600) 31.0 2.40 5.4 2.4 8.0
625 (750) 36.0 3.10 5.5 3.2 9.5
800 (960) 45.0 3.80 6.4 2.7 13.0
990 (1200) 45.0 4.70 6.4 3.0 16.0
1100 (1320) 45.0 6.50 6.4 3.3 17.0
1300 (1560) 60.0 5.70 8.0 2.6 20.0
1600 (1920) 62.0 7.10 8.0 3.0 23.0
1900 (2280) 65.0 8.50 8.0 3.4 26.0

All values are theoretically typical.
Values within parenthesis are for 60Hz operation only.
Copper losses at 25C ambient temperature at full load


Copyright © 2008 RAF Tabtronics LLC.
Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts.  A copy of the license is included here "GNU Free Documentation License".

© 2007 RAF Tabtronics LLC
PO Box 128, Geneseo, NY 14454-0128
e-mail: info@tabtronics.com