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Why is a toroidal transformer about half the size of a laminated transformer?
There are 2 factors that contribute:
1) In a laminated transformer core the individual E- and I-shaped laminates are stamped out of grain oriented steel. The magnetic flux travels easily along the grain but less well across the grain, which must be passed as part of the path around the bobbin. (See Fig 1)
In a toroidal transformer the core is wound like a roll of tape from grain oriented steel. The magnetic flux will go with the grain all the way around the core. (See Fig 2)
As a consequence, a laminated transformer core can be used with a flux density of 1000 to 1200 Gauss (1.0-1.2 Tesla). A toroidal transformer core is normally calculated with a flux density of 1500 to 1600 Gauss (1.5-1.6 Tesla) which results in a weight reduction of about (1.2/1.5 x 100 =) 20%.
2) On a toroidal transformer core the copper wires are wound all around the circumference which allows for many turns before a new layer of the winding must begin.
With a laminated transformer a bobbin is used to wind the primary and secondary windings. The width of the bobbin is limited as it must fit into the core (See Fig 3). As a result, many layers of windings must be wound and the length of the wire will increase with each layer and the average turn-length will be longer as more layers are needed. The weight of one turn of copper increases with the length of that turn so the total weight of copper for the whole winding will be higher than for a winding on a toroidal core where the (virtual) bobbin is much wider and fewer layers are needed with lower average weight per turn as a result (see Fig 4).
A secondary, less important, effect also comes into play. With the longer average turn-length in the laminated transformer the resistance in the winding increases so either a heavier wire must be used or more turns are needed to compensate for the voltage drop in the winding.
The actual weight savings for the toroidal winding compared to the laminated transformer winding is dependent on the actual design of a specific transformer but our experience over the years is that the toroidal transformer comes out at about 50% of the weight of a laminated transformer.
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