# Calculation of toroidal transformers

Before the designers of radio electronic equipment, the task is to create such devices that would be distinguished by their small size and minimum weight. Practice has shown that it is best to apply toroidal transformers... In comparison with armor cores made of W-shaped plates, they have less weight and dimensions, and also differ in better conditions for cooling the winding and increased efficiency. In addition, with a uniform distribution of windings around the core perimeter, there is practically shielding of transformers is no longer necessary. Due to the fact that the complete calculation of power transformers on toroidal cores is too cumbersome and complicated, the drives have a table with which it will be easier for a radio amateur to calculate a toroidal transformer with a power of up to 120 VA. The accuracy of the calculation is quite sufficient for amateur purposes. The calculation of the parameters of a toroidal transformer, which are not included in the table, is similar to the calculation of transformers on an E-shaped core. The table can be used when calculating transformers on cores made of cold-rolled steel E810, E320, E380 with a tape thickness of 0.35-0.5 mm and steel 3340, E350, E360 with a tape thickness of 0.05-0.1 mm at a power supply frequency of 50 Hz.

When winding transformers, it is permissible to use only interwinding and external insulation: although the interlayer insulation makes it possible to achieve a more even laying of the winding wire, due to the difference in the outer and inner core diameters, when using it, the thickness of the winding in the inner diameter inevitably increases. For winding toroidal transformers, it is necessary to use winding wires with increased mechanical and electrical insulation strength. When winding manually, you should use PELSHO, PESHO wires. In extreme cases, you can use the PEV-2 wire.
Suitable as interwinding and external insulation are a PTFE film with a thickness of 0.01–0.02 mm, a lacquered cloth LShSS with a thickness of 0.06–0.12 mm, or cambric mite.
An example of calculating a transformer Given: supply voltage Uc = 220V, output voltage Un — 24 V, load current In = 1.8A
1. Determine the power of the secondary winding P = Un * In = 24 * 1.8 = 43.2W
2. Determine the overall power of the transformer. Pg = P / µ = 43.2 / 0.92 = 48 W. The value of the efficiency and other data necessary for the calculation is selected according to the table from the required column of a number of overall capacities.
3. Find the cross-sectional area of the core Scalc = Pg1 / 2 / 1.2 = 481/2 / 1.2 = 5.8 cm2
4. The size of the core is selected Dc is the outer diameter of the core, dc is the inner diameter of the core, h is the height of the core

 Pg, W overall power of the transformer w1, the number of turns per volt for steels E310, E320, E330 w2, the number of turns per volt for steels E340, E350, E360 S, cm2 cross-sectional area of the core ð A / mm2, permissible current density in the windings µ %, efficiency transformer to 10 41 / S 38 / S Pg1 / 2 4,5 0,8 10-30 38 / S 32 / S Pg1 / 2 / 1.1 4,0 0,9 30-50 33.3 / S 29 / S Pg1 / 2 / 1.2 3,5 0,92 50-120 32 / S 28 / S Pg1 / 2 / 1.25 3,0 0,95

The closest standard type of core is OL50 / 80-40, the cross-sectional area of which is S = 8-5 / 2 * 4 = 6 cm2 (not less than the calculated one).
5. When determining the inner diameter of the core, the following condition must be met: dc> = d'c, where d'c = (2.4 * S) 1/2 = (2.4 * 6) 1/2 = 3.8 cm , i.e. 5> 3.8
6. Suppose that the core is made of steel E320, then the number of turns per volt is determined by the formula: w1 = 33.3 / S = 33.3 / 6 = 5.55 turns per volt.
7. Find the calculated number of turns of the primary and secondary windings Wi-1 = w1 * Uc = 5.55 * 220 = 1221 turns, W1-2 = w1 * Un = 5.55 * 24 = 133 turns.
Since the magnetic flux of leakage in toroidal transformers is very small, the voltage drop in the windings is determined practically only by their active resistance, as a result of which the relative magnitude of the voltage drop in the windings of a toroidal transformer is much less than in rod and armored transformers. Therefore, to compensate for losses on the resistance of the secondary overcasting, it is necessary to increase the number of its turns by only 3%. W1-2 = 133 * 1.03 = 137 turns.
8. Determine the diameters of the wires of the windings d1 = 1.13 (I1 / ð) 1/2, where I1 is the current of the primary winding of the transformer, determined from the formula: I1 = P2 / UC = 1.1 * 48/220 = 0.24 A ...
d1 = 1.13 * (0.24 / 3.5) = 0.299mm.
Select the closest wire diameter upward (0.31 mm); d2 = 1.13 * (In / ð) = 1.19 * (1.2 / 3.5) = 0.8mm
The transformers calculated on the basis of the table below were tested after production under constant maximum load for several hours and showed good results.

Ing. G. Martynikhin