Mains transformer calculations

Calculation of a small mains transformer

In vintage radio repair, it sometimes happens that the mains power transformer is damaged and needs to be replaced or rewound. This operation may require a recalculation of the transformer, which is done in 2 steps. The pages of this calculator are based on a simplified model and some formulas proposed by Marthe Douriou in her book given in the bibliography mentioned below.
This engineer wrote several technical books under a male pseudonym, then under her real name. At the same time, she produced articles in the magazine "L'Antenne" and then in "Le Haut-Parleur".

1. Pre-calculation: Based on the 4 parameters below, the dimensions of the transformer are roughly determined.
   The choice of these parameters will depend, in vintage radio troubleshooting, on what is available in the workshop. We choose from the available values equal to or immediately greater than the theoretical values found during the pre-calculation.
   
   
   • the mains frequency: We limit ourselves here to 2 values: 50 Hz (Europe, Asia, Africa), and 60 Hz in North America.
   • the admissible current density in the copper wires that make up the transformer. This choice is economic. The higher the admitted density, the lower the weight of copper required will be, but the higher the thermal heating due to the Joule effect in the copper will be.
   • the efficiency is the ratio between the total power delivered at the output and the power consumed at the primary, therefore drawn from the mains. In practice, a value around 0.85 or 85% is accepted.
   • the nature of the core. This determines the efficiency mentioned above, but also the dimensions and weight of the transformer. Here again, production cost considerations come into play. We go from the cheapest, the simple lamination, to the double C core, the most expensive. This nature determines the maximum admissible induction in the transformer. In a poor material, an induction of one Tesla should not be exceeded, otherwise the material will saturate at high powers and have a non-linear behavior.
     
     
2. Final calculation. In this second and final phase, the diameters of the copper wires and the cross-section of the iron core available are entered into the tool to display the number of turns of each winding. The copper must then fit on the winding former. Amateurs without high-performance winding machines adopt a safety coefficient. This is applied here.
   

1st phase: pre-calculation

Primary (V)

U

Transformer image

Secondary (V/I)

n	V(volts)	I(A)
1
2
3
4
5
6