When a new power transformer for a rectifier is to be built or an old one rewound, simple calculations must first made. For power transformer of 100-200-watt rating, the design procedure is as follows.
Taking in to consideration the maximum voltage and maximum current to be given by the secondary winding of the transformer (V2 and I2), we find the secondary circuit power:
P2 = V2I2
When the transformer is provided with several secondary windings, P2 is equal to the sum of powers of all secondary windings. Assuming s transformer efficiency of 80%, the power of the primary winding is determined
P1 = P2/0.8 = 1.25P2
Power is transferred from the primary to the secondary circuit via the magnetic flux. Hence the cross sectional area ‘S’ of a transformer core depends upon the amount of power to be transferred and is proportional to it. When the core is to be made of ordinary transformer steel, S is given by the following formula
S= (P1)1/2
Where S is given in square centimetres and P1 in watts.
From the value of S is determined the number of turns per volt referring to w’. When transformer steel is used, this number is given by the following equation:-
w’ =50/S
If the transformer core is made of lower-grade materials, e.g., tin, roof steel, steel wire (such materials must be first annealed to make them soft), the values of S and w’ should be increased by 20-30%.
The number of turns in all the winding can now be calculated:-
W1 = w’ *V1
W2 = w’ *V2
When current flows through a transformer winding, considerable part of the voltage may be lost because of voltage drop in the winding. Hence it is recommended to wind 5-10% turns more than the calculated value.
The current through the primary winding is as follows
I1=P1/V1
The diameter of the winding wires is determined from the current value; an average current density of 2 amperes per sq. millimetre is usually allowed in small transformers. With such current density the wire diameter (not considering its insulation) is calculated for any winding, the result being expressed in millimeters.
d= 0.8(I) 1/2
If no wire of required diameter is available, the winding can be made with several thinner wires, connected in parallel. The total cross sectional area of such wires must not be less than the computed area of the required wire. The cross sectional area of a wire is given by the following equation
Q= 0.8d2
Filament windings are usually made with a few turns of thick wire and are placed on top of all the other windings. The current density for such filament windings can be increased up to 2.5 and even 3 A/mm2, because these windings are subjected to better cooling. In this case a coefficient of 0.7 or 0.65 should be substituted for 0.8 in the formula used for wire diameter.
In conclusion, check the location of windings in the space provided for them. The total cross-sectional area made up by the turns of each winding can be found by multiplying the number of turns by the cross sectional area of the wire. The latter is taken as 0.8d2ins , where d2ins stands for diameter of wire, allowance have been made for the insulation. The cross sectional areas of all the windings are added up. Then the total area thus determined is increased two or three times in order to make an approximate allowance for such factors as loose parts of windings, coil forms, insulating spacers between the windings and between separate selections of windings. The area of core openings must not be less than the value arrived at by calculation.
NOTE:- These steps are well tested by an expert and transformer designed by these calculations is working properly.
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