Electrical transformer formulas pdf

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However, CAM and FEA are still based on Maxwell’s equations, Ampere’s law, Faraday’s law, and Gauss’s law, which together with Lenz’s law, are the basis of magnetic circuit analysis. The designer first needs several known factors to design a transformer. Once these factors are known, design can begin. The designer first starts with the primary voltage and frequency.

Since they are a known factor, they are the first numbers to be plugged into the equations. The transformer losses in watts are estimated and added to this sum to give a total power the primary coil must supply. These losses are dissipated as heat. Here, the permissible temperature rise must be kept in mind.

Each type of core material will have a loss chart whereby one can find the loss in watts per pound by looking up the operating flux density and frequency. Next, one selects the type of iron by what efficiency is stated, and the value of losses to the user. Once the iron is selected, the flux density is selected for that material. In this case, one looks for a core material with high permeability and a high flux density.

Of course, the better each become, the material goes up in price due to the manufacturing cost of the material, and their different compositions. In other words, a grain-oriented silicon steel conducts magnetic flux 1500 times better than a vacuum. B-H Curve for M-19 CRNO Steel. The designer refers to B-H curves for each type of steel. They select a flux density where the knee either starts on the curve, or slightly up on it. The start of the knee is where saturation starts and permeability is at its highest. As saturation starts, the permeability curve starts dropping off rapidly to zero, and the primaries inductance falls rapidly.

By selecting this point on the knee, it will give a transformer with the lowest weight possible for that material. One needs to find the core area in square centimeters or inches, and match it to the total power in watts or volt-amperes. The larger the core, the more power it will handle. Once this core size is calculated, one then finds the number of turns for the primary.

For sine wave operation, the designer then uses either the two short formulas, or they begin using the long formulas which are more exact, and whereby all the factors can be changed. For square wave operation, refer to the notes at the end of the equations section. Either way, it’s time to use a transformer design sheet. The design sheet has places to write the details such as the flux density, the number of turns, calculate the turns per layer, and thickness of the coil. Once the number of turns of the primary are calculated, the secondary windings numbers can be calculated with the same turns per volt figure. If the primary has 120 turns for 120 volts input, we would have 1 turn per volt.