I am learning about transformers and one of the items to calculate is the impedance. I need to calculate regular 60 Hz Core and Coil Shell Type Transformers Al wire in secundary, Cu Wire primary and use Epoxy paper for insulation.
It's pretty difficult to calculate the impedances (there's more than one) entirely from the transformer's design data. It's easier and more usual to decide on an equivalent circuit (there are plenty available depending on how well you want to model the transformer) and then to determine the parameters by a mix of calculation and measurement. A pretty basic equivalent circuit which refers all impedances to the primary side, has the primary terminals connected first by Xm and Rc in parallel (the magnetising reactance and core loss resistance) and then by a third parallel branch containg a series connection of leakage reactance Xl, winding resistance Rw and an ideal transformer of turns ratio Np/Ns. Xm is best obtained from an open circuit test but could be calculated as the inductance of the primary winding. For the latter you'd need to know core dimensions, number of winding turns and the magnetising characteristic of the core iron. If you have conductor sizes and conductivities you can calculate the winding resistance Rw, referring the secondary part to the primary by multiplying it by (Np/Ns)?. You can deduce Rc from the losses measured on open circuit at nominal voltage and Rw from dc resistance measurements on the windings. If you know the specific hysteresis and eddy current losses of the core material, you can also have a good stab at calculating Rc. The leakage reactance is quite difficult to calculate from first principles - even designers usually resort to some empirical factors. Basically it's determined from the short circiut test which is at nominal secondary current. The ratio of primary volts to secondary surrent (referred of course) on secondary short circuit will get you close to Xl - you can adjust for Rw which can be determined from the losses on short circuit (core losses are absent here!) or by the two methods indicated above. It's normally Xl that's referred to as the transformer reactance and together with Rc and Rw, the impedance.
