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Darlington gives an equivalent transform that can eliminate an ideal transformer altogether. This technique requires that the transformer is next to (or capable of being moved next to) an "L" network of same-kind impedances. The transform in all variants results in the "L" network facing the opposite way, that is, topologically mirrored. [2]
An ideal transformer is linear, lossless and perfectly coupled. Perfect coupling implies infinitely high core magnetic permeability and winding inductance and zero net magnetomotive force (i.e. i p n p − i s n s = 0). [3] [c] Ideal transformer connected with source V P on primary and load impedance Z L on secondary, where 0 < Z L < ∞.
Real transformer equivalent circuit. One case of voltage regulation is in a transformer. The unideal components of the transformer cause a change in voltage when current flows. Under no load, when no current flows through the secondary coils, V nl is given by the ideal model, where V S = V P *N S /N P.
The voltage (, blue) and current (, red) waveforms in an ideal inductor to which an alternating current has been applied. The current lags the voltage by 90° The current lags the voltage by 90° When a sinusoidal alternating current (AC) is passing through a linear inductance, the induced back- EMF is also sinusoidal.
The ratio of the voltage bases on either side of a transformer is selected to be the same as the ratio of the transformer voltage ratings. With these two rules, a per-unit impedance remains unchanged when referred from one side of a transformer to the other. This allows the ideal transformer to be eliminated from a transformer model.
To match the impedances, both cables must be connected to a matching transformer with a turns ratio of 2:1. In this example, the 300-ohm line is connected to the transformer side with more turns; the 75-ohm cable is connected to the transformer side with fewer turns. The formula for calculating the transformer turns ratio for this example is: