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I am assuming that we are referring to an ordinary power transformer working at 50-60 Hz of alternating current circuit system. Saturation in these Transformers is the result of the magnetic field in the iron core reaching the saturation phase. At low current levels on the input side (currents are measured in amperes or amps) the magnetic filed produced in the core increases linearly with the current. Consequently, the current produced in the output coils is proportional to the input currents. If the amount of current in the input coil is large, the magnetic field in the core will not be a smooth sine wave, but a sine wave with tops and bottoms chopped as the magnetic core reaches saturation at the peak current level. This happens even if the input current remains a sine wave. The current induced in the output is directly proportional to the magnetic field and hence has the same shape - chopped off sine wave. Here are some of the implications:

1. Energy transfer from input to output is now limited by the chopping process which limits the peak current that can be induced into the output coil.

2. Energy transfer efficiency goes down - more energy may be poured in, but output energy does not increase significantly. Transformer will heat up as input coils experience greater currents. There will also be greater heating of the magnetic core due to magnetic hysteresis effects.

3. The output current has a chopped sine wave shape and hence has more 'harmonics' - waves with frequencies that are multiples of the input waves. The output current wave shape resembles a square wave more than the input sine wave. This is akin to waves produced by Electric Guitar distortion equipment. While this may not be important in some applications such as heating, it is usually unacceptable in audio transformers.

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