Term Gain for Amplifiers and Efficiency for Transformers

Amplifier gain = Output/input

Transformer Efficiency = Output/input

But there is a hidden agenda- In amplifier the energy is increased (you have a secondary power pumped in) But that is not the case in transformer.

Transformers are passive components. The ratio of windings between the primary and secondary windings can step up or step down the AC voltage on the primary side.

However, like any passive system there are losses. The more signal loss, the lower the efficiency of the transformer.

There is a lot more to this than that, but discussing transformers in a complete and meaningful way is a big subject in itself and there are books on the subject.

Understand that transformers do not produce gain. While you might be able to step up an AC voltage to a higher potential, you also produce proportionally less drive current minus any insertion loss in the transformer.

You can easily "feel" those losses if you put your hand on a working power transformer. It will be warm or in some cases even hot.

Because your talking about two different devices. In their use the amplifier we would want to know it's gain how much it amplifies the signal. On a transformer is efficiency or how well transforms the power.

As has been said in different words by experts here....

An Amplifier amplifies an input, but has some power available from elsewhere. eg: an audio amplifier.

A Transformer transforms power from one level of voltage and current to another. It has no access to any other power source except the input.

Why think of these two devices together? They are quite different...

Transformer Efficiency is actually = Output power /input power, it is a measure of how efficient power is being transferer from primary to secondary side, it is always less than 1 (100%).

Amplifier gain can be voltage gain or current gain, can be more or less than 1, can also be negative value.