Transformers (AC)

Transformers are AC/AC Power Conditioning Circuits. The principle is:

$$I_{in}\to \Phi \to I_{out}$$

where $\Phi$ is a coupled magnetic flux.

The idea is that there are two coils, which generate a magnetic field that couples 2 electromagnetic fields outside of the device. The coils are related to the input and output voltages, such that:

$$\frac{V_{in}}{V_{out}}=\frac{N_{in}}{N_{out}}$$

where $N$ is the number of coils. This lets us control the input and output voltage and current easily.

The efficiency is expressed as:

$$\eta P_{in}=P_{out}$$

In schematic form:

Some applications include microwaves and old CRT televisions.

Example

What is $I_{in}$ if $V_{in}=120{\text{ V}}_{\text{RMS}}$, $V_{out}=12{\text{ V}}_{\text{RMS}}$, $I_{out}=1{\text{ A}}_{\text{RMS}}$, $\eta =97\%$?

We have:

$$\begin{array}{rl}{P}_{in}\cdot \eta & =P_{out}\\ \eta & =\frac{V_{out}\cdot I_{out}}{V_{in}\cdot I_{in}}\\ \therefore I_{in}& =\frac{12\times 1}{120\times 0.97}=103{\text{ mA}}_{\text{RMS}}\end{array}$$