## 3.6 Transformers

We have assumed thus far that we have AC input to many of our circuits, but we surely can’t use 120V AC in our circuits, so we must find a way to step this voltage down. Transformers are ideally suited for this; recalling from Chapter 1, transformers are basically two coils of wire or two inductors in close proximity or wound around a common core material. Figure 3.47 shows the schematic symbol for a transformer. There is a primary on the left with turns N1; this is the input to the transformer. The output is on the right; this is called the secondary with turns N2. Finally, the ratio of turns of coil on the primary to the secondary is called the "turns-ratio" and is simply N2/N1.

### 3.6.1 The Step Up/Down Action

The formula that defines the relationship from input voltage to output is

**Equation 3.3:** Transformer equation.

- Vout = Vin* N2/N1

Figure 3.47 Transformer schematic symbol.

If N2/N1 is equal to 1.0 then there is no change to the voltage; if N2/N1 > 1 then there is step up. similarly if N2/N1 < 1 then there is a step down. Hence, say you want to make a 12V AC supply; you would need a 10:1 step down transformer. Of course, not only the ratio of turns is important, but the number of turns and the overall resistance of the wire. The number of turns is going to control the impedance and inductance of the primary and secondary; additionally the number of turns is proportional to amount of resistance of the primary and secondary windings. For example, if you tried to make a transformer yourself with 10 turns on the primary and 100 turns on the secondary and then plugged it in, I guarantee you would blow your circuit breaker—why? The reason is that 10 turns of any wire is going to have nearly 0 resistance thus, a huge amount of current will flow; hence, real transformers typically have thousands of turns in their primaries and secondaries to control current flow and set inductance properly.