Tutorial 10  Transformers 

Learning Objective 
To understand the concept of power matching. To apply the ideas to transformer matching. To demonstrate power matching practically. 

Key Question 
How do we model transformers? What is meant by transformer matching? 

TransformersElectric locomotives take their power from a variety of systems. In most modern electrified railways the power is supplied to the locomotive by a 25 000 V overhead line at 50 Hz ac. However the motors work at about 1500 V, so there needs to be a way of reducing the voltage. This could be done using a resistor, but it would be extremely wasteful. So it's done with a transformer.
The transformer is a machine that is simplicity itself. It consists of:
The two coils are electrically completely different circuits. Either of the coils can act as a primary. The laminated core is made up of layers of soft iron separated by an insulating layer of varnish or glue. This reduces losses from eddy currents. Soft iron loses its magnetism immediately the current is turned off. Therefore the magnetic field can change forwards to backwards as the current changes.
The ratio of the input voltage to the output voltage is the same as the ratio of the number of turns on the primary to the number of turns on the secondary. We can write this as:
In Physics code:
If N_{1} is greater than N_{2}, we have a stepdown transformer, because the voltage is reduced. A stepup transformer increases the voltage. If a transformer is 100 % efficient (and it nearly is) we can say that: power in = power out Equation:
Therefore we can say that when the voltage is lower, the current is bigger. We can rewrite the transformer equation in terms of current to give us:
In practice, the transformer is about 97 % efficient. When a large transformer is transferring a lot of energy, even 3 % losses produce a fair amount of heat. Therefore the transformer is cooled with oil, which is pumped to heat exchangers. The giant transformers here step the output voltage of a power station from 25 000 V to 132 000 V for transmission.
What are the sources of inefficiency in a transformer?
This is called hysteresis, shown on the graph below:
A few points to note:
Transformers can only work with alternating current; they cannot work with direct current. 



Transformer MatchingTransformers are normally associated with stepping up and stepping down commercial mains electricity as we have seen above. However they also have an important use in impedance matching. We saw earlier that for maximum transfer from a Thévenin source that the load matched the internal resistance.
For an alternating current, reactance is important as a result of the inductance of coils of wire. The load may have a certain impedance.
For maximum power transfer in an AC circuit, the impedance of the load must match the internal impedance of the supply. We can achieve this with a transformer, and the turns ratio (N_{1} ÷ N_{2}) is given by:
With stereo radio receivers, it is essential to use a decent aerial. If there isn’t one, the radio won’t pick up anything, or at best it will be very hissy, which is not pleasant to listen to. There are two kinds of aerial available: · A balanced ribbon aerial; · An unbalanced antenna connected by a coaxial cable.
The input impedance for a balanced aerial is 300 ohms, while that for an unbalanced aerial is 75 ohms. If you connect a ribbon aerial to a 75 ohm socket, the signal will be weak. You need a matching transformer called a balun (from balancedunbalanced).
We can work out the turns ratio, knowing that the source resistance is 300 ohms and the load (input impedance) is 75 ohms:
The schematic is like this:




Impedance matching in an audio systemThere are many incidences of where a source might not be properly matched with its load. Consider an audio amplifier that can drive a 2 ohm load to 50 W. We can work out the current easily enough. Most loudspeakers are 8 ohms. So if we connect the supply directly to the loudspeaker, we get only 32 W. You can see that the possible power transfer is a lot less.
So we need to increase the voltage to the loudspeaker so that it transfers 50 W of power. We know that:
So rearranging:
V = 20 V
So we need to increase the voltage from 10 V to 20 V using a 1:2 turns ratio. So if the primary has 1000 turns, the secondary has 2000 turns.
We can show the consistency of the result using the equation:
In other words we can say that the primary has half the number of turns as the secondary.
The transformer is actually a lot more complex than what is in this tutorial. To look at the transformer in more detail, click HERE.




