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?

## Transformers

Electric 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:

• A primary coil connected to the alternating power source.  This provides the changing magnetic field.

• A secondary coil connected to the load (in this case, the rectifier and control equipment in the locomotive).

• A laminated soft iron core. 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 N1 is greater than N2, we have a step-down transformer, because the voltage is reduced.  A step-up 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?

• The coils will have a certain value of resistance.  If the currents are large, the energy loss is large, since P = I2R.

• With the laminated soft iron core, there are still eddy currents, even though they are much reduced.  These will heat up the core.

• Transformers are inductive devices.  Therefore there is a certain reactance as well as resistance. We will look at this later.

• Work has to be done in building up the magnetic field in the core.  It takes energy to line up all the domains.  The energy recovered as the magnetic field falls is less than what is put in.

This is called hysteresis, shown on the graph below: A few points to note:

• The area within the loop is the energy lost.

• All magnetic materials have a certain remanance, meaning that the material is magnetised, even when the current is zero.  In soft iron, the remanance is low.

• There is a value of current at which all the tiny molecular magnets are lined up.  The magnetic field cannot increase further.  This is called saturation

Transformers can only work with alternating current; they cannot work with direct current.

 Question 1 A transformer has a primary of 3600 turns and a secondary of 150 turns.  It takes 1.5 amps from the 240 V mains.  What is the output voltage and current?

### Transformer Matching

Transformers 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 (N1 ÷ N2) 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 balanced-unbalanced). 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: Question 2 Why is there an impedance in the transformer?

#### Impedance matching in an audio system

There 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.

 Question 3 An audio amplifier can drive a 2 ohm load to 50 W.  Work out the current in the amplifier above. Question 4 Show that the voltage is 10 V Question 5 Most loudspeakers are 8 ohms.  Show that the power transfer is 32 W for an 8 ohm load.