Tutorial 9 - Power Transfer and Load Matching

Learning Objective

To understand the concept of power matching.

To apply the ideas to transformer matching.

Key Question

What are the ideas behind power matching?

## Power Transfer and Matching

In Tutorial 7 we looked at a power supply with an internal resistance.  In Tutorial 8 we saw that Thévenin’s Theorem told us that any complicated power supply can be represented as:

a simple perfect battery in series with an internal resistor, r. We know that the graph of the voltage across the resistor, R against a current is like this: Question 1 What is the significance of: (a) The gradient; (b) The y-axis intercept; (c) The x-axis intercept?

If we plot the graph of power against resistance, we get: From this graph, we see that:

• the maximum power transfer occurs when the load is the same as the internal resistance.

• In this case the internal resistance is 1.5 ohms and the external resistance = 1.5 ohms.

We can measure the efficiency of the power transfer using the equation: Question 2 Calculate the power transferred across each resistor, using the EMF as 4.5 V.  (Hint: You will need to work out the current from the power graph) Question 3 Show that when the maximum power is transferred, the efficiency = 50 %.

The graph of efficiency against resistance looks like this: We see the following from this graph:

• When the resistance is lower than the internal resistance, the energy transfer is very inefficient.

• When the resistance is the same as the internal resistance, the energy transfer is 50 % efficient.

• If the external resistance is much higher than the internal resistance, then the efficiency increases to a very high percentage.

If we want maximum power transfer, we need to match the load so that it is equal to the internal resistance of the source.  This is the case regardless of whether we have a simple source or a complex source of many EMFs and resistances.  We use Thévenin’s Theorem to simplify the source into a simple battery in series with an internal resistance.

 Question 4 What is the energy efficiency in this circuit if the external resistance is 10 ohms? Question 5 If we have a perfect battery with zero internal resistance, do you think we would get any maximum useful power transfer? Question 6 An amplifier is modelled on a Thévenin voltage source that has an internal resistance of 8 ohms and has an EMF of 15 V.  Calculate: a.      The maximum power  transfer; b.      The power transferred when the load is 16 ohms. c.      The efficiency of the power transfer at 16 ohms.