7.02 Equivalent circuits.

In electrical systems we sometimes need to connect two fairly complex circuits together. In these cases, it is often important to know, what the voltage across the connection point will be and how much current will flow from one circuit to another. The calculations required to determine this for the original circuits, can be very complicated due to the large number of components in each circuit. Also, it may then be necessary to repeat these calculation many times, if we want to analyse the connection of several optional circuits to one main circuit.

Fortunately there is a simpler solution. If we just want to know the output voltage across the connection between the circuits and the current through it, then both circuits can be "mimicked", with equivalent circuits, consisting of just two components in each. This obviously makes the subsequent calculations a great deal simpler. There will however, be initial calculations required, to find the values of the two components in each circuit. However, once the equivalent circuits have been determined, they can be used to quickly calculate output voltages and currents, when any two such circuits are connected together. It is important to point out, that the equivalent circuit obviously cannot perform the same function as the original circuit, (or else why bother with the complicated circuit in the first place!). It only "mimics" the original circuit with respect to predicting the correct output voltage and current when a load is connected to it.

You will already be familiar this idea, if you have ever connected pieces of audio equipment together. Amplifiers, cd players etc. are complicated pieces of equipment that contain many components. However all you need to know, to decide if it safe to connect say a cd player to an amplifier, is the cd players impedance and output voltage.
Note, impedance is a characteristic of a.c. circuits. As we are only currently considering d.c. circuits, our equivalent circuits will contain resistance not impedance.

The next pages introduce Thevenin and Norton's Theorems, which describe how to produce two different equivalent circuits. Either equivalent circuit can be used to determine the output voltage and current from the original circuit, when a resistive load is connected to its output.