Wires and Cables

6.1 Which way?

Plain old metal wires turn up a lot in electrical systems, electronics, and even in computing and optoelectronics. The metal patterns used for microwave ‘striplines’, and even the connections inside integrated circuits are essentially ‘cables’ or ‘wires’. There is also a serious sub-industry as part of the Hi-Fi equipment business that sells fancy connecting cables, often at high prices. Given how many cables there are, and the wide range of tasks they perform, it is seems a good idea to look at their properties with some care.

In general, metal cables and wires serve two purposes.

To carry electrical power from place to place.
To carry information-bearing signals from place to place.

Now in order to communicate a signal we have to transfer some energy from place to place. This is because a signal without energy cannot have an effect upon a receiver. Hence it doesn’t matter whether the wires are for simple power or signal transfer, power or energy has to be transferred in both cases. We therefore need to establish how this can take place.

To get an initial idea of what is going on, consider the situation shown in figure 6·1.

This shows a wire hung between two houses. It is being used to send signals from one house to the other. The transmitter is a switch (Morse Key) and a battery, the receiver is a light bulb. (We are deliberately making this as simple as possible to avoid all the details of fancy signal communications equipment!) With stunning originality and imagination, we can call the houses ‘A’ and ‘B’. (We could call them ‘Dunpayin’ or whatever, but that would just make the following equations longer to type!)

An eavesdropper wants to find out, “Which house are the signals being sent from?” Can he tell this by examining the signals on the wire? For his eavesdropping he just has a voltmeter and a current meter which he can attach. By using the voltmeter he can determine the potential difference between the wire and the ground. Using the current meter he can determine which way any currents flow in the wire. Note that, as is usual, EM signals on wires actually require a conducting ‘loop’. This provides a complete circuit for the current to flow around. In between the signal source and its destination this also means there are two conductors, and any applied voltage will appear as a potential difference between them. In this case one of the conductors is actually the ground (earth) upon which both houses sit. So the eavesdropper also measures voltages with reference to the ground. In the situation described he only notices the current in the wire and ignores the current flow in the ground.

Now

so for power to flow from house to house (i.e. from transmitter to receiver – or from battery to light bulb in this case) we require the product of the observed voltage and the observed current to be non zero. The voltmeter and ammeter used by the eavesdropper are ‘center zero’ types that show both a magnitude and a sign. The transmitter (battery) can be two possible locations, and can be arranged to apply either a positive or a negative potential to the wire, There are therefore four possible situations which may arise whenever the switch is closed and energy flows from battery to bulb. These are illustrated in figures 6·2a to 6·2d.

The results obtained by observing the meters in each case can be listed as follows if we define a flow of conventional current from A to B as having a positive sign we can draw up the following table of results.

Figure	Observed voltage	Conventional Current Flow	Sign of
6·2a	+ve	A to B (+ve)	+ve
6·2b	–ve	B to A (–ve)	+ve
6·2c	+ve	B to A (-ve)	–ve
6·2d	–ve	A to B (+ve)	–ve

By looking at this table we can see that we can’t decide where the signal source is located simply by examining the current or voltage alone. However by considering their product (i.e. the power) we obtain a value whose sign tells us where the signal is coming from. This is because

tells us the rate and direction of energy flow along the wires. Although in this case we aren’t noticing the current flow in the ground we would find that it would tell us the same thing if we could find the very low current density and voltage in the ground itself since both of these always have to opposite sign to the wire’s.