Click here to purchase the entire book in PDF format. Hysteresis Let's look a little more carefully about the behaviour of analog recording tape when we try to put a signal on it. If tape were perfect, it would have a linear transfer function like the one shown in Figure 6.57. In this case, the signal that we get off the tape is identical to the signal we try to put on it. This is a lovely idea. Unfortunately, it is very far from the way tape actually behaves as we'll see... Figure 6.57: A perfectly linear transfer function where the output signal is identical to the input signal. This is how we would like analog tape to behave. Unfortunately, it doesn't. Let's start with a piece of analog tape that has no magnetic signal on it. Therefore $M=0$. We'll start with the tape in a place that has no magnetic field, and we'll slowly apply a magnetic field with a positive polarity (indicating that it's pointing in a given direction - we don't know that direction, but we do know that a negative field would be in the opposite direction) to it from an external source like a permanent magnet. Figure 6.58 shows how the tape magnetization will behave if we do this. If we apply a small magnetic field, a smaller field will be stored on the tape. As we apply more and more external magnetic field, more and more strength will be stored on the tape. Eventually, you'll notice that there is a nearly-linear relationship between the applied field and the stored field. If we increase the magnetic field even more, we'll start getting closer to the maximum magnetism that can be stored on the tape - the point of saturation, so the curve gets more and more horizontal. No matter how much further we try to push the tape, we can never get a bigger magnetic field from the tape. Figure 6.58: Now we have a tape that has been magnetized to its saturation point. What happens if we try to de-magnetize it. One way to do this is to put it in a weak magnetic field with the same polarity. The applied field, $H$ will cause the tape to have a magnetism more like the applied field than the one it had. However, the tape doesn't automatically have the same magnetism as the applied field. In fact, it will maintain some amount of magnetism as can be seen in Figure 6.59. As we apply a weaker and weaker field, we will pull the tape back to less and less of a magnetic signal. Eventually, we'll get to $H = 0$ - in other words, no magnetic field is applied to the tape. However, some magnetism is left on the tape. The amount of the remaining field is the tape's retentivity, as we have seen already in Section 6.3.2. Figure 6.59: So, now the tape is in a space free of a magnetic field, but it's still magnetized. If we now start applying a stronger and stronger external magnetic field, but with a polarity opposite to the one we applied before, we'll be bringing the magnetism on the tape closer and closer to 0 - essentially undoing everything we did. This behaviour is shown in Figure 6.60. You'll also note that, if the strength of the external field is increased more and more, we'll eventually reach the saturation of the tape, but in the opposite polarity. Figure 6.60: If we reduce the strength of the external field, we'll start reducing the magnetic field on the tape just as we did in the positive direction. This is shown in Figures 6.60 and 6.61. The final curve that results is called a hysteresis loop. The word comes from the Greek word hystéresis meaning ``a state of delay''[Woram, 1989]. Figure 6.61: Hysteresis loop