 From your previous study of oscillators, you've learned that frequency stability is of the utmost importance. You might ask why all of the concern about frequency stability. As an example, let's consider a radio broadcast station. I have here a book of FCC regulations governing the operation of radio broadcast stations. One particular regulation prohibits the frequency of the station from changing more than a few cycles, and it's a pretty stiff regulation. But it must be so, so that the station will not interfere with another station operating on a nearby frequency. Now for this reason, the oscillator producing this frequency must be one with the very best frequency stability. An oscillator capable of producing such an output is the crystal controlled oscillator. We're not going to study the oscillator circuit in this lesson, but we will study the characteristics of the crystals used in such a circuit. And here I might add that the crystal will be used as the frequency determining device of the oscillator in much the same manner as a coil and capacitor was used in oscillator circuits previously covered. Now some of the items that we're going to discuss are the use of crystals. Types of crystal substance is used, crystal cutting, types of crystal cuts, crystal characteristics. You'll see the purpose of a crystal holder, the frequency stability of crystals, and a little bit later we'll discuss overtone crystals. Now there are many types of crystal substances, but not all are suitable for use in oscillator circuits. A crystal used in oscillator circuits must possess a characteristic known as piezoelectricity or the piezoelectric effect. Let's look at a definition of the piezoelectric effect. Now the piezoelectric effect is defined as the property of a crystal by which mechanical stress produces electric charges and conversely electric charges produce mechanical stresses. Now at this time you should complete item one of your TVI guide. Now this is saying nothing more than if a voltage is applied to the crystal it will vibrate. The amplitude of these vibrations are such or much greater at one frequency than at any other frequency. Now this one particular frequency is called the natural resonant frequency of the crystal. Now let's look at some of the crystal substances that possess the piezoelectric characteristics. They are Rochelle salt, tourmaline, and quartz. Now we should include these substances in item two of the TVI guide, the A part of item two. Now of these three Rochelle salts exhibits the piezoelectric effect to the greatest degree. However quartz crystal is most generally used because it has a greater mechanical strength. Now at this time let's complete the B part of item two. The substance most often used in oscillators is, go ahead and complete that blank. It is quartz crystal. Remember it has a greater mechanical strength. Now I want to show you a piece of quartz crystal in its natural form. Now if we were to examine this carefully we can see that the quartz crystal has a hexagonal cross-section. That is to say it has six sides. Also quartz crystal in its natural form has pointed ends. This one doesn't because a primary cut has already been made on this crystal. Now let's take a look at this drawing so that we can determine more about the quartz crystal. There are two views. The top view indeed shows us that the quartz crystal has a hexagon shape, six sides. While the lower view points out that indeed the quartz crystal in its natural form does have pointed ends. Now quartz crystal in its natural form cannot possibly be used in oscillator circuits. It must be cut in a specific manner to exhibit its piezoelectric properties. I know all of you at one time or another have heard of diamond cutting. The reason a diamond is cut is to give it brilliance. And the manner in which it's cut will determine its degree of brilliance. A piece of diamond in its natural form would never be used in a diamond ring. Just as a piece of quartz crystal would never be used in an oscillator circuit. Now when a piece of crystal is going to be cut, imaginary lines are used as the reference points for cutting. And these imaginary lines are known as crystal axes. Let's take a look at this drawing of a crystal and see the exact location of the crystal axes. The axes passing from point to point are end to end and directly through the crystal is known as the z-axis. Remember from end to end directly through the center. The axes passing through the corners of the crystals is known as the x-axis. Remember it goes through the corners. While the axis perpendicular to the faces of the crystal is known as the y-axis going through the faces. Now let's remember these are only imaginary lines and are used as reference points when cutting the crystal. Then at this time complete item three in your TVI guide by labeling the axes there. Now all crystals are not cut in exactly the same manner. Just as all diamonds are not cut exactly the same. The properties which a crystal exhibit are dependent on the manner in which it's cut. Now there are many different cuts but we're only going to examine three basic cuts. Let's go to this chart and see exactly how we make these three particular cuts. The first cut is made perpendicular to the x-axis which you will recall passed through the corners of the crystal. It's perpendicular to that axis and parallel to the z-axis. Now to get a more realistic view of this cut let's go to a mock-up. Remember we're considering the x-axis passing through the corners of the crystal. The cut is made perpendicular to this x-axis and parallel to the z-axis. And the cut would look something like this. You can see that it's only a small portion of the natural crystal. Now since this cut was made in reference to the x-axis it is known as an x-cut crystal. Okay let's go back to the chart and see how another cut is made. For this cut we will use the y-axis which passed through the face of the crystal. This cut will be taken perpendicular to the y-axis and it also is parallel to the z which you will recall ran through the center of the crystal. Remember perpendicular to the y parallel to the z. And again to get a more realistic view of this cut let's go back to the mock-up. Remember the y-axis passed through the face of the crystals in this manner. We'll cut perpendicular to that and parallel to the z-axis. And we come up with our second cut which in this case since we took it in reference to the y-axis would be known as a y-cut crystal. Then let's go back to our chart for the third and final cut. Now this time we're going to cut at an angle from the z-axis. Recall the z-axis passes through the center of the crystal from end to end. And for this cut we'll cut at a 35 degree angle from the z-axis. Remember 35 degrees from this z-axis. Okay back to the mock-up once more. Now in this case the crystal cut is taken right in or made right into the face of the crystal. Remember the z-axis is running down through the crystal in this manner. And we'll cut at a 35 degree angle from this z-axis. And removing the cut from the crystal. Again only a small portion of the natural crystal. We call this cut an AT-cut. An AT-cut crystal. Okay let's go back to our chart once more and I want you to complete item four in the TVI guide. Now we've seen from the mock-up what these three cuts look like. Let's go over and I want to show you the actual cuts now. I have here three crystal cuts. Now as you can see they look like small thin wafers and each cut looks very similar. Each cut looks very similar. Now all crystals look the same but not all will exhibit the same characteristics. Now you'll recall earlier we mentioned the resonant frequency of the crystal. Not all crystals naturally will have the same resonant frequency. Its frequency will be dependent upon its thickness. Let's take a look at two pieces of crystal cuts and compare this difference in thicknesses. As you can see the thinner cut here, the thicker cut here. We're indicating here that the vibration of this thinner cut or the frequency is greater than this cut. Now this will always hold true. The thinner the crystal cut the higher the frequency of oscillation. Okay then at this time let's refer to item five in our TVI guide. You read along with me and then complete that statement. In order to increase the frequency of a crystal it should be cut. We just saw that. It should be cut thinner. Now another characteristic which will be different for the various crystal cuts is the temperature coefficient of the crystal. The temperature coefficient. Now this is a new term so let's define it. Temperature coefficient is the relationship between temperature and frequency change. Then at this time complete item six in your TVI guide. Temperature coefficient is actually the effect that a changing temperature will have on the frequency of the crystal. Now let's compare the temperature coefficients of the three cuts that we just considered. The X, Y, and A-T cut crystals. To do that we'll use this chart. On the left we're indicating the type of crystal cut, the X, Y, and A-T. Let's begin then with the X cut. The temperature coefficient of the X cut is negative. This means that if temperature about the crystal increases the crystal frequency will decrease. A negative temperature coefficient. An increase in temperature, a decrease in frequency. The Y cut crystal has a positive temperature coefficient. If temperature increases the frequency increases also. A positive temperature coefficient. The A-T cut crystal has a zero temperature coefficient. That is to say as long as the temperature ranges between 40 to 50 degrees centigrade. Remember as long as the temperature is within this range the frequency of oscillation will remain the same. Then the A-T cut has a zero temperature coefficient. Now at this time you should complete the chart in item 7 of your TVI guide. Now from this you should be able to reason that the A-T cut crystal would be extensively used. Now there are a few other crystal cuts with better frequency stability. But these will not be discussed in this lesson. Now when an extremely high degree of frequency stability must be maintained the crystal will be placed in a temperature oven. A temperature oven. A temperature oven is nothing more than a thermostatically controlled container used to maintain the crystal temperature in its proper range. And in doing so of course we have a high degree of frequency stability. Then let's go to item 8 in our TVI guide. When a high degree of frequency stability is to be maintained a crystal will be placed in a temperature oven. Temperature oven. Nothing more than a thermostatically controlled container. Now in order for a crystal to be used in an oscillator circuit it first must be placed in a holder. Now the crystal holder will support the crystal physically and provide the electrodes by which this voltage is applied to the electrodes. The holder must allow the crystal maximum freedom of vibration at all times. Let's look at this drawing of a typical holder. The crystal will be placed in the holder between two parallel plates. The plates have an air gap between them which allows room for the crystal to vibrate. The two plates then are connected to the pins. Now these are the pins that will allow the voltage to be applied to the plates. And also the pins will allow the crystal to be connected into a circuit in much the same manner as a vacuum tube. The spring will keep a constant pressure on the plates and hold them firmly in place. The crystal holder cover usually indicates the fundamental frequency for which this particular crystal was cut. In this case the crystal was cut to oscillate at a fundamental frequency of 430 kilocycles. Now so far we've seen the physical characteristics of the crystals. Let's now see how the crystal reacts electrically. To do this we'll look at the electrical equivalent of a crystal and its holder. The crystal itself, when vibrating, acts very similar to a series resonant circuit containing resistance, inductance, and capacitance. Remember this is when the crystal is vibrating. Now when the crystal is placed in the holder the capacitance of the holder will be placed in parallel like this. CH, the capacitance of the holder. So this capacitance represents the holder capacitance. This represents the vibrating crystal. Now at this time you should complete item nine of your TVI guide. Now just because this vibrating crystal is equivalent to or is the equivalent of a series LC tank circuit I don't want you to think that it's the same thing because the crystal will be far superior to the LC tank circuit. Now the Q of the crystal circuit is many times greater than that of the LC circuit. Let's take a look at the comparison between the Q of a crystal and an ordinary LC tank circuit. The Q of an LC tank circuit is seldom greater than 2000 whereas the Q of the crystal is sometimes as great as 30,000. And as comparing these two you can see that the Q of the crystal would be many times greater than that of the LC tank circuit. Now because of the high Q this would mean that the crystal would have better frequency stability because its bandwidth is much more narrow than that of the LC tank circuit. Then at this time let's complete item ten in our TVI guide. The Q of a crystal is than that of an LC tank circuit. Go ahead and complete that statement. Now let's look at some of the values both physical and electrical of a typical crystal. Physical size, a typical crystal would have a thickness of about 0.025 inches. The width would be about 1.3 inches. The length would be 1.08 inches. And with these physical characteristics the resonant frequency or the fundamental frequency would be 430 kilocycles. Now with this physical dimensions or these physical dimensions let's look at the electrical value. The vibrating crystal would have an inductance of about 3.3 Henry. A capacitance of 0.042 micro microfarads. The capacitance of the crystal holder would be about 5.8 micro microfarads. And this crystal would have a Q of around 23,000. Now let's remember these values were for a crystal cut for a fundamental frequency of 430 kilocycles and will not hold true for all crystals but it does give us an idea of relative values. Since the crystal is going to be used in an oscillator circuit as the frequency determining device it must be represented on the schematic diagram. Let's take a look then at the schematic symbol for our crystal. These two plates represent the crystal holder while this area would represent the crystal itself. Now this is the schematic symbol of a crystal used in oscillator circuits. So while looking at this complete item 11 in your TVI guide. Earlier in the lesson we discussed the various crystal cuts and how each was different from the other. However they do have one thing in common. That is they can be made to oscillate at frequencies other than that frequency for which they were cut. Now when a crystal is used in a circuit in this manner it's referred to as an overtone crystal. An overtone crystal. Now getting a crystal to act as an overtone crystal is nothing more than causing it to oscillate at a harmonic of the frequency for which it was cut. And I might add here that the crystals will oscillate only at odd harmonics of their fundamental frequencies. Now for example if a crystal was cut for a frequency of 10 megacycles it can be made to oscillate at 30 megacycles. The third harmonic or the third overtone. You might ask how is this accomplished? Simply by increasing the feedback to the point where the crystal is shocked into vibrations at the odd harmonic rather than the fundamental frequency. And let's determine what's happening when this is true. Now here we're indicating the distortions that exist in the crystal when it's oscillating at its fundamental frequency. Here is representing the crystal at rest. No oscillations. Here the crystal is deformed to produce one alternation. And here it's deformed in the opposite manner to produce the other alternation. Now this is when it's oscillating at its fundamental frequency. Notice that the deformities are opposite for each alternation. Now here we're representing the crystal when it's made to oscillate in the third overtone. Now let's notice that the crystal breaks up into three layers when it's oscillating at the third overtone. Now this is representing the deformed layers to produce one alternation. Here the deformed layers for the other alternation. And let's notice that the deformities are opposite for each alternation. Now if the crystal is made to operate on the fifth overtone it breaks down into five layers. If it's made to operate in the seventh it breaks down into seven layers and so on. But I might hasten to add that a crystal cut for a fundamental frequency is limited to only a few overtones. When higher overtone modes are desired then a crystal is precision ground and mounted in a special holder and it would be used specifically for these higher overtones. Then let's start for just a moment and complete item 12 in our TVI guide. A crystal which is specially cut in ground to oscillate at more than one frequency is called an overtone crystal. An overtone crystal. Now let's recap a few of the points that we've discussed in this lesson. First we saw the use of the crystals. Now we said that the crystal must exhibit the piezoelectric effect. And we defined the piezoelectric effect as the property of a crystal by which mechanical stress produces electric charges and conversely by which electric charges produce mechanical stress. Then we saw the three substances used. Rochelle salts, tourmaline and quartz. We said that Rochelle salts exhibits the piezoelectric effect to the greatest degree but that quartz is most generally used because of its mechanical strength. Then we saw the three basic crystal cuts that we were considering. The x-cut which is made perpendicular to the x-axis. The y-cut which is made perpendicular to the y-axis. And the at-cut which is made at a 35 degree angle from the z-axis. And then we defined temperature coefficient as the relationship between a temperature change and a frequency change. And then we gave you the schematic symbol for a crystal. This represented the crystal holder, this the crystal itself. Now in concluding we can say that the one big advantage of the crystal is its frequency stability. Remember it has a very high Q giving us a very narrow bandwidth. Then we have one more TBI guide item to complete, item 13. The main asset of a crystal oscillator is its frequency stability. Frequency stability. That just about concludes the lesson on the characteristics of crystals, so until another time, so long.