19.1 How Sound Is Produced by Speakers

As we mentioned in Chapter 18, sound is the result of vibrations (i.e., oscillating motions) in the air. These vibrations are produced in electronics with a speaker when the speaker oscillates back and forth. The speaker oscillates back and forth because it is connected to a magnet and a coil. When the electricity in the coil oscillates between more positive and more negative charges, the magnet is attracted to and repelled from the coil, moving the speaker back and forth.

The frequency of this oscillation will determine the pitch of the sound (i.e., how high or low the sound is). If the frequency is higher (shorter periods), then the pitch is higher. If the frequency is lower (longer periods), then the pitch is lower.

Now, compared to the blinking lights we worked with in Chapter 18, sounds that you can hear are all of a much higher frequency. The bottom end of the hearable audio is about 20 Hz—that is, 20 cycles per second. The top end is about 20 kHz (i.e., 20,000 Hz). These values vary by individual, but this is a pretty good guide for most people. If we tried to blink an LED that fast, we just would not be able to see it—it would just look like a dimmer-than-normal light.

19.2 Graphing Electricity

Now, when we deal with circuits that are oscillating quickly, we need to have a way to visualize what is happening. With circuits that have one or two states, we don’t need to visualize much—we just need to calculate what the values are. However, with circuits that are continually oscillating (such as sound circuits), it is helpful to be able to graph what the voltages are at different points in time.

There are several ways to graph electricity. One of the most common ways is to plot time on the x-axis and voltage on the y-axis. This gives a visible representation of how the voltage is varying within the circuit. Now, because each point on a circuit has a different voltage, you have to specify which point on the circuit you are graphing. For instance, if you take the 555 oscillator circuit from Chapter 18 (i.e., Figure 18-2), the two places whose voltages you might want to graph are (a) right before the capacitor and (b) right after the output pin.

These will give very different graphs, but both of them are instructive. The graph of (a) will show you what the input side of the circuit looks like, and the graph of (b) will show you what the output side of the circuit looks like.

Notice that Figure 19-1 changes fairly smoothly (except when it changes directions). This is because capacitor charging causes the voltageto change smoothly over time. It charges up until it reaches ofsupply voltage and then discharges down to of supply voltage. It does this over and over again as you can see on the graph.

The output, however, is either on or off. Therefore, Figure 19-2 shows a very jagged graph. This is known as a square wave , because it is basically rectangular. The voltage just goes from zero to the target voltage almost instantly, and then after it stays there a bit, the voltage goes back down again just as instantaneously as it rose.

In addition to graphing voltage, we can also graph current in the same way, though it is harder to measure. Because voltage can be measured with simple probes and measuring current requires replacing a wire, most of the time, people just focus on voltage measurements.

Special devices known as oscilloscopes can be used to measure voltage changes over time. Graphs such as those in Figures 19-1 and 19-2 can be made by hooking up an oscilloscope to the circuit while it is in operation.¹ Oscilloscopes used to cost thousands of dollars, but now you can pick up a small handheld oscilloscope for under $50.

Usage of an oscilloscope is outside the scope of this book, but the basics are simple enough. An oscilloscope usually has an active probe and a ground probe. You hook up the ground probe to the ground on your circuit, and you hook up the active probe to the point on the circuit that you want to measure. Then, you look at the screen, and it will graph for you what the voltage is at that point over a period of time. Most oscilloscopes have all sorts of adjustments, such as how wide of a voltage range you want to measure and how long of a time window you want to show on the screen. In any case, oscilloscopes provide graphical views of oscillating voltages.

19.3 Outputting a Tone to Headphones

In this section, we are going to modify the circuit in Figure 18-2 to add in a headphone output. Figure 19-3 shows the final circuit, and Figure 19-4 shows how to build it. This circuit has several changes to our original circuit that we will discuss in this section.

The first changes to this circuit are to the RC time circuit. Because we want the circuit to be in audio range, we are making a much higher frequency (i.e., a shorter period). To do this, we swapped out the electrolytic capacitor for a ceramic disk capacitor of 100 nF. Then, we dropped the resistors down to 10 kΩ each. This will make a tone with a period of 0.003 seconds. Taking the reciprocal gives us a frequency of about 333 Hz. This is well within hearing range for most people. You can adjust the resistors and capacitors how you wish for different tone frequencies. We are merely using the equations from Chapter 18 to determine the period and frequency.

The strange change is in the output circuit. When we were blinking the LED, we just used a medium-sized resistor to limit output current. Here, however, we are using a combination of a capacitor and a resistor. This looks like an RC time circuit—and it would be, if it had a constant voltage going to it. However, in this circuit, the voltage going to the RC circuit is fluctuating, and that introduces a whole host of new considerations.

19.4 AC vs. DC

In Chapter 3, we introduced the ideas of direct current (DC) and alternating current (AC). In DC circuits, the circuit has a more-or-less constant voltage. Our power supply is at a certain voltage, our output is at a certain voltage, and so on. In AC circuits, however, the voltage oscillates back and forth. These oscillations introduce a whole new set of considerations.

In pure AC circuits, voltage and current actually swing both to positive and negative values. What is a negative current? A negative current happens when the electricity flows in the opposite direction. Thus, in a pure AC circuit, electricity flows back and forth, switching between directions while it is running, spending about even time in each direction.

Some components, such as speakers, assume that they are going to receive or process pure ACs. That is, they expect the current to switch direction at some point. As mentioned earlier, the speaker is driven by changing voltages in a coil, which alters the attraction of the coil to a magnet. These variations in attraction and repulsion move the coil back and forth, which moves the speaker cone, which vibrates the air, which vibrates your eardrum, which you hear. Speakers expect the oscillating current to go back and forth each direction about evenly.

However, in our circuit, the voltage only swings between a positive voltage and 0 V. If you look at the graph in Figure 19-2, notice that while the voltage goes up to a positive voltage, the lowest that it ever goes is zero. Therefore, it is not a pure AC circuit, because it is not centered around 0 V. Instead, the AC has a DC bias voltage . That is, the output voltage can be thought of as a combination of an AC voltage signal added to a DC voltage.

19.5 Using Capacitors to Separate AC and DC Components

Sometimes having a DC bias is good, and sometimes we need to separate out our AC and DC signals. Capacitors are excellent at this. Capacitors are said to allow AC to flow and to block DC. This is a simplistic view, and we will get a little more nuanced in future chapters, but it works for now.

To understand why this happens, let’s remember what a capacitor does physically. It stores charge—like a small battery. Remember, even though the pathway between the plates of a capacitor is blocked, when a positive charge accumulates on one side, it pulls electrons onto the other side, which means that the other side beyond the capacitor gets more positive as well. Do you remember what happens when the capacitor first starts charging? The capacitor basically acts as a short circuit. As the capacitor fills up, it starts acting more and more like a resistor, preventing current from flowing.

Thus, when given a constant voltage, once the capacitor is nearly full, it essentially stops getting more charge (or comes very close to it). Therefore, once it is full, it is basically blocking any more current from flowing. Since what goes onto one side of the capacitor affects what is on the other side, this same blockage will block the transmission of the current to the other side as well. Thus, in the long run, if you have a DC voltage, the capacitor will eventually block current flow. Thus, the current on the other side of the capacitor will be zero.

However, now consider what happens if the voltage changes. If the voltage changes, then the capacitor will allow current to flow through. If the voltage goes up, then the capacitor has more storage available (since the amount of storage depends on voltage). While it is charging to the new level, current will be flowing. If the voltage goes down, then the capacitor will actually have to discharge back into the circuit.

Now, if the capacitor discharges back into the circuit, which way is the current flowing? Well, that means the current from the capacitor is now flowing in the opposite direction!

Thus, what ends up happening is that the capacitor winds up only sending changes in voltage to the other side of the circuit! While the capacitor is charging and discharging, charge is moving through both sides of the capacitor. Thus, when the voltage (and therefore the charge) on the capacitor is changing, current is indeed flowing. Now, when the voltage stays the same, no electrons move, no matter what the voltage is. Therefore, even though you have a positive voltage on one side, if the voltage is not changing, no current is flowing. Therefore, on an unchanging current, the voltage on the other side of the capacitor will be zero.

Since the changes go up and down, but the DC bias voltage does not go up and down, this has the effect of sending AC through the capacitor, but blocking the DC bias voltage.

Therefore, capacitors are often used in series in a circuit to couple together parts of the circuit that are pure AC with other parts of the circuit that have a DC bias. Since the output of the 555 is DC biased and speakers generally are optimized for pure AC output, the capacitor in our output circuit filters out the DC bias and gives a pure AC signal.

A capacitor used in this way is known as a coupling capacitor .

Alternatively , if for some reason you wanted only the DC component, you could wire the capacitor to go to ground. This sends the AC part of the signal to ground, leaving only the DC component in the circuit. In such a scenario, the capacitor is being used as a filter capacitor .

Now, using a coupling capacitor does add in a small amount of distortion, both because DC bias voltage does have some effect on the signal and because different capacitor values are optimal for coupling different frequencies. For audio applications, a capacitor somewhere between 10 nF and 10 μF should be used.

19.6 Speaker Wattage

Next in the circuit is the R3 resistor. The R3 resistor is there to limit the output signal to the headphones. Headphones and speakers are all a little strange—there is very little standardization. Different headphones have different resistances in the speakers and different tolerances for how much wattage can be put through them. Speakers are usually rated by (a) how much resistance they normally add to the circuit, (b) how loud they are at a given wattage of power, and (c) what their maximum wattage is. Even though there is quite a bit of variance, for headphones, you can be fairly safe by estimating that the headphones will act as 16 Ω resistors and that they can consume a maximum of 20 mW.

The output of the 555 timer is 1.7 V less than my supply voltage. So, for a 5 V source, the output will be 3.2 V. However, since we have now centered it on 0 V, the output will actually only be half of that—1.6 V. We can usethe formula from Chapter 10 to determine how many watts this will supply. If the speaker is 16 Ω, then the power used by the headphonewithout the extra resistor will be = 0.16 W = 160 mW. Therefore, the R3 resistor pulls out some of that power.

With the resistor, the combined power usage of the resistor and the headphone speaker is 166 Ω. Therefore, the power here is = 0.015 W = 15 mW. Remember, though, that this is the combined power of both the resistor and our speaker. The speaker is only supplying about of the resistance, so it is only using up to of the power, or 1.5 mW.

Now, the calculation for this is relatively easy because we are working with square waves. The calculation becomes harder for different types of output, because you have to take into account the shape of the wave. However, we won’t go into that in this book. This calculation using the peak voltage provides a simple method which will give you a good starting point, and you can judge for yourself if you need more or less resistance for your own circuits.

19.7 Sound Control

Now, as I mentioned, all headphones are different, and, with the exception of having a coupling capacitor, they all have different ranges and need different amounts of power. Usually this is accommodated by having a volume control.

This is usually done with a variable resistor. On a variable resistor, you usually turn a knob and the resistance changes. Variable resistors go by different names—variable resistor, adjustable resistor, rheostat, and trimming resistors, though they each have slight differences. Trimming resistors are the easiest to use for this, but probably the hardest to find.

To use a variable resistor, you would need to find one with the right range of values and then simply replace the output resistor R3 with your variable resistor.

A more common type of component which can be used as a variable resistor is a potentiometer. A potentiometer is basically a variable voltage divider. The symbol for the potentiometer is shown in Figure 19-5. It has three leads—input, ground, and output. When you turn the knob, it adjusts the relative resistance of each side of the voltage divider to vary what is coming out of the output.

Potentiometers were built for working as a variable voltage divider. Figure 19-6 shows what this looks like. Essentially, the user controls a knob which alters the voltage coming out by changing the voltage division between the resistors.

However, you can also use a potentiometer as a simple variable resistor by just hooking up one side of the potentiometer. Figure 19-7 shows this configuration.

The simplest way of using the potentiometer for a volume control is simply setting it up like Figure 19-7, with the input coming from the coupling capacitor and the output going to the speaker. Potentiometers vary widely in how much resistance they offer, so if we were to add one as a volume control, we would need to make sure its resistance range approximately matches what is needed (around 150 Ω).

19.8 Review

19.9 Apply What You Have Learned