24.1 An Amplification Parable

As we noted in Chapter 10, physics tells us that we can’t actually increase the power of something. What we can do, though, is use a smaller power signal to control a larger power source, and that is what we refer to as amplification.

Let’s say that we have a dam on a river. The river wants to go downstream, but it is blocked by the dam. Let’s say that we have a giant named Andre, which is able to lift the dam using his strength. If Andre lifts the dam a little bit, a little bit of water flows. If Andre lifts the dam a lot, all of the water can flow. The power of the water itself is actually more than Andre’s power. Therefore, Andre can “amplify” his power by raising and lowering the dam.

Let’s say that at the end of the riverbed was a structure that Andre wanted to destroy, but Andre himself isn’t strong enough to do it. However, the river is strong enough to do it. Therefore, rather than try to destroy the structure on his own, Andre decides to raise the dam and let the river’s power do it.

Note that Andre didn’t actually increase the amount of power in the river. Instead, he (a being with lesser power) controlled the operation of the river (a higher-powered entity) by adjusting the dam (the physical resistance against the water). Thus, he amplified the effects of his actions by controlling the resistance on the higher-powered current.

24.2 Amplifying with Transistors

A very common method of amplifying power output in projects is with transistors . The term “transistor” is short for “transconductance varistor,” which means that it is an electrically controlled variable resistor. In other words, it helps you amplify a signal in your project the same way that the dam allowed Andre to amplify his power. The transistor operates as a controllable electric dam, allowing a smaller-powered electric signal to control a higher-powered electric signal by adjusting resistance.

Another way you can think of it is like an outdoor faucet—the water going through the faucet is controlled by the wheel knob on the top, which provides a variable amount of resistance to the flow. The faucet can be fully on, fully off, or somewhere in between, all based on where the knob is set. The knob setting is like the input current—a specific level of input current will control the amount of flow that comes out.

There are many different types of transistors, with a wide variety of ways in which they work. What they all have in common is that they have three (sometimes four) terminals, and one of the terminals acts as a control valve for the flow of electricity between the other two.

The main way that the types of transistors differ is in whether the knob on the faucet is controlled by voltage or by current. The transistors operated by current are known as bipolar junction transistors (BJTs), and the ones operated by voltage are known as field effect transistors (FETs).

As a gross overgeneralization, FETs are most useful for lower-power switching applications, while BJTs are most useful for power amplification. This chapter will cover BJTs.

BJTs come in two basic forms based on whether the knob is normally closed but turned on by positive current (an NPN transistor) or whether the knob is normally open but closed off by positive current (a PNP transistor). Here we will focus on NPN transistors.

24.3 Parts of the BJT

A BJT has three terminals—the collector, the base, and the emitter. In BJT NPN transistors, a small positive current comes in at the base (which you can think of as the knob of a faucet), and it controls the current moving from the collector to the emitter. The more current that comes through the base, the more current is allowed to flow between the collector and the emitter.

Figure 24-1 shows what an NPN BJT looks like in a schematic. The collector is at the top right of this diagram. The emitter is the line with the arrow pointing out. The current being controlled is the current between the collector and the emitter. The base is the horizontal line coming into the middle of the transistor. The base acts as a knob which can limit the flow of current between the collector and emitter.

Figure 24-2 shows a conceptual picture of how the transistor operates. The connection from the base to the emitter operates as a diode, and the connection from the collector to the emitter operates as a variable resistor, offering resistances from zero (completely open dam) to infinity (completely closed dam). The resistance of the variable resistor is based on the current flowing through the base. The variable resistor is adjusted so that, under certain conditions, the current flowing from the collector to emitter is a certain multiple of the current flowing from the base to the emitter.

When we talk about the voltages and currents flowing through the resistor, there are special names you need to remember and keep in mind. Each of the legs of the transistor is named by the first letter of its role. The collector is C, the emitter is E, and the base is B. Then, each of the voltages/currents is labeled based on which leg it is going from and to. Therefore, V_BE is the voltage difference between the base and the emitter, V_CE is the voltage difference between the collector and the emitter, and V_CB is the voltage difference between the collector and the base. I_BE is the current flowing between the base and the emitter, and I_CE is the current flowing between the collector and the emitter. The total current coming out of the emitter is I_BE + I_CE. Take time to think about these designations as we are going to be using them extensively when we talk about transistors and their usage in a circuit.

A photo of a transistor can be seen in Figure 24-3. This is the transistor we will focus on in this chapter—the 2N2222A (sometimes called the PN2222A). It is important to read the datasheet to find out information about your transistor—especially to know which transistor leg is which! For the picture in Figure 24-3, the collector is on the right, the base is in the middle, and the emitter is on the left. Note that some other transistors have different pin configurations, which is why it is so important to check the datasheets. For instance, the P2N2222A (very similar name!) has the collector and emitter pins reversed!

Transistors can also come in a variety of shapes and sizes, known as packages . The package depicted in Figure 24-3 is known as a TO-92 package. Other packages you might see are a TO-18 package (which looks like a tiny metal cylinder) or a package similar to an integrated circuit.

24.4 NPN Transistor Operation Basics

To fully understand NPN transistor operation requires a lot of complicated mathematics. However, you can get a “good enough” understanding of it just by remembering a few simple rules.

Rule 6: The Transistor Cannot Amplify More Than the Collector Can Supply

This is mostly a reminder that the amplification comes from the collector current. If the collector can’t supply the amplification, it won’t happen. Basically, we need to think of the transistor as controlling a resistor from the collector to the emitter which will adjust itself to maintain the ratio (beta) between the base-emitter current and the collector-emitter current. Thus, it can’t provide less resistance than no resistance.

24.5 The Transistor as a Switch

One of the issues with transistors is that it takes a while before using a transistor becomes intuitive. Transistors, as we will see in the forthcoming chapters, wind up needing a lot of special considerations. Because of this, many people don’t use transistors directly and instead choose to only use integrated circuits (see Chapter 11). Integrated circuits, since they are based on the needs of a circuit instead of simple physical properties, tend to be much easier to work with. Most of the guess work has been taken out, and the chips are built so that they can be inserted into a circuit in a straightforward way. Even though some people opt to use integrated circuits instead of using transistors directly, it is worthwhile to understand their operation. It is always better to choose an option because you understand your available alternatives instead of choosing an option because that choice is the only one you understand.

Now, when we think of buttons and switches, most people naturally put the switch at the beginning of the circuit that is being turned on or off. Figure 24-4 shows what this looks like. However, it is just as valid to place the switch at the end, as shown in Figure 24-5.

When using transistors as a switch, we almost always place them at the end of a circuit. The reason for this should become clear as we examine circuits.

The first circuit we will look at is Figure 24-6. In this circuit, there is no real need for a transistor—we could just as easily have put the switch where the transistor is. However, understanding how this setup works will help us understand other transistor circuits. In this circuit, the base is controlled by a small signal (the size of the signal is set by the size of the resistor). When the base turns on, it switches on the connection from the collector to the emitter, which controls current to the motor (the diode is simply a snubber diode as described in Chapter 20).

If the emitter of a transistor is simply connected directly to ground as it is in this example, the easiest way to analyze the circuit is by looking at the flow of current through the base. When the switch is closed, current will flow from the voltage source, through the resistor, across the transistor to ground. How much current? Well, this is actually a simple question. Remember that the junction from the base to the emitter can be treated as a simple diode (Rules 2 and 3). Therefore, we have a very simple circuit to analyze—voltage source to resistor to diode to ground. The voltage source is 5 V, and we have a diode (0.6 V) in the circuit path, so the voltage going through the resistor will be 4.4 V. Since the resistor is a 1 kΩ resistor, then, using Ohm’s law, the current will be , or 4.4 mA.

Since the current going through the base (I_BE) is 4.4 mA, how much current is flowing from the collector to the emitter? We will assume for our exercises that the beta of transistors is exactly 100. According to Rule 5, that means that the current going from the collector to the emitter is 100 times the base current. Therefore, the current going from the collector to the emitter can be determined by I_CE = β⋅I_BE = 100⋅4.4 = 440mA. Therefore, the current going from the collector to the emitter is 440 mA. Because the current at the collector is 440 mA, that means that the current going through the motor is also 440 mA.

Depending on the current we wanted flowing through the motor, we could choose other resistor values to set the current to the appropriate level. However, because of Rule 6, the collector current will be limited by the motor’s characteristics as well.

So why did we put the transistor at the end of the circuit? Let’s imagine that we added one component to the circuit—a resistor after the emitter before the ground. All of a sudden, the circuit is a lot harder to analyze. Why? Well, we can no longer determine the base current by simply looking at the current path through the base. The voltage across that final resistor will not be based on the base current, but based on the combined current from both the base and the collector. Thus, when there are components after the emitter, in order to analyze the base current, you have to analyze how the components after the base respond to the combined current of the base and collector, but we won’t know that until after you calculate the base current. It is possible to do this, but the math isn’t fun. Instead, by connecting the emitter directly to ground, we simplify our calculations because we know the voltage after the emitter—since it is connected to ground, it will be zero.

Thus, by connecting the emitter directly to ground, we can analyze the current flow from the base independently of the current flow from the collector. Additionally, connecting the emitter to ground will automatically make sure our DC circuits follow Rule 4 and make it easy to analyze when the transistor turns on and off by Rule 2.

Just as we have looked at several common resistor circuit patterns, there are also several common transistor circuit patterns. The transistor pattern we are looking at in this chapter is known as a common emitter circuit. This is because the “interesting” parts of the circuit are at the base (which provides the current to be amplified) and the collector (where the preceding circuit enjoyed the amplified current) and the emitter is connected to a common reference point (the ground in this case).

24.6 Connecting a Transistor to an Arduino Output

To understand why we would use a transistor for a switch in the first place, let’s imagine that we have a motor just like in Figure 24-6, but in this case we want it to be controlled by an output pin from an Arduino running on an ATmega328/P.

Now, on this chip, output pins put out 5 V, but their current rating maxes out at 40 mA. However, motors usually require much more current than that. If we wanted our motor to use as much current as in Figure 24-6, it would blow out the chip if we tried to connect it directly to the output.

However, we can instead wire the output of the Arduino to the base of a transistor. Then, the current coming out of the Arduino will be much smaller than the current used by the motor.

Figure 24-7 shows how this is configured. The schematic for this setup is almost identical to that of Figure 24-6. The only difference is that the electrical output of the Arduino is being used to control the base current instead of a mechanical switch. We can even calculate exactly how much current will be used. Since there is a diode (in the transistor), the resistor will be using 4.4 V. Therefore, since , then . With a beta of 100, that means that our motor can source 440 mA.

24.7 Stabilizing Transistor Beta With a Feedback Resistor

As we mentioned earlier, the transistor’s beta is not a very stable parameter. If we mass-produced something with a transistor, each device would wind up having a transistor with a different beta. Additionally, as the device was used, the beta would drift, meaning that things such as the temperature of the transistor would affect the beta, so it wouldn’t even have the same value the entire time it was turned on!

In order to get around this, engineers have developed ways of stabilizing the actual gain of a circuit even when the transistor’s beta shifts. The way that this is achieved depends greatly on the type of circuit used. In a common emitter circuit like the one we have been looking at in this chapter, we can add a resistor to the emitter to stabilize the transistor’s gain. I know that I just said not to do this because it is hard to analyze the effects. However, if you add a single resistor to the emitter, other people have worked out the math for you in order to make this work easily.

Now, to imagine why adding a resistor to the output stabilizes the transistor beta, we have to think about what happens when you do this. Without the resistor, when the transistor beta increases, it simply increases the current flow at the collector. Since the emitter is connected to ground, there aren’t any more real effects. However, if I add a resistor to the emitter, then increasing the current flow at the collector will also increase the voltage at the emitter. Now, since the voltage between the base and the emitter (V_BE) must be at 0.6 V, this will actually reduce the current in the base.

This is known as feedback—where the output of the circuit comes back in some way to affect the input. Sometimes, feedback occurs because the output is wired back to the input, but in this case, the resistor simply increases the voltage at the emitter, causing the base to pull back.

What the final effect of adding a resistor to the base will do is to limit the gain of the transistor to a fixed value that won’t change either due to manufacturing issues or due to changes during operation as the transistor beta changes due to temperature. Additionally, the computation for this is very simple. If your transistor beta varies between 50 and 200, you can add a resistor to the emitter which will limit the actual transistor gain below 50, and it will keep this value very stable even as the transistor’s beta drifts. In such a configuration, the most stable gain you can get for a given transistor beta is about of the transistor’s lowest beta.

The equation for the effect that a feedback resistor has on a transistor circuit depends on the circuit design itself—there isn’t a one-size-fits-all rule. However, feedback resistors are usually fairly small compared to the rest of the circuit.

For most circuits, simply start with a small feedback resistor (10–100 Ω). The feedback resistor will usually improve the stability of your design, even if you can’t calculate exactly how that affects the beta of the transistor. It means that your design will likely continue to work even with different transistors and operating at different temperatures. Just know that while you add stability, this will also limit the gain (which is sometimes problematic with motors).

24.8 A Word of Caution

One thing to keep in mind with transistors is that they can get very hot! Transistors have a maximum current rating, and that often is based on the amount of heat that they are able to dissipate. Transistors that are able to handle large currents are called power transistors , and usually have an attachment for a heatsink, which helps them dissipate heat to the air more efficiently.

If you build a circuit similar to the one in this chapter, be sure to keep in mind both the specs of the motor (how much voltage and current is required for it to operate) and the specs of the transistor (how much current the transistor can handle). If the motor doesn’t have enough voltage or current, it might not turn on, and if the transistor can’t handle the current, it could easily burn out.

Review

In this chapter, we learned the following:

Apply What You Have Learned