10.1 Important Terms Related to Power

One of the interesting things about work, energy, and power is that they can take on a number of forms that are all basically equivalent. For instance, we can have mechanical energy, chemical energy, and electrical energy (as well as others). We can also perform mechanical work, chemical work, and electrical work. All these types of energy and work can be converted to each other. They are all also measured in joules. Therefore, we have a common unit of energy for any sort of task we want to accomplish.

Now, when we actually apply energy to perform work, we do not get a 100% conversion rate. In other words, if we want to do 100 joules of work, we will probably need more than 100 joules of energy to perform the task. That’s because the process of converting energy into work (as well as converting between different types of energy and work) is inefficient—not all of the energy gets directed to the task we want to perform. There is no perfectly efficient process of converting energy to work. Additionally, there is no way to create energy from nothing—any time you need additional energy, you will need a source for it.

When energy is converted to work, all of the energy does something, even if it isn’t work on the task you want. Usually, the inefficiencies get converted to heat. So, if I have a process that is only 10% efficient and I give that process 80 joules of energy, then that process will do only 8 joules of work, leaving 72 joules of energy that is converted to heat.

Work and energy are usually the quantities we care about for systems that do a fixed task (i.e., require a fixed amount of energy). In electronics, however, we are usually building systems that stay on for sustained periods of time. Therefore, instead of measuring energy, we measure power, which is the continuous delivery of energy (or the continuous usage of energy in doing work).

As we mentioned, power is measured in watts, where a watt is 1 joule per second. So, if you have a 100 W light bulb, that bulb uses 100 joules of energy each second. True, 100 W incandescent light bulbs are very inefficient, which is why they get so hot—the energy that is not converted to light gets converted to heat instead. Today, incandescent bulbs are rarely used for that very reason. For instance, the LED bulbs that are labeled as “100 W” equivalent generally use about 11 W, but they are as bright as the old 100 W incandescents. What this means is that in an incandescent light, less than 11 W of energy was being put toward actually giving off light, and the rest was wasted as heat, which is why they got quite so hot.¹

10.2 Power in Electronics

So we have a basic idea about what power is in general. In electronics, there are a few equivalent ways of calculating power.

The first is to multiply the number of volts being consumed by the number of amps of current going through a device:

(10.1)

Here, P indicates power measured in watts, V indicates volts, and I indicates current measured in amps. So, if my circuit is on a 9-volt battery and I measure that the battery is delivering 20 mA to the circuit, then that means I can calculate the amount of power that my circuit is using (don’t forget to convert milliamps to amps first!):

So our circuit uses 0.18 watt of power.

You can also measure the amount of power that individual components use. For instance, let’s say that a resistor has a 3 V voltage drop and has 12 mA of current running through it. Therefore, the resistor uses up 3 ∗ 0.012 = 0.036 watt of power.

The second way of calculating power comes from applying Ohm’s law. Ohm’s law say

(10.2)

So, if we have the equation P = V ∗ I, Ohm’s law allows us to replace V with I ∗ R. Therefore, our new equation becomes

(10.3)

Or we can simplify it further and say that

(10.4)

We can also substitute I = V/R and wind up with a third equation for power:

(10.5)

So, if we have 15 mA running through a 200 Ω resistor, then we can calculate the amount of power being used using Equation 10.4:

10.3 Component Power Limitations

Now, if you think about it, the resistor in the previous example isn’t actually doing anything. It is just sitting there. Therefore, since we are not accomplishing any work by going through the resistor, the energy gets converted to heat. Electronic components are usually rated for how much power they can dissipate, or easily get rid of. Most common resistors, for instance, are rated between 1/16 W and 1/2W (most that I’ve seen for sale are 1/4 W). This means that they will continue to work as long as their power consumption stays under their limit. If the power consumption goes too high, they will not be able to handle the increased heat and will break (and possibly catch fire!).

So far, our projects have dealt with low enough power that this isn’t a concern. In fact, using 9 V batteries, it is hard to generate more than 1/4W of power—you would have to have less than 350 Ω of resistance on the whole circuit and have the entire voltage drop occur on the resistor.

In any case, whenever you are building circuits, you should keep in mind how much power the component is rated to handle and how much power it is actually consuming. You can use any of the equations given here to calculate power consumption. The component itself should have information on its maximum ability to handle power consumption and dissipation.

10.4 Handling Power Dissipation with Heatsinks

As we mentioned earlier, when power dissipates without doing any work, it is converted to heat. Some devices need to dissipate large quantities of heat under regular workloads. One common device that often needs to dissipate heat is the voltage regulator, like the 7805 regulator we will encounter in Chapter 12.

The way that this regulator performs its job is essentially by dissipating power until the voltage is at the right level. When used with any serious amount of current, this can actually get very, very hot. As such, the back side of these contains a metal plate which is used to dissipate heat. Additionally, it has a metal tab with a hole that can be used to attach a heatsink.

A heatsink is a metal structure with a large surface area that helps an electronic component dissipate heat. By being made of metal, it quickly moves the heat into itself. By having a large surface area, it can transfer the heat to the air, where it will then disperse into the environment.

Figure 10-1 shows a 7805 chip next to its heatsink. To attach the heatsink, just screw it into the 7805. On the 7800 series of regulators, the tab is electrically connected to ground, so it should not produce a voltage. However, other types of chips in the same TO-220 package may actually have a voltage on the tab. In such a case, it would be wise to buy an isolation kit to electrically isolate the chip from the heatsink; otherwise, incidental contact with the heatsink could cause a short circuit. The isolation kit will only allow heat, not electricity, flow into the heatsink.

10.5 Transforming Power

As we have discussed, energy (and therefore power) can be transformed among a variety of forms—mechanical, electrical, chemical, and so on. In any case, always remember that energy is only reduced or lost, never gained.

The essence of energy transformation is at the heart of what makes batteries work. A battery contains energy stored in a chemical form. Chemical reactions in the battery allow electrons to move. By drawing the electrons through a specific path (drawing them to the positive from the negative), this reaction generates electrical energy. So we have a conversion from chemical energy (the reaction of the chemicals in the battery) into electrical energy (the pull of the electrons through the circuit).

This can also go the other way. Electrical energy can be used to stimulate chemical reactions. A common one is the separation of water into hydrogen and oxygen.

The same conversion can happen with mechanical energy. In an electric motor, electrical energy is converted into mechanical energy in the motor. But the reverse also can occur. A power generator is made by converting mechanical energy into electrical energy.

Power and energy are known as conserved quantities , because, although they are transformed, they are never created or lost. Note that when we talk about power lost through inefficiencies, the power actually isn’t lost in total; it is merely converted to heat. You can think of heat as power that is applied in a nonspecific direction. Energy is lost when it is transformed not because it disappears but rather because all processes which channel one form of energy into another are imperfect.

In Section 10.2, “Power in Electronics,” we noted that, in electronics, the power (measured in watts) is determined by both the voltage and the current—by multiplying them together. Therefore, what will be conserved in electronics will not be the voltage or the current individually, but their product. What this means is that we can, at least in theory, increase the voltage without needing a power gain, but at the cost of current. Likewise, we can, at least in theory, increase the current without needing a power gain, at the cost of voltage. In both of these cases, rather than transforming electrical power to another form of power altogether, we are transforming it into a different configuration of electrical power.

Devices that convert electrical power between different voltage/current configurations are known as transformers . A step-up transformer is one that converts a low voltage to a higher voltage (at the cost of current), and a step-down transformer is one that converts a high voltage to a lower voltage (but can supply additional current).

Technically, for DC circuits, these are usually known as DC-DC power converters or boost converters instead of being called transformers, but the same rules apply—the total number of watts delivered can never increase, but the voltage can be converted up and down at the expense or gain of the current.²

So, if I had a source of 12 V and 2 A, then I would have 12 ∗ 2 = 24 W. Therefore, it may be possible to convert that to 24 V, but I would only be able to get 1 A of current (24 ∗ 1 = 24). However, I could drop the voltage to get more current. If I needed 4 A, I could reduce the voltage to 6 V.

Also remember that in doing these transformations, there is always some amount of power loss as well, but these calculations will give you what the maximum possibilities are. The actual mechanisms that these devices employ for doing power conversions are outside the scope of this book.

10.6 Amplifying Low-Power Signals

Many devices, especially integrated circuits, are only capable of processing and generating low-power signals. Microcontrollers (like the ATmega328/P) have limits to how much power they can send or receive. The ATmega328/P can only source up to 40 mA per pin and only about 200 mA total across all pins simultaneously. At 5 V, 40 mA would yield a maximum of 0.2 W. Therefore, if you want to turn on a device that requires more power than that, you will need to amplify your signal.

Now, as we discussed previously, you can’t actually create more power out of nothing. What you can do is, instead of trying to create power, you can instead control power. We will discuss several specific techniques on how to do this starting in Chapter 24, but the essential idea is that you can amplify a signal by using a small signal to control a larger one.

Think about your car. The way that you control your car is by taking a low-power signal, such as the gas pedal, and using it to control a high-power signal, such as the engine. My foot is not directly powering the car. My foot is merely using the pedals to tell another power source—the engine—how much of its energy it should move. My foot doesn’t actually interact directly with the engine at all, except as a valve to unleash or not unleash the power available in the gas tank and engine.

In the same way, since the output signals from the microcontrollers are low power, instead of using these signals directly, we will use the signals to control larger sources of power. Devices which can do this include relays, optocouplers, transistors, op-amps, and darlington arrays. We will cover more about amplification starting in Chapter 24.

10.7 Review

10.8 Apply What You Have Learned