Chapter 4

Working with Inductors

In This Chapter

Unravelling the mystery of induction

Discovering reactance

Combining inductors in series and parallel

Using inductors in electronic circuits

Nearly a century ago, when radio was brand new and the invention of the transistor was another quarter of a century away, a book was published called A Course in Electrical Engineering, written by Chester L. Dawes. Technology moves so quickly that you’d think that an electrical engineering book written in 1920 would be completely obsolete today. But here’s how Chapter 1 begins:

Magnets and magnetism are involved in the operation of practically all electrical apparatus. Therefore an understanding of their underlying principles is essential to a clear conception of the operation of all such apparatus.

On the face of it magnets don’t seem to have much to do with today’s solid-state computing or LCD televisions. Yet electricity and magnetism are closely related and the relationship between electric current and magnetism still forms the core of many different types of essential circuits and everyday gadgets. For example, a power adapter that converts 230 VAC from a wall outlet to a safer level of 9 V uses a transformer that relies on magnetism to step down the voltage. An analogue multimeter (the kind with a needle that moves with voltage, current or resistance and which we describe in Book I, Chapter 8) relies on magnetism to deflect the needle. Plus, electric motors use magnetism to convert electric current into motion.

In this chapter, we look at a special class of component called inductors, which exploit the nature of magnetism and its relationship to electric current. Inductors are sort of like cousins to capacitors (which we discuss in Chapter 3 of this minibook), in that you use them to do similar things and they play by similar rules. For example, an important characteristic of a capacitor is its ability to oppose changes in voltage. Inductors have a similar ability to oppose changes, but in current not voltage.

This chapter is a bit different from the others in this minibook, because it contains no construction projects. The practical applications for inductors are in circuits that you may not be ready to build yet, such as radio tuners or power supplies. We explain the important concepts of how inductors work in this chapter so that later, when you come to use an inductor in a circuit, you know what it does. You can then use this chapter to refresh your memory as and when the need arises.

What Is Magnetism?

When Albert Einstein was 5-years-old and sick in bed, his father gave him a compass to play with. Young Albert saw that no matter how he spun the compass around, the needle always swung back to point north, and he was amazed. Years later, he wrote that this compass launched his lifelong interest in physics. He realised then that ‘something [was] behind things, something deeply hidden’.

In the case of the compass, that deeply hidden thing that Einstein marvelled at was magnetism. Although everyone is familiar with magnetism, exactly what it is remains mysterious.

A magnetic field extends through space and attracts or repels certain materials. Materials that are strongly affected by magnetic fields are called magnetic and materials that create magnetic fields are called magnets.

Pointing to the north and south of magnetism

Magnetic fields and electric fields are distinct things, but they’re closely related and have much in common. For example, magnetic fields are polarised in much the same way that electric fields are polarised. Electric fields exist between electric charges of opposite polarity (negative and positive) and magnetic fields exist between opposite magnetic poles, called north and south.

Just as opposite electric charges attract and like charges repel, opposite magnetic poles attract and like magnetic poles repel. That’s why if you take two strong magnets and try to push the two north poles together or the two south poles together, the magnet fights back and you can’t connect them. But if you turn one of the magnets around and try to hook up the north pole with the south pole, the magnets attract each other and you have trouble keeping them apart.

A magnetic field has a distinct shape that you can visualise by using a simple experiment that’s still done in schools. All you need is a bar magnet, some iron filings and a piece of paper. Put the paper over the magnet and sprinkle the filings on the paper. The filings line up to reveal the shape of the magnetic field, as shown in Figure 4-1. As you can see, the filings align themselves from one pole of the magnet to the other.

Figure 4-1: Iron filings revealing the shape of a magnetic field.

Pondering permanent magnets

A permanent magnet is a material that creates its own magnetic field. Some naturally occurring materials, such as lodestone, are inherently magnetic and produce magnetic fields on their own. But most permanent magnets are made from materials that aren’t inherently magnetic, but become so when they’re exposed to a powerful magnetic field.

You probably have several permanent magnets around your home, such as on your refrigerator holding up your children’s pictures or your shopping list.

Examining Electromagnets

Whereas permanent magnets create a magnetic field all by themselves (see the preceding section), an electromagnet relies on the key relationship between electricity and magnetism to create a magnetic field. Specifically, whenever electric current flows, a magnetic field is created by the moving charges. In short, an electron in motion becomes a magnet.

As we say several times in this book, electrons are always in motion, and so, you may wonder, aren’t little magnets everywhere? The answer is yes, in the same sense that electric current is everywhere. But when the motion of electrons within a material is random, the magnetic fields created by the electrons are oriented randomly, and so they end up just cancelling each other out. But when you give the electrons a nudge with voltage, they all start moving in the same direction. This strengthens and organises the magnetic fields so they can combine to form one large magnetic field.

The magnetic field created by current flowing through a single wire is measurable but small. If you coil the wire tightly, however, as shown in Figure 4-2, the magnetic fields are strengthened because of their proximity to one another. For example, you can create a simple electromagnet by wrapping a metre or so of small, insulated wire around a pencil, a ballpoint pen or any other rigid tube or cylinder.

Figure 4-2: An electromagnet.

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The strength of the magnetic field of such a coil depends on several factors, the most important being:

The number of turns in the coil: More turns makes for a stronger magnetic field.

The amount of current flowing through the electromagnet: Increasing the current increases the strength of the electromagnet exponentially. For example, if you double the current the electromagnet is four times as strong.

The material used for the core that the electromagnet is wrapped around: Any coil wrapped around an iron core is about ten times as strong as the same coil wrapped around an inert core such as air, plastic or wood.

The polarity of an electromagnet is easy to determine: the negative side of the coil is the magnet’s north pole and the positive side is the south pole.

Inducing Current

Electromagnets are possible because a moving current creates a magnetic field. Interestingly enough, the reverse is also true: a moving magnetic field creates an electric current. In other words, if you wave a magnet over a wire, you create a current in the wire. This effect is called electromagnetic induction, or sometimes just magnetic induction.

You can increase the strength of the current induced in a wire by coiling the wire into turns so that you expose a greater length of wire to the magnetic field. Whether the magnet or the coil moves, a current is induced in the coil if the coil is moving relative to the magnet, provided of course that the coil passes through the magnet’s magnetic field.

Whenever current is flowing, voltage exists. Thus, in addition to causing current to flow through the coil, electromagnetic induction creates a voltage across the coil.

Resisting change: Inductance

An inductor is a coil that’s designed for use in electronic circuits. Inductors take advantage of an important characteristic of coils called self-inductance, also called just inductance. Inductors are simple devices, consisting of nothing more than a coil of wire, often wrapped around an iron core. But their ability to exploit the idea of self-inductance is a stroke of genius.

Self-inductance is similar to electromagnetic induction (which we describe in the previous section), but with a subtle twist. Whereas electromagnetic induction refers to the ability of a coil to generate a current when it moves across a magnetic field, self-inductance refers to the ability of a coil to create the very magnetic field that then induces the voltage. In other words, with self-inductance, the coil feeds back upon itself. A voltage applied across the coil causes current to flow, which creates a magnetic field, which in turn creates more voltage.

Inductance happens only when the current running through the coil changes, because only a moving magnetic field induces voltage in a coil. Whenever the current changes in a coil, the magnetic field created by the current grows or shrinks, depending on whether the current increases or decreases. When the magnetic field grows or shrinks, it’s effectively moving, and so a voltage is inducted in the coil as a result of this movement. When the current stays steady, no inductance occurs.

Self-inductance is a tricky concept to get your mind around, and so don’t panic if it doesn’t make sense to you straight away. We took a while to get this concept clear at first. Therefore, we go over the idea in more detail, point by point, in the following list:

When voltage is applied across a coil, the voltage causes current to flow through the coil. Remember, current always requires voltage, and voltage always results in a current when applied across a conductor.

The current flowing through the coil creates a magnetic field around the coil. Keep in mind that the coil that creates the magnetic field is itself within the field and can therefore be influenced by it.

If the current flowing through the coil changes, the magnetic field created by the current also changes. The magnetic field grows or shrinks, depending on whether the current increases or decreases. Either way, the changing magnetic field is in effect moving.

The magnetic field is moving, which means that voltage is induced in the coil. This voltage is additional, on top of the voltage that’s driving the main current through the coil.

The amount of voltage induced by the changing magnetic field depends on the speed in which the current changes. The faster the current changes, the more the magnetic field moves and therefore the more voltage is induced.

The polarity of the induced voltage depends on whether the current is increasing or decreasing. This is because the direction of movement in the magnetic field depends on whether the field is growing or shrinking, and the voltage induced by a moving magnetic field depends on which direction the field is moving, according to the following rules:

• When the current increases, the polarity of the induced voltage is opposite to the polarity of the voltage driving the coil. This inducted voltage is often called back voltage, because it has the opposite polarity to the supply voltage.

• When the current decreases, the resulting self-induced voltage has the same polarity as the supply voltage.

The induced voltage creates a current in the coil that flows with or against the main coil current, depending on whether the coil current is decreasing or increasing, according to the following rules:

• When the coil current is increasing, the additional current flows against the main coil current. This has the effect of pushing back against the increasing main current, which effectively slows down the rate at which the current can change.

• When the coil current is decreasing, the additional current flows with the main coil current, thus counteracting the decrease in coil current.

When the coil current stops changing, self-inductance stops. Thus, when current is steady, an inductor is simply a straight conductor. (It’s also an electromagnet (check out the earlier section ‘Examining Electromagnets’), because the current travelling through it produces a magnetic field.)

Self-inductance means that an inductor is said to oppose changes in current. If the current increases, an opposite voltage is induced across the coil, which slows the rate at which the current can increase. If the current decreases, a forward voltage is induced across the coil, which slows the rate at which the current decreases. An inductor applies equal opposition to increases and decreases in current.

This ability to oppose changes in current is useful in electronic circuits, as we explain later in the section ‘Putting Inductors to Work’.

Here are some additional important details concerning inductors:

Inductors can’t stop changes in current; they can only slow them down. Measuring how much an inductor can slow down a change in current is the topic of the next section.

The magnetic field from one inductor can spill over into a nearby inductor and induce voltage in it as well. To prevent this from happening, many inductors have special shielding around them to keep them magnetically isolated.

If you use unshielded inductors in your circuits, be sure to space them as far apart as possible.

Regarding henrys

Inductance is only a momentary occurrence. Exactly how momentary depends on the amount of inductance an inductor has.

Inductance is measured in units called henrys. One henry is the amount of inductance necessary to induce 1 V when the current in the coil changes at a rate of 1 ampere per second.

As you may guess, 1 henry is a fairly large inductor. Inductors in the single-digit henry range are often used when dealing with household current (230 VAC at 50 Hz). But for most electronics work, you use inductances measured in thousandths of a henry (millihenrys, abbreviated mH) or in millionths of a henry (microhenrys, abbreviated μH).

Here are a few factoids about inductors and henrys:

Abbreviation: The letter L is often used to represent inductance in formulas. In addition, inductors in schematic diagrams are usually referenced by ‘L’. For example, if a circuit calls for three inductors, they’re identified L1, L2 and L3.

Name: The henry is named after Joseph Henry, who discovered self-inductance and invented the inductor. Note that the plural of henry is henrys, not henries.

  Schematics: The symbol used to represent inductors in a schematic diagram is shown in the margin.

Calculating RL Time Constants

In Chapter 3 of this minibook, you discover how to calculate the RC time constant for a resistor-capacitor circuit. Well, you can do a similar calculation for inductors, except that instead of being called the RC time constant, it’s known as the RL time constant (L is the symbol for inductance).

The RL time constant indicates the amount of time necessary to conduct 63.2% of the current that results from a voltage applied across an inductor. (If you’re thinking that you’ve seen 63.2% before, you’re right! It’s the same percentage used to calculate time constants in resistor-capacitor networks. The value 63.2% derives from the calculus equations used to determine the exact time constants for both resistor-capacitor and resistor-inductor networks.)

Here’s the formula for calculating an RL time constant:

In other words, the RL time constant in seconds is equal to the inductance in henrys divided by the resistance of the circuit in ohms.

For example, suppose that the resistance is 100 Ω and the capacitance is 100 mH. Before you do the multiplication, you first need to convert the 100 mH to henrys. Because 1 mH is 1 1-thousandth of a henry, 100 mH is equivalent to 0.1 H. Dividing 0.1H by 100Ω gives you a time constant of 0.001 second (s), or one millisecond (ms).

The following table gives you a helpful approximation of the percentage of current that an inductor passes after the first five time constants. For all practical purposes, you can consider the current fully flowing after five time constants have elapsed.

RL Time Constant Interval	Percentage of Total Current Passed
1	62.3%
2	86.5%
3	95.0%
4	98.2%
5	99.3%

Thus, in the example circuit in which the resistance is 100 Ω and the inductance is 0.1 H, you can expect current to be flowing at full capacity within 5 ms of when the voltage is applied.

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Calculating Inductive Reactance

Although inductors oppose changes in current (as we discuss in the earlier section ‘Resisting change: Inductance’), they don’t oppose all changes equally.

Inductors present more opposition to fast current changes than they do to slower changes. Or, put another way, inductors oppose current changes in higher-frequency signals more than they do in lower-frequency signals.

The degree to which an inductor opposes current change at a particular frequency is called the inductor’s reactance. Like resistance, inductive reactance is measured in ohms (check out Chapter 2 of this minibook for more details), and can be calculated with the following formula:

Here, the symbol XL represents the inductive reactance in ohms, f represents the frequency of the signal in hertz (cycles per second) and L equals the inductance in henrys. Oh, and π is the mathematical constant you heard so much about at school, whose value is approximately 3.14.

For example, suppose you want to know the reactance of a 1 mH inductor to a 60 Hz sine wave. The maths looks like this:

Thus, a 1 mH inductor has a reactance of about a third of an ohm at 60 Hz.

How much reactance does the same inductor have at 20 kHz? Much more:

Increase the frequency to 100 MHz and see how much resistance the inductor has:

At low frequencies, inductors are much more likely to let current pass than at high frequencies. As the next section explains, you can exploit this characteristic to create circuits that block frequencies above or below certain values.

Combining Inductors

Just like resistors and capacitors (the subjects of Chapters 2 and 3 of this minibook, respectively), you can combine inductors in series or parallel and use simple equations to calculate the total inductance of the circuit.

For the calculations to be valid, however, the inductors must be shielded. If they aren’t shielded, they’re not only affected by their own magnetic fields, but also by the magnetic fields of other inductors around them. In that case, all bets are off.

You calculate inductor combinations just like resistor combinations (from Chapter 2 of this minibook), using exactly the same formulas except substituting henrys for ohms. Here are the formulas:

Series inductors: Just add up the value of each individual inductor.

Two or more identical parallel inductors: Add them up and divide by the number of inductors.

Two parallel and unequal inductors: Use this formula:

Three or more parallel and unequal inductors: Use this formula:

Here’s an example in which three inductors valued at 20 mH, 100 mH and 50 mH are connected in parallel:

Therefore, the total inductance of this circuit is 12.5 mH.

Putting Inductors to Work

Here are a few common uses for inductors in real-life circuits:

Smoothing voltage in a power supply: The final stage of a typical power-supply circuit that converts 230 VAC household current to a useable direct current is often a filter circuit that removes any residual irregularities in the voltage due to the fact that it was derived from a 50 Hz AC input.

Filters: Select frequencies to be allowed to pass or to be blocked. You’re probably familiar with the tone settings on a stereo system, which let you bump up the bass, tone down the midrange and ease up the upper range just for brightness. Three different types of filters exist:

• High-pass filters allow only frequencies above a certain value to pass.

• Low-pass filters allow only frequencies below a certain value to pass.

• Band-pass filters allow only frequencies that fall between an upper and a lower value to pass.

Radio-tuning circuits: You can use coils to help a radio-tuning circuit tune to a particular frequency signal and hold it.

Transformers: The simplest transformer consists of a pair of inductors placed next to each other. The transformer serves two functions: it can increase or decrease voltage and it can electrically isolate one part of a circuit from another. For more about transformers, flip to Book IV, Chapter 1.