Definition of Alternating Current

AC is the abbreviation for alternating current. Alternating current is an electrical current which changes in both magnitude and direction. The term, magnitude, refers to the quantitative value of the current in a circuit — in other words, how much current is flowing. The term, direction, refers to the direction current flows in a circuit.

Generating an AC Waveform

The simple dc circuit in Figure 1.2 can be used to simulate alternating current. The circuit consists of a variable dc power supply, a resistor, and a galvanometer. The galvanometer is an ammeter with a center scale value of zero amperes. If current flows in the circuit in a counter-clockwise direction, the meter needle will deflect to the left. If current flows in a clockwise direction, the meter needle will deflect to the right.

With the circuit configuration as shown in Figure 1.3, electron current flow will be in a counter-clockwise direction. If the power supply voltage is increased, the galvanometer needle will deflect to the left to some maximum current value. As the voltage is decreased to zero volts, current flow in the circuit will decrease to zero amperes.

Therefore, a current flow has been predicted which changes in magnitude. This meets one of the two specified criteria for alternating current. To meet the other criterion, a change in direction, the polarity of the battery can be reversed as in Figure 1.4. Notice that current now flows in a clockwise direction.

As the power supply voltage is increased, the galvanometer needle deflects to the right to some maximum value. As the voltage is decreased to zero volts, current flow in the circuit decreases to zero amperes.

Plotting an AC Waveform

This alternating current can be represented in graphical form, as shown in Figure 1.5. Notice that the axes of this graph are specified to plot current versus time. Time is plotted on the horizontal, or X axis. Current is plotted on the vertical, or Y axis. The vertical axis is divided into a positive (+) current value above the X axis and a negative (–) current value below the X axis. This polarity designation is used simply to differentiate between direction of current flow.

For this application, current flow in a counter-clockwise direction will be designated as positive current, and current flow in the opposite, clockwise direction, will be designated a negative current. The polarity and direction selections are arbitrary.

With the circuit connected as in Figure 1.3, current, I, flows in a counter-clockwise direction, with current flow increasing and decreasing. Note that the direction of current stays the same. Only the value of the current is changed. Current in this direction is plotted in the top half of the graph to indicate positive current as shown in Figure 1.6.

With the battery reversed as shown in Figure 1.4, current now flows in a clockwise direction. The current always flows in the same direction. The magnitude of the current increases and decreases following the magnitude of the applied voltage, and the current is plotted in the negative (–) portion of the graph of Figure 1.7. This indicates negative current or, more precisely, a current that is flowing in a direction opposite to the direction originally chosen for positive current. Note the two distinguishing characteristics of this waveform. First, there is a change in current value — in this example, the change is continuous. Second, the direction of current flow has changed. This change in direction is indicated by the waveform crossing the X axis into the negative half of the graph. If these two criteria are met, the waveform can be categorized as an ac waveform.

The particular waveform shown in Figure 1.7 is only one type of an ac waveform, a sine wave. Other ac waveforms which meet the specified criteria for an ac waveform will be introduced later.

AC Voltages

If there is current flow in a circuit, a difference in potential, or voltage, must be present. The voltage, E, that produces an alternating current must change in the same manner as the current as shown by the diagrams in Figure 1.8.

The polarity of the voltage must change to cause current to change direction. A voltage that causes an alternating current is called an ac voltage.

Summary of DC and AC Voltages and Currents

The difference between dc and ac voltages and currents can now be summarized.

DC is direct current — a current which flows in only one direction. It can change in magnitude, and if it does, it generally is called pulsating dc. A dc voltage is a voltage that produces a direct current. It does not change in polarity.

AC is alternating current — a current which changes in both magnitude and direction. AC voltage is a voltage that produces an alternating current. It changes in amplitude and polarity. Amplitude is the magnitude or value of an ac voltage.

CONTRASTING DC AND AC WAVEFORMS

A comparison of some different types of dc and ac voltage waveforms should help you understand the differences between the two.

The waveform in Figure 1.9a is a dc waveform because it does not change polarity. Note that the amplitude remains at a constant level. A plot of the current versus time in a circuit with the voltage of Figure 1.9a applied would also be a constant value as a result of a fixed value of dc voltage.

The waveform in Figure 1.9b is also a dc waveform. It has a polarity opposite to that of the waveform in Figure 1.9a, but it too does not change in amplitude.

The waveform in Figure 1.10a is a dc waveform, and it is a pulsating waveform. The entire waveform is in the positive portion of the graph, and never crosses the X axis. If the line graph had crossed the X axis into the opposite half of the graph, and if this voltage were applied to a circuit, then it would have caused the circuit current to change direction, and it would no longer be considered a dc voltage. This is the most important point in distinguishing between dc and ac waveforms.

The waveform in Figure 1.10b is a dc waveform that is constantly changing amplitude. This type of waveform is often referred to as an ac waveform riding on a steady state or constant dc voltage or current (indicated by the dotted line). The output from signal–amplifier circuits often looks like the one in Figure 1.10b. There is a steady-state dc voltage at the output displaced from zero when there is no signal being amplified. When a signal is amplified it rides on top of the dc voltage and swings the dc voltage above and below its steady-state value. In many circuits, resistive and capacitive coupling circuits are used to remove, or block, the dc component of the waveform. The resultant waveform then looks like Figure 1.11a.

Both waveforms in Figure 1.11 are ac waveforms. Both are constantly changing in amplitude and direction. Figure 1.11a shows a typical sine waveform. Figure 1.11b shows an ac square waveform, commonly called a square wave. Note that the square wave maintains a constant amplitude for a period of time and then almost instantly changes to the same constant amplitude of opposite polarity for the same period of time. So the periods of time are equal and the constant amplitudes of opposite polarity are equal, and the changes are almost instantaneous or step-like.

The AC Generator

An ac generator is a device which generates an ac voltage by rotating a loop of conductor material through a magnetic field. To understand the operation of an ac generator, some basic understanding of magnetic theory is necessary.

Magnetic Lines of Force

It is generally known that magnets have north poles and south poles, and that they attract other materials with magnetic properties. If two magnets are brought close to one another, then a magnetic field exists between their two poles. If these two poles are unlike, one a north pole and the other a south pole, the direction of the flux lines is from the north pole to the south pole, as shown in the diagram of Figure 1.12. The stronger the magnets, the stronger the magnetic field between the two poles.

Iron filings can be used to indicate the presence of the flux lines between north and south magnetic poles as shown in Figure 1.13. The magnets are placed on the table with north and south poles as shown, a sheet of plexiglas is placed over them and iron filings are sprinkled on top. The iron fillings, because they are magnetic material, align themselves with the flux lines of the magnetic field. These lines are important because they are used to explain how to generate ac.

Electromagnetic Induction

In 1831, Michael Faraday, a British physicist, discovered that if a moving magnetic field passes through a conductor, a voltage will be induced in the conductor, and if the conductor is connected in a circuit, a current will flow.

Conversely, if a moving conductor passes through a magnetic field, a voltage will also be induced in the conductor causing current to flow as shown in Figure 1.14, by generating an electromotive force by a process called electromagnetic induction. The direction of current flow in the conductor depends on the direction of the magnetic field and the direction of motion of the conductor through the field. This fact is summarized in what is known as the left-hand rule for generators.

Figure 1.15 is a drawing illustrating this rule. The thumb points in the direction of motion of the conductor through the magnetic field. The forefinger points in the direction of the lines of magnetic field. And the index finger points in the direction of electron current flow. Electron current flow will be used throughout this book unless otherwise noted. Electron flow with its moving negative charges is opposite from the conventional current flow direction which was used by Ben Franklin when he assumed that positive charges were moving to constitute current flow.

A practical application of this concept is the ac single loop rotary generator shown in Figure 1.16. In this type of generator, a single loop of wire is rotated in a circular motion in a magnetic field. The direction of the magnetic field flux lines is as shown.

There are 360 degrees in any circle, and various points of rotation can be defined in terms of degrees. For this example, the loop is assumed closed and the current flow in the loop as a result of the induced voltage at four points of rotation of the loop, A, B, C, and D as shown in Figure 1.16, will be analyzed.

The circular motion of the loop will be started at point A or 0 degrees; continue to point B at 90 degrees; go to point C, 180 degrees; pass through point D, 270 degrees; and return to point A at 360 degrees, or 0 degrees. The arrow in the drawing of Figure 1.16 indicates the direction in which the conductor is moving through the stationary magnetic field.

As shown in Figure 1.17, at point A, 0°, and point C, 180°, the conductor is moving parallel to the lines of flux. It cuts no flux lines; therefore, no voltage is induced and no current will flow in the wire. However, at point B, 90°, and point D, 270°, the conductor is moving perpendicular to the flux lines;

therefore, a maximum voltage is induced and a maximum current flows in the loop.

Changing Directions of Current Flow

An important point is that while the wire loop rotates from 0 degrees through 180 degrees, current flows in one direction. While the wire loop rotates from 180 degrees through 360 degrees, current flows in the opposite direction.

This fact is explained by the left hand rule for generators using electron flow which is shown in Figure 1.15. If one were using conventional current then the right hand rule for generators as shown in Figure 1.18 explains the direction of conventional current that flows. These diagrams show the relationship between the magnetic field, the direction of movement of the conductor, and the direction of current flow in the conductor.

Plotting an AC Generator Output Waveform

Based on this discussion of an ac single loop generator, a graph of the current flow in the wire loop through 360 degrees of rotation will be plotted on a graph.

As shown in Figure 1.19, the axes of the graph are defined in current on the Y, or vertical axis, and degrees of rotation at points A, B, C, and D on the X, or horizontal axis. Notice that the Y axis shows positive current above the origin (zero axis), and negative current below the origin. This is simply to distingush between opposite directors of current flow.

As shown in Figure 1.17 with the loop at 0 degrees, no flux lines are being cut. Therefore, no current flows in the loop. This current value is plotted at the 0 current level at point A on the graph of Figure 1.19.

After 90 degrees of rotation, as shown in Figure 1.17, a maximum amount of flux is being cut and a maximum current flows in the loop. Therefore, a maximum current level is plotted at point B on the graph.

At 180 degrees of rotation, the loop is again moving parallel to the flux lines. Therefore, no current flows. The value is plotted at point C on the graph.

At 270 degrees, a maximum current again flows, but now the current flows in the opposite direction to the direction at point B because the conductor is moving in the opposite direction. This maximum current is plotted at point D in the negative area of the graph to distinguish it from current flow in the opposite direction during the previous 180 degrees of rotation.

At 360 degrees, current again decreases to zero and is plotted at 0 degrees at point A.

If the rotation should continue through another 360 degrees, the current flow would be identical to the previous rotation and identical points would be plotted on the graph.

Between the four points plotted for each cycle of loop rotation, current flow is not linear. It’s a smooth, continuously changing waveform called a sine wave. When the current values at the four points A, B, C, and D are connected as shown in Figure 1.19, a waveform called a sinusoidal waveform is the result.

It is the type of waveform most commonly found in ac, and it will be the primary type of waveform studied throughout this book. The characteristics of the waveform will be explained in detail in following chapters.

Cycle Alternations

One cycle of a sinusoidal waveform can also be described in terms of alternations. Each cycle has two alternations: a positive alternation and a negative alternation. The positive alternation occurs while current is flowing in the same direction which is defined as the positive direction. The negative alternation occurs while current flows in the opposite direction.

Cycle alternations are identified in Figure 1.21.

Cycle Identification

There are several cycles of an ac waveform in the diagram of Figure 1.22. The first cycle begins at point A and continues for 360 degrees to point B. The second cycle starts at point B where the first cycle ends and continues for the next 360 degrees to point C.

The remaining part of the waveform between points C and D should be recognized as not being a complete cycle. It is only one-half of a cycle: 180 degrees of a cycle.

To generate the complete waveform, the loop of the generator would have to be rotated two complete turns and one-half of the next turn.

Nonstandard Cycles

It should be understood that it is not necessary for all waveforms to begin at zero degrees and continue through 360 degrees to be defined as a cycle. The waveform in Figure 1.23 begins at the 90-degree point. A cycle will be completed at the following 90-degree point and another cycle at the following 90-degree point.

One cycle of a waveform may be observed beginning at any degree point. It must continue from that point through a 360-degree change to be a complete cycle. For example, observe the waveform in Figure 1.24 which begins at the 135-degree point. A cycle will be completed when it progresses through a 360-degree change and returns to 135 degrees.

If a waveform is observed beginning at a negative peak as in Figure 1.25, one cycle would be completed at the next negative peak.

Cycle Defined

Repetitious waveforms which are not sinusoidal have cyclic properties as shown in Figure 1.26. In each example the waveform has completed one cycle when it reaches a point where repetition of the waveform begins.

A cycle of a waveform can now be defined as a waveform that begins at any electrical degree point and progresses through a 360-degree change.

The square waves in Figure 1.27 also have cyclic characteristics.

Voltage Considerations in Cycle Identification

When identifying cycles, you should pay particular attention to the voltage values and the waveform shape at the beginning and end of each cycle of a waveform. The repetitious sawtooth waveform in Figure 1.28 can be divided in cycles using this criteria. Notice the value of the voltage and slope of the waveform at the start and end of each cycle are the same.

Frequency Defined

From previous discussion, you should now understand that any waveform which is repetitious can be described in terms of cycles. The rate at which a waveform cycles is called the frequency of the waveform. The frequency of the waveform is defined as the number of cycles occurring in each second of time. The unit of frequency, cycles per second, is often abbreviated cps.

For example, Figure 1.29 shows three sinusoidal waveforms, each having a different frequency. In Figure 1.29a, only one cycle occurs in one second of time. The frequency of this waveform is one cycle per second

In Figure 1.29b, three cycles occur in one second. In this example, the frequency is three cycles per second.

In Figure 1.29c, five cycles occur in one-half second. If the waveform is repetitious, 10 cycles must occur in one second. Therefore, the frequency is 10 cycles per second.

Unit of Frequency: Hertz

In recent years, the unit of frequency, cycles per second, has been replaced by the term hertz, abbreviated Hz. The unit hertz was adopted to honor the German physicist, Heinrich Hertz, who made important discoveries in the area of electromagnetic waves in the late nineteenth century.

One hertz is simply one cycle per second. Applying the newer terminology to the waveform of Figure 1.29, the waveform of Figure 1.29a has a frequency of one hertz, the waveform of Figure 1.29b has a frequency of three hertz, and the frequency of Figure 1.29c is 10 hertz.

Frequency Prefixes

Prefixes are often used to simplify the writing of high frequencies. The common prefixes used are:

k for kilo or thousand

M for mega or million

G for giga or billion

For example, a radio station broadcasting at 820,000 hertz (Hz) can have its frequency described as 820 kilohertz (kHz).

A 1,210,000 hertz signal could be written as 1.21 megahertz (MHz).

A radar system operating at 27,000,000,000 hertz may be specified as 27 gigahertz (GHz).

Period Defined

The frequency of a waveform is determined by the lengh of time of one cycle. This time of one cycle of a waveform is defined as the period of the waveform.

The symbol T is used to represent time and period. Remember that the terms are synonomous. The period or time of a waveform is simply the time required to complete one cycle of the waveform. T has units of seconds.

Period Calculation Examples

Let’s return to the examples in Figure 1.29 and determine the period of each of the three waveforms.

The waveform in Figure 1.29a has a frequency of one hertz. One cycle occurs in one second of time. Therefore, the time of one cycle, the period, of this waveform is one second.

In Figure 1.29b the waveform has a frequency of three hertz. One cycle occurs during each one-third of a second time interval. Therefore, the period of one cycle is one-third second or 0.333 second. The waveform in Figure 1.29c has five cycles occurring in one-half of a second. The waveform repeats itself every one-tenth of a second. Each cycle occupies a one-tenth second time interval; therefore the period, T, of the waveform is one-tenth (0.1) second.

Period or Time Equation

There is a mathematical relationship between the period and frequency of a waveform. This mathematical relationship is expressed by this equation:

(1–1)

The time of one cycle or period, T, of a waveform in seconds can be determined by dividing the number one by the frequency of the waveform in hertz. This equation is normally simplified by writing it in this form:

(1–2)

You must remember that to obtain the period of a waveform in seconds, the frequency in hertz must be used in the equation. Attempts to calculate the period of a waveform by leaving the zeroes out of the frequency value will result in an incorrect answer.

Using equation 1–2 to find the period of a waveform when the frequency is known is a common technical electronic solution. For example, find the time of one cycle when the frequency is known to be 50 hertz.

The time of one cycle is 20 milliseconds. If the known frequency is a larger value, the solution can at first appear difficult, but the technique is identical to the previous example. For example, what is the time of one cycle when the frequency is 650,000 hertz? Using equation 1–2:

The time of one cycle is 1.54 microseconds.

a. dc

b. pulsating dc

c. ac

d. pulsating dc

e. ac square wave

f. dc square wave

a. 3 cycles

b. 4½ cycles

c. 1 cycle

d. 1½ cycles

e. 1¾ cycles

f. 2 cycles

a. 

b. 

c. 

d. 

e. 

f. 

a. f = 105 Hz

b. f = 60 Hz

c. f = 8,500 Hz

d. f = 16.8 kHz

e. f = 320 kHz

f. f = 6.1 MHz

a. 

b. 

c. 

d. 

e. 

f. 

a. f = 40 Hz

b. f = 1.5 kHz

c. f = 63 kHz

d. f = 118 kHz

e. f = 0.8 MHz

f. f = 1.5 MHz

a. T = 0.015 s

b. T = 37.2 ms

c. T = 37.2 μs

d. T = 0.000008 s

e. T = 48 ms

f. T = 7.35 μs

a. f = 30 Hz

b. f = 300 Hz

c. f = 63.8 kHz

d. f = 20 kHz

e. f = 1,700 Hz

f. f = 22 MHz