AC电路教程：第六版，2007更新

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《电气电路教程第二卷 - 交流》（Lessons in Electric Circuits Volume II - AC, Sixth Edition, Last Update July 25, 2007）是Tony R. Kuphaldt撰写的一本专业IT教材，专注于交流电理论和应用。本书作为开放源代码的一部分，遵循设计科学许可协议（Design Science License），允许读者自由复制、分发和修改，旨在促进知识共享，且没有商业保证或特定用途适用性的承诺。该书第六版于2007年7月更新，提供了清晰易懂的内容，特别注重对交流电路的基本原理和概念的讲解。第一版在2000年6月发布，所有的插图采用标准的ASCII格式，确保了广泛的计算机兼容性，以便所有用户都能阅读理解。第二版在同年9月推出，进一步改进了图形设计，将源文件转换成TeXinfo格式，便于在线查看和打印。作为一本协作开发的教材，它旨在帮助学生和工程师深入理解交流电路的分析方法，包括欧姆定律、基尔霍夫定律、相量分析、功率计算、变压器工作原理等核心主题。书中还涵盖了谐振、滤波、电机控制等实用技术，适合进行电子工程、电力系统分析以及信号处理领域的学习。由于本书是开源作品，读者可以在www.ibiblio.org/obp/electricCircuits找到完整版本，并参与到持续的改进和讨论中，这体现了现代教育理念中的互动性和社区参与。《电气电路教程第二卷 - 交流》是一本兼具学术严谨性和实用性，且不断发展的IT教育资源。

1.2. AC WAVEFORMS

Time

(the sine wave)

Figure 1.8:

Graph of AC voltage over time (the si ne wave).

Table 1.1:

Trigonometric “sine” function.

Angle (

) sin(angle) wave Angle (

) sin(angle) wave

0 0.0000 zero 180 0.0000 zero

15 0.2588 + 195 -0.2588 -

30 0.5000 + 210 -0.5000 -

45 0.7071 + 225 -0.7071 -

60 0.8660 + 240 -0.8660 -

75 0.9659 + 255 -0.9659 -

90 1.0000 +peak 270 -1.0000 -peak

105 0.9659 + 285 -0.9659 -

120 0.8660 + 300 -0.8660 -

135 0.7071 + 315 -0.7071 -

150 0.5000 + 330 -0.5000 -

165 0.2588 + 345 -0.2588 -

180 0.0000 zero 360 0.0000 zero

CHAPTER 1. BASIC AC THEORY

Mathematically, the rate of magnetic ﬂux change due to a rotating magnet follows that of a

sine function, so the voltage produced by the coils follows that same function.

If we were to follow the changing voltage produced by a coil in an alternator from any

point on the sine wave graph to that point when the wave shape begins to repeat itself, we

would have marked exactly one cycle of that wave. This is most easily shown by spanning the

distance between identical peaks, but may be measured between any corresponding points on

the graph. The degree marks on the horizontal axis of the graph represent the domain of the

trigonometric sine function, and also the angular position of our s imple two-pole alternator

shaft as it rotates: Figure

1.9

one wave cycle

Alternator shaft

position (degrees)

0 90 180 270 360

(0)

90 180 270 360

(0)

one wave cycle

Figure 1.9:

Alternator voltage as function of shaft position ( time).

Since the horizontal axis of this graph can mark the passage of time as well as shaft position

in degrees, the dimension marked for one cycle is often measured in a unit of time, most often

seconds or fractions of a second. When expressed as a measurement, this is often called the

period of a wave. The period of a wave in degrees is always 360, but the amount of time one

period occupies depends on the rate voltage oscillates back and forth.

A more popular measure for describing the alternating rate of an AC voltage or current

wave than period is the rate of that back-and-forth oscillation. This is called frequency. The

modern unit for frequency is the Hertz (abbreviated Hz), which represents the number of wave

cycles completed during one second of time. In the United States of America, the standard

power-line frequency is 60 Hz, meaning that the AC voltage oscillates at a rate of 60 complete

back-and-forth cycles every second. In Europe, where the power system frequency is 50 Hz,

the AC voltage only completes 50 cycles every second. A radio station transmitter broadcasting

at a frequency of 100 MHz generates an AC voltage oscillating at a rate of 100 million cycles

every second.

Prior to the canonization of the Hertz unit, frequency was simply expressed as “cycles per

second.” Older meters and electronic equipment often bore frequency units of “CPS” (Cycles

Per Second) instead of Hz. Many people believe the change from self-explanatory units like

CPS to Hertz constitutes a step backward in clarity. A similar change occurred when the unit

of “Celsius” replaced that of “Centigrade” for metric temperature measurement. The name

Centigrade was based on a 100-count (“Centi-”) scale (“-grade”) representing the melting and

boiling points of H

O, respectively. The name Celsius, on the other hand, gives no hint as to

the unit’s origin or meaning.

1.2. AC WAVEFORMS

Period and frequency are mathematical reciprocals of one another. That is to say, if a wave

has a period of 10 seconds, its frequency will be 0.1 Hz, or 1/10 of a cycle per second:

Frequency in Hertz =

Period in seconds

An instrument called an oscilloscope, Figure 1.10, is used to display a changing voltage over

time on a graphical screen. You may be familiar with the appearance of an ECG or EKG (elec-

trocardiograph) machine, used by physicians to graph the oscillations of a patient’s heart over

time. The ECG is a special-purpose oscilloscope expressly designed for medical use. General-

purpose oscilloscopes have the ability to display voltage from virtually any voltage source,

plotted as a graph with time as the independent variable. The relationship between period

and frequency is very useful to know when displaying an AC voltage or current waveform on

an oscilloscope screen. By measuring the period of the wave on the horizontal axis of the oscil-

loscope screen and reciprocating that time value (in seconds), you can determine the frequency

in Hertz.

trigger

timebase

s/div

DC GND AC

GNDDC

V/div

vertical

OSCILLOSCOPE

16 divisions

@ 1ms/div =

a period of 16 ms

Frequency =

period

1 1

16 ms

= = 62.5 Hz

Figure 1.10:

Time period of sinewave is shown on oscill oscope.

Voltage and current are by no means the only physical variables subject to variation over

time. Much more common to our everyday experience is sound, which is nothing more than the

alternating compression and decompression (pressure waves) of air molecules, interpreted by

our ears as a physical sensation. Because alternating current is a wave phenomenon, it shares

many of the properties of other wave phenomena, like sound. For this reason, sound (especially

structured music) provides an excellent analogy for relating AC concepts.

In musi cal terms, frequency is equivalent to pitch. Low-pitch notes such as those produced

by a tuba or bassoon consist of air molecule vibrations that are relatively slow (low frequency).

CHAPTER 1. BASIC AC THEORY

High-pitch notes such as those produced by a ﬂute or whistle consist of the same type of vibra-

tions in the air, only vibrating at a much faster rate (higher frequency). Figure 1.11 is a table

showing the actual frequencies for a range of common musical notes.

C (middle)

Note Musical designation

C sharp (or D flat) C

or D

D D

D sharp (or E flat) D

or E

E E

F F

F sharp (or G flat) F

or G

G G

G sharp (or A flat) G

or A

A A

A sharp (or B flat) A

or B

B B

A sharp (or B flat) A

or B

A A

220.00

440.00

261.63

Frequency (in hertz)

293.66

233.08

246.94

277.18

311.13

329.63

349.23

369.99

392.00

415.30

466.16

493.88

523.25

Figure 1.11:

The frequency in Hertz (Hz) is shown f or various musical notes.

Astute observers will notice that all notes on the table bearing the same letter designation

are related by a frequency ratio of 2:1. For example, the ﬁrst frequency shown (designated with

the letter “A”) is 220 Hz. The next highest “A” note has a frequency of 440 Hz – exactly twice as

many sound wave cycles per second. The same 2:1 ratio holds true for the ﬁrst A sharp (233.08

Hz) and the next A sharp (466.16 Hz), and for all note pairs found i n the table.

Audibly, two notes whose frequencies are exactly double each other sound remarkably sim-

ilar. This similarity in sound is musically recognized, the shortest span on a musical scale

separating such note pairs being called an octave. Following this rule, the next highest “A”

note (one octave above 440 Hz) will be 880 Hz, the next lowest “A” (one octave below 220 Hz)

will be 110 Hz. A view of a piano keyboard helps to put this scale into perspective: Figure 1.12

As you can see, one octave is equal to seven white keys’ worth of distance on a piano key-

board. The familiar musical mnemonic (doe-ray-mee-fah-so-lah-tee) – yes, the same pattern

immortalized in the whimsical Rodgers and Hammerstein song sung in The Sound of Music –

covers one octave from C to C.

While electromechanical alternators and many other physical phenomena naturally pro-

duce sine waves, this is not the only kind of alternating wave in existence. Other “waveforms”

of AC are commonly produced within electronic circuitry. Here are but a few sample waveforms

and their common designations in ﬁgure 1.13

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