What is alternating current (AC)?
Most students of electricity begin their
study with what is known as direct current (DC), which is
electricity flowing in a constant direction, and/or possessing a voltage
with constant polarity. DC is the kind of electricity made by a battery
(with definite positive and negative terminals), or the kind of charge
generated by rubbing certain types of materials against each other.
As useful and as easy to understand as DC
is, it is not the only "kind" of electricity in use. Certain sources of
electricity (most notably, rotary electro-mechanical generators)
naturally produce voltages alternating in polarity, reversing positive
and negative over time. Either as a voltage switching polarity or as a
current switching direction back and forth, this "kind" of electricity
is known as Alternating Current (AC):
Whereas the familiar battery symbol is
used as a generic symbol for any DC voltage source, the circuit with the
wavy line inside is the generic symbol for any AC voltage source.
One might wonder why anyone would bother
with such a thing as AC. It is true that in some cases AC holds no
practical advantage over DC. In applications where electricity is used
to dissipate energy in the form of heat, the polarity or direction of
current is irrelevant, so long as there is enough voltage and current to
the load to produce the desired heat (power dissipation). However, with
AC it is possible to build electric generators, motors and power
distribution systems that are far more efficient than DC, and so we find
AC used predominately across the world in high power applications. To
explain the details of why this is so, a bit of background knowledge
about AC is necessary.
If a machine is constructed to rotate a
magnetic field around a set of stationary wire coils with the turning of
a shaft, AC voltage will be produced across the wire coils as that shaft
is rotated, in accordance with Faraday's Law of electromagnetic
induction. This is the basic operating principle of an AC generator,
also known as an alternator:
Notice how the polarity of the voltage
across the wire coils reverses as the opposite poles of the rotating
magnet pass by. Connected to a load, this reversing voltage polarity
will create a reversing current direction in the circuit. The faster the
alternator's shaft is turned, the faster the magnet will spin, resulting
in an alternating voltage and current that switches directions more
often in a given amount of time.
While DC generators work on the same
general principle of electromagnetic induction, their construction is
not as simple as their AC counterparts. With a DC generator, the coil of
wire is mounted in the shaft where the magnet is on the AC alternator,
and electrical connections are made to this spinning coil via stationary
carbon "brushes" contacting copper strips on the rotating shaft. All
this is necessary to switch the coil's changing output polarity to the
external circuit so the external circuit sees a constant polarity:
The generator shown above will produce
two pulses of voltage per revolution of the shaft, both pulses in the
same direction (polarity). In order for a DC generator to produce
constant voltage, rather than brief pulses of voltage once every 1/2
revolution, there are multiple sets of coils making intermittent contact
with the brushes. The diagram shown above is a bit more simplified than
what you would see in real life.
The problems involved with making and
breaking electrical contact with a moving coil should be obvious
(sparking and heat), especially if the shaft of the generator is
revolving at high speed. If the atmosphere surrounding the machine
contains flammable or explosive vapors, the practical problems of
spark-producing brush contacts are even greater. An AC generator
(alternator) does not require brushes and commutators to work, and so is
immune to these problems experienced by DC generators.
The benefits of AC over DC with regard to
generator design is also reflected in electric motors. While DC motors
require the use of brushes to make electrical contact with moving coils
of wire, AC motors do not. In fact, AC and DC motor designs are very
similar to their generator counterparts (identical for the sake of this
tutorial), the AC motor being dependent upon the reversing magnetic
field produced by alternating current through its stationary coils of
wire to rotate the rotating magnet around on its shaft, and the DC motor
being dependent on the brush contacts making and breaking connections to
reverse current through the rotating coil every 1/2 rotation (180
degrees).
So we know that AC generators and AC
motors tend to be simpler than DC generators and DC motors. This
relative simplicity translates into greater reliability and lower cost
of manufacture. But what else is AC good for? Surely there must be more
to it than design details of generators and motors! Indeed there is.
There is an effect of electromagnetism known as mutual induction,
whereby two or more coils of wire placed so that the changing magnetic
field created by one induces a voltage in the other. If we have two
mutually inductive coils and we energize one coil with AC, we will
create an AC voltage in the other coil. When used as such, this device
is known as a transformer:
The fundamental significance of a
transformer is its ability to step voltage up or down from the powered
coil to the unpowered coil. The AC voltage induced in the unpowered
("secondary") coil is equal to the AC voltage across the powered
("primary") coil multiplied by the ratio of secondary coil turns to
primary coil turns. If the secondary coil is powering a load, the
current through the secondary coil is just the opposite: primary coil
current multiplied by the ratio of primary to secondary turns. This
relationship has a very close mechanical analogy, using torque and speed
to represent voltage and current, respectively:
If the winding ratio is reversed so that
the primary coil has less turns than the secondary coil, the transformer
"steps up" the voltage from the source level to a higher level at the
load:
The transformer's ability to step AC
voltage up or down with ease gives AC an advantage unmatched by DC in
the realm of power distribution. When transmitting electrical power over
long distances, it is far more efficient to do so with stepped-up
voltages and stepped-down currents (smaller-diameter wire with less
resistive power losses), then step the voltage back down and the current
back up for industry, business, or consumer use use.
Transformer technology has made
long-range electric power distribution practical. Without the ability to
efficiently step voltage up and down, it would be cost-prohibitive to
construct power systems for anything but close-range (within a few miles
at most) use.
As useful as transformers are, they only
work with AC, not DC. Because the phenomenon of mutual inductance relies
on changing magnetic fields, and direct current (DC) can only
produce steady magnetic fields, transformers simply will not work with
direct current. Of course, direct current may be interrupted (pulsed)
through the primary winding of a transformer to create a changing
magnetic field (as is done in automotive ignition systems to produce
high-voltage spark plug power from a low-voltage DC battery), but pulsed
DC is not that different from AC. Perhaps more than any other reason,
this is why AC finds such widespread application in power systems.
- REVIEW:
- DC stands for "Direct Current,"
meaning voltage or current that maintains constant polarity or
direction, respectively, over time.
- AC stands for "Alternating Current,"
meaning voltage or current that changes polarity or direction,
respectively, over time.
- AC electromechanical generators, known
as alternators, are of simpler construction than DC
electromechanical generators.
- AC and DC motor design follows
respective generator design principles very closely.
- A transformer is a pair of
mutually-inductive coils used to convey AC power from one coil to the
other. Often, the number of turns in each coil is set to create a
voltage increase or decrease from the powered (primary) coil to the
unpowered (secondary) coil.
- Secondary voltage = Primary voltage
(secondary turns / primary turns)
- Secondary current = Primary current
(primary turns / secondary turns)
AC waveforms
When an alternator produces AC voltage,
the voltage switches polarity over time, but does so in a very
particular manner. When graphed over time, the "wave" traced by this
voltage of alternating polarity from an alternator takes on a distinct
shape, known as a sine wave:
In the voltage plot from an
electromechanical alternator, the change from one polarity to the other
is a smooth one, the voltage level changing most rapidly at the zero
("crossover") point and most slowly at its peak. If we were to graph the
trigonometric function of "sine" over a horizontal range of 0 to 360
degrees, we would find the exact same pattern:
Angle Sine(angle)
in degrees
0 ............... 0.0000 -- zero
15 ............... 0.2588
30 ............... 0.5000
45 ............... 0.7071
60 ............... 0.8660
75 ............... 0.9659
90 ............... 1.0000 -- positive peak
105 .............. 0.9659
120 .............. 0.8660
135 .............. 0.7071
150 .............. 0.5000
165 .............. 0.2588
180 .............. 0.0000 -- zero
195 .............. -0.2588
210 .............. -0.5000
225 .............. -0.7071
240 .............. -0.8660
255 .............. -0.9659
270 .............. -1.0000 -- negative peak
285 .............. -0.9659
300 .............. -0.8660
315 .............. -0.7071
330 .............. -0.5000
345 .............. -0.2588
360 .............. 0.0000 -- zero
The reason why an electromechanical
alternator outputs sine-wave AC is due to the physics of its operation.
The voltage produced by the stationary coils by the motion of the
rotating magnet is proportional to the rate at which the magnetic flux
is changing perpendicular to the coils (Faraday's Law of Electromagnetic
Induction). That rate is greatest when the magnet poles are closest to
the coils, and least when the magnet poles are furthest away from the
coils. 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 simple
two-pole alternator shaft as it rotates:
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 H2O,
respectively. The name Celsius, on the other hand, gives no hint as to
the unit's origin or meaning.
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:
An instrument called an oscilloscope
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
(electrocardiograph) 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 oscilloscope screen and reciprocating that time
value (in seconds), you can determine the frequency in Hertz.
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 musical 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). High-pitch notes such as those produced by a flute or
whistle consist of the same type of vibrations in the air, only
vibrating at a much faster rate (higher frequency). Here is a table
showing the actual frequencies for a range of common 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 in the
table.
Audibly, two notes whose frequencies are
exactly double each other sound remarkably similar. 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:
As you can see, one octave is equal to
eight white keys' worth of distance on a piano keyboard. The
familiar musical mnemonic (doe-ray-mee-fah-so-lah-tee-doe) -- 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 produce 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:
These waveforms are by no means the only
kinds of waveforms in existence. They're simply a few that are common
enough to have been given distinct names. Even in circuits that are
supposed to manifest "pure" sine, square, triangle, or sawtooth
voltage/current waveforms, the real-life result is often a distorted
version of the intended waveshape. Some waveforms are so complex that
they defy classification as a particular "type" (including waveforms
associated with many kinds of musical instruments). Generally speaking,
any waveshape bearing close resemblance to a perfect sine wave is termed
sinusoidal, anything different being labeled as non-sinusoidal.
Being that the waveform of an AC voltage or current is crucial to its
impact in a circuit, we need to be aware of the fact that AC waves come
in a variety of shapes.
- REVIEW:
- AC produced by an electromechanical
alternator follows the graphical shape of a sine wave.
- One cycle of a wave is one
complete evolution of its shape until the point that it is ready to
repeat itself.
- The period of a wave is the
amount of time it takes to complete one cycle.
- Frequency
is the number of complete cycles that a wave completes in a given
amount of time. Usually measured in Hertz (Hz), 1 Hz being equal to
one complete wave cycle per second.
- Frequency = 1/(period in seconds)
Measurements of AC magnitude
So far we know that AC voltage alternates
in polarity and AC current alternates in direction. We also know that AC
can alternate in a variety of different ways, and by tracing the
alternation over time we can plot it as a "waveform." We can measure the
rate of alternation by measuring the time it takes for a wave to evolve
before it repeats itself (the "period"), and express this as cycles per
unit time, or "frequency." In music, frequency is the same as pitch,
which is the essential property distinguishing one note from another.
However, we encounter a measurement
problem if we try to express how large or small an AC quantity is. With
DC, where quantities of voltage and current are generally stable, we
have little trouble expressing how much voltage or current we have in
any part of a circuit. But how do you grant a single measurement of
magnitude to something that is constantly changing?
One way to express the intensity, or
magnitude (also called the amplitude), of an AC quantity is to
measure its peak height on a waveform graph. This is known as the
peak or crest value of an AC waveform:
Another way is to measure the total
height between opposite peaks. This is known as the peak-to-peak
(P-P) value of an AC waveform:
Unfortunately, either one of these
expressions of waveform amplitude can be misleading when comparing two
different types of waves. For example, a square wave peaking at 10 volts
is obviously a greater amount of voltage for a greater amount of time
than a triangle wave peaking at 10 volts. The effects of these two AC
voltages powering a load would be quite different:
One way of expressing the amplitude of
different waveshapes in a more equivalent fashion is to mathematically
average the values of all the points on a waveform's graph to a single,
aggregate number. This amplitude measure is known simply as the
average value of the waveform. If we average all the points on the
waveform algebraically (that is, to consider their sign, either
positive or negative), the average value for most waveforms is
technically zero, because all the positive points cancel out all the
negative points over a full cycle:
This, of course, will be true for any
waveform having equal-area portions above and below the "zero" line of a
plot. However, as a practical measure of a waveform's aggregate
value, "average" is usually defined as the mathematical mean of all the
points' absolute values over a cycle. In other words, we
calculate the practical average value of the waveform by considering all
points on the wave as positive quantities, as if the waveform looked
like this:
Polarity-insensitive mechanical meter
movements (meters designed to respond equally to the positive and
negative half-cycles of an alternating voltage or current) register in
proportion to the waveform's (practical) average value, because the
inertia of the pointer against the tension of the spring naturally
averages the force produced by the varying voltage/current values over
time. Conversely, polarity-sensitive meter movements vibrate uselessly
if exposed to AC voltage or current, their needles oscillating rapidly
about the zero mark, indicating the true (algebraic) average value of
zero for a symmetrical waveform. When the "average" value of a waveform
is referenced in this text, it will be assumed that the "practical"
definition of average is intended unless otherwise specified.
Another method of deriving an aggregate
value for waveform amplitude is based on the waveform's ability to do
useful work when applied to a load resistance. Unfortunately, an AC
measurement based on work performed by a waveform is not the same as
that waveform's "average" value, because the power dissipated by
a given load (work performed per unit time) is not directly proportional
to the magnitude of either the voltage or current impressed upon it.
Rather, power is proportional to the square of the voltage or
current applied to a resistance (P = E2/R, and P = I2R).
Although the mathematics of such an amplitude measurement might not be
straightforward, the utility of it is.
Consider a bandsaw and a jigsaw, two
pieces of modern woodworking equipment. Both types of saws cut with a
thin, toothed, motor-powered metal blade to cut wood. But while the
bandsaw uses a continuous motion of the blade to cut, the jigsaw uses a
back-and-forth motion. The comparison of alternating current (AC) to
direct current (DC) may be likened to the comparison of these two saw
types:
The problem of trying to describe the
changing quantities of AC voltage or current in a single, aggregate
measurement is also present in this saw analogy: how might we express
the speed of a jigsaw blade? A bandsaw blade moves with a constant
speed, similar to the way DC voltage pushes or DC current moves with a
constant magnitude. A jigsaw blade, on the other hand, moves back and
forth, its blade speed constantly changing. What is more, the
back-and-forth motion of any two jigsaws may not be of the same type,
depending on the mechanical design of the saws. One jigsaw might move
its blade with a sine-wave motion, while another with a triangle-wave
motion. To rate a jigsaw based on its peak blade speed would be
quite misleading when comparing one jigsaw to another (or a jigsaw with
a bandsaw!). Despite the fact that these different saws move their
blades in different manners, they are equal in one respect: they all cut
wood, and a quantitative comparison of this common function can serve as
a common basis for which to rate blade speed.
Picture a jigsaw and bandsaw
side-by-side, equipped with identical blades (same tooth pitch, angle,
etc.), equally capable of cutting the same thickness of the same type of
wood at the same rate. We might say that the two saws were equivalent or
equal in their cutting capacity. Might this comparison be used to assign
a "bandsaw equivalent" blade speed to the jigsaw's back-and-forth blade
motion; to relate the wood-cutting effectiveness of one to the other?
This is the general idea used to assign a "DC equivalent" measurement to
any AC voltage or current: whatever magnitude of DC voltage or current
would produce the same amount of heat energy dissipation through an
equal resistance:
In the two circuits above, we have the
same amount of load resistance (2 Ω) dissipating the same amount of
power in the form of heat (50 watts), one powered by AC and the other by
DC. Because the AC voltage source pictured above is equivalent (in terms
of power delivered to a load) to a 10 volt DC battery, we would call
this a "10 volt" AC source. More specifically, we would denote its
voltage value as being 10 volts RMS. The qualifier "RMS" stands
for Root Mean Square, the algorithm used to obtain the DC
equivalent value from points on a graph (essentially, the procedure
consists of squaring all the positive and negative points on a waveform
graph, averaging those squared values, then taking the square root of
that average to obtain the final answer). Sometimes the alternative
terms equivalent or DC equivalent are used instead of "RMS,"
but the quantity and principle are both the same.
RMS amplitude measurement is the best way
to relate AC quantities to DC quantities, or other AC quantities of
differing waveform shapes, when dealing with measurements of electric
power. For other considerations, peak or peak-to-peak measurements may
be the best to employ. For instance, when determining the proper size of
wire (ampacity) to conduct electric power from a source to a load, RMS
current measurement is the best to use, because the principal concern
with current is overheating of the wire, which is a function of power
dissipation caused by current through the resistance of the wire.
However, when rating insulators for service in high-voltage AC
applications, peak voltage measurements are the most appropriate,
because the principal concern here is insulator "flashover" caused by
brief spikes of voltage, irrespective of time.
Peak and peak-to-peak measurements are
best performed with an oscilloscope, which can capture the crests of the
waveform with a high degree of accuracy due to the fast action of the
cathode-ray-tube in response to changes in voltage. For RMS
measurements, analog meter movements (D'Arsonval, Weston, iron vane,
electrodynamometer) will work so long as they have been calibrated in
RMS figures. Because the mechanical inertia and dampening effects of an
electromechanical meter movement makes the deflection of the needle
naturally proportional to the average value of the AC, not the
true RMS value, analog meters must be specifically calibrated (or mis-calibrated,
depending on how you look at it) to indicate voltage or current in RMS
units. The accuracy of this calibration depends on an assumed waveshape,
usually a sine wave.
Electronic meters specifically designed
for RMS measurement are best for the task. Some instrument manufacturers
have designed ingenious methods for determining the RMS value of any
waveform. One such manufacturer produces "True-RMS" meters with a tiny
resistive heating element powered by a voltage proportional to that
being measured. The heating effect of that resistance element is
measured thermally to give a true RMS value with no mathematical
calculations whatsoever, just the laws of physics in action in
fulfillment of the definition of RMS. The accuracy of this type of RMS
measurement is independent of waveshape.
For "pure" waveforms, simple conversion
coefficients exist for equating Peak, Peak-to-Peak, Average (practical,
not algebraic), and RMS measurements to one another:
In addition to RMS, average, peak
(crest), and peak-to-peak measures of an AC waveform, there are ratios
expressing the proportionality between some of these fundamental
measurements. The crest factor of an AC waveform, for instance,
is the ratio of its peak (crest) value divided by its RMS value. The
form factor of an AC waveform is the ratio of its peak value divided
by its average value. Square-shaped waveforms always have crest and form
factors equal to 1, since the peak is the same as the RMS and average
values. Sinusoidal waveforms have crest factors of 1.414 (the square
root of 2) and form factors of 1.571 (π/2). Triangle- and sawtooth-shaped
waveforms have crest values of 1.732 (the square root of 3) and form
factors of 2.
Bear in mind that the conversion
constants shown here for peak, RMS, and average amplitudes of sine
waves, square waves, and triangle waves hold true only for pure
forms of these waveshapes. The RMS and average values of distorted
waveshapes are not related by the same ratios:
This is a very important concept to
understand when using an analog meter movement to measure AC voltage or
current. An analog movement, calibrated to indicate sine-wave RMS
amplitude, will only be accurate when measuring pure sine waves. If the
waveform of the voltage or current being measured is anything but a pure
sine wave, the indication given by the meter will not be the true RMS
value of the waveform, because the degree of needle deflection in an
analog meter movement is proportional to the average value of the
waveform, not the RMS. RMS meter calibration is obtained by "skewing"
the span of the meter so that it displays a small multiple of the
average value, which will be equal to be the RMS value for a particular
waveshape and a particular waveshape only.
Since the sine-wave shape is most common
in electrical measurements, it is the waveshape assumed for analog meter
calibration, and the small multiple used in the calibration of the meter
is 1.1107 (the form factor π/2 divided by the crest factor 1.414: the
ratio of RMS divided by average for a sinusoidal waveform). Any
waveshape other than a pure sine wave will have a different ratio of RMS
and average values, and thus a meter calibrated for sine-wave voltage or
current will not indicate true RMS when reading a non-sinusoidal wave.
Bear in mind that this limitation applies only to simple, analog AC
meters not employing "True-RMS" technology.
- REVIEW:
- The amplitude of an AC waveform
is its height as depicted on a graph over time. An amplitude
measurement can take the form of peak, peak-to-peak, average, or RMS
quantity.
- Peak
amplitude is the height of an AC waveform as measured from the zero
mark to the highest positive or lowest negative point on a graph. Also
known as the crest amplitude of a wave.
- Peak-to-peak
amplitude is the total height of an AC waveform as measured from
maximum positive to maximum negative peaks on a graph. Often
abbreviated as "P-P".
- Average
amplitude is the mathematical "mean" of all a waveform's points over
the period of one cycle. Technically, the average amplitude of any
waveform with equal-area portions above and below the "zero" line on a
graph is zero. However, as a practical measure of amplitude, a
waveform's average value is often calculated as the mathematical mean
of all the points' absolute values (taking all the negative
values and considering them as positive). For a sine wave, the average
value so calculated is approximately 0.637 of its peak value.
- "RMS" stands for Root Mean Square,
and is a way of expressing an AC quantity of voltage or current in
terms functionally equivalent to DC. For example, 10 volts AC RMS is
the amount of voltage that would produce the same amount of heat
dissipation across a resistor of given value as a 10 volt DC power
supply. Also known as the "equivalent" or "DC equivalent" value of an
AC voltage or current. For a sine wave, the RMS value is approximately
0.707 of its peak value.
- The crest factor of an AC
waveform is the ratio of its peak (crest) to its RMS value.
- The form factor of an AC
waveform is the ratio of its peak (crest) value to its average value.
- Analog, electromechanical meter
movements respond proportionally to the average value of an AC
voltage or current. When RMS indication is desired, the meter's
calibration must be "skewed" accordingly. This means that the accuracy
of an electromechanical meter's RMS indication is dependent on the
purity of the waveform: whether it is the exact same waveshape as the
waveform used in calibrating.
Simple AC circuit calculations
Over the course of the next few chapters,
you will learn that AC circuit measurements and calculations can get
very complicated due to the complex nature of alternating current in
circuits with inductance and capacitance. However, with simple circuits
involving nothing more than an AC power source and resistance, the same
laws and rules of DC apply simply and directly.
Series resistances still add, parallel
resistances still diminish, and the Laws of Kirchhoff and Ohm still hold
true. Actually, as we will discover later on, these rules and laws
always hold true, it's just that we have to express the quantities
of voltage, current, and opposition to current in more advanced
mathematical forms. With purely resistive circuits, however, these
complexities of AC are of no practical consequence, and so we can treat
the numbers as though we were dealing with simple DC quantities.
Because all these mathematical
relationships still hold true, we can make use of our familiar "table"
method of organizing circuit values just as with DC:
One major caveat needs to be given here:
all measurements of AC voltage and current must be expressed in the same
terms (peak, peak-to-peak, average, or RMS). If the source voltage is
given in peak AC volts, then all currents and voltages subsequently
calculated are cast in terms of peak units. If the source voltage is
given in AC RMS volts, then all calculated currents and voltages are
cast in AC RMS units as well. This holds true for any calculation
based on Ohm's Laws, Kirchhoff's Laws, etc. Unless otherwise stated, all
values of voltage and current in AC circuits are generally assumed to be
RMS rather than peak, average, or peak-to-peak. In some areas of
electronics, peak measurements are assumed, but in most applications
(especially industrial electronics) the assumption is RMS.
- REVIEW:
- All the old rules and laws of DC (Kirchhoff's
Voltage and Current Laws, Ohm's Law) still hold true for AC. However,
with more complex circuits, we may need to represent the AC quantities
in more complex form. More on this later, I promise!
- The "table" method of organizing
circuit values is still a valid analysis tool for AC circuits.
AC phase
Things start to get complicated when we
need to relate two or more AC voltages or currents that are out of step
with each other. By "out of step," I mean that the two waveforms are not
synchronized: that their peaks and zero points do not match up at the
same points in time. The following graph illustrates an example of this:
The two waves shown above (A versus B)
are of the same amplitude and frequency, but they are out of step with
each other. In technical terms, this is called a phase shift.
Earlier we saw how we could plot a "sine wave" by calculating the
trigonometric sine function for angles ranging from 0 to 360 degrees, a
full circle. The starting point of a sine wave was zero amplitude at
zero degrees, progressing to full positive amplitude at 90 degrees, zero
at 180 degrees, full negative at 270 degrees, and back to the starting
point of zero at 360 degrees. We can use this angle scale along the
horizontal axis of our waveform plot to express just how far out of step
one wave is with another:
The shift between these two waveforms is
about 45 degrees, the "A" wave being ahead of the "B" wave. A sampling
of different phase shifts is given in the following graphs to better
illustrate this concept:
Because the waveforms in the above
examples are at the same frequency, they will be out of step by the same
angular amount at every point in time. For this reason, we can express
phase shift for two or more waveforms of the same frequency as a
constant quantity for the entire wave, and not just an expression of
shift between any two particular points along the waves. That is, it is
safe to say something like, "voltage 'A' is 45 degrees out of phase with
voltage 'B'." Whichever waveform is ahead in its evolution is said to be
leading and the one behind is said to be lagging.
Phase shift, like voltage, is always a
measurement relative between two things. There's really no such thing as
a waveform with an absolute phase measurement because there's no
known universal reference for phase. Typically in the analysis of AC
circuits, the voltage waveform of the power supply is used as a
reference for phase, that voltage stated as "xxx volts at 0 degrees."
Any other AC voltage or current in that circuit will have its phase
shift expressed in terms relative to that source voltage.
This is what makes AC circuit
calculations more complicated than DC. When applying Ohm's Law and
Kirchhoff's Laws, quantities of AC voltage and current must reflect
phase shift as well as amplitude. Mathematical operations of addition,
subtraction, multiplication, and division must operate on these
quantities of phase shift as well as amplitude. Fortunately, there is a
mathematical system of quantities called complex numbers ideally
suited for this task of representing amplitude and phase.
Because the subject of complex numbers is
so essential to the understanding of AC circuits, the next chapter will
be devoted to that subject alone.
- REVIEW:
- Phase shift
is where two or more waveforms are out of step with each other.
- The amount of phase shift between two
waves can be expressed in terms of degrees, as defined by the degree
units on the horizontal axis of the waveform graph used in plotting
the trigonometric sine function.
- A leading waveform is defined
as one waveform that is ahead of another in its evolution. A
lagging waveform is one that is behind another. Example:
-
- Calculations for AC circuit analysis
must take into consideration both amplitude and phase shift of voltage
and current waveforms to be completely accurate. This requires the use
of a mathematical system called complex numbers.
Principles of radio
One of the more fascinating applications
of electricity is in the generation of invisible ripples of energy
called radio waves. The limited scope of this lesson on
alternating current does not permit full exploration of the concept,
some of the basic principles will be covered.
With Oersted's accidental discovery of
electromagnetism, it was realized that electricity and magnetism were
related to each other. When an electric current was passed through a
conductor, a magnetic field was generated perpendicular to the axis of
flow. Likewise, if a conductor was exposed to a change in magnetic flux
perpendicular to the conductor, a voltage was produced along the length
of that conductor. So far, scientists knew that electricity and
magnetism always seemed to affect each other at right angles. However, a
major discovery lay hidden just beneath this seemingly simple concept of
related perpendicularity, and its unveiling was one of the pivotal
moments in modern science.
This breakthrough in physics is hard to
overstate. The man responsible for this conceptual revolution was the
Scottish physicist James Clerk Maxwell (1831-1879), who "unified" the
study of electricity and magnetism in four relatively tidy equations. In
essence, what he discovered was that electric and magnetic fields
were intrinsically related to one another, with or without the presence
of a conductive path for electrons to flow. Stated more formally,
Maxwell's discovery was this:
A changing electric field
produces a perpendicular magnetic field, and
A changing magnetic field
produces a perpendicular electric field.
All of this can take place in open space,
the alternating electric and magnetic fields supporting each other as
they travel through space at the speed of light. This dynamic structure
of electric and magnetic fields propagating through space is better
known as an electromagnetic wave.
There are many kinds of natural radiative
energy composed of electromagnetic waves. Even light is electromagnetic
in nature. So are X-rays and "gamma" ray radiation. The only difference
between these kinds of electromagnetic radiation is the frequency of
their oscillation (alternation of the electric and magnetic fields back
and forth in polarity). By using a source of AC voltage and a special
device called an antenna, we can create electromagnetic waves (of
a much lower frequency than that of light) with ease.
An antenna is nothing more than a device
built to produce a dispersing electric or magnetic field. Two
fundamental types of antennae are the dipole and the loop:
While the dipole looks like nothing more
than an open circuit, and the loop a short circuit, these pieces of wire
are effective radiators of electromagnetic fields when connected to AC
sources of the proper frequency. The two open wires of the dipole act as
a sort of capacitor (two conductors separated by a dielectric), with the
electric field open to dispersal instead of being concentrated between
two closely-spaced plates. The closed wire path of the loop antenna acts
like an inductor with a large air core, again providing ample
opportunity for the field to disperse away from the antenna instead of
being concentrated and contained as in a normal inductor.
As the powered dipole radiates its
changing electric field into space, a changing magnetic field is
produced at right angles, thus sustaining the electric field further
into space, and so on as the wave propagates at the speed of light. As
the powered loop antenna radiates its changing magnetic field into
space, a changing electric field is produced at right angles, with the
same end-result of a continuous electromagnetic wave sent away from the
antenna. Either antenna achieves the same basic task: the controlled
production of an electromagnetic field.
When attached to a source of
high-frequency AC power, an antenna acts as a transmitting
device, converting AC voltage and current into electromagnetic wave
energy. Antennas also have the ability to intercept electromagnetic
waves and convert their energy into AC voltage and current. In this
mode, an antenna acts as a receiving device:
While there is much more that may
be said about antenna technology, this brief introduction is enough to
give you the general idea of what's going on (and perhaps enough
information to provoke a few experiments).
- REVIEW:
- James Maxwell discovered that changing
electric fields produce perpendicular magnetic fields, and visa-versa,
even in empty space.
- A twin set of electric and magnetic
fields, oscillating at right angles to each other and traveling at the
speed of light, constitutes an electromagnetic wave.
- An antenna is a device made of
wire, designed to radiate a changing electric field or changing
magnetic field when powered by a high-frequency AC source, or
intercept an electromagnetic field and convert it to an AC voltage or
current.
- The dipole antenna consists of
two pieces of wire (not touching), primarily generating an electric
field when energized, and secondarily producing a magnetic field in
space.
- The loop antenna consists of a
loop of wire, primarily generating a magnetic field when energized,
and secondarily producing an electric field in space.
Contributors
Contributors to this chapter are listed
in chronological order of their contributions, from most recent to
first. See Appendix 2 (Contributor List) for dates and contact
information.
Duane Damiano
(February 25, 2003): Pointed out magnetic polarity error in DC generator
illustration.
Mark D. Zarella
(April 28, 2002): Suggestion for improving explanation of "average"
waveform amplitude.
John Symonds
(March 28, 2002): Suggestion for improving explanation of the unit
"Hertz."
Jason Starck
(June 2000): HTML document formatting, which led to a much
better-looking second edition.
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