From electric to electronic
Electric circuits are connections of
conductive wires and other devices whereby the uniform flow of electrons
occurs. Electronic circuits add a new dimension to electric circuits in
that some means of control is exerted over the flow of electrons
by another electrical signal, either a voltage or a current.
In and of itself, the control of electron
flow is nothing new to the student of electric circuits. Switches
control the flow of electrons, as do potentiometers, especially when
connected as variable resistors (rheostats). Neither the switch nor the
potentiometer should be new to your experience by this point in your
study. The threshold marking the transition from electric to electronic,
then, is defined by how the flow of electrons is controlled
rather than whether or not any form of control exists in a circuit.
Switches and rheostats control the flow of electrons according to the
positioning of a mechanical device, which is actuated by some physical
force external to the circuit. In electronics, however, we are dealing
with special devices able to control the flow of electrons according to
another flow of electrons, or by the application of a static voltage. In
other words, in an electronic circuit, electricity is able to control
electricity.
Historically, the era of electronics
began with the invention of the Audion tube, a device controlling
the flow of an electron stream through a vacuum by the application of a
small voltage between two metal structures within the tube. A more
detailed summary of so-called electron tube or vacuum tube
technology is available in the last chapter of this volume for those who
are interested.
Electronics technology experienced a
revolution in 1948 with the invention of the transistor. This
tiny device achieved approximately the same effect as the Audion tube,
but in a vastly smaller amount of space and with less material.
Transistors control the flow of electrons through solid semiconductor
substances rather than through a vacuum, and so transistor technology is
often referred to as solid-state electronics.
Active versus passive devices
An active device is any type of
circuit component with the ability to electrically control electron flow
(electricity controlling electricity). In order for a circuit to be
properly called electronic, it must contain at least one active
device. Components incapable of controlling current by means of another
electrical signal are called passive devices. Resistors,
capacitors, inductors, transformers, and even diodes are all considered
passive devices. Active devices include, but are not limited to, vacuum
tubes, transistors, silicon-controlled rectifiers (SCRs), and TRIACs. A
case might be made for the saturable reactor to be defined as an active
device, since it is able to control an AC current with a DC current, but
I've never heard it referred to as such. The operation of each of these
active devices will be explored in later chapters of this volume.
All active devices control the flow of
electrons through them. Some active devices allow a voltage to control
this current while other active devices allow another current to do the
job. Devices utilizing a static voltage as the controlling signal are,
not surprisingly, called voltage-controlled devices. Devices
working on the principle of one current controlling another current are
known as current-controlled devices. For the record, vacuum tubes
are voltage-controlled devices while transistors are made as either
voltage-controlled or current controlled types. The first type of
transistor successfully demonstrated was a current-controlled device.
Amplifiers
The practical benefit of active devices
is their amplifying ability. Whether the device in question be
voltage-controlled or current-controlled, the amount of power required
of the controlling signal is typically far less than the amount of power
available in the controlled current. In other words, an active device
doesn't just allow electricity to control electricity; it allows a
small amount of electricity to control a large amount of
electricity.
Because of this disparity between
controlling and controlled powers, active devices may be
employed to govern a large amount of power (controlled) by the
application of a small amount of power (controlling). This behavior is
known as amplification.
It is a fundamental rule of physics that
energy can neither be created nor destroyed. Stated formally, this rule
is known as the Law of Conservation of Energy, and no exceptions to it
have been discovered to date. If this Law is true -- and an overwhelming
mass of experimental data suggests that it is -- then it is impossible
to build a device capable of taking a small amount of energy and
magically transforming it into a large amount of energy. All machines,
electric and electronic circuits included, have an upper efficiency
limit of 100 percent. At best, power out equals power in:
Usually, machines fail even to meet this
limit, losing some of their input energy in the form of heat which is
radiated into surrounding space and therefore not part of the output
energy stream.
Many people have attempted, without
success, to design and build machines that output more power than they
take in. Not only would such a perpetual motion machine prove
that the Law of Energy Conservation was not a Law after all, but it
would usher in a technological revolution such as the world has never
seen, for it could power itself in a circular loop and generate excess
power for "free:"
Despite much effort and many unscrupulous
claims of "free energy" or over-unity machines, not one has ever
passed the simple test of powering itself with its own energy output and
generating energy to spare.
There does exist, however, a class of
machines known as amplifiers, which are able to take in
small-power signals and output signals of much greater power. The key to
understanding how amplifiers can exist without violating the Law of
Energy Conservation lies in the behavior of active devices.
Because active devices have the ability
to control a large amount of electrical power with a small amount
of electrical power, they may be arranged in circuit so as to duplicate
the form of the input signal power from a larger amount of power
supplied by an external power source. The result is a device that
appears to magically magnify the power of a small electrical signal
(usually an AC voltage waveform) into an identically-shaped waveform of
larger magnitude. The Law of Energy Conservation is not violated because
the additional power is supplied by an external source, usually a DC
battery or equivalent. The amplifier neither creates nor destroys
energy, but merely reshapes it into the waveform desired:
In other words, the current-controlling
behavior of active devices is employed to shape DC power from the
external power source into the same waveform as the input signal,
producing an output signal of like shape but different (greater) power
magnitude. The transistor or other active device within an amplifier
merely forms a larger copy of the input signal waveform out of
the "raw" DC power provided by a battery or other power source.
Amplifiers, like all machines, are
limited in efficiency to a maximum of 100 percent. Usually, electronic
amplifiers are far less efficient than that, dissipating considerable
amounts of energy in the form of waste heat. Because the efficiency of
an amplifier is always 100 percent or less, one can never be made to
function as a "perpetual motion" device.
The requirement of an external source of
power is common to all types of amplifiers, electrical and
non-electrical. A common example of a non-electrical amplification
system would be power steering in an automobile, amplifying the power of
the driver's arms in turning the steering wheel to move the front wheels
of the car. The source of power necessary for the amplification comes
from the engine. The active device controlling the driver's "input
signal" is a hydraulic valve shuttling fluid power from a pump attached
to the engine to a hydraulic piston assisting wheel motion. If the
engine stops running, the amplification system fails to amplify the
driver's arm power and the car becomes very difficult to turn.
Amplifier gain
Because amplifiers have the ability to
increase the magnitude of an input signal, it is useful to be able to
rate an amplifier's amplifying ability in terms of an output/input
ratio. The technical term for an amplifier's output/input magnitude
ratio is gain. As a ratio of equal units (power out / power in,
voltage out / voltage in, or current out / current in), gain is
naturally a unitless measurement. Mathematically, gain is symbolized by
the capital letter "A".
For example, if an amplifier takes in an
AC voltage signal measuring 2 volts RMS and outputs an AC voltage of 30
volts RMS, it has an AC voltage gain of 30 divided by 2, or 15:
Correspondingly, if we know the gain of
an amplifier and the magnitude of the input signal, we can calculate the
magnitude of the output. For example, if an amplifier with an AC current
gain of 3.5 is given an AC input signal of 28 mA RMS, the output will be
3.5 times 28 mA, or 98 mA:
In the last two examples I specifically
identified the gains and signal magnitudes in terms of "AC." This was
intentional, and illustrates an important concept: electronic amplifiers
often respond differently to AC and DC input signals, and may amplify
them to different extents. Another way of saying this is that amplifiers
often amplify changes or variations in input signal
magnitude (AC) at a different ratio than steady input signal
magnitudes (DC). The specific reasons for this are too complex to
explain at this time, but the fact of the matter is worth mentioning. If
gain calculations are to be carried out, it must first be understood
what type of signals and gains are being dealt with, AC or DC.
Electrical amplifier gains may be
expressed in terms of voltage, current, and/or power, in both AC and DC.
A summary of gain definitions is as follows. The triangle-shaped "delta"
symbol (Δ) represents change in mathematics, so "ΔVoutput
/ ΔVinput" means "change in output voltage divided by change
in input voltage," or more simply, "AC output voltage divided by AC
input voltage":
If multiple amplifiers are staged, their
respective gains form an overall gain equal to the product
(multiplication) of the individual gains:
Decibels
In its simplest form, an amplifier's
gain is a ratio of output over input. Like all ratios, this form of
gain is unitless. However, there is an actual unit intended to represent
gain, and it is called the bel.
As a unit, the bel was actually devised
as a convenient way to represent power loss in telephone system
wiring rather than gain in amplifiers. The unit's name is derived
from Alexander Graham Bell, the famous American inventor whose work was
instrumental in developing telephone systems. Originally, the bel
represented the amount of signal power loss due to resistance over a
standard length of electrical cable. Now, it is defined in terms of the
common (base 10) logarithm of a power ratio (output power divided by
input power):
Because the bel is a logarithmic unit, it
is nonlinear. To give you an idea of how this works, consider the
following table of figures, comparing power losses and gains in bels
versus simple ratios:
It was later decided that the bel was too
large of a unit to be used directly, and so it became customary to apply
the metric prefix deci (meaning 1/10) to it, making it decibels,
or dB. Now, the expression "dB" is so common that many people do not
realize it is a combination of "deci-" and "-bel," or that there even is
such a unit as the "bel." To put this into perspective, here is another
table contrasting power gain/loss ratios against decibels:
As a logarithmic unit, this mode of power
gain expression covers a wide range of ratios with a minimal span in
figures. It is reasonable to ask, "why did anyone feel the need to
invent a logarithmic unit for electrical signal power loss in a
telephone system?" The answer is related to the dynamics of human
hearing, the perceptive intensity of which is logarithmic in nature.
Human hearing is highly nonlinear: in
order to double the perceived intensity of a sound, the actual sound
power must be multiplied by a factor of ten. Relating telephone signal
power loss in terms of the logarithmic "bel" scale makes perfect sense
in this context: a power loss of 1 bel translates to a perceived sound
loss of 50 percent, or 1/2. A power gain of 1 bel translates to a
doubling in the perceived intensity of the sound.
An almost perfect analogy to the bel
scale is the Richter scale used to describe earthquake intensity: a 6.0
Richter earthquake is 10 times more powerful than a 5.0 Richter
earthquake; a 7.0 Richter earthquake 100 times more powerful than a 5.0
Richter earthquake; a 4.0 Richter earthquake is 1/10 as powerful as a
5.0 Richter earthquake, and so on. The measurement scale for chemical pH
is likewise logarithmic, a difference of 1 on the scale is equivalent to
a tenfold difference in hydrogen ion concentration of a chemical
solution. An advantage of using a logarithmic measurement scale is the
tremendous range of expression afforded by a relatively small span of
numerical values, and it is this advantage which secures the use of
Richter numbers for earthquakes and pH for hydrogen ion activity.
Another reason for the adoption of the
bel as a unit for gain is for simple expression of system gains and
losses. Consider the last system example where two amplifiers were
connected tandem to amplify a signal. The respective gain for each
amplifier was expressed as a ratio, and the overall gain for the system
was the product (multiplication) of those two ratios:
If these figures represented power
gains, we could directly apply the unit of bels to the task of
representing the gain of each amplifier, and of the system altogether:
Close inspection of these gain figures in
the unit of "bel" yields a discovery: they're additive. Ratio gain
figures are multiplicative for staged amplifiers, but gains expressed in
bels add rather than multiply to equal the overall system
gain. The first amplifier with its power gain of 0.477 B adds to the
second amplifier's power gain of 0.699 B to make a system with an
overall power gain of 1.176 B.
Recalculating for decibels rather than
bels, we notice the same phenomenon:
To those already familiar with the
arithmetic properties of logarithms, this is no surprise. It is an
elementary rule of algebra that the antilogarithm of the sum of two
numbers' logarithm values equals the product of the two original
numbers. In other words, if we take two numbers and determine the
logarithm of each, then add those two logarithm figures together, then
determine the "antilogarithm" of that sum (elevate the base number of
the logarithm -- in this case, 10 -- to the power of that sum), the
result will be the same as if we had simply multiplied the two original
numbers together. This algebraic rule forms the heart of a device called
a slide rule, an analog computer which could, among other things,
determine the products and quotients of numbers by addition (adding
together physical lengths marked on sliding wood, metal, or plastic
scales). Given a table of logarithm figures, the same mathematical trick
could be used to perform otherwise complex multiplications and divisions
by only having to do additions and subtractions, respectively. With the
advent of high-speed, handheld, digital calculator devices, this elegant
calculation technique virtually disappeared from popular use. However,
it is still important to understand when working with measurement scales
that are logarithmic in nature, such as the bel (decibel) and Richter
scales.
When converting a power gain from units
of bels or decibels to a unitless ratio, the mathematical inverse
function of common logarithms is used: powers of 10, or the antilog.
Converting decibels into unitless ratios
for power gain is much the same, only a division factor of 10 is
included in the exponent term:
Because the bel is fundamentally a unit
of power gain or loss in a system, voltage or current gains and
losses don't convert to bels or dB in quite the same way. When using
bels or decibels to express a gain other than power, be it voltage or
current, we must perform the calculation in terms of how much power gain
there would be for that amount of voltage or current gain. For a
constant load impedance, a voltage or current gain of 2 equates to a
power gain of 4 (22); a voltage or current gain of 3 equates
to a power gain of 9 (32). If we multiply either voltage or
current by a given factor, then the power gain incurred by that
multiplication will be the square of that factor. This relates back to
the forms of Joule's Law where power was calculated from either voltage
or current, and resistance:
Thus, when translating a voltage or
current gain ratio into a respective gain in terms of the bel
unit, we must include this exponent in the equation(s):
The same exponent requirement holds true
when expressing voltage or current gains in terms of decibels:
However, thanks to another interesting
property of logarithms, we can simplify these equations to eliminate the
exponent by including the "2" as a multiplying factor for the
logarithm function. In other words, instead of taking the logarithm of
the square of the voltage or current gain, we just multiply the
voltage or current gain's logarithm figure by 2 and the final result in
bels or decibels will be the same:
The process of converting voltage or
current gains from bels or decibels into unitless ratios is much the
same as it is for power gains:
Here are the equations used for
converting voltage or current gains in decibels into unitless ratios:
While the bel is a unit naturally scaled
for power, another logarithmic unit has been invented to directly
express voltage or current gains/losses, and it is based on the
natural logarithm rather than the common logarithm as bels
and decibels are. Called the neper, its unit symbol is a
lower-case "n."
For better or for worse, neither the
neper nor its attenuated cousin, the decineper, is popularly used
as a unit in American engineering applications.
- REVIEW:
- Gains and losses may be expressed in
terms of a unitless ratio, or in the unit of bels (B) or decibels
(dB). A decibel is literally a deci-bel: one-tenth of a bel.
- The bel is fundamentally a unit for
expressing power gain or loss. To convert a power ratio to
either bels or decibels, use one of these equations:
-
- When using the unit of the bel or
decibel to express a voltage or current ratio, it must
be cast in terms of the an equivalent power ratio. Practically,
this means the use of different equations, with a multiplication
factor of 2 for the logarithm value corresponding to an exponent of 2
for the voltage or current gain ratio:
-
- To convert a decibel gain into a
unitless ratio gain, use one of these equations:
-
- A gain (amplification) is expressed as
a positive bel or decibel figure. A loss (attenuation) is expressed as
a negative bel or decibel figure. Unity gain (no gain or loss; ratio =
1) is expressed as zero bels or zero decibels.
- When calculating overall gain for an
amplifier system composed of multiple amplifier stages, individual
gain ratios are multiplied to find the overall gain ratio. Bel
or decibel figures for each amplifier stage, on the other hand, are
added together to determine overall gain.
Absolute dB scales
It is also possible to use the decibel as
a unit of absolute power, in addition to using it as an expression of
power gain or loss. A common example of this is the use of decibels as a
measurement of sound pressure intensity. In cases like these, the
measurement is made in reference to some standardized power level
defined as 0 dB. For measurements of sound pressure, 0 dB is loosely
defined as the lower threshold of human hearing, objectively quantified
as 1 picowatt of sound power per square meter of area.
A sound measuring 40 dB on the decibel
sound scale would be 104 times greater than the threshold of
hearing. A 100 dB sound would be 1010 (ten billion) times
greater than the threshold of hearing.
Because the human ear is not equally
sensitive to all frequencies of sound, variations of the decibel
sound-power scale have been developed to represent physiologically
equivalent sound intensities at different frequencies. Some sound
intensity instruments were equipped with filter networks to give
disproportionate indications across the frequency scale, the intent of
which to better represent the effects of sound on the human body. Three
filtered scales became commonly known as the "A," "B," and "C" weighted
scales. Decibel sound intensity indications measured through these
respective filtering networks were given in units of dBA, dBB, and dBC.
Today, the "A-weighted scale" is most commonly used for expressing the
equivalent physiological impact on the human body, and is especially
useful for rating dangerously loud noise sources.
Another standard-referenced system of
power measurement in the unit of decibels has been established for use
in telecommunications systems. This is called the dBm scale. The
reference point, 0 dBm, is defined as 1 milliwatt of electrical power
dissipated by a 600 Ω load. According to this scale, 10 dBm is equal to
10 times the reference power, or 10 milliwatts; 20 dBm is equal to 100
times the reference power, or 100 milliwatts. Some AC voltmeters come
equipped with a dBm range or scale (sometimes labeled "DB") intended for
use in measuring AC signal power across a 600 Ω load. 0 dBm on this
scale is, of course, elevated above zero because it represents something
greater than 0 (actually, it represents 0.7746 volts across a 600 Ω
load, voltage being equal to the square root of power times resistance;
the square root of 0.001 multiplied by 600). When viewed on the face of
an analog meter movement, this dBm scale appears compressed on the left
side and expanded on the right in a manner not unlike a resistance
scale, owing to its logarithmic nature.
An adaptation of the dBm scale for audio
signal strength is used in studio recording and broadcast engineering
for standardizing volume levels, and is called the VU scale. VU
meters are frequently seen on electronic recording instruments to
indicate whether or not the recorded signal exceeds the maximum signal
level limit of the device, where significant distortion will occur. This
"volume indicator" scale is calibrated in according to the dBm scale,
but does not directly indicate dBm for any signal other than steady
sine-wave tones. The proper unit of measurement for a VU meter is
volume units.
When relatively large signals are dealt
with, and an absolute dB scale would be useful for representing signal
level, specialized decibel scales are sometimes used with reference
points greater than the 1mW used in dBm. Such is the case for the dBW
scale, with a reference point of 0 dBW established at 1 watt. Another
absolute measure of power called the dBk scale references 0 dBk
at 1 kW, or 1000 watts.
- REVIEW:
- The unit of the bel or decibel may
also be used to represent an absolute measurement of power rather than
just a relative gain or loss. For sound power measurements, 0 dB is
defined as a standardized reference point of power equal to 1 picowatt
per square meter. Another dB scale suited for sound intensity
measurements is normalized to the same physiological effects as a 1000
Hz tone, and is called the dBA scale. In this system, 0 dBA is
defined as any frequency sound having the same physiological
equivalence as a 1 picowatt-per-square-meter tone at 1000 Hz.
- An electrical dB scale with an
absolute reference point has been made for use in telecommunications
systems. Called the dBm scale, its reference point of 0 dBm is
defined as 1 milliwatt of AC signal power dissipated by a 600 Ω load.
- A VU meter reads audio signal
level according to the dBm for sine-wave signals. Because its response
to signals other than steady sine waves is not the same as true dBm,
its unit of measurement is volume units.
- dB scales with greater absolute
reference points than the dBm scale have been invented for high-power
signals. The dBW scale has its reference point of 0 dBW defined
as 1 watt of power. The dBk scale sets 1 kW (1000 watts) as the
zero-point reference.
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