Anatomy of a Waveform

 
Radios transmit and receive signals over vast distances in the form of EM waves, at
a particular frequency level that differentiates them from other EM waves in the
frequency spectrum, such as infrared (IR) or X-rays (discussed later in this chapter).
The sinusoidal waveform is the most common waveform and is used to represent all
types of waves. Figure 2.1 shows the key properties of a sinusoidal wave. A cycle is the smallest portion of a waveform that, if repeated, represents the
entire waveform.Waveforms can be described as having the following properties:
1. a = Amplitude
The measurement of a waveform above a center reference.With EM
waves this is usually measured in volts or watts.
2. v = Velocity of Propagation
The velocity of propagation of a wave is the velocity that a wave
travels through a medium, and is usually measured in meters per second.3. τ = Period
The period of a wave is the time it takes for one cycle to pass a
fixed point and is usually measured in seconds. It is designated by the
Greek letter tau (τ).
4. λ = Wavelength
The wavelength of a wave is the distance that the wave will propagate
in one cycle and is usually measured in meters and designated by
the Greek letter lambda (λ).
5. f = Frequency
The frequency of a wave is the rate at which individual cycles pass a
given point and is usually measured in cycles per second or Hertz (Hz),
named after Heinrich Hertz, who discovered EM waves.
All of these properties except amplitude are related by the following formula:
f = 1/τ = v /λ
The velocity of propagation for EM waves is relatively constant, and for practical
purposes is equal to the speed of light (3.00 × 108 m/s). Substituting this
constant for velocity yields the following:
f = (3.00 × 108 m/s) / λ
Therefore, frequency (f ) and wavelength (λ) can be used interchangeably by
using the preceding formula to convert one to the other.
Some of the most common types of signals transmitted via radio are audio signals
such as voice or music.True audio signals like voice are usually near-random
signals and very hard to graph and conceptualize. For this discussion, assume that
the input signal being transmitted is a 1 KHz sinusoidal wave. Also assume that the
audio signal has already hit a microphone, thus converting the acoustical signal into
an electric signal. If you want to transmit this 1 KHz electrical signal from point A
to point B using a conductive medium such as copper wires, you only need to
connect a pair of wires to each endpoint—one wire is the point of reference or
ground, and the other wire carries the alternating signal voltage from point A to
point B. However, transmitting this signal without wires is more complicated: the
signal needs to be transmitted without interference.
Modulating a Radio Signal
To transmit a 1 KHz wave without wires, it must first be modulated onto a carrier
wave with a frequency many times higher than the input signal.There are several
reasons why the desired signal must be modulated onto a much higher carrier
signal. The first reason is for better transmission. Most of the radio signals transmitted
are low-frequency signals.These signals do not propagate well as EM
waves.Therefore, modulation is used to increase the frequency to allow more
effective transmission.
The second reason is to allow multiple signals to be transmitted at the same
time without interference.Your voice is in the same frequency range as my voice.
Assume we both try to use a two-way radio to talk to our remote friends simultaneously.
If we did not modulate our signals onto different carrier waves, our
signals would get mixed together and it would be impossible to distinguish on
the remote end. However, if we modulated our signals onto carrier waves of different
frequencies, our signals would not interfere with one another and we
could talk simultaneously. Each specific carrier frequency is called a channel (discussed
later in this chapter).
A third reason to modulate signals onto high frequency carrier waves is due
to restrictions on antenna size.The length of an antenna is based on the length of
the wave it was designed to transmit or receive.The simplest antennas are a fraction
of the wavelength, usually one-half or one-quarter of the wavelength. Since
lower frequencies have longer wavelengths, the antennas designed for low frequencies
are bigger. For example, 60 Hz is at the very lowest range of human
hearing.The wavelength of a 60 Hz wave traveling at the speed of light is 3107
miles, or the distance from Boston, MA to San Francisco, CA.Therefore, a onehalf
wavelength dipole antenna would be approximately 1,500 miles long—not a
feasible length for an antenna. Antenna design is discussed in more depth later in
this chapter.
When talking about modulation, we are talking about a minimum of two
waves, the signal and the carrier. Certain properties of the carrier waveform are
modified (modulated) to represent the signal waveform.The signal wave is also
called the modulating wave because it is the wave that modifies (or modulates) the
carrier wave.The modulating wave can be anything from analog audio to a computer-
generated digital square wave.The carrier wave is called the modulated wave
because it is the wave that is being changed by the modulating or signal wave.
Almost all carrier waves are a periodic sinusoidal wave with a frequency many
times higher than the frequency of the modulating wave.
There are many types of modulation. Some were developed to carry analog
waveforms, however, since the invention of the computer, many types of modulation
have been developed to carry digital waveforms.The following sections discuss
a few widely used types of modulation. Analog Modulation Schemes
There are two analog modulation schemes that are widely used and familiar to
anyone who has ever tuned a modern audio broadcast radio.These two forms of
modulation are:
 Amplitude Modulation (AM)
 Frequency Modulation (FM)
AM is the modulation of the amplitude of the carrier wave. Figure 2.2 illustrates
the AM modulated signal. Digital Modulation Schemes
Most sources of information that are transmitted are analog signals. Human
speech, music, video, and pictures are all analog by nature. However, because
computers use binary to store and process information, analog sources of information
must be digitized.This means that the signal is represented by a code of
1s and 0s that the computer uses to recreate the original signal as closely as possible.
The error introduced when the signal is digitized is called a quantization
error. If the digitizing encoding technology is designed well, the resulting signal so
closely resembles the original signal that the differences are imperceptible to
humans (such as music stored on CDs).
As computers continue to take a more active role in capturing, storing, transmitting,
and modifying these signals, more information can successfully be digitized
to satisfy the growing demand to transmit information over the air.This
results in a growing need for modulation schemes that are designed to carry digital
information. One advantage of digital signals is the increased ease of compression. Most
analog signals, once digitized, require less space to store physically and less bandwidth
to transmit due to various types of compression techniques.
Digital signals are commonly referred to as bit streams and are graphically represented
as a square wave (see Figure 2.4). In its simplest form, digital modulation
is easier to conceptualize and to perform than analog modulation, because there
are only two signal states to distinguish between: a bit value of one and a bit
value of zero. However, digital modulation schemes get very complex as we try
to maximize transmission speeds and bandwidth by combining various types of
modulation.This section looks briefly at the following types of digital modulation
in their simplest forms:
1. On/Off Keying (OOK)
2. Frequency Shift Keying (FSK)
3. Phase Shift Keying (PSK)
4. Pulse Amplitude Modulation (PAM)
OOK is the simplest form of modulation, digital or analog, and is the modulation
used on the first radios built by Marconi and is the basis for Morse Code.
OOK simply involves making (on) or breaking (off ) the connection between the
carrier signal’s oscillator and the antenna in order to represent the digital signal.
Figure 2.4 illustrates OOK modulation. FSK is similar to OOK, but instead of alternating between the carrier frequency
(on) to no frequency (off ), FSK alternates from the carrier wave frequency
to the carrier wave frequency plus an offset frequency.The detection of
this frequency change yields the transmitted digital signal. Figure 2.5 illustrates
FSK modulation. PSK differs from OOK and FSK in that it does not change the frequency of
the carrier wave. PSK changes the phase of the carrier wave in reference to the
digital modulating wave.The detection of these phase shifts yields the transmitted
digital signal. In its simplest form, PSK shifts the phase by one-half of a wavelength,
or 180 degrees. Figure 2.6 illustrates PSK modulation.