Lesson 17: Communications Systems, EM Spectrum, and Signals
Objectives:
(a) Describe the four components of a communications system and the impact on security of using free space as a
communication medium.
(b) Identify communication applications for various bands of the electromagnetic spectrum ranging from extremely low
frequency (ELF) to extremely high frequency (EHF).
(c) Explain the basic properties of a sinusoidal electromagnetic signal (period, frequency, wavelength, phase, and amplitude)
and describe their mathematical relationship.
(d) Define and calculate bandwidth of transmitted signals.
(e) Plot simple (sinusoidal) electromagnetic signals in the time and frequency domains; interpret time- and frequency-domain
plots to determine the associated signals.
Connection to Cyber Security
This chapter marks the beginning of the third part of EC312. In Part I: The Host, we examined how data are stored and accessed
in memory at the machine level and examined the resulting threats against a specific computer, focusing on the buffer overflow
attack. In Part II: Networks, we concentrated on understanding how the Controller Area Network (
CAN) works and how networks are just as important and vulnerable as the individual host computers that reside on them. In
Part III: Wireless, we will gain an appreciation for communicating in an environment without physical connections to every
computer, router, etc. in the network, leading up to how wireless communication systems can be hacked.
1. Communication Systems
The purpose of a communications system is to transmit information over a distance. This “information” could be audio (such
as speech or music), video, sensor data (temperature, pressure), or other data (e.g., text, stock prices, photos, etc.). “Over a
distance” may mean from here to the other side of the world via a satellite, or from one computer to another in a network, or
from your computer’s CPU to its RAM.
Any communications system consists of the following basic components, which are shown in the following figure. There are
four main components:
• Transmitter – converts information into an electronic form suitable for the channel
• Channel – the physical medium through which an electronic signal travels
o e.g., wire, fiber-optic cable, free space (i.e., air), water (sonar)
• Receiver – converts the received signal back to a usable form
• Noise – undesired, random corrupting energy
The information is passed to the transmitter which in turn transmits it into the communication channel. The receiver produces
a “recovered” information signal, which may not be the same signal that was transmitted. This is because a significant,
though undesired, occurrence in all communication systems is noise, which is random energy that enters the system and
interferes with (corrupts) the transmitted message. If the noise is strong enough, the information signal may not get through at
all. You’ve all heard what noise sounds like, for example on a telephone (we sometimes refer to it as static). If the static is
very powerful you will only hear a small portion (or none) of the words that are spoken to you. This relationship between the
useful signal and corrupting noise that impacts it will be formalized in lesson 19.
Noise can be divided into two broad categories:
•
External noise is noise introduced into the transmission channel from outside sources. Examples include:
o Industrial noise arising from man-made electrical sources (e.g., motors, generators, switches)
o Atmospheric noise due to naturally occurring disturbances in earth’s atmosphere (e.g., lightning)
o Extraterrestrial noise due to solar and cosmic activity.
•
Internal noise is noise introduced by the electronics inside the receiver itself. Examples include:
o
o
Thermal noise
Semiconductor noise
For the third block of this course, we will focus on communications systems in which our channel or medium is free space.
Free space can refer to a perfect vacuum (as you might recall from physics), or to the atmosphere (as opposed to transmission
through a wire or other material). Signals that propagate in free space are often referred to as “wireless” or “over-the-air”
signals, and all signals in free space are part of the electromagnetic spectrum. With wireless routers and satellites part of
almost every network, especially in military applications, understanding the electromagnetic spectrum is critical to cyber
security.
2. Data Flow
Communications systems range from the very simple to the complex. And with complexity comes cost. Systems which have
a requirement to both transmit and receive may have a transceiver which is capable of both. In designing a communications
system, it is important to consider the data flow required between devices so that they include the correct components, but are
not unnecessarily complex. Communication between two devices will be in one of three modes: simplex, half duplex, or full
duplex.
2.1 Simplex Signals transmitted in one direction. Only one of two devices on a link can transmit. Examples of simplex
devices are keyboards and televisions. Remember that a keyboard is an example of an input device. It cannot accept any
outputs. Similarly, your television (before smart TV!) does not transmit any information back to the cable company. The
simplex mode can used the entire capacity of a communications channel to send data in one direction.
2.2 Half Duplex Both stations may transmit, but not at the same time. Military Radios are an example of duplex devices.
Half duplex mode works in cases where there is no need for communication at the same time and the entire capacity of the
channel can be used in one direction at a time.
2.3 Full Duplex In full duplex mode, both stations can transmit and receive simultaneously. One common example of full
duplex communication is the telephones network. Both users can talk and listen at the same time however the capacity of the
channel but must be divided in the two directions.
3. Electromagnetic Spectrum
The electromagnetic spectrum is the range of all possible frequencies of electromagnetic waves. The spectrum is broken into
regions/ranges and classified by frequency and/or wavelength. The frequency (f ) of an electromagnetic wave is a measure of
how rapidly it oscillates. Frequency is measured in Hertz (1 Hz = 1 cycle/sec).
The period (T) of an electromagnetic wave is the length of time required to complete one cycle. The period is measured in
seconds, and is the reciprocal of the frequency in Hz (T = 1/f). Wavelength (λ) is the physical distance between the peaks of
one cycle of a transmitted wave as it moves through the medium, and is measured in meters (m). The following plots show an
EM wave’s voltage as a function of time (left plot), and as a function of distance (right plot).
For electromagnetic waves traveling in air (or vacuum), we will assume that they travel at the speed of light (c) which is
roughly 3 x 108 m/s. The wavelength is inversely proportional to the frequency, and is related to the speed of light by:
𝑐𝑐
𝜆𝜆 =
𝑓𝑓
Practice Problem 17.1
What is the wavelength of an FM radio station whose broadcast frequency is 101.1 MHz?
Solution:
Practice Problem 17.2
What is the frequency of a signal whose wavelength is 8 cm?
Solution:
3.1 Frequency Bands The specific bands of frequencies in the EM spectrum is shown in the following figure. In this course,
we are concerned with communications in the frequency ranges from ELF to EHF.
To transmit signals effectively, the characteristics of the transmission medium and the EM wave behavior in the frequency
bands are considered and matched.
For example, a communication system transmitting to a submarine will have water as the transmission medium. Lower
frequency, longer wave length waves from VLF band do not attenuate as quickly in water as higher frequency bands, so the
transmission frequency will be selected from the VLF band.
You should be familiar with the frequency ranges for communications from ELF to EHF.
• Extremely low frequency (ELF) 30 Hz to 300 Hz. Power line frequencies and low end of human audio.
• Voice frequency (VF) 300 Hz to 3000 Hz. Typical range associated with human voice.
• Human hearing 20 Hz to 20 kHz. (You may try a demo at https://www.youtube.com/watch?v=qNf9nzvnd1k)
• Very low frequency (VLF) 3 kHz to 30 kHz. Used for communications with submerged submarines.
• Low frequency (LF) 30 kHz to 300 kHz. Long range radio navigation.
• Medium frequency (MF) 300 kHz to 3000 kHz. AM radio and long range communication.
• High frequency (HF) 3 MHz to 30 MHz. Known as “short wave”, used by two-way radio.
• Very high frequency (VHF) 30 MHz to 300 MHz. Radio communications and FM radio.
• Ultra high frequency (UHF) 300 MHz to 3000 MHz. TV, military and cell phones.
• Super high frequency (SHF) 3 GHz to 30 GHz. Microwave. Satellite communications and radar.
• Extremely high frequency (EHF) 30 GHz to 300 GHz. Satellite communications.
3.2 Bandwidth The range of frequencies contained in a signal is its bandwidth. Bandwidth is the amount of the frequency
spectrum occupied by a signal regardless of where it is in the spectrum. It is the difference between the upper and lower
frequency limits of the signal.
If a signal occupies the range of frequencies between approximately 300 Hz and 3000 Hz. The following figure demonstrates
that for that signal, it’s bandwidth would be 2700 Hz.
3.3 Federal Communications Commission (FCC)
The electromagnetic spectrum is crowded; everyone wants some bandwidth. The FCC was established by the
Communications Act of 1934 to regulate interstate and foreign communication. The FCC:
• Allocates bands of frequencies for specific uses
• Sets limitations on broadcast power
• Monitors broadcasts to detect unlicensed operations and technical violations
• Auctions spectrum usage
The FCC controls which portions of the EM spectrum are used for various purposes (e.g. FM radio, AM radio, broadcast TV,
satellite communications). The FCC also makes sure that transmissions do not interfere with each other (two transmitters
physically close to each other transmitting in the same frequency range can destroy each other’s signals). For example,
Washington D.C. can have an FM station that transmits at 101.1 MHz (the FM station called FM101), but Baltimore cannot
have an FM station that transmits at 101.1 MHz because it is too close to the Washington D.C. station (approximately 35
miles away).
Because the spectrum is a non-renewable resource in a society that is increasingly connected it is incredibly precious. To give
you an idea of its value, 400 MHz of spectrum was auctioned by the FCC in 2015 and sold for $44.9 billion dollars!
Typical bandwidths:
•
•
•
AM Radio Station – 10 kHz
FM Radio Station – 180 kHz
Broadcast TV Station – 6 MHz
4. Signals as a Function of Time and Frequency
Recall that the purpose of a communications system is to transmit information over a distance. The block diagram for a
communication system is again shown below.
Thus far, we’ve covered that during the final section of this course we’re going to focus on free space as our channel or
medium, which means we’re considering the electromagnetic spectrum. Why do we care?
Information can be in various forms. We transmit information in the form of a signal.
4.1 Time Domain (Sinusoidal Wave) Earlier in this chapter, we discussed some basic properties of sinusoidal
(electromagnetic) waves. A sinusoidal voltage waveform can be expressed mathematically in the following way:
vm (=
t ) Vm sin(2π f mt + θ m )
f=
m
1
Tm
This equation is plotted in the following figure. Note that a cosine is a sine wave with a phase shift of π/2 radians (which is
90°).
Amplitude (Vm) – distance from average to peak (in volts)
Peak-to-peak Voltage (Vpp) – distance from maximum value to minimum value (in volts)
Period (Tm) – time to complete one cycle (in seconds)
Frequency (fm) - number of cycles in one second (in Hz)
Phase (θm)– Left/right shift with respect to the t = 0 axis (in radians)
A sinusoidal wave is one way to represent the sound the tuning fork makes as a function of time. This is referred to as its
“time domain” representation. If the amplitude of the signal is 2 Volts, then the equation for the tuning fork signal could be:
vm (t ) = 2 cos(2π 440t )
This signal can also be represented in terms of its frequency content (i.e., which frequencies are present in the signal) in the
“frequency domain.”
4.2 Frequency Domain (Frequency Spectrum) To display a signal in the frequency domain, we determine the frequency
content of the signal (which can be done using Fourier theory or, for this class, when the signals we will analyze are
composed of sinusoids it can be done by inspection). The frequency content is then displayed on a plot of magnitude vs.
frequency. (magnitude is the absolute value of amplitude). Since our tuning fork is a very simple tone with a single frequency
component of 440 Hz and an amplitude of 2V, the frequency domain plot looks like this:
Both the time-domain (sine or cosine wave) and the frequency-domain displays represent the important characteristics of the
tuning fork as far as a communication system is concerned– they’re just different ways to express the same signal. For
communication engineers, the primary interest is what portion of the frequency spectrum does the signal occupy and how
strong is the signal (magnitude); for our purposes, phase offset (if present) is not part of the frequency plot,, so a sine or
cosine with the same amplitude (positive or negative) and any phase offset have the same frequency plot.
Suppose we had a slightly more complicated signal. Suppose
𝑣𝑣𝑚𝑚 (𝑡𝑡) = 2𝑠𝑠𝑠𝑠𝑠𝑠(2𝜋𝜋440𝑡𝑡) − 3𝑠𝑠𝑠𝑠𝑠𝑠�2𝜋𝜋900𝑡𝑡 + 𝜋𝜋�4� + 5𝑐𝑐𝑐𝑐𝑐𝑐�2𝜋𝜋1100𝑡𝑡 + 2𝜋𝜋�7�
In this case, there are three sinusoids (i.e., there are three frequencies in the
signal) so the frequency plot will have three spikes, at the three frequencies
given, with heights corresponding to the magnitudes of the amplitudes
given. Again, the phases given are not considered in this plot.
Part of the benefit of a frequency domain representation is that certain
signal attributes, like bandwidth, are easy to visualize. For instance, in the
above graph, you can quickly see the bandwidth is:
BW = 1100 Hz – 440 Hz = 660 Hz.