Transcript Antenna fundamentals and RF Propagation

TLEN 5830 Wireless Systems
Lecture Slides
01-September-2016
Primary Overview Topics:
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Software Defined Radio architecture (for context)
Finish overview topics
Decibels Review
Complete Signals Overview
SNR: Signal-to-Noise Ratio
Antenna Fundamentals
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Additional reference materials
Required Textbook:
Antennas and Propagation for Wireless Communication Systems, by Simon R.
Saunders and Alejandro Aragon-Zavala, ISBN 978-0-470-84879-1; March 2007
(2nd edition).
Optional References:
Wireless Communications and Networks, by William Stallings, ISBN 0-13040864-6, 2002 (1st edition);
Wireless Communication Networks and Systems, by Corey Beard & William
Stallings (1st edition); all material copyright 2016
Wireless Communications Principles and Practice, by Theodore S. Rappaport,
ISBN 0-13-042232-0 (2nd edition)
Acknowledgements: Several of the Antenna slides are from Michael Borsuk,
Michael Borsuk & Associates.
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Software Defined Radio architecture
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Signal-to-Noise Ratio: Most important wireless communications metric
• Ratio of the power in a signal to the power contained in
the noise that is present at a particular point in the
transmission
• Typically measured at a receiver
• Signal-to-noise ratio (SNR, or S/N)
signal power
( SNR) dB  10 log 10
noise power
• A high SNR means a high-quality signal, low number of
required intermediate repeaters
• SNR sets upper bound on achievable data rate
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Electromagnetic spectrum of telecommunications
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Decibels Review
As a signal propagates along a transmission medium, there will be
a loss, or attenuation, of signal strength. It is customary to express
gains, losses, and relative levels in decibels because:
• Signal strength often falls off logarithmically, so loss is easily
expressed in terms of the decibel, which is a logarithmic
unit of measure
• The net gain or loss in the transmission path can be
calculated by simple addition and subtraction
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Antenna Fundamentals
(restart at slide 24)
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Antenna Fundamentals
• An antenna is an electrical conductor or
system of conductors
– Transmission - radiates electromagnetic energy
into space
– Reception - collects electromagnetic energy from
space
• In two-way communication, the same antenna
can be used for transmission and reception
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Antenna Radiation Patterns
• Radiation pattern
– Graphical representation of radiation properties of an
antenna
– Depicted as two-dimensional cross section
• Beam width (or half-power beam width)
– Measure of directivity of antenna
• Reception pattern
– Receiving antenna’s equivalent to radiation pattern
• Sidelobes
– Extra energy in directions outside the mainlobe
• Nulls
– Very low energy in between mainlobe and sidelobes
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Antenna Radiation Patterns
Also termed
isotropic
radiation
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Types of Antennas
• Isotropic antenna (idealized)
– Radiates power equally in all directions
• Dipole antennas
– Half-wave dipole antenna (or Hertz antenna)
– Quarter-wave vertical antenna (or Marconi antenna)
• Parabolic Reflective Antenna
• Directional Antennas
– Arrays of antennas
• In a linear array or other configuration
– Signal amplitudes and phases to each antenna are adjusted to
create a directional pattern
– Very useful in modern systems
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Simple Antennas
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Radiation Pattern in Three Dimensions
y
y
x
Side view (xy-plane)
z
z
Side view (zy-plane)
x
Top view (xz-plane)
(a) Simple dipole
y
y
x
Side view (xy-plane)
z
Side view (zy-plane)
(b) Directed antenna
TLEN 5830 Wireless Systems
z
x
Top view (xz-plane)
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Parabolic Reflective Antennas
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Antenna Gain
• Antenna gain
– Power output, in a particular direction, compared
to that produced in any direction by a perfect
omnidirectional antenna (isotropic antenna)
• Effective area
– Related to physical size and shape of antenna
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Antenna Gain
• Relationship between antenna gain and effective
area
G=
•
•
•
•
•
4p Ae
l
2
4p f Ae
2
=
c
2
G = antenna gain
Ae = effective area
f = carrier frequency
c = speed of light 3  108 m/s)
λ = carrier wavelength
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Spectrum Considerations for Signal Transmission
• Controlled by regulatory bodies
– Carrier frequency
– Signal Power
– Multiple Access Scheme
• Divide into time slots –Time Division Multiple Access
(TDMA)
• Divide into frequency bands – Frequency Division
Multiple Access (FDMA)
• Different signal encodings – Code Division Multiple
Access (CDMA)
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Spectrum Considerations for Signal Transmission
• Federal Communications Commission (FCC) in the
United States regulates spectrum
–
–
–
–
–
–
Military
Broadcasting
Public Safety
Mobile
Amateur
Government exclusive, non-government exclusive, or
both
– Many other categories
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Spectrum Considerations for Signal Transmission
• Industrial, Scientific, and Medical (ISM) bands
– Can be used without a license
– As long as power and spread spectrum regulations
are followed
• ISM bands are used for
– WLANs
– Wireless Personal Area networks
– Internet of Things
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Signal Propagation Modes
• Ground-wave propagation
• Sky-wave propagation
• Line-of-sight propagation
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Propagation Modes
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Ground Wave Propagation
• Follows contour of the earth
• Can propagate considerable distances
• Frequencies up to 2 MHz
• Example
– AM radio
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Sky Wave Propagation
• Signal reflected from ionized layer of atmosphere
back down to earth
• Signal can travel a number of hops, back and forth
between ionosphere and earth’s surface
• Reflection effect caused by refraction
• Examples
– Amateur radio
– CB radio
– AM radio at night
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Line-of-Sight Propagation
• Transmitting and receiving antennas must be within line
of sight
– Satellite communication – signal above 30 MHz not reflected by
ionosphere
– Ground communication – antennas within effective line of site
due to refraction
• Refraction – bending of microwaves by the atmosphere
– Velocity of electromagnetic wave is a function of the density of
the medium
– When wave changes medium, speed changes
– Wave bends at the boundary between mediums
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Antenna Overview
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•The ionosphere is composed of various “layers”: D (44-55 miles up), E (65-75 miles up), F1
(90-120 miles), and F2 (200 miles).
•The D layer is good at absorbing AM Broadcast frequencies (0.5 – 1.7 MHz) during the day,
but it disappears at night.... the E and F layers bounce the waves back to the earth during
nighttime hours. Many AM stations shut down or reduce power at night to avoid
interference.
•Communication between most two points on Earth is possible at most times of the day
with low attenuation at some frequency in the Short Wave band: 3 – 30 MHz. Most short
wave licenses have multiple frequencies assigned to take advantage of time of day and
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But wait, isn’t EM propagation subject to the 1/R2 rule?*
•In general, free space electromagnetic waves spread out in three dimensions and are
attenuated by the square of the distance from the source. The most general condition
is “from an isotropic source” or radiation equally in all directions—a situation that is
not usually the case, but radio waves not affected by anything else do always observe
the inverse square law as does even “beams” of radio in free space (when not affected
by other factors).
•Ionospheric reflection and absorption are special but very important cases.
•How waves are launched and received by antennas, the interactions with the Earth,
obstacles, and the Ionosphere must all be taken into account.
•In free space from an isotropic antenna energy travels outward equally in straight
lines with this power density, S:
Siso(R) = Prad/4R2 watts/square meter
Prad is the total power radiated and R is the distance from the source.
Under these special conditions, radio is attenuated as per the inverse square law. That
is, the energy is spread out as the area of its coverage increases.
*Some of the background for this and the following slides are taken from Foundations of Electrical Engineering by J. R.
Cogdell, 1996 Prentice Hall, pages 594 – 608.
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FACTORS AFFECTING RADIO WAVE PROPAGATION
Polarization. Electromagnetic waves consist of electric and magnetic waves that at
every point in wave have directions. While the E and M field vectors are perpendicular
to each other, they have a specific orientation at each point in space. Polarization is
important because most antennas produce and receive only one polarization. Circular
polarization is a special case and produces a signal receivable well by both “horizontal”
and vertical” polarized antennas. Having the correct polarization is often critical for
radio communications as cross polarization losses can be over 10 dB.
Surface Waves. Lower frequencies can follow the curvature of the Earth. Losses may
be due to resistive losses in the soil in addition to the 1/R2 loss. Surface waves do not
have to be line of sight but bend with the Earth.
Frequency Dependence. In general, lower frequencies (below 50 MHz) propagate via
surface waves and/or ionosphere reflections and can not be particularly polarity
sensitive.
Frequencies above 50 MHz, while occasionally subject to spectacular (or annoying)
“skip” conditions, require strict antenna polarization and propagate line of sight—that
is, they do not curve in general with the Earth or over obstacles such as mountains.
They do penetrate buildings via reflections.
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Radio Wave Phenomena. There are many. Here are some:
•Reflection can occur from the Earth’s surface, bodies of water, building, and at low
frequencies, the ionosphere. Radar is based on this phenomena. Multipath distortion is
when a signal interferes with itself because of reflections.
•Depolarization occurs when a wave loses its polarization—usually due to a reflection. This
can be good or bad depending on the antennas used.
•Refraction is bending of a wave towards the direction of denser material. Since the
atmosphere is denser at lower levels, refraction extends the “radio horizon” slightly beyond
pure line of sight.
•Diffraction occurs when waves spread into a shadow region behind an obstacle. This is a
well known wave phenomena (think ocean waves) that allows radio signals to go around
and into buildings.
•Scattering occurs when radio waves bounce off multiple small objects. Ocean waves or
even dust particles in the air effect propagation, depending on the wavelength. Often
scattering as well as attenuation due to matter, such as rain or atmospheric gases, can
occur for high microwave frequencies.
•Doppler Shift is a change of frequency that occurs due to the source, reflecting object, or
receiver moving. This can allow the police to measure your speed or make aircraft
communications on microwave frequencies impossible.
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Reflection, Scattering and Diffraction
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ANTENNAS
VLA New Mexico, Keith Stanley
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An antenna is a structure that couples between a
guided and a free electromagnetic wave.
from Foundations of Electrical Engineering, J. R. Cogdell
•Antennas are really just unshielded transmission lines optimized for coupling to free
space. Optimization includes size, shape, height, and other physical and electrical
characteristics such as physical or artificial ground (counterpoise).
•Transmitting and Receiving antennas can be identical in design but often physical
details are different (e.g. thicker components to minimize ohmic losses when used for
transmitting).
•Frequency of Signal, Polarization, Gain, Radiation (or acceptance) Patterns, Drive
Impedance are specification factors.
•Different types used for fixed, mobile, portable, use on towers or buildings, etc.
determines physical size.
•Radiating elements get very inefficient when sized less than an appreciable fraction
of a wavelength (e.g. less than ¼ wavelength in size).
•Other issues: affixed to device, removable, possible to locate remotely from
equipment, proximity to other antennas (pattern interaction, front end overload*).
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*Front end overload
What is it?
Front end overload is where a receiver is not capable of ignoring strong signals which are outside of the
specific frequency range it is designed to receive but usually in the same general part of the spectrum.
Although, for example, a wireless LAN should not pick up anything outside of its specific channel, a
strong signal on the nearby cordless telephone frequencies may be able to overload the receiver
circuitry.
What are the effects of front end overload?
This type of interference usually causes a reduction of sensitivity of the receiver (called “desense”),
although in extreme cases intermodulation distortion can occur or even the receiving device can be
rendered inoperative until action is taken regarding the offending transmitter.
Who's fault is it?
As the equipment suffering the problem should be able to reject nearby signals, it is the fault of that
equipment itself. Usually it is due to the first amplifier stage within the receiver being driven into nonlinearity by the strong nearby signal. Often but not always, low end cost equipment will be more likely to
suffer from this problem.
What can I do about it?
With regard to your wireless LAN access point, cordless phones, and even microwave oven—all within
the general 2.4 GHz band—it is best to locate these units some distance apart. (Of course, if you notice
anything due to the microwave, it is probably leaking energy and should be replaced for safety reasons.)
It might be best to do some frequency management of your own and avoid purchasing a 2.4 GHz
cordless phone, for example, if you have a IEEE 802.11b or IEEE 802.11g wireless LAN.
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THE BASIC MATHEMATICS OF ANTENNAS
1. How well an antenna couples energy into electromagnetic waves is
called the Radiation Efficiency, η (Greek letter eta).
η = Prad/Pin
2. The GAIN of an antenna describes how well it can focus the energy
rather than radiate (or accept) radio waves isotropically*. Some parabolic
reflector antennas (such as the ones at the VLA) can have gains well
over 30 dB.
G = η S(R)/Siso(R)
S(R) is the Power Density, usually in units of microwatts per square meter,
μw/m2. This is the usual measure of the electromagnet field strengths,
especially with respect to radio.
Siso(R) is the field strength produced by substituting (or calculating) what
would be radiated from a perfect isotropic antenna. Some antennas are
spec’ed as compared to a dipole antenna, in which case Sd(R) is used.
*Isotropic = independent (equal) in all directions, as radiation from a point source.
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THE FIELD POWER DENSITY, S(R)
•The field power density is the measure of how much signal is “out there.”
The higher S, the more signal an antenna used for receiving can couple from
the field. You still have to take into account the result of the transmission
line loss, noise and interference, and the performance of the receiver
circuitry.
•Since EM fields in free space obey the inverse square law, combining this
with the previous two equations gives the well known relationship
describing the field strength produced by an antenna at any distance, R.
S(R) = PinG/4πR2
•Field strength meters are quite common for a wide range of frequencies,
and calibrated test antennas (even quiet antenna ranges are available) to
test antenna performance.
•Pin is not the whole story since the drive impedance, Zin, of the antenna
determines how well the feed-line can couple energy into it.
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Transmitting Antenna Example:
An antenna used for a microwave point to point link has a gain of 22 dB. We need
to have a minimum power density of 2 μw/m2 at 10 miles away.
10 miles = 16.1 Km
22 dB = a ratio of 158, so
Pin = 4πR2S(R)/G
= 41.1 watts.
You would need to supply
The antenna with 41.1 watts.
At right: the “Meet Me” room in this
new office building terminates
facilities from many different telco's,
said to be the most interconnections
anywhere in the world.
Reference Calif State University
Rooftop microwave antennas at One Wilshire in
Los Angeles.
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RECEIVING ANTENNA MATH
We have an intuitive feeling that bigger antennas work better. It is true, and assuming that
a receiving antenna is correctly oriented towards the transmitting antenna and that the
polarization of the two antennas are the same, then:
Pav = Aeff S(R) watts
Where Pav is the available power that the antenna receives, and Aeff is the Effective Area of
the antenna—a measure of its size. Understanding the details of Aeff is a little difficult, but
the the concept is really simple: the antenna works better if there is more metal. It’s kind of
thinking that a bigger ladle scoops up more soup, but the devil is in the details. For us it’s
good enough to realize that the higher the gain, the bigger Aeff must be (and must have
been). With that in mind, we get:
Aeff = λ2Gr/4π square meters
Where λ is the wavelength of your signal. The more gain, the bigger the effective area. FYI,
the above formula comes from Maxwell’s equations applied to conservation of energy. You
can’t be more basic than that. The formula says that the effective area goes up with gain
and as the square with wavelength. That means that antennas for higher frequencies don’t
work very well unless they have huge gains. That’s one reason microwaves systems use
dishes. Since higher gains are as the result of directionality, omnidirectional microwave
systems (such as wireless LANs) have very low range, and cell phones work better than PCS.
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Receiving Antenna Example:
Let’s look at the receiving end of the link from the
top of One Wilshire from the previous example.
Let’s say the receiving antenna is identical, and the
frequency is 5020 MHz, in the 5005 – 5060 MHz
FIXED SERVICE (point to point microwave) band in
the US.
λ = 300/5020 = 5.97 cm
G = 158
S(R) = 2 μw/m2
Aeff = λ2Gr/4π = 4.50 x 10-2 m2
Pav = Aeff S(R) = .0901 μw
Actually we might be interested in the voltage the
antenna couples to the transmission
line. Let’s say the receiver which is attached to a very short feed-line and is mounted
right behind the antenna so that there is no transmission line losses. We know that
P = V2/R. Therefore, V = square root of PxR. So for a 50 ohm feed-line, V = 2.12 mv,
which is a pretty strong signal. This is a good link.
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LET’S PUT IT ALL TOGETHER – THE ENTIRE HOP
•If we combine the formulas from the last two examples, we get:
•Prec = PinGtGr/(4πR/λ)2
•Where Gt and Gr are the gains of the transmitting and receiving antennas respectively. It makes
sense that the link doesn’t care (for this formula) which antenna has more gain; it’s the product
of the gains that matters*. So the numerator is the power from the transmitter antenna times
the total gain.
•The denominator of the above formula is called the space loss and is often given in dB. Notice
that the formula calculates the distance (to be applied to the inverse square rule as we would
expect) as R/λ or how many wavelengths apart the two antennas are.
•For the examples we just did with the antennas 10 miles apart and a frequency of 5020 MHz,
R/λ = 2.69 x 105 or 269,000 wavelengths.
The space loss is (4πR/λ)2 = 1.143 x 1013
130.6 dB
•The signal loses 130.6 dB in its hop between the two antennas. Good thing we have a total gain
of 44 dB, a factor of 25,000. If we used isotropic antennas, we would have needed over 1
million watts for this link instead of just 41.1 watts. Again, think of your wireless LAN, where
both the AP and your laptop might be using omnidirectional antennas.
•For all it’s worth, your cell phone antenna probably has a gain of 2 dB or less.
*The respective gains do matter if you are concerned with interfering signals.
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LOTS OF KINDS OF ANTENNAS – YOU SHOULD KNOW A LITTLE
ABOUT EACH
Reflector Type: The real antenna is a small approximately close to 0 dB gain
antenna—called the feed—at the focus of (usually) a parabolic reflector. These
antennas are usually described in terms of the diameter of the parabola (e.g.
“a 3 meter dish”).
It’s not all that hard to calculate the ideal gain of such antennas; it’s roughly 2π
times the area of the antenna dish (given in number of wavelengths at the
operating frequency). This formula assumes that about half the energy
impinging on the dish is actually reflected into the feed due to roughness in the
dish and assuming that the feed is at the correct position at the focus of the
dish.
So for our antenna of the earlier examples, if you assume a feed gain of 0 dB:
G = 22 dB = 158 times = ½ π2 (D/λ)2
If you plug in the numbers, you find that the diameter of the dish must have
been 33.8 cm, about the size of home TV satellite dishes.
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Typical Studio Transmitter 950 MHz
Link antenna – WSUM, Madison
WI.
G = (approximately) 2π x The Area of the dish in square wavelengths
G = π2 (D/λ)2/2 (answer as a ratio)
G = 20 log10B + 20 log10F + 7.5 dB
The 2nd formula simplifies the calculation with B the diameter of the dish in
feet and F the operating frequency and gives the answer in dB.
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LOW GAIN ANTENNAS
Quarter wavelength long “whip” antennas have a very modest
gain, only 0.85 dBi but are practical. They have the advantage of
radiating horizontally. That’s where the gain comes from since
no energy goes straight up or down. The simplest whip is ¼
wavelength long, but somewhat higher gains can be achieved
by increasing its length. 5/8 wavelength is a common size.
Often two quarter wavelength segments are cascaded to
increase the gain by 3 dB and focus the radiation pattern even
more. This sort of antenna is common on mobile cell antennas.
Note the inductor at the mid-point of the antenna to couple
the two ¼ wavelength elements.
Two quarter length segments feed in the middle is a “dipole”
antenna. Dipoles are used by everything from FM broadcast
transmitters to calibrated test equipment. The gain of a dipole
is theoretically 2.14 dBi = 0 dBd.
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A VERY BIG WHIP ANTENNA
AM Broadcasts wavelengths are from 150
to 600 meters!
Often the entire tower is a 1/4th or 5/8
wavelength antenna, and sometimes a
number of such 40 – 200 meter towers
are constructed in a field to provide some
gain and directionality to avoid
interference with neighboring areas.
It is also not uncommon for much higher
frequency antennas to be mounted on the
¼ wavelength radiating towers.
Note the insulator at the bottom of this
200 meter high AM broadcast antenna
and the VHF, UHF, and microwave
antennas mounted at various heights.
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Left: A tunable dipole in which the element
lengths (rightmost part) can be mechanically
adjusted to quarter wavelengths at the
operating frequency.
Above: A Yaggi antenna (named for the
Japanese inventor) is a number dipoles
aligned to focus the signal in one direction.
Gains of up to 20 dB or more are possible in
one direction as 3 dB gain is achieved each
time the number of elements are doubled.
This one has circular polarization for
communication with satellites.
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Amateur Radio installation including a number of short wave Yaggi type antennas
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TV antennas are Yaggi’s made to work over a broad range of frequency. They have little gain but
a very wide frequency range. Notice that this TV antenna intended for use in Spain has vertical
polarization. TV stations in the United Stations require horizontal antennas.
One type of such antennas is the log periodic, a very common for commercial short wave
operation where one large antenna must cover many frequencies to allow world wide
communication. You see these at government and military installations.
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FM radio stations require both horizontal and vertical polarization to accommodate
listeners’ horizontally polarized rooftop antennas and vertical “whip” antenna
automobile installations.
A typical FM station will have a number of circular or diagonally polarized antennas on
one tower to provide some gain and lower the radiation pattern. Gains of 6 dB
requiring four such antennas or 9 dB with eight antennas are common.
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Notice the 5 antenna (little more than 6 dB gain) FM radio station in the background and the
many “whips”. Most of these are co-linear types which are multiple quarter wavelength long to
provide gains in the 6 – 10 dB range or multiple vertically polarized dipoles on the same mast
for the same purpose. Or, as on the right, the dipoles can be placed to make the pattern more
omnidirectional.
The microwave dish is a link for the Boulder County Sheriff Department’s emergency services
communication center (the E911 AP) to a transmitter located in the green building. The
Sheriff’s Department maintains a network of such sites throughout the county.
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These two curves are typical antenna patterns from tower side mounted antennas
such as for cell/PCS sites, TV or FM radio stations. The curve is the field strength (in dB)
at a given distance, usually where the signal is just strong enough to provide good
coverage. For example, north might be up and the curve shows the field strength (in
microwatts/meter) for each direction from the transmitter at say 30 miles, the limits
that the station wants to be heard (and sell advertising for). Let’s hope that the
population center is west of the transmitter site. Cell phone site curves would look
very similar, but the contour would be for a much smaller range.
Here TV station KAUP is comparing their antenna patterns for their old analog
broadcasts versus their new digital/HDTV transmitter site.
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The curve on the left is for a 5.3 GHz 28
dBi gain High Performance Parabolic
Dish Wireless LAN Antenna for IEEE
802.11a wireless LANs. The dB scale
shows relative power in the horizontal
direction. The radiation off the back of
the dish is down 35 dB from the favored
direction.
Full specs for this antenna are at:
http://www.hyperlinktech.com/web/hg5328d.php
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DISTANCE TO THE HORIZON
D  4.124 H
The distance to the horizon (in kilometers) increases with the
height of the antenna above the ground (in meters) according to
the above approximation.
The maximum “line of sight” distance between two radio sites
requires that both antennas be elevated.
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QUIZ QUESTIONS
1. All else being equal, what happens to the gain of an antenna if
the “Effective Area” (Capture Area) is doubled?
2. All else being equal, what is the gain of an antenna if the
frequency is doubled?
3. All else being equal, what happens to the through the air
losses if the frequency is doubled?
4. What is the approximate gain of your cell phone’s antenna?
5. Have you recognized the type of any antennas around campus or
home in the last few days? (Extra credit for reporting on this
in class or via e-mail for the distant students.)
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CLASS EXAMPLE: MICROWAVE LINK FADE MARGIN CALULATION*
1. Free Space Loss
You will have more opportunities to do this in later courses, but we might as well take
a quick look at the procedure now. It will give you some exposure of how wireless
links are engineered while reinforcing your feel how real radio systems work.
Earlier in the lecture, we saw that the Free Space Loss was calculated as follows:
FSL = (4πR/λ)2
where R/λ is the number of wavelengths at the operating frequency between the
two antennas. Since FSL is usually given in dB, an additional conversion to that
measure is necessary.
A more common statement (with English units and the result in dB) for FSL is as
follows:
FSL = 36.6 + 20 log F + 20 log D
where F = Frequency in MHz, and D = Distance between the antennas in miles.
*Notes adapted from a paper given at the 2004 FCC Broadband Forum paper
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The “American” restatement of the Free Space Loss formula makes the calculation easy.
Notice that at any distance the 2.4 GHz IEEE 802.11g wireless LANs will be 8 dB stronger
than the 5.8 GHz IEEE 802.11a type. Note that doubling the distance has the same effect as
doubling the frequency. This formula uses MHz. Add 60 dB for GHz.
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2. Fresnel Zone
We know that at EM radiation at microwave frequencies travel in straight lines (called,
“line of sight”) and need a clear path: that is one without obstacles.
The Fresnel (please pronounce this correctly—it’s fra-nell) zone is a calculation of how
wide a swath the radio signal path needs to be clear. This is because the signal is not
pencil thin; it spreads out. We wouldn’t want it as thin as a laser anyway since then
the aiming of the antennas would be too critical and subject to loss in wind or even if a
bird flew between them. But we are worried that there is something that will “reflect”
the signal along the path.
This is not purely a simple calculation as there are more than one Fresnel Zone, but
usually engineers calculate the “First Fresnel Zone” as an estimate.
The Fresnel zones at any point in the path are:
Fn = 72.1*SQRT((nd1d2)/fD)
where Fn = nth Fresnel zone radius in feet, d1 = distance from one end of path a
reflection (obstacle) point in miles, D = total length of path in miles, d2 = D - d1, and f =
frequency in GHz. Notice that F gets smaller as the square root of F.
Usually engineers are happy if nothing penetrates the 1st Fresnel zone within 40% of
the beam at any point, or in other words less than 0.6F1 is clear of obstructions.
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20%
60%
20%
Fn = 72.1*SQRT((nd1d2)/fD). You don’t want anything penetrating the 1st Fresnel Zone
maximally within 0.6 F1. The site engineers ensure that the antennas are high enough and that
the path avoids obstacles, sometimes requiring a zig-zag path around anything that might
penetrate the Fresnel Zone.
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3. Antenna Gain
We have already looked at this for dishes where G can be very big.
G = 20 log10B + 20 log10F + 7.5 dB
Where B is the diameter of the dish in feet and F is in GHz.* Other types of antennas vary
between a little more than 0 dBi (whips and dipoles) and maybe between 10 and 20 dB
(Yaggi’s).
4. Transmit Power and Receiver Sensitivity – System Operating Margin
These are equipment specifications. The transmit power in watts is what the transmit
applies to the feed-line, not the signal actually delivered to the antenna which will be less.
The receiver sensitivity is a minimum signal level (sometimes given in dBm but more usually
given in microvolts applied to the input port of the receiver equipment), again after the
losses in the receiver transmission line. For most radio equipment, one to 10 microvolts are
required minimally.
5. Feed line losses
At microwave frequencies, the loss per meter can be very high. It’s always better to use
short lengths of cable, better cables, or even locate receivers and transmitters near the
antennas, sometimes on the towers themselves.
*In the Wilshire One Bldg example: B = 1 foot, F = 5.02 GHz. G was approx 22 dB.
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NCAR ON TABLE MESA, BOULDER COLORADO
© University Corporation for Atmospheric Research, all rights reserved
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6. Multipath Interference
This is when some of the signal arrives at the receive antenna after being
reflected off the ground, from atmospheric reflections, or a passing aircraft. This
is usually destructive to the signal. Siting, antenna height, etc., and other design
schemes are employed to minimize these possibilities. Multipath is responsible
for your FM radio sounding poorly even when the signal is strong—as here in
Boulder because of reflections off the Flatirons—and accounts for “ghosts” on
analog TV reception.
7. Signal-to-Noise Radio
S/N (usually in dB). This is a more critical number than “Receiver Sensitivity” (as
in optical fiber calculations) since as you probably know various wireless systems
will test the “connection” during the initial session set-up or even every second
or so for reliable packet reception and step down the data rate to provide for
error free performance.
This is why your IEEE 802.11g wireless lap top connection might show 54 Mbps
sometimes but 36 Mbps down to 11 Mbps or less if you stray too far from the
wireless Access Point.
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How much more signal is presented to the receiver than required is the System
Operating Margin, usually given in dB (just like for optical fibers). But you have
to take into account the minimum S/N ratio required as well.
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The receiver and transmitter will test the reliability of packet exchange and only provide
the full data rate when the SNR is adequate.
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The calculation of the SYSTEM OPERATING MARGIN (also called FADE MARGIN) puts all the
factors together.
Here two dishes each with 24 dB gain are 20 miles apart. A receiver sensitivity of -83 dBm
provides the minimally adequate S/N level. The actual installation has a transmitter power of 24
dBm or 1/4 watt, and the feed-lines have losses of 1 dB each.
The FADE MARGIN is 23 dB, a factor of 200 times the minimum signal required.
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So why so high a “fade margin”?
1. Transmit power is pretty cheap, but gain in antennas is cheaper.
2. Shorter antenna spacing is very expensive as is making the towers
higher. These are to be avoided.
3. Most engineers agree that 20 dB is a minimum fade margin to take care
of real world factors, but some installations have margins of as low as 10
dB. It’s hard to get a microwave engineer to accept a design of less than
14 dB margin (or 25 times the power).
4. The real world factors include interference (from other transmitters or
even electrical equipment), antennas misaimed or worries about their
becoming out of aim or even shaking in the wind, atmospheric conditions
(skip or even dirt or rain) which can account for a daily variation of up to
+/- 6 dB, and ice on the antenna or water in the feed-line*. 14 dB margin
doesn’t seem so high if you consider these factors.
*It is not uncommon to find gallons of water leaking out of replaced air gap feed lines.
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Picture Credit: Royal Army, UK
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Additional reference materials
Required Textbook:
Antennas and Propagation for Wireless Communication Systems, by Simon R.
Saunders and Alejandro Aragon-Zavala, ISBN 978-0-470-84879-1; March 2007
(2nd edition).
Optional References:
Wireless Communications and Networks, by William Stallings, ISBN 0-13040864-6, 2002 (1st edition);
Wireless Communication Networks and Systems, by Corey Beard & William
Stallings (1st edition); all material copyright 2016
Wireless Communications Principles and Practice, by Theodore S. Rappaport,
ISBN 0-13-042232-0 (2nd edition)
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