A Practical Introduction to Radio Physics:What is a wave?, Polarization

<< Where to Begin:Purpose of this book, Fitting wireless into your existing network, Wireless networking protocols

Network Design:Designing the physical network, Mesh networking with OLSR, Estimating capacity >>

A Practical Introduction to

Radio Physics

Wireless communications make use of electromagnetic waves to send sig-

nals across long distances. From a user s perspective, wireless connections

are not particularly different from any other network connection: your web

browser, email, and other applications all work as you would expect. But

radio waves have some unexpected properties compared to Ethernet cable.

For example, it s very easy to see the path that an Ethernet cable takes: lo-

cate the plug sticking out of your computer, follow the cable to the other end,

and you ve found it! You can also be confident that running many Ethernet

cables alongside each other won t cause problems, since the cables effec-

tively keep their signals contained within the wire itself.

But how do you know where the waves emanating from your wireless card

are going? What happens when these waves bounce off of objects in the

room or other buildings in an outdoor link? How can several wireless cards

be used in the same area without interfering with each other?

In order to build stable high-speed wireless links, it is important to understand

how radio waves behave in the real world.

What is a wave?

We are all familiar with vibrations or oscillations in various forms: a pendu-

lum, a tree swaying in the wind, the string of a guitar - these are all examples

of oscillations.

Chapter 2: A Practical Introduction to Radio Physics

What they have in common is that something, some medium or object, is

swinging in a periodic manner, with a certain number of cycles per unit of

time. This kind of wave is sometimes called a mechanical wave, since it is

defined by the motion of an object or its propagating medium.

When such oscillations travel (that is, when the swinging does not stay

bound to one place) then we speak of waves propagating in space. For ex-

ample, a singer singing creates periodic oscillations in his or her vocal cords.

These oscillations periodically compress and decompress the air, and this

periodic change of air pressure then leaves the singers mouth and travels, at

the speed of sound. A stone plunging into a lake causes a disturbance, which

then travels across the lake as a wave.

A wave has a certain speed, frequency, and wavelength. These are con-

nected by a simple relation:

Speed = Frequency * Wavelength

The wavelength (sometimes referred to as lambda, ) is the distance meas-

ured from a point on one wave to the equivalent part of the next, for example

from the top of one peak to the next. The frequency is the number of whole

waves that pass a fixed point in a period of time. Speed is measured in

meters/second, frequency is measured in cycles per second (or Hertz, ab-

breviated Hz), and wavelength is measured in meters.

For example, if a wave on water travels at one meter per second, and it oscil-

lates five times per second, then each wave will be twenty centimeters long:

1 meter/second = 5 cycles/second * W

W = 1 / 5 meters

W = 0.2 meters = 20 cm

Waves also have a property called amplitude. This is the distance from the

center of the wave to the extreme of one of its peaks, and can be thought of

as the "height" of a water wave. The relationship between frequency, wave-

length, and amplitude are shown in Figure 2.1.

Waves in water are easy to visualize. Simply drop a stone into the lake and

you can see the waves as they move across the water over time. In the case

of electromagnetic waves, the part that might be hardest to understand is:

"What is it that is oscillating?"

In order to understand that, you need to understand electromagnetic forces.

Chapter 2: A Practical Introduction to Radio Physics

time: 1 second

wavelength (

)

amplitude

wavelength (

)

Figure 2.1: Wavelength, amplitude, and frequency. For this wave, the frequency is 2

cycles per second, or 2 Hz.

Electromagnetic forces

Electromagnetic forces are the forces between electrical charges and cur-

rents. Our most direct access to those is when our hand touches a door

handle after walking on synthetic carpet, or brushing up against an electrical

fence. A more powerful example of electromagnetic forces is the lightning we

see during thunderstorms. The electrical force is the force between electri-

cal charges. The magnetic force is the force between electrical currents.

Electrons are particles that carry a negative electrical charge. There are

other particles too, but electrons are responsible for most of what we need to

know about how radio behaves.

Let us look at what is happening in a piece of straight wire, in which we push

the electrons from one and to the other and back, periodically. At one mo-

ment, the top of the wire is negatively charged - all the negative electrons are

gathered there. This creates an electric field from plus to minus along the

wire. The next moment, the electrons have all been driven to the other side,

and the electric field points the other way. As this happens again and again,

the electric field vectors (arrows from plus to minus) are leaving the wire, so

to speak, and are radiated out into the space around the wire.

What we have just described is known as a dipole (because of the two poles,

plus and minus), or more commonly a dipole antenna. This is the simplest

form of omnidirectional antenna. The motion of the electric field is commonly

referred to as an electromagnetic wave.

Let us come back to the relation:

Speed = Frequency * Wavelength

Chapter 2: A Practical Introduction to Radio Physics

In the case of electromagnetic waves, the speed is c, the speed of light.

c = 300,000 km/s = 300,000,000 m/s = 3*108 m/s

c=f*

lectromagnetic waves differ from mechanical waves in that they require no

medium in which to propagate. Electromagnetic waves will even propagate

through the vacuum of space.

Powers of ten

In physics, math, and engineering, we often express numbers by powers of

ten. We will meet these terms again, e.g. in Giga-Hertz (GHz), Centi-meters

(cm), Micro-seconds ( s), and so on.

Powers of Ten

10-9

Nano-

1/1000000000

10-6

1/1000000

Micro-

Milli-

10-3

1/1000

Centi-

10-2

1/100

Kilo-

103

1 000

Mega-

106

1 000 000

Giga-

109

1 000 000 000

Knowing the speed of light, we can calculate the wavelength for a given fre-

quency. Let us take the example of the frequency of 802.11b wireless net-

working, which is

f = 2.4 GHz

= 2,400,000,000 cycles / second

wavelength lambda ( ) =

c/f

3*108 / 2.4*109

1.25*10-1 m

12.5 cm

Frequency and wavelength determine most of an electromagnetic wave s be-

havior, from antennas that we build to objects that are in the way of the networks

we intend to run. They are responsible for many of the differences between dif-

Chapter 2: A Practical Introduction to Radio Physics

ferent standards we might be choosing. Therefore, an understanding of the basic

ideas of frequency and wavelength helps a lot in practical wireless work.

Polarization

Another important quality of electromagnetic waves is polarization. Polari-

zation describes the direction of the electrical field vector.

If you imagine a vertically aligned dipole antenna (the straight piece of wire),

electrons only move up and down, not sideways (because there is no room

to move) and thus electrical fields only ever point up or down, vertically. The

field leaving the wire and traveling as a wave has a strict linear (and in this

case, vertical) polarization. If we put the antenna flat on the ground, we

would find horizontal linear polarization.

direction of propagation

electric field

magnetic field

Figure 2.2: Electric field and complementary magnetic field components of an elec-

tromagnetic wave. Polarization describes the orientation of the electric field.

Linear polarization is just one special case, and is never quite so perfect: in gen-

eral, we will always have some component of the field pointing other directions

too. The most general case is elliptic polarization, with the extremes of linear

(only one direction) and circular polarizations (both directions at equal strength).

As one can imagine, polarization becomes important when aligning anten-

nas. If you ignore polarization, you might have very little signal even though

you have the strongest antennas. We call this polarization mismatch.

The electromagnetic spectrum

Electromagnetic waves span a wide range of frequencies (and, accordingly,

wavelengths). This range of frequencies and wavelengths is called the elec-

tromagnetic spectrum. The part of the spectrum most familiar to humans is

probably light, the visible portion of the electromagnetic spectrum. Light lies

roughly between the frequencies of 7.5*1014 Hz and 3.8*1014 Hz, correspond-

ing to wavelengths from circa 400 nm (violet/blue) to 800 nm (red).

Chapter 2: A Practical Introduction to Radio Physics

We are also regularly exposed to other regions of the electromagnetic spec-

trum, including Alternating Current (AC) or grid electricity at 50/60 Hz, Ul-

traviolet (on the higher frequencies side of visible light), Infrared (on the lower

frequencies side of visible light), X-Rays / Roentgen radiation, and many oth-

ers. Radio is the term used for the portion of the electromagnetic spectrum

in which waves can be generated by applying alternating current to an an-

tenna. This is true for the range from 3 Hz to 300 GHz, but in the more nar-

row sense of the term, the upper frequency limit would be 1 GHz.

When talking about radio, many people think of FM radio, which uses a fre-

quency around 100 MHz. In between radio and infrared we find the region of

microwaves - with frequencies from about 1 GHz to 300 GHz, and wave-

lengths from 30 cm to 1 mm.

The most popular use of microwaves might be the microwave oven, which in

fact works in exactly the same region as the wireless standards we are deal-

ing with. These regions lie within the bands that are being kept open for gen-

eral unlicensed use. This region is called the ISM band, which stands for

Industrial, Scientific, and Medical. Most other parts of the electromagnetic

spectrum are tightly controlled by licensing legislation, with license values

being a huge economic factor. This goes especially for those parts of the

spectrum that are suitable for broadcast (TV, radio) as well as voice and data

communication. In most countries, the ISM bands have been reserved for

unlicensed use.

Approximate frequency in Hz

104

106

108

1010

1012

1014

1016

1018

1020

1022

1024

microwave

visible light

X rays

ultraviolet

radio

gamma rays

infrared

104

102

100

10-2

10-4

10-6

10-8

10-10

10-12

10-14

10-16

Approximate wavelength in meters

Figure 2.3: The electromagnetic spectrum.

The frequencies most interesting to us are 2.400 - 2.495 GHz, which is used

by the 802.11b and 802.11g radio standards (corresponding to wavelengths

of about 12.5 cm). Other commonly available equipment uses the 802.11a

standard, which operates at 5.150 - 5.850 GHz (corresponding to wave-

lengths of about 5 to 6 cm).

Chapter 2: A Practical Introduction to Radio Physics

Bandwidth

A term you will meet often in radio physics is bandwidth. Bandwidth is sim-

ply a measure of frequency range. If a range of 2.40 GHz to 2.48 GHz is

used by a device, then the bandwidth would be 0.08 GHz (or more commonly

stated as 80MHz).

It is easy to see that the bandwidth we define here is closely related to the

amount of data you can transmit within it - the more room in frequency

space, the more data you can fit in at a given moment. The term bandwidth is

often used for something we should rather call a data rate, as in "my Internet

connection has 1 Mbps of bandwidth", meaning it can transmit data at 1

megabit per second.

Frequencies and channels

Let us look a bit closer at how the 2.4GHz band is used in 802.11b. The

spectrum is divided into evenly sized pieces distributed over the band as in-

dividual channels. Note that channels are 22MHz wide, but are only sepa-

rated by 5MHz. This means that adjacent channels overlap, and can inter-

fere with each other. This is represented visually in Figure 2.4.

Channel

2.412

2.417 2.422 2.427 2.432 2.437 2.442 2.447 2.452 2.457 2.462 2.467 2.472

2.484

Center Frequency

(GHz)

22 MHz

Figure 2.4: Channels and center frequencies for 802.11b. Note that channels 1, 6,

and 11 do not overlap.

For a complete list of channels and their center frequencies for 802.11b/g

and 802.11a, see Appendix B.

Behavior of radio waves

There are a few simple rules of thumb that can prove extremely useful when

making first plans for a wireless network:

· The longer the wavelength, the further it goes

· The longer the wavelength, the better it travels through and around things

· The shorter the wavelength, the more data it can transport

Chapter 2: A Practical Introduction to Radio Physics

All of these rules, simplified as they may be, are rather easy to understand by

example.

Longer waves travel further

Assuming equal power levels, waves with longer wavelengths tend to travel

further than waves with shorter wavelengths. This effect is often seen in FM

radio, when comparing the range of an FM transmitter at 88MHz to the range

at 108MHz. Lower frequency transmitters tend to reach much greater dis-

tances than high frequency transmitters at the same power.

Longer waves pass around obstacles

A wave on water which is 5 meters long will not be stopped by a 5 mm piece

of wood sticking out of the water. If instead the piece of wood were 50 me-

ters big (e.g. a ship), it would be well in the way of the wave. The distance a

wave can travel depends on the relationship between the wavelength of the

wave and the size of obstacles in its path of propagation.

It is harder to visualize waves moving "through" solid objects, but this is the

case with electromagnetic waves. Longer wavelength (and therefore lower

frequency) waves tend to penetrate objects better than shorter wavelength

(and therefore higher frequency) waves.

For example, FM radio (88-

108MHz) can travel through buildings and other obstacles easily, while

shorter waves (such as GSM phones operating at 900MHz or 1800MHz)

have a harder time penetrating buildings. This effect is partly due to the dif-

ference in power levels used for FM radio and GSM, but is also partly due to

the shorter wavelength of GSM signals.

Shorter waves can carry more data

The faster the wave swings or beats, the more information it can carry -

every beat or cycle could for example be used to transport a digital bit, a '0'

or a '1', a 'yes' or a 'no'.

There is another principle that can be applied to all kinds of waves, and

which is extremely useful for understanding radio wave propagation. This

principle is known as the Huygens Principle, named after Christiaan Huy-

gens, Dutch mathematician, physicist and astronomer 1629 - 1695.

Imagine you are taking a little stick and dipping it vertically into a still lake's

surface, causing the water to swing and dance. Waves will leave the center

of the stick - the place where you dip in - in circles. Now, wherever water par-

ticles are swinging and dancing, they will cause their neighbor particles to do

Chapter 2: A Practical Introduction to Radio Physics

the same: from every point of disturbance, a new circular wave will start. This

is, in simple form, the Huygens principle. In the words of wikipedia.org:

"The Huygens' principle is a method of analysis applied to problems of

wave propagation in the far field limit. It recognizes that each point of an

advancing wave front is in fact the center of a fresh disturbance and the

source of a new train of waves; and that the advancing wave as a whole

may be regarded as the sum of all the secondary waves arising from

points in the medium already traversed. This view of wave propagation

helps better understand a variety of wave phenomena, such as diffrac-

tion."

This principle holds true for radio waves as well as waves on water, for sound

as well as light - only for light the wavelength is far too short for human be-

ings to actually see the effects directly.

This principle will help us to understand diffraction as well as Fresnel zones,

the need for line of sight as well as the fact that sometimes we seem to be

able to go around corners, with no line of sight.

Let us now look into what happens to electromagnetic waves as they travel.

Absorption

When electromagnetic waves go through 'something' (some material), they

generally get weakened or dampened. How much they lose in power will de-

pend on their frequency and of course the material. Clear window glass is

obviously transparent for light, while the glass used in sunglasses filter out

quite a share of the light intensity and also the ultraviolet radiation.

Often, an absorption coefficient is used to describe a material s impact on

radiation. For microwaves, the two main absorbent materials are:

· Metal. Electrons can move freely in metals, and are readily able to swing

and thus absorb the energy of a passing wave.

· Water. Microwaves cause water molecules to jostle around, thus taking

away some of the wave s energy1.

For the purpose of practical wireless networking, we may well consider metal

and water perfect absorbers: we will not be able to go through them (al-

1. A commonly held myth is that water "resonates" at 2.4 GHz, which is why that frequency is

used in microwave ovens. Actually, water doesn t appear to have any particular "resonant" fre-

quency. Water spins and jostles around near radio, and will heat when in the presence of high

power radio waves at just about any frequency. 2.4 GHz is an unlicensed ISM frequency, and so

was a good political choice for use in microwave ovens.

Chapter 2: A Practical Introduction to Radio Physics

though thin layers of water will let some power pass). They are to microwave

what a brick wall is to light. When talking about water, we have to remember

that it comes in different forms: rain, fog and mist, low clouds and so forth all

will be in the way of radio links. They have a strong influence, and in many

circumstances a change in weather can bring a radio link down.

There are other materials that have a more complex effect on radio absorp-

tion. For trees and wood, the amount of absorption depends on how much

water they contain. Old dead dry wood is more or less transparent, wet fresh

wood will absorb a lot.

Plastics and similar materials generally do not absorb a lot of radio energy-

but this varies depending on the frequency and type of material. Before you

build a component from plastic (e.g. weather protection for a radio device

and its antennas), it is always a good idea to measure and verify that the ma-

terial does not absorb radio energy around 2.4 GHz. One simple method of

measuring the absorption of plastic at 2.4 GHz is to put a sample in a micro-

wave oven for a couple of minutes. If the plastic heats up, then it absorbs

radio energy and should not be used for weatherproofing.

Lastly, let us talk about ourselves: humans (as well as other animals) are

largely made out of water. As far as radio networking is concerned, we may

well be described as big bags of water, with the same strong absorption. Ori-

enting an office access point in such a way that its signal must pass through

many people is a key mistake when building office networks. The same goes

for hotspots, cafe installations, libraries, and outdoor installations.

Reflection

Just like visible light, radio waves are reflected when they come in contact

with materials that are suited for that: for radio waves, the main sources of

reflection are metal and water surfaces. The rules for reflection are quite

simple: the angle at which a wave hits a surface is the same angle at which it

gets deflected. Note that in the eyes of a radio wave, a dense grid of bars

acts just the same as a solid surface, as long as the distance between bars is

small compared to the wavelength. At 2.4 GHz, a one cm metal grid will act

much the same as a metal plate.

Although the rules of reflection are quite simple, things can become very

complicated when you imagine an office interior with many many small metal

objects of various complicated shapes. The same goes for urban situations:

look around you in city environment and try to spot all of the metal objects.

This explains why multipath effects (i.e. signal reaching their target along

different paths, and therefore at different times) play such an important role in

wireless networking. Water surfaces, with waves and ripples changing all the

Chapter 2: A Practical Introduction to Radio Physics

time, effectively make for a very complicated reflection object which is more

or less impossible to calculate and predict precisely.

i= r

Figure 2.5: Reflection of radio waves. The angle of incidence is always equal to the

angle of reflection. A parabolic uses this effect to concentrate radio waves spread

out over its surface in a common direction.

We should also add that polarization has an impact: waves of different po-

larization in general will be reflected differently.

We use reflection to our advantage in antenna building: e.g. we put huge pa-

rabolas behind our radio transmitter/receiver to collect and bundle the radio

signal into a fine point.

Diffraction

Diffraction is the apparent bending of waves when hitting an object. It is the

effect of "waves going around corners".

Imagine a wave on water traveling in a straight wave front, just like a wave

that we see rolling onto an ocean beach. Now we put a solid barrier, say a

wooden solid fence, in its way to block it. We cut a narrow slit opening into

that wall, like a small door. From this opening, a circular wave will start, and it

will of course reach points that are not in a direct line behind this opening, but

also on either side of it. If you look at this wavefront - and it might just as well

be an electromagnetic wave - as a beam (a straight line), it would be hard to

explain how it can reach points that should be hidden by a barrier. When

modeled as a wavefront, the phenomenon makes sense.

Chapter 2: A Practical Introduction to Radio Physics

Diffraction

Straight wave front

Figure 2.6: Diffraction through a narrow slit.

The Huygens Principle provides one model for understanding this behavior.

Imagine that at any given instant, every point on a wavefront can be consid-

ered the starting point for a spherical "wavelet". This idea was later extended

by Fresnel, and whether it adequately describes the phenomenon is still a

matter of debate. But for our purposes, the Huygens model describes the

effect quite well.

Diffraction

Potential spherical wavelets

Figure 2.7: The Huygens Principle.

Through means of the effect of diffraction, waves will "bend" around corners

or through an opening in a barrier. The wavelengths of visible light are far too

small for humans to observe this effect directly. Microwaves, with a wave-

length of several centimeters, will show the effects of diffraction when waves

hit walls, mountain peaks, and other obstacles. It seems as if the obstruction

causes the wave to change its direction and go around corners.

Chapter 2: A Practical Introduction to Radio Physics

Figure 2.8: Diffraction over a mountain top.

Note that diffraction comes at the cost of power: the energy of the diffracted

wave is significantly less than that of the wavefront that caused it. But in

some very specific applications, you can take advantage of the diffraction

effect to circumvent obstacles.

Interference

When working with waves, one plus one does not necessarily equal two. It

can also result in zero.

Figure 2.9: Constructive and destructive interference.

This is easy to understand when you draw two sine waves and add up the

amplitudes. When peak hits peak, you will have maximum results (1 + 1 = 2).

This is called constructive interference. When peak hits valley, you will

have complete annihilation ((1 + (-)1 = 0) - destructive interference.

You can actually try this with waves on water and two little sticks to create

circular waves - you will see that where two waves cross, there will be areas

of higher wave peaks and others that remain almost flat and calm.

Chapter 2: A Practical Introduction to Radio Physics

In order for whole trains of waves to add up or cancel each other out per-

fectly, they would have to have the exact same wavelength and a fixed phase

relation, this means fixed positions from the peaks of the one wave to the

other's.

In wireless technology, the word Interference is typically used in a wider

sense, for disturbance through other RF sources, e.g. neighboring channels.

So, when wireless networkers talk about interference they typically talk about

all kinds of disturbance by other networks, and other sources of microwave.

Interference is one of the main sources of difficulty in building wireless links,

especially in urban environments or closed spaces (such as a conference

space) where many networks may compete for use of the spectrum.

Whenever waves of equal amplitude and opposite phase cross paths, the

wave is annihilated and no signal can be received. The much more common

case is that waves will combine to form a completely garbled waveform that

cannot be effectively used for communication. The modulation techniques

and use of multiple channels help to deal with the problem of interference,

but does not completely eliminate it.

Line of sight

The term line of sight, often abbreviated as LOS, is quite easy to under-

stand when talking about visible light: if we can see a point B from point A

where we are, we have line of sight. Simply draw a line from A to B, and if

nothing is in the way, we have line of sight.

Things get a bit more complicated when we are dealing with microwaves.

Remember that most propagation characteristics of electromagnetic waves

scale with their wavelength. This is also the case for the widening of waves

as they travel. Light has a wavelength of about 0.5 micrometers, microwaves

as used in wireless networking have a wavelength of a few centimeters.

Consequently, their beams are a lot wider - they need more space, so to

speak.

Note that visible light beams widen just the same, and if you let them travel

long enough, you can see the results despite of their short wavelength. When

pointing a well focussed laser at the moon, its beam will widen to well over

100 meters in radius by the time it reaches the surface. You can see this

effect for yourself using an inexpensive laser pointer and a pair of binoculars

on a clear night. Rather than pointing at the moon, point at a distant moun-

tain or unoccupied structure (such as a water tower). The radius of your

beam will increase as the distance increases.

Chapter 2: A Practical Introduction to Radio Physics

The line of sight that we need in order to have an optimal wireless connection

from A to B is more than just a thin line - its shape is more like that of a cigar,

an ellipse. Its width can be described by the concept of Fresnel zones.

Understanding the Fresnel zone

The exact theory of Fresnel (pronounced "Fray-nell") zones is quite compli-

cated. However, the concept is quite easy to understand: we know from the

Huygens principle that at each point of a wavefront new circular waves start,

We know that microwave beams widen as they leave the antenna. We know

that waves of one frequency can interfere with each other. Fresnel zone the-

ory simply looks at a line from A to B, and then at the space around that line

that contributes to what is arriving at point B. Some waves travel directly from

A to B, while others travel on paths off axis. Consequently, their path is

longer, introducing a phase shift between the direct and indirect beam.

Whenever the phase shift is one full wavelength, you get constructive inter-

ference: the signals add up optimally. Taking this approach and calculating

accordingly, you find there are ring zones around the direct line A to B which

contribute to the signal arriving at point B.

Fresnel radius

Line of sight

Partial obstruction

Figure 2.10: The Fresnel zone is partially blocked on this link, although the visual line

of sight appears clear.

Note that there are many possible Fresnel zones, but we are chiefly con-

cerned with zone 1. If this area were partially blocked by an obstruction, e.g.

a tree or a building, the signal arriving at the far end would be diminished.

When building wireless links, we therefore need to be sure that these zones

be kept free of obstructions. Of course, nothing is ever perfect, so usually in

wireless networking we check that about 60 percent of the radius of the first

Fresnel zone should be kept free.

Here is one formula for calculating the first Fresnel zone:

r = 17.31 * sqrt((d1*d2)/(f*d))

...where r is the radius of the zone in meters, d1 and d2 are distances from

the obstacle to the link end points in meters, d is the total link distance in

meters, and f is the frequency in MHz. Note that this gives you the radius

Chapter 2: A Practical Introduction to Radio Physics

of the zone, not the height above ground. To calculate the height above

ground, you need to subtract the result from a line drawn directly between

the tops of the two towers.

For example, let s calculate the size of the first Fresnel zone in the middle of

a 2km link, transmitting at 2.437 GHz (802.11b channel 6):

r = 17.31 sqrt((1000 * 1000) / (2437 * 2000))

r = 17.31 sqrt(1000000 / 4874000)

r = 7.84 meters

Assuming both of our towers were ten meters tall, the first Fresnel zone

would pass just 2.16 meters above ground level in the middle of the link. But

how tall could a structure at that point be to clear 60% of the first zone?

r = 0.6 * 17.31 sqrt((1000 * 1000) / (2437 * 2000))

r = 0.6 * 17.31 sqrt(600000 / 4874000)

r = 4.70 meters

Subtracting the result from 10 meters, we can see that a structure 5.3 meters

tall at the center of the link would block up to 40% of the first Fresnel zone.

This is normally acceptable, but to improve the situation we would need to

position our antennas higher up, or change the direction of the link to avoid

the obstacle.

Power

Any electromagnetic wave carries energy - we can feel that when we enjoy

(or suffer from) the warmth of the sun. The amount of energy received in a

certain amount of time is called power. The power P is of key importance for

making wireless links work: you need a certain minimum power in order for a

receiver to make sense of the signal.

We will come back to details of transmission power, losses, gains and radio

sensitivity in Chapter 3. Here we will briefly discuss how the power P is de-

fined and measured.

The electric field is measured in V/m (potential difference per meter), the

power contained within it is proportional to the square of the electric field

P ~ E2

Practically, we measure the power by means of some form of receiver, e.g.

an antenna and a voltmeter, power meter, oscilloscope, or even a radio card

and laptop. Looking at the signal s power directly means looking at the

square of the signal in Volts.

Chapter 2: A Practical Introduction to Radio Physics

Calculating with dB

By far the most important technique when calculating power is calculating

with decibels (dB). There is no new physics hidden in this - it is just a con-

venient method which makes calculations a lot simpler.

The decibel is a dimensionless unit2, that is, it defines a relationship between

two measurements of power. It is defined by:

dB = 10 * Log (P1 / P0)

where P1 and P0 can be whatever two values you want to compare. Typi-

cally, in our case, this will be some amount of power.

Why are decibels so handy to use? Many phenomena in nature happen to

behave in a way we call exponential. For example, the human ear senses a

sound to be twice as loud as another one if it has ten times the physical signal.

Another example, quite close to our field of interest, is absorption. Suppose

a wall is in the path of our wireless link, and each meter of wall takes away

half of the available signal. The result would be:

meters

1 (full signal)

meter

1/2

meters

1/4

meters

1/8

meters

1/16

1/2n = 2-n

meters

This is exponential behavior.

But once we have used the trick of applying the logarithm (log), things be-

come a lot easier: instead of taking a value to the n-th power, we just multiply

by n. Instead of multiplying values, we just add.

Here are some commonly used values that are important to remember:

double power

-3

half the power

+10

order of magnitude (10 times power)

-10

one tenth power

2. Another example of a dimensionless unit is the percent (%) which can also be used in all

kinds of quantities or numbers. While measurements like feet and grams are fixed, dimension-

less units represent a relationship.

Chapter 2: A Practical Introduction to Radio Physics

In addition to dimensionless dB, there are a number of relative definitions

that are based on a certain base value P0. The most relevant ones for us

are:

dBm

relative to P0 = 1 mW

dBi

relative to an ideal isotropic antenna

An isotropic antenna is a hypothetical antenna that evenly distributes power

in all directions. It is approximated by a dipole, but a perfect isotropic an-

tenna cannot be built in reality. The isotropic model is useful for describing

the relative power gain of a real world antenna.

Another common (although less convenient) convention for expressing

power is in milliwatts. Here are equivalent power levels expressed in milli-

watts and dBm:

0 dBm

3 dBm

100

20 dBm

30 dBm

Physics in the real world

Don t worry if the concepts in this chapter seem challenging. Understanding

how radio waves propagate and interact with the environment is a complex

field of study in itself. Most people find it difficult to understand phenomenon

that they can t even see with their own eyes. By now you should understand

that radio waves don t travel in a straight, predictable path. To make reliable

communication networks, you will need to be able to calculate how much

power is needed to cross a given distance, and predict how the waves will

travel along the way.

There is much more to learn about radio physics than we have room for here.

For more information about this evolving field, see the resources list in Ap-

pendix A.

Table of Contents: