1. Cambium College Radio Wave Propagation and Antennas/Reflectors
David Hensley
Senior Engineer Network & Systems

2. Before we get started… This presentation has some math.
In fact, this presentation has some algebra.
Don’t worry. This presentation ends well.
It ends with addition and subtraction.
It’s just like life.
Sometimes we have to schedule our pain.
Sometimes we have to suffer a little before life gets easier.
If you’ve always wondered how you’d ever use what you’d learned in your freshman algebra class, this is it!

3. Radio Wave Propagation and Antennas/Reflectors
Parts of a Radio
Conversation
Wave Properties
Radio Waves
Antennas
Decibels
Link Budget
For further study

4. Parts of a Radio formatter demodulator receiver antenna channel
transmitter
modulator
transmit
receive
input
information
output
Start with an example like an iPhone
Input information can be voice or data
Formatter converts the input information into a binary stream—a stream of ones and zeroes.
The modulator converts the stream of ones and zeros:
Adds additional binary digits (redundant information) for error detection and error correction
Chooses the right method of varying the carrier wave that’s appropriate for the channel (the correct modulation mode)
Produces an information stream composed of symbols
The transmitter produces a wave that carries the information from the transmitter to the receiver—this is the carrier wave
There can be one or more carrier waves
The transmitter antenna focuses the carrier wave so that it can be sent from the transmitter to the receiver with intent
The channel carries the carrier wave through thin air!
There may be obstructions, objects, etc. in the channel
The channel may have varying characteristics like temperature, pressure, density, etc.
The receiver antenna captures and focuses the carrier wave with intent (extreme prejudice)
Focuses the wanted signal
Rejects the unwanted signal
The receiver removes the carrier wave and provides the demodulator with the information stream, in symbol format
The demodulator converts the information stream in symbol format to an information stream of binary digits
The demodulator can detect errors that were sent
The demodulator can often correct errors that were sent: this is called Forward Error Correction
The demodulator strips off any additional binary digits that were used to “protect” the information stream
The formatter converts the binary stream into the output information format—voice or data

5. It’s like a conversation! (Radio waves are like sound waves)
The speaker or transmitter (mouth) must be intelligible:
Language
Volume
Pitch
Tone of voice
Direction
Oxford comma
The channel must be clear:
Extraneous noises, music, conversations, etc.
Objects in the way
The listener or receiver (ear) must be available:
Sensitivity
Distraction
“Eats, shoots and leaves!”
It’s mostly all about delivering enough power to the receiver

6. Wave Properties Drop a rock into a pond. What happens?
Waves travel or radiate or propagate outwards in a big circle
Take a point source, radiating radio energy in all directions.
Capture or receive the signal. What do you have?
point source
capture area

7. Properties of Waves
What happens to radio waves as they travel in free space?
They get smaller
Their amplitude gets smaller
This is called attenuation or loss
Amplitude
How tall is the wave?
Frequency or Wavelength
How often does the wave repeat?
Phase
How far did the wave
start from a reference
starting point?

8. Radio Waves As the signal propagates, it gets spread out over
the area of a sphere.
What’s the surface area of a sphere? (4πR2)
The amount of power we can capture is related to the part of the area captured
Pt (λ / 4πR)2
Pt is Power transmitted, Watts
λ is the wavelength of the signal, meters
R is the distance between the transmitter and receiver, meters
Assuming that our transmitter and receiver have no focus or gain
point source
capture area

9. Let’s be more intentional
Then the amount of power we can capture is
Pr = Gt Gr Pt (λ / 4πR)2
Pr is Power received, Watts
Gt is transmitter antenna Gain (output/input ratio)
Gr is receiver antenna Gain (output/input ratio)
Pt is Power transmitted, Watts
λ is the wavelength of the signal, meters
R is the distance between the transmitter and receiver, meters
The Free Space Path Loss is the power lost between transmitter and receiver
FSPL = (4πR / λ)2 = (4πRf / c)2
f is the signal’s frequency, Hertz
c is the speed of light in a vacuum, 300 x 106 meters per second
point source
capture area

10. How do we make antennas with large gain, Gt or Gr?
Make them bigger!
This is useful, but it becomes impractical (after a while)
There is a point of diminishing returns
Large antennas on tall towers are similar to sails on sail boats
Focus the energy by reflecting captured signal to a single point
Use a parabolic reflector
A parabola has a focus
Collect the signal and reflects it to a single point
the signal can be two, three, ten, or even thousands of times stronger

11. So what’s all of this look like at home?
Here’s an example using your home Wi-Fi Access Point
Notice:
the farther we get away from the Access Point, the weaker the received power
These power levels are small!
10-6 Watts or microwatts or μW or millionths of a Watt
10-9 Watts or nano Watts or nW or billionths of a Watt
Go watch “Powers of Ten” (1977) on YouTube right now!
There’s a way to make these power levels easier to understand: the decibel or dB!
Power transmitted, Pt, mW
Transmitter antenna gain, Gt
distance, R, m
Receiver antenna gain, Gr
Power received, Pr, W 20
3.165 10 1
62.6E-6
15.7E-6 30
7.0E-6 50
2.5E-6
100
626.3E-9
200
156.6E-9

12. But first, we have to agree on the following…
Multiplication and Division are difficult!
Addition and Subtraction are easy!
Dealing with thousandths, millionths, billionths, picos, and femtos is hard!
Wait. Where does multiplication and division show up in the radio?
Antennas amplify (or increase) the signal—these are multipliers
Antennas can magnify (or multiply) the signal by two or three or ten or a thousand times
The channel attenuates (or reduces) the signal—this is a divider
Channels can decrease (or divide) the signal by
A thousand
A million
A billion
Or more!

13. Decibel or dB! 10 log( P / P0 ) dB A decibel is a ratio of two things:
Compare one thing to another
Compare a measured quantity to a reference quantity
In our case,
We are comparing power levels
We are comparing our measured quantity to 1 (one) milliwatt
1 milliwatt or a thousandth of a Watt or 10-3 Watts
The ratio is received power divided by one milliwatt (or referenced to a mW)
Pr / 1 mW
It’s called a dBm
1 mW is the reference Power
To make the math easier, we take the logarithm of Pr / 1 mW and multiply it by ten
10 log( Pr / 1 mW )
10 log( P / P0 ) dB

14. Example Power Levels in milliwatts, Watts, and dBm
Observations (rules of thumb)
1000 mW is 1 Watt
Double the power (in Watts) add 3 dB
Halve the power (in Watts) subtract 3 dB
Multiply the power by ten (in Watts) add 10 dB
Dividing the power by ten (in Watts) subtract 10 dB
Antenna gains and channel losses become easier
An antenna with 1000 times gain has 30 dB of gain (add 30 dB)
A channel that divides the signal by one million has 60 dB of loss (subtract 60 dB)
A channel that divides the signal by one billion has 90 dB of loss (subtract 90 dB)
Free Space Path Loss becomes easier
(4πR / λ)2 = (4πRf / c)2 becomes 20 log( R ) + 20 log( f ) dB mW W
dBm
0.1
0.0001
-10.0 1
0.001
0.0 2
0.002
3.0 5
0.005
7.0 10
0.01
10.0 20
0.02
13.0
100
20.0
200
0.2
23.0
1000
30.0
2000
33.0
As an exercise, you can create your own chart just using these four rules for power levels
3 dB and half/double are approximations
Rules of them are often wrong!

15. Let’s go back to the parts of a radio and create a Link Budget
Link Budget, 2.4 GHz, varying distance between AP and client
distance
R, distance, m 10
100
500
1000
frequency
f, frequency, GHz
2.4E+9
AP transmit Power
Pt, transmit power, dBm 13
AP antenna Gain
Gt, Tx antenna gain, dBi 5
 Free Space Path Loss
FSPL, dB
-60
-80
-94
-100
client antenna Gain
Gr, Rx antenna gain, dBi
client received Power
Pr, received Power, dBm
-42
-62
-76
-82
Pr = Pt + Gt + FSPL + Gr

16. In the end, it’s all about…
Getting sufficient power to the receiver
Shorter distances
Choosing a lower frequency
Bigger antennas
Antennas that focus
More sensitive receivers
One transmitter and multiple receivers (receiver diversity)
Multiple transmitters and multiple receivers (Multiple Input Multiple Output or MIMO)

17. For Further Study
Digital Communications, Fundamentals and Applications, Bernard Sklar
Networks, The Definitive Guide, Matthew Gast
Building Wireless Community Networks, Rob Flickenger
Wikipedia!
Parabolic reflector
Friis transmission equation
Decibel
dBm (not dbm)
Link budget
Power of 10
Modulation
Trellis modulation
Radio propagation
Sphere
Frequency
Wavelength
Speed of light
Antenna (radio)
Parabola
Logarithm
Half-power point
Radio wave
Wave
Longitudinal wave
Directional antenna
Serial comma
Radio receiver
MIMO
Isotropic radiator
Wi-Fi
IEEE