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**Cambium College Radio Wave Propagation and Antennas/Reflectors**

David Hensley Senior Engineer Network & Systems

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**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!

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**Radio Wave Propagation and Antennas/Reflectors**

Parts of a Radio Conversation Wave Properties Radio Waves Antennas Decibels Link Budget For further study

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**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

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**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

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**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

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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?

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**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

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**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

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**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

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**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

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**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!

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**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

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**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!

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**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

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**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)

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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

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