Dr. Tahseen Al-Doori Lesson 3 Radio Frequency Components, Measurements, and Mathematics.

Dr. Tahseen Al-DooriDr. Tahseen Al-Doori

Lesson 3Lesson 3

Radio Frequency Components, Radio Frequency Components, Measurements, and Mathematics Measurements, and Mathematics


ObjectivesObjectives

The Components of RF CommunicationsThe Components of RF Communications – TransmitterTransmitter– ReceiverReceiver– AntennaAntenna– Isotropic RadiatorIsotropic Radiator– Intentional Radiator (IR)Intentional Radiator (IR)– Equivalent Isotropically Radiated Power (EIRP)Equivalent Isotropically Radiated Power (EIRP)


ObjectivesObjectives Units of Power and ComparisonUnits of Power and Comparison

– WattWatt– MilliwattMilliwatt– Decibel (dB)Decibel (dB)– dBidBi– dBddBd– dBmdBm

RF MathematicsRF Mathematics System Operating Margin (SOM)/Link BudgetSystem Operating Margin (SOM)/Link Budget Fade MarginFade Margin Inverse Square LawInverse Square Law


RF Components RF Components

Many components contribute to the Many components contribute to the successful transmission and reception of an successful transmission and reception of an RF signal. RF signal. Figure 1Figure 1 shows the key shows the key components that will be covered in this components that will be covered in this section. In addition to understanding the section. In addition to understanding the function of the components, it is important to function of the components, it is important to understand how the strength of the signal is understand how the strength of the signal is specifically affected by each of the specifically affected by each of the components.components.


TransmitterTransmitter The transmitter is the initial component in the The transmitter is the initial component in the

creation of the wireless medium. The computer creation of the wireless medium. The computer hands the data off to the transmitter, and it is the hands the data off to the transmitter, and it is the transmitter’s job to begin the RF communication.transmitter’s job to begin the RF communication.

The transmitter will take the data provided and The transmitter will take the data provided and modify the AC signal using a modulation technique modify the AC signal using a modulation technique to encode the data into the signal. This modulated to encode the data into the signal. This modulated AC signal is now a carrier signal, containing the AC signal is now a carrier signal, containing the data to be transmitted. The carrier signal is then data to be transmitted. The carrier signal is then transported either directly to the antenna or transported either directly to the antenna or through a cable to the antenna.through a cable to the antenna.


In addition to generating a signal at a specific In addition to generating a signal at a specific frequency, the transmitter is responsible for frequency, the transmitter is responsible for determining the amplitude, or what is more determining the amplitude, or what is more commonly referred to as the power level, of the commonly referred to as the power level, of the signal. signal.

The higher the amplitude of the wave, the more The higher the amplitude of the wave, the more powerful the wave is and the further it will travel. powerful the wave is and the further it will travel. The power levels that the transmitter is allowed to The power levels that the transmitter is allowed to generate are determined by the local regulatory generate are determined by the local regulatory body, such as the Federal Communications body, such as the Federal Communications Commission (FCC) in the United States. Commission (FCC) in the United States.


Although we are explaining the transmitter Although we are explaining the transmitter and receiver separately, and although and receiver separately, and although functionally they are different components, functionally they are different components, typically they are one device that is referred typically they are one device that is referred to as a transceiver (transmitter/receiver). to as a transceiver (transmitter/receiver).

Typical wireless devices that have Typical wireless devices that have transceivers built into them are access transceivers built into them are access points, bridges, and client adapters.points, bridges, and client adapters.


AntennaAntenna An antenna provides two functions in a communication An antenna provides two functions in a communication

system. system. When connected to the transmitter, it collects the AC signal When connected to the transmitter, it collects the AC signal

that it receives from the transmitter and directs, or radiates, that it receives from the transmitter and directs, or radiates, the RF waves away from the antenna in a pattern specific the RF waves away from the antenna in a pattern specific to the antenna type. to the antenna type.

When connected to the receiver, it takes the RF waves that When connected to the receiver, it takes the RF waves that it receives through the air and directs the AC signal to the it receives through the air and directs the AC signal to the receiver. The receiver converts the AC signal to bits and receiver. The receiver converts the AC signal to bits and bytes. As you will see later, the signal that is received is bytes. As you will see later, the signal that is received is much less than the signal that is generated. much less than the signal that is generated.

This signal loss is analogous to two people trying to talk to This signal loss is analogous to two people trying to talk to each other from opposite ends of a football field. Due to each other from opposite ends of a football field. Due to distance alone (free space), the yelling from one end of the distance alone (free space), the yelling from one end of the field may be heard as barely louder than a whisper on the field may be heard as barely louder than a whisper on the other end.other end.


The signal of an antenna is usually compared or The signal of an antenna is usually compared or referenced to an referenced to an isotropic radiatorisotropic radiator . .

An isotropic radiator is a An isotropic radiator is a point sourcepoint source that that radiates signal equally in all directions. The sun is radiates signal equally in all directions. The sun is probably one of the best examples of an isotropic probably one of the best examples of an isotropic radiator. It generates equal amounts of energy in radiator. It generates equal amounts of energy in all directions. all directions.

Unfortunately, it is not possible to manufacture an Unfortunately, it is not possible to manufacture an antenna that is a perfect isotropic radiator. The antenna that is a perfect isotropic radiator. The structure of the antenna itself influences the output structure of the antenna itself influences the output of the antenna, similar to the way the structure of a of the antenna, similar to the way the structure of a lightbulb affects the bulb’s ability to emit light lightbulb affects the bulb’s ability to emit light equally in all directions.equally in all directions.


There are two ways to increase the power output from an There are two ways to increase the power output from an antenna. antenna.

The first is to generate more power at the transmitter, as The first is to generate more power at the transmitter, as stated in the previous section. The other is to direct, or stated in the previous section. The other is to direct, or focus, the RF signal that is radiating from the antenna. This focus, the RF signal that is radiating from the antenna. This is similar to how you can focus light from a flashlight. If you is similar to how you can focus light from a flashlight. If you remove the lens from the flashlight, the bulb is typically not remove the lens from the flashlight, the bulb is typically not very bright and radiates in almost all directions. To make very bright and radiates in almost all directions. To make the light brighter, you could use more powerful batteries, or the light brighter, you could use more powerful batteries, or you could put the lens back on. The lens is not actually you could put the lens back on. The lens is not actually creating more light. It is focusing the light that was radiating creating more light. It is focusing the light that was radiating in all different directions into a narrow area. in all different directions into a narrow area.

Some antennas radiate waves as the bulb without the lens Some antennas radiate waves as the bulb without the lens does, while some radiate focused waves as the flashlight does, while some radiate focused waves as the flashlight with the lens does. with the lens does.


ReceiverReceiver The receiver is the final component in the wireless The receiver is the final component in the wireless

medium. medium. The receiver takes the carrier signal that is The receiver takes the carrier signal that is

received from the antenna and translates the received from the antenna and translates the modulated signals into 1s and 0s. It then takes this modulated signals into 1s and 0s. It then takes this data and passes it to the computer to be data and passes it to the computer to be processed. The job of the receiver is not always processed. The job of the receiver is not always an easy one. The signal that is received is a much an easy one. The signal that is received is a much less powerful signal than what was transmitted less powerful signal than what was transmitted due to the distance it has traveled and the effects due to the distance it has traveled and the effects of free space path loss. of free space path loss.

The signal is also often altered due to interference The signal is also often altered due to interference from other RF sources and multipath.from other RF sources and multipath.


Intentional Radiator (IR)Intentional Radiator (IR)

intentional radiator (IR) isintentional radiator (IR) is “a device that “a device that intentionally generates and emits radio intentionally generates and emits radio frequency energy by radiation or induction.”frequency energy by radiation or induction.”

Basically, it’s something that is specifically Basically, it’s something that is specifically designed to generate RF as opposed to designed to generate RF as opposed to something that generates RF as a byproduct something that generates RF as a byproduct of its main function, such as a motor that of its main function, such as a motor that incidentally generates RF noise. incidentally generates RF noise.


Regulatory bodies such as the FCC limit the Regulatory bodies such as the FCC limit the amount of power that is allowed to be generated amount of power that is allowed to be generated by an IR. by an IR.

The IR consists of all the components from the The IR consists of all the components from the transmitter to the antenna but not including the transmitter to the antenna but not including the antenna, as see in Fig 1antenna, as see in Fig 1

The power output of the IR is thus the sum of all The power output of the IR is thus the sum of all the components from the transmitter to the the components from the transmitter to the antenna, again not including the antenna.antenna, again not including the antenna.


The components making up the IR include the The components making up the IR include the transmitter, all cables and connectors, and any transmitter, all cables and connectors, and any other equipment (grounding, lightning arrestors, other equipment (grounding, lightning arrestors, amplifiers, attenuators, etc.) between the amplifiers, attenuators, etc.) between the transmitter and the antenna. transmitter and the antenna.

The power of the IR is measured at the connecter The power of the IR is measured at the connecter that provides the input to the antenna. Since this is that provides the input to the antenna. Since this is the point where the IR is measured and regulated, the point where the IR is measured and regulated, we often refer to this point alone as the IR. Using we often refer to this point alone as the IR. Using the flashlight analogy, the IR is all of the the flashlight analogy, the IR is all of the components up to the lightbulb socket but not the components up to the lightbulb socket but not the bulb and lens. This is the raw power, or signal, bulb and lens. This is the raw power, or signal, that is provided, and now the bulb and lens can that is provided, and now the bulb and lens can focus the signal. focus the signal.


Equivalent Isotropically Radiated Equivalent Isotropically Radiated Power (EIRP)Power (EIRP)

Equivalent isotropically radiated power (EIRP) is the Equivalent isotropically radiated power (EIRP) is the highest RF signal strength that is transmitted from a highest RF signal strength that is transmitted from a particular antenna. particular antenna.

To understand this better, think of our flashlight example To understand this better, think of our flashlight example for a moment. Let’s assume that the bulb without the lens for a moment. Let’s assume that the bulb without the lens generates 1 watt of power. When you put the lens on the generates 1 watt of power. When you put the lens on the flashlight, it focuses that 1 watt of light. If you were to look flashlight, it focuses that 1 watt of light. If you were to look at the light now, it would appear much brighter. If you were at the light now, it would appear much brighter. If you were to measure the brightest point of the light that was being to measure the brightest point of the light that was being generated by the flashlight, due to the effects of the lens, it generated by the flashlight, due to the effects of the lens, it may be equal to the brightness of an 8 watt bulb. So by may be equal to the brightness of an 8 watt bulb. So by focusing the light, you are able to make the equivalent focusing the light, you are able to make the equivalent isotropically radiated power of the focused bulb equal to 8 isotropically radiated power of the focused bulb equal to 8 watts.watts.


Units of Power and Comparison Units of Power and Comparison When an 802.11 wireless network is designed, two When an 802.11 wireless network is designed, two

key components are coverage and performance. A key components are coverage and performance. A good understanding of RF power, comparison, good understanding of RF power, comparison, and RF mathematics can be very helpful during and RF mathematics can be very helpful during the network design phase.the network design phase.

Here, I will introduce you to an assortment of units Here, I will introduce you to an assortment of units of power and units of comparison. It is important to of power and units of comparison. It is important to know and understand the different types of units of know and understand the different types of units of measurement and how they relate to each other.measurement and how they relate to each other.

Some of the numbers that you will be working with Some of the numbers that you will be working with will represent actual units of power and others will will represent actual units of power and others will represent relative units of comparison. Actual units represent relative units of comparison. Actual units are ones that represent a known or set value.are ones that represent a known or set value.


Comparative units of measurement are Comparative units of measurement are useful when working with units of power. useful when working with units of power.

As you will see later, we can use these As you will see later, we can use these comparative units of power to compare the comparative units of power to compare the area that one access point can cover versus area that one access point can cover versus another access point. another access point.

Using simple mathematics, we can Using simple mathematics, we can determine things such as how many watts determine things such as how many watts are needed to double the distance of a are needed to double the distance of a signal from an access point.signal from an access point.


Units of PowerUnits of Power Units of ComparisonUnits of Comparison

Watts (W)Watts (W) Decibal (dB)Decibal (dB)

Milliwatts (mW)Milliwatts (mW) dBidBi

dBmdBm dBddBd


Decibel (dB)Decibel (dB)

The first thing you should know about the decibel The first thing you should know about the decibel (dB) is that it is a unit of comparison, not a unit of (dB) is that it is a unit of comparison, not a unit of power. power.

Therefore, it is used to represent a difference Therefore, it is used to represent a difference between two values. between two values.

In wireless networking, decibels are often used to In wireless networking, decibels are often used to either compare the power of two transmitters or, either compare the power of two transmitters or, more often, compare the difference or loss more often, compare the difference or loss between the EIRP output of a transmitter and the between the EIRP output of a transmitter and the amount of power received by the receiver.amount of power received by the receiver.


Let’s look at an example: Let’s look at an example: An access point transmits data at 100 mW. An access point transmits data at 100 mW.

Laptop1 receives the signal at a power level of 10 Laptop1 receives the signal at a power level of 10 mW, and laptop2 receives the signal at a power mW, and laptop2 receives the signal at a power level of 1 mW. The difference between the signal level of 1 mW. The difference between the signal from the access point (100 mW) to laptop1 (10 from the access point (100 mW) to laptop1 (10 mW) is 100:10, or a 10:1 ratio, or 1 bel. The mW) is 100:10, or a 10:1 ratio, or 1 bel. The difference between the signal from laptop1 (10 difference between the signal from laptop1 (10 mW) to laptop2 (1 mW) is 10:1, also a 10:1 ratio, mW) to laptop2 (1 mW) is 10:1, also a 10:1 ratio, or 1 bel. So the power difference between the or 1 bel. So the power difference between the access point and laptop2 is 2 bels. access point and laptop2 is 2 bels.


Bels can be looked at mathematically using logarithms. Not Bels can be looked at mathematically using logarithms. Not everyone understands or remembers logarithms, so we will everyone understands or remembers logarithms, so we will review them. review them.

First, we need to look at raising a number to a power. If First, we need to look at raising a number to a power. If you take 10 and raise it to the third power (10^3 = y), what you take 10 and raise it to the third power (10^3 = y), what you are actually doing is multiplying three 10s (10 × 10 × you are actually doing is multiplying three 10s (10 × 10 × 10). If you do the math, you will calculate that y is equal to 10). If you do the math, you will calculate that y is equal to 1,000. So the completed formula is 10^3 =1,000. When 1,000. So the completed formula is 10^3 =1,000. When calculating logarithms, you change the formula to 10^y = calculating logarithms, you change the formula to 10^y = 1,000. Here you are trying to figure out what power 10 1,000. Here you are trying to figure out what power 10 needs to be raised to in order to get to 1,000. You know in needs to be raised to in order to get to 1,000. You know in this example that the answer is 3. this example that the answer is 3.

You can also write this equations as y = log10(1,000). You can also write this equations as y = log10(1,000). So the complete equation is 3 = log10(1,000). Here are So the complete equation is 3 = log10(1,000). Here are

some examples of power and log formulas:some examples of power and log formulas:


10^1=1010^1=10 log10(10)=1log10(10)=1 10^2=10010^2=100 log10(100)=2log10(100)=2 10^3=100010^3=1000 log10(1000)=3log10(1000)=3 10^4=10,00010^4=10,000 log10(10,000)=4log10(10,000)=4


ExampleExample

Now let’s go back and calculate the bels from the Now let’s go back and calculate the bels from the access point to the laptop2 example using access point to the laptop2 example using logarithms. logarithms.

Remember that bels are used to calculate the ratio Remember that bels are used to calculate the ratio between two powers. So let’s refer to the power of between two powers. So let’s refer to the power of the access point as Pap and the power of laptop1 the access point as Pap and the power of laptop1 as PL1 . So the formula for this example would be as PL1 . So the formula for this example would be y = log10(Pap/PL1). If you plug in the power y = log10(Pap/PL1). If you plug in the power values, the formula becomes y = log10(100/1), or values, the formula becomes y = log10(100/1), or y = log10(100). y = log10(100).

So this equation is asking 10 raised to what power So this equation is asking 10 raised to what power equals 100. The answer is 2 bels (102 = 100).equals 100. The answer is 2 bels (102 = 100).


To calculate decibels, all you need to do is To calculate decibels, all you need to do is multiply bels by 10. So the formulas for bels multiply bels by 10. So the formulas for bels and decibels are as follows:and decibels are as follows:

bels = log10(P1/P2)bels = log10(P1/P2) decibels = 10 × log10(P1/P2)decibels = 10 × log10(P1/P2)


Now let’s go back and calculate the decibels Now let’s go back and calculate the decibels of the access point to laptop2 example. of the access point to laptop2 example.

So the formula now is So the formula now is

y = 10 × log10(Pap/PL1). y = 10 × log10(Pap/PL1). If you plug in the power values, the formula If you plug in the power values, the formula

becomes becomes

y = 10 × log10(100/1), or y = 10 × log10(100/1), or

y = 10 × log10(100). y = 10 × log10(100).

So the answer is 20 decibels.So the answer is 20 decibels.


Now that you have learned about decibels, Now that you have learned about decibels, you are probably still wondering why you you are probably still wondering why you can’t just work with milliwatts. can’t just work with milliwatts.

You can if you want, but since power You can if you want, but since power changes are logarithmic, the differences changes are logarithmic, the differences between values can become extremely between values can become extremely large and more difficult to deal with. large and more difficult to deal with.

It is easier to say that a 100 mW signal It is easier to say that a 100 mW signal decreased by 70 decibels than to say that it decreased by 70 decibels than to say that it decreased to .00001 milliwatts. decreased to .00001 milliwatts.


dBidBi The gain or increase of power from an antenna The gain or increase of power from an antenna

when compared to what an isotropic radiator when compared to what an isotropic radiator would generate is known as decibels isotropic would generate is known as decibels isotropic (dBi). Another way of phrasing this is “decibel gain (dBi). Another way of phrasing this is “decibel gain relative to an isotropic radiator.” relative to an isotropic radiator.”

Since you are comparing two antennas, and since Since you are comparing two antennas, and since antennas are measured in gain, not power, you antennas are measured in gain, not power, you can conclude that dBi is a comparative can conclude that dBi is a comparative measurement and not a power measurement. measurement and not a power measurement.

The dBi value is measured at the strongest point The dBi value is measured at the strongest point or the focus point of the antenna signal. Since or the focus point of the antenna signal. Since antennas always focus their energy more in one antennas always focus their energy more in one direction than another, the dBi value of an antenna direction than another, the dBi value of an antenna is always a positive gain and not a loss. is always a positive gain and not a loss.


A common antenna used on access points A common antenna used on access points is the half-wave dipole antenna. is the half-wave dipole antenna.

The half-wave dipole antenna is a small, The half-wave dipole antenna is a small, typically rubber-encased, general purpose typically rubber-encased, general purpose antenna and has a dBi value of 2.14.antenna and has a dBi value of 2.14.

Any time you see dBi, think antenna gain.Any time you see dBi, think antenna gain.


dBddBdThe antenna industry uses two different dB scales to describe The antenna industry uses two different dB scales to describe

the gain of antennas. the gain of antennas. The first scale, which you just learned about, is dBi.The first scale, which you just learned about, is dBi. The other scale used to describe antenna gain is decibels The other scale used to describe antenna gain is decibels

dipole (dBd), or “decibel gain relative to a dipole antenna.” dipole (dBd), or “decibel gain relative to a dipole antenna.” So a dBd value is the increase in gain of an antenna when So a dBd value is the increase in gain of an antenna when

it is compared to the signal of a dipole antenna. Like dBi, it is compared to the signal of a dipole antenna. Like dBi, since dBd is comparing two antennas, and since antennas since dBd is comparing two antennas, and since antennas are measured in gain, not power, you can also conclude are measured in gain, not power, you can also conclude that dBd is a comparative measurement and not a power that dBd is a comparative measurement and not a power measurement. measurement.

The definition of dBd seems simple enough, but what The definition of dBd seems simple enough, but what happens when you want to compare two antennas and one happens when you want to compare two antennas and one is represented with dBi and the other with dBd? is represented with dBi and the other with dBd?


This is actually quite simple. This is actually quite simple. A standard dipole antenna has a dBi value of 2.14. A standard dipole antenna has a dBi value of 2.14.

If an antenna has a value of 3 dBd, this means If an antenna has a value of 3 dBd, this means that it is 3 dB greater than a dipole antenna. Since that it is 3 dB greater than a dipole antenna. Since the value of a dipole antenna is 2.14 dBi, all you the value of a dipole antenna is 2.14 dBi, all you need to do is add 3 plus 2.14. So a 3 dBd antenna need to do is add 3 plus 2.14. So a 3 dBd antenna is equal to a 5.14 dBi.is equal to a 5.14 dBi.

When working with 802.11 equipment, it is not When working with 802.11 equipment, it is not often that you will have an antenna with a dBd often that you will have an antenna with a dBd value. 802.11 antennas typically are measured value. 802.11 antennas typically are measured using dBi. On the rare occasion that you do run using dBi. On the rare occasion that you do run into one, just add 2.14 and you now know the into one, just add 2.14 and you now know the antenna’s dBi value.antenna’s dBi value.


dBmdBm dBm provides a comparison, but instead of dBm provides a comparison, but instead of

comparing a signal to another signal, it is used to comparing a signal to another signal, it is used to compare a signal to 1 milliwatt of power. compare a signal to 1 milliwatt of power.

dBm means “decibels relative to 1 milliwatt.” So dBm means “decibels relative to 1 milliwatt.” So what you are doing is setting dBm to 0 (zero) and what you are doing is setting dBm to 0 (zero) and equating that to 1 milliwatt of power. equating that to 1 milliwatt of power.

Since dBm is a measurement that is compared to Since dBm is a measurement that is compared to a known value, 1 milliwatt, then dBm is actually a a known value, 1 milliwatt, then dBm is actually a measure of power. measure of power.

You can now state that 0 dBm is equal to 1 You can now state that 0 dBm is equal to 1 milliwatt. Using the formula milliwatt. Using the formula

dBm = 10 × log10(PmW), dBm = 10 × log10(PmW), you can determine that 100 mW of power is equal you can determine that 100 mW of power is equal

to 20 dBm. to 20 dBm.


RF MathematicsRF MathematicsTo convert:To convert:

mW to dBm use this formula:mW to dBm use this formula:dBm=10Log(mW)dBm=10Log(mW)

dBm to mW use this formuladBm to mW use this formulamW=10^(dBm/10)mW=10^(dBm/10) dBi to dBddBi to dBddBd=dBi-2.14dBd=dBi-2.14

mW to dBWmW to dBWdBW=10Log(mW/1)dBW=10Log(mW/1)


ExercisesExercises

1. convert the following:1. convert the following: 400mW ______dBm400mW ______dBm 14dBm ______mW14dBm ______mW 7dBW ______dBm7dBW ______dBm 250mW ______dBW250mW ______dBW


CalculatorCalculator

http://www.terabeam.com/support/http://www.terabeam.com/support/calculations/index.phpcalculations/index.php


Decibels: Do them in your headDecibels: Do them in your head

The 1,3,10 Rule for converting between The 1,3,10 Rule for converting between whole decibels and actual powers without a whole decibels and actual powers without a calculator!calculator!

dBdB IncreaseIncrease DecreaseDecrease

1 dB1 dB x 1.25x 1.25 x 0.8x 0.8

3 dB3 dB x2x2 x 0.5x 0.5

10 dB10 dB x10x10 x 0.1x 0.1


ExampleExample

35dB35dB = 30dB+3dB+3dB-1dB= 30dB+3dB+3dB-1dB

= 1000x2x2x0.8= 1000x2x2x0.8

=3200mW or 3.2W=3200mW or 3.2W Try it:Try it:

1.1. Convert 24dBm to _______mWConvert 24dBm to _______mW

2.2. Convert 0.5W to _______dBmConvert 0.5W to _______dBm

3.3. Convert 47dBm to ______WConvert 47dBm to ______W


To add or not to addTo add or not to add

In mW you just add and subtract normally.In mW you just add and subtract normally. In dBm you convert to mW then add then In dBm you convert to mW then add then

convert to dBm.convert to dBm. 37 dBm + 37 dBm=? dBm37 dBm + 37 dBm=? dBm


Q1Q1

2 dBd is equal to how many dBi?2 dBd is equal to how many dBi? 5 dBi5 dBi 4.41 dBi4.41 dBi 4.14 dBi4.14 dBi The value cannot be calculated.The value cannot be calculated. To convert any dBd value to dBi, simply add To convert any dBd value to dBi, simply add

2.14 to the dBd value. 2.14 to the dBd value.


Q2Q223 dBm is equal to how many mW?23 dBm is equal to how many mW? 200 mW200 mW 14 mW14 mW 20 mW20 mW 23 mW23 mW 400 mW 400 mW To convert to mW, first calculate how many 10s To convert to mW, first calculate how many 10s

and 3s are needed to add up to 23, which is 0 + 10 and 3s are needed to add up to 23, which is 0 + 10 + 10 + 3. To calculate the mW, you must multiply 1 + 10 + 3. To calculate the mW, you must multiply 1 × 10 × 10 × 2, which calculates to 200 mW. × 10 × 10 × 2, which calculates to 200 mW.


Q3Q3A wireless bridge is configured to transmit at A wireless bridge is configured to transmit at

100 mW. The antenna cable and connectors 100 mW. The antenna cable and connectors produce a 3 dB loss and are connected to a produce a 3 dB loss and are connected to a 16 dBi antenna. What is the EIRP?16 dBi antenna. What is the EIRP?

20 mW20 mW 30 dBm30 dBm 2,000 mW2,000 mW 36 dBm36 dBm 8 W 8 W


To reach 100 mW, you can use 10s and 2s and To reach 100 mW, you can use 10s and 2s and multiplication and division. multiplication and division.

Multiplying by two 10s will accomplish this. Multiplying by two 10s will accomplish this. This means that on the dBm side, you must add This means that on the dBm side, you must add

two 10s, which equals 20 dBm. two 10s, which equals 20 dBm. Then subtract the 3 dB of cable loss for a dBm of Then subtract the 3 dB of cable loss for a dBm of

17. 17. Since you subtracted 3 from the dBm side, you Since you subtracted 3 from the dBm side, you

must divide the 100 mW by 2, giving you a value must divide the 100 mW by 2, giving you a value of 50 mW. of 50 mW.

Now add in the 16 dBi by adding a 10 and two 3s Now add in the 16 dBi by adding a 10 and two 3s to the dBm column, giving a total dBm of 33. to the dBm column, giving a total dBm of 33.

Since you added a 10 and two 3s, you must Since you added a 10 and two 3s, you must multiply the mW column by 10 and two 2s, giving a multiply the mW column by 10 and two 2s, giving a total mW of 2,000, or 2 W. total mW of 2,000, or 2 W.


Q4Q4

Which of the following are valid calculations Which of the following are valid calculations when using the rule of 10s and 3s? (Choose when using the rule of 10s and 3s? (Choose all that apply.)all that apply.)

Multiply dBm by 3 and add 2 to mW.Multiply dBm by 3 and add 2 to mW. Add 10 to dBm and multiply mW by 10.Add 10 to dBm and multiply mW by 10. Add 3 to dBm and multiply mW by 3.Add 3 to dBm and multiply mW by 3. Subtract 10 from dBm and divide mW by 10.Subtract 10 from dBm and divide mW by 10. Divide dBm by 10 and subtract 10 from mW. Divide dBm by 10 and subtract 10 from mW.


The only valid calculations are as follows: The only valid calculations are as follows: Add 3 to dBm and multiply mW by 2.Add 3 to dBm and multiply mW by 2. Subtract 3 from dBm and divide mW by 2.Subtract 3 from dBm and divide mW by 2. Add 10 to dBm and multiply mW by 10.Add 10 to dBm and multiply mW by 10. Subtract 10 from dBm and divide mW by 10. Subtract 10 from dBm and divide mW by 10.


System Operating Margin (SOM)/ System Operating Margin (SOM)/ Link BudgetLink Budget

SOM is the calculation of the amount of RF SOM is the calculation of the amount of RF signal that is received minus the amount of signal that is received minus the amount of signal required by the receiver.signal required by the receiver.

The figure on next slide shows all the The figure on next slide shows all the components and their effects on the SOM, components and their effects on the SOM, and this is called and this is called receiver sensitivityreceiver sensitivity..

Manufacturers determine the receiver Manufacturers determine the receiver sensitivity for each speed supported by the sensitivity for each speed supported by the wireless card.wireless card.


Different speeds use different modulation Different speeds use different modulation techniques and encoding methods and techniques and encoding methods and some encoding methods are more some encoding methods are more susceptible to corruption. susceptible to corruption.

The manufacturers carries out tests to The manufacturers carries out tests to determine the least signal required by the determine the least signal required by the receiver to be acceptable as a proper signal.receiver to be acceptable as a proper signal.

They look at the figures above and below They look at the figures above and below the threshold. Then give the Rx of the card.the threshold. Then give the Rx of the card.

The lower No. the weaker the signal the The lower No. the weaker the signal the more reliable the card.more reliable the card.


1Mbps1Mbps -94 dBm-94 dBm

2 Mbps2 Mbps -93 dBm-93 dBm

5.5 Mbps5.5 Mbps -92 dBm-92 dBm






As you can see we are dealing with negative nos.Therefore, -71 dBm is the highest Rx


Typically, the faster the speed, the higher Typically, the faster the speed, the higher the receiver sensitivity.the receiver sensitivity.

Have you noticed that we are dealing with Have you noticed that we are dealing with negative nos., and so far we have been negative nos., and so far we have been working with positive dBm. working with positive dBm.

WHY?WHY?


Case 1Case 1

The Diagram below shows simple summary The Diagram below shows simple summary of gains and losses in an office.of gains and losses in an office.


Until now we have worked primarily with Until now we have worked primarily with calculating the IR and EIRP. calculating the IR and EIRP.

It is the effect of free space path loss that It is the effect of free space path loss that makes the values negative, as you will see makes the values negative, as you will see in the calculations based upon the earlier in the calculations based upon the earlier diagram.diagram.


The link budget is equal to the received The link budget is equal to the received signal minus the receive sensitivity. signal minus the receive sensitivity.

In this example, the received signal is the In this example, the received signal is the sum of all components, which issum of all components, which is

20 dBm + 5 dBi – 73.98 dB + 2.14 dBi = –46.84 dBm20 dBm + 5 dBi – 73.98 dB + 2.14 dBi = –46.84 dBm

If the receive sensitivity of the laptop’s radio If the receive sensitivity of the laptop’s radio is –71 dBm, then the link budget isis –71 dBm, then the link budget is

––46.84 dBm – (–71 dBm) = 24.16 dBm46.84 dBm – (–71 dBm) = 24.16 dBm


Case 2Case 2


Let’s look at the SOM of a point-to-point Let’s look at the SOM of a point-to-point wireless network, as seen in the Figurewireless network, as seen in the Figure . .

In this case, the two antennas are 10 In this case, the two antennas are 10 kilometers apart. kilometers apart.

In addition to the effects of the antennas and In addition to the effects of the antennas and cables, there are also lightning arrestors.cables, there are also lightning arrestors.

Assume that the receiver sensitivity is –80 Assume that the receiver sensitivity is –80 dBm. dBm.


In this configuration, the calculation for the link budget is as In this configuration, the calculation for the link budget is as follows:follows:

TransceiverTransceiver 10 dBm10 dBm 10' LMR 600 cable10' LMR 600 cable –.44 dB–.44 dB Lightning arrestorLightning arrestor –.1 dB–.1 dB 50' LMR 600 cable50' LMR 600 cable –2.21 dB–2.21 dB Parabolic antennaParabolic antenna +25 dBi+25 dBi FSPLFSPL –120 dB–120 dB Parabolic antennaParabolic antenna +25 dBi+25 dBi 50' LMR 600 cable50' LMR 600 cable –2.21 dB–2.21 dB Lightning arrestorLightning arrestor –.1 dB–.1 dB 10' LMR 600 cable10' LMR 600 cable –.44 dB–.44 dB Total signalTotal signal –65.5 dBm–65.5 dBm So the SOM isSo the SOM is ––65.5 dBm – (–80 dBm) = 14.5 dBm65.5 dBm – (–80 dBm) = 14.5 dBm


Fade MarginFade Margin Fade margin is a level of desired signal Fade margin is a level of desired signal

above what is required. Also called the above what is required. Also called the comfort zone.comfort zone.

If a receiver has a receive sensitivity of –80 If a receiver has a receive sensitivity of –80 dBm, then as long as the signal received is dBm, then as long as the signal received is greater than –80 dBm, the transmission will greater than –80 dBm, the transmission will be successful. be successful.

The problem is that the signal being The problem is that the signal being received fluctuates due to many outside received fluctuates due to many outside influences. influences.


In order to accommodate for the fluctuation, In order to accommodate for the fluctuation, it is a common practice to add 10 to 20 dBs it is a common practice to add 10 to 20 dBs to the receive sensitivity value. The to the receive sensitivity value. The additional value that is added is known as additional value that is added is known as the fade margin. the fade margin.


ExampleExample

Receiver has a sensitivity of –80 dBm and a signal Receiver has a sensitivity of –80 dBm and a signal is typically received at –76 dBm. Then under is typically received at –76 dBm. Then under normal circumstances, this communication is normal circumstances, this communication is successful. successful.

However, due to outside influences, the signal However, due to outside influences, the signal may fluctuate by ± 5 dBm. This means that most of may fluctuate by ± 5 dBm. This means that most of the time, the communication is successful, but on the time, the communication is successful, but on those occasions that the signal has fluctuated to –those occasions that the signal has fluctuated to –81 dBm, the communication will be unsuccessful. 81 dBm, the communication will be unsuccessful.


By adding a fade margin of 10 dBm, you are By adding a fade margin of 10 dBm, you are now stating that for your needs, the receive now stating that for your needs, the receive sensitivity is –70 dBm, and you will plan sensitivity is –70 dBm, and you will plan your network so that the received signal is your network so that the received signal is greater than –70 dBm. greater than –70 dBm.

If the received signal fluctuates, you have If the received signal fluctuates, you have already built in some padding, in this case already built in some padding, in this case 10 dBm. 10 dBm.


If you look back at the diagram and added a fade If you look back at the diagram and added a fade margin of 10 dBm to the receive sensitivity of –80 margin of 10 dBm to the receive sensitivity of –80 dBm, then the amount of signal required for the dBm, then the amount of signal required for the link would be –70 dBm. link would be –70 dBm.

Since the signal is calculated to be received at –Since the signal is calculated to be received at –65.5 dBm, you will have a successful 65.5 dBm, you will have a successful communication. communication.

However if you chose a fade margin of 15 dBm, However if you chose a fade margin of 15 dBm, the amount of signal required would be –65 dBm, the amount of signal required would be –65 dBm, and based upon the configuration in the diagram, and based upon the configuration in the diagram, you would not have enough signal to satisfy the you would not have enough signal to satisfy the link budget plus the 15 dBm fade margin.link budget plus the 15 dBm fade margin.


Conclusion of Fade MarginConclusion of Fade Margin

Since RF communications can be affected Since RF communications can be affected by many outside influences, it is common to by many outside influences, it is common to have a fade margin to provide a level of link have a fade margin to provide a level of link reliability. By increasing the fade margin, reliability. By increasing the fade margin, you are essentially increasing the reliability you are essentially increasing the reliability of the link.of the link.


Inverse Square LawInverse Square Law

Earlier we learned about the 6 dB rule, which Earlier we learned about the 6 dB rule, which states that a +6 dB change in signal will double the states that a +6 dB change in signal will double the usable distance of a signal and a –6 dB change in usable distance of a signal and a –6 dB change in signal will halve the usable distance of a signal.signal will halve the usable distance of a signal.

This rule and these numbers are actually based This rule and these numbers are actually based upon the Inverse Square Law, originally developed upon the Inverse Square Law, originally developed by Isaac Newton. This law states that the change by Isaac Newton. This law states that the change in power is equal to 1 divided by the square of the in power is equal to 1 divided by the square of the change in distance.change in distance.


What this means is that if you are receiving What this means is that if you are receiving a signal at a certain power level and a a signal at a certain power level and a certain distance (D) and you were to double certain distance (D) and you were to double the distance (2 × D), then the new power the distance (2 × D), then the new power level will change by 1 / (2 × D)^2. level will change by 1 / (2 × D)^2.

If at a distance of 1 feet (call this D) you If at a distance of 1 feet (call this D) you were receiving a signal of 4 mW, then at a were receiving a signal of 4 mW, then at a distance of 2 feet (2 × D) the power would distance of 2 feet (2 × D) the power would change by 1 / 2^2, which is 1/4. change by 1 / 2^2, which is 1/4.

So the power at 2 feet is 4 mW × 1/4, which So the power at 2 feet is 4 mW × 1/4, which is equal to 1 mW.is equal to 1 mW.


To see how this relates to the 6 dB rule, To see how this relates to the 6 dB rule, using the rule of 10s and 3s, consider that to using the rule of 10s and 3s, consider that to change from 4 mW to 1 mW, you would change from 4 mW to 1 mW, you would need to divide the mW column by 2 twice.need to divide the mW column by 2 twice.

This would require you to subtract 3 twice This would require you to subtract 3 twice from the dBm column, giving you a –6 dBm from the dBm column, giving you a –6 dBm change caused by the doubling of the change caused by the doubling of the distance of the signal.distance of the signal.

Dr. Tahseen Al-Doori Lesson 3 Radio Frequency Components, Measurements, and Mathematics.

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Transcript of Dr. Tahseen Al-Doori Lesson 3 Radio Frequency Components, Measurements, and Mathematics.