The fi rst thing you should know about the decibel (dB) is that it is a unit of comparison, not a unit of power. Therefore, it is used to represent a difference between two values. In other words, a dB is a relative expression and a measurement of change in power. In wire- less networking, decibels are often used either to compare the power of two transmitters or, more often, to compare the difference or loss between the EIRP output of a transmitter’s antenna and the amount of power received by the receiver’s antenna.
Decibel is derived from the term bel. Employees at Bell Telephone Laboratories needed a way to represent power losses on telephone lines as power ratios. They defi ned a bel as the ratio of 10 to 1 between the power of two sounds. Let us look at an example: An access point transmits data at 100 mW. Laptop1 receives the signal from the AP at a power level of 10 mW, and laptop2 receives the signal from the AP at a power level of 1 mW. The differ- ence between the signal from the access point (100 mW) to laptop1 (10 mW) is 100:10, or a 10:1 ratio, or 1 bel. The difference between the signal from laptop1 (10 mW) to laptop2 (1 mW) is also a 10:1 ratio, or 1 bel. So the power difference between the access point and laptop2 is 2 bels.
Bels can be looked at mathematically by using logarithms. Not everyone understands or remembers logarithms, so we will review them. First, we need to look at raising a number to a power. If you take 10 and raise it to the third power (103 = y), what you are actually doing is multiplying three 10s (10 × 10 × 10). If you do the math, you will calculate that y is equal to 1,000. So the solution is 103 = 1,000. When calculating logarithms, you change the formula to 10y = 1,000. Here you are trying to fi gure out what power 10 needs to be raised to in order to get to 1,000. You know in this example that the answer is 3. You can also write this equation as y = log10(1,000) or y = log101,000. So the complete equation is 3 = log10(1,000). Here are some examples of power and log formulas:
101 = 10 log10(10) = 1 102 = 100 log10(100) = 2 103 = 1,000 log10(1,000) = 3 104 = 10,000 log10(10,000) = 4
Now, let’s go back and calculate the bels from the access point to the laptop2 example by using logarithms. Remember that bels are used to calculate the ratio between two pow- ers. So let’s refer to the power of the access point as PAP and the power of laptop2 as PL2. So, the formula for this example would be y = log10(PAP/PL2). If you plug in the power val- ues, the formula becomes y = log10(100/1), or y = log10(100). So this equation is asking, 10 raised to what power equals 100? The answer is 2 bels (102 = 100).
OK, so this is supposed to be a section about decibels, but so far we have covered just bels. In certain environments, bels are not exact enough, which is why we use decibels
instead. A decibel is equal to 1/10 of a bel. To calculate decibels, all you need to do is multiply bels by 10. So the formulas for bels and decibels are as follows:
bels = log10(P1/P2)
decibels = 10 × log10(P1/P2)
Now let us go back and calculate the decibels for the example of the access point to laptop2. So the formula now is y = 10 × log10(PAP/PL2). If you plug in the power values, the formula becomes y = 10 × log10(100/1), or y = 10 × log10(100). So the answer is +20 deci- bels. +20 decibels is the equivalent of +2 bels.
You do not need to know how to calculate logarithms for the CWNA exam.
These examples are here only to give you some basic understanding of what they are and how to calculate them. Later in this chapter, you will learn how to calculate decibels without using logarithms.
Now that you have learned about decibels, you are probably still wondering why you cannot just work with milliwatts. You can if you want, but because power changes are cal- culated using logarithmic formulas, the differences between values can become extremely large and more diffi cult to deal with. It is easier to say that a 100 mW signal decreased by 70 decibels than to say that it decreased to 0.00001 milliwatts. Because of the scale of the numbers, you can see why decibels can be easier to work with.
Why Should You Use Decibels?
In Chapter 2, you learned that there are many behaviors that can adversely affect a wave.
One of the behaviors that you learned about was free space path loss.
If a 2.4 GHz access point is transmitting at 100 mW, and a laptop is 100 meters (0.1 kilome- ter) away from the access point, the laptop is receiving only about 0.000001 milliwatts of power. The difference between the numbers 100 and 0.000001 is so large that it doesn’t have much relevance to someone looking at it. Additionally, it would be easy for someone to accidentally leave out a zero when writing or typing 0.00001 (as we just did).
If you use the FSPL formula to calculate the decibel loss for this scenario, the formula would be
decibels = 32.4 + (20log10(2,400)) + (20log10(0.1))
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dBi
Earlier in this chapter, we compared an antenna to an isotropic radiator. Theoretically, an isotropic radiator can radiate an equal signal in all directions. An antenna cannot do this because of construction limitations. In other instances, you do not want an antenna to radiate in all directions because you want to focus the signal of the antenna in a particular direction. Whichever the case may be, it is important to be able to calculate the radiating power of the antenna so that you can determine how strong a signal is at a certain distance from the antenna. You may also want to compare the output of one antenna to that of another.
The gain, or increase, of power from an antenna when compared to what an isotropic radiator would generate is known as decibels isotropic (dBi). Another way of phrasing this is decibel gain referenced to an isotropic radiator or change in power relative to an antenna. Since antennas are measured in gain, not power, you can conclude that dBi is a relative measurement and not an absolute power measurement. dBi is simply a measure- ment of antenna gain. The dBi value is measured at the strongest point, or the focus point, of the antenna signal. Because antennas always focus their energy more in one direction than another, the dBi value of an antenna is always a positive gain and not a loss. There are, however, antennas with a dBi value of 0, which are often referred to as no-gain, or unity-gain, antennas.
A common antenna used on access points is the half-wave dipole antenna. The half- wave dipole antenna is a small, typically rubber-encased, general-purpose omnidirectional antenna. A 2.4 GHz half-wave dipole antenna has a dBi value of 2.14.
Any time you see dBi, think antenna gain.
dBd
The antenna industry uses two dB scales to describe the gain of antennas. The fi rst scale, which you just learned about, is dBi, which is used to describe the gain of an antenna rela- tive to a theoretical isotropic antenna. The other scale used to describe antenna gain is deci- bels dipole (dBd), or decibel gain relative to a dipole antenna. So a dBd value is the increase in gain of an antenna when it is compared to the signal of a dipole antenna. As you will learn in Chapter 4, dipole antennas are also omnidirectional antennas. Therefore, a dBd value is a measurement of omnidirectional antenna gain and not unidirectional antenna gain. Because dipole antennas are measured in gain, not power, you can also conclude that dBd is a relative measurement and not a power measurement.
The defi nition of dBd seems simple enough, but what happens when you want to com- pare two antennas and one is represented with dBi and the other with dBd? This is actually quite simple. A standard dipole antenna has a dBi value of 2.14. If an antenna has a value of 3 dBd, this means that it is 3 dB greater than a dipole antenna. Because the value of a
dipole antenna is 2.14 dBi, all you need to do is add 3 to 2.14. So a 3 dBd antenna is equal to a 5.14 dBi antenna.
Don’t forget that dB, dBi, and dBd are comparative, or relative, measure- ments and not units of power.
The Real Scoop on dBd
When working with 802.11 equipment, it is not often that you will have an antenna with a dBd value. 802.11 antennas typically are measured using dBi. On the rare occasion that you do run into an antenna measured with dBd, just add 2.14 to the dBd value and you will know the antenna’s dBi value.
dBm
Earlier when you read about bels and decibels, you learned that they measured differences or ratios between two signals. Regardless of the type of power that was being transmitted, all you really knew was that the one signal was greater or less than the other by a particu- lar number of bels or decibels. dBm also provides a comparison, but instead of compar- ing a signal to another signal, it is used to compare a signal to 1 milliwatt of power. dBm means decibels relative to 1 milliwatt. So, what you are doing is setting dBm to 0 (zero) and equating that to 1 milliwatt of power. Because dBm is a measurement that is compared to a known value, 1 milliwatt, it is actually a measure of absolute power. Because decibels (rela- tive) are referenced to 1 milliwatt (absolute), think of a dBm as an absolute assessment that measures change of power referenced to 1 milliwatt. You can now state that 0 dBm is equal to 1 milliwatt. Using the formula dBm = 10 × log10(PmW), you can determine that 100 mW of power is equal to +20 dBm.
If you happen to have the dBm value of a device and want to calculate the corresponding milliwatt value, you can do that too. The formula is PmW = 10(dBm ÷ 10).
Remember that 1 milliwatt is the reference point and that 0 dBm is equal to 1 mW. Any absolute power measurement of +dBm indicates amplitude greater than 1 mW. Any abso- lute power measurement of –dBm indicates amplitude less than 1 mW. For example, we stated earlier that the transmission amplitude of most 802.11 radios usually ranges from 1 mW to 100 mW. A transmission amplitude of 100 mW is equal to +20 dBm. Because of FSPL, received signals will always measure below 1 mW. A very strong received signal is
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It might seem a little ridiculous to have to deal with both milliwatts and dBm. If mil- liwatts are a valid measurement of power, why not just use them? Why do you have to, or want to, also use dBm? These are good questions that are asked often by students. One rea- son is simply that dBm absolute measurements are often easier to grasp than measurements in the millionths and billionths of a single milliwatt. Most 802.11 radios can interpret received signals from –30 dBm (1/1,000th of 1 mW) to as low as –100 dBm (1/10 of a bil- lionth of 1 mW). The human brain can grasp –100 dBm much easier than 0.0000000001 milliwatts. During a site survey, WLAN engineers will always determine coverage zones by recording the received signal strength in –dBm values.
Another very practical reason to use dBm can be shown using the FSPL formula again.
Following are two FSPL equations. The fi rst equation calculates the decibel loss of a 2.4 GHz signal at 100 meters (0.1 kilometer) from the RF source, and the second calculates the decibel loss of a 2.4 GHz signal at 200 meters (0.2 kilometer) from the RF source:
FSPL = 32.4 + (20log10(2,400)) + (20log10(0.1)) = 80.00422 dB FSPL = 32.4 + (20log10(2,400)) + (20log10(0.2)) = 86.02482 dB
In this example, by doubling the distance from the RF source, the signal decreased by about 6 dB. If you double the distance between the transmitter and the receiver, the received signal will decrease by 6 dB. No matter what numbers are chosen, if the distance is doubled, the decibel loss will be 6 dB. This rule also implies that if you increase the ampli- tude by 6 dB, the usable distance will double. This 6 dB rule is very useful for comparing cell sizes or estimating the coverage of a transmitter. The 6 dB rule is also useful for under- standing antenna gain, because every 6 dB of extra antenna gain will double the usable dis- tance of an RF signal. Remember, if you were working with milliwatts this rule would not be relevant. By converting milliwatts to dBm, you have a more practical way to compare signals.
Remember the 6 dB rule: +6 dB doubles the distance of the usable signal;
–6 dB halves the distance of the usable signal.
Using dBm also makes it easy to calculate the effects of antenna gain on a signal. If a transmitter generates a +20 dBm signal and the antenna adds 5 dBi of gain to the signal, then the power that is radiating from the antenna (EIRP) is equal to the sum of the two numbers, which is +25 dBm.