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CWNP CWNA – Components and Measurements of RF Part 3

The 6 dB Rule Now there is this idea of the six-DB rule. They call it the inverse square law. So let’s think about it. Let me put my antenna at the top this time. Let’s think about the power. We know that we have our best power where the antenna begins, and that power is going to go down as we move away from the antenna. So basically, the inverse square law says that if I double the distance from the source to wherever I am, my total DBMS…

1. The 6 dB Rule

Now there is this idea of the six-DB rule. They call it the inverse square law. So let’s think about it. Let me put my antenna at the top this time. Let’s think about the power. We know that we have our best power where the antenna begins, and that power is going to go down as we move away from the antenna.

So basically, the inverse square law says that if I double the distance from the source to wherever I am, my total DBMS are going to decrease by about six. Now again, you figure out what that double is. If I measured it while I was here, 10 feet away, and then measured it again when I was 20 feet away, that would tell me that I would decrease the signal strength by six DB. And as I move further away, right, we can keep using the rule of six to get a good idea of when we’d be too far away due to the loss that we wouldn’t have the signal anymore.

Now we could double the distance between the transmitter and the receiver. Well, I guess that’s basically what I said. If you double it, then the received signal decreases by six DBS, and we can measure that. But if I said, “Okay, let’s add six DBS to the signal strength,” then that means I’m going to double the distance that I can use this particular antenna for.

So we use it to compare the cell sizes. And again, the idea of cell sizes when we’re talking about coverage inside an office is where I was putting an access point and basically mapping out how far that signal can be used at a usable rate. And so that circle that I created is called a cell. And then I can decide, okay, well, maybe I can put another cell here and get more coverage, hopefully even some overlapping coverage. But that’s part of why we use it: to figure out where the access points need to be, or B, so we can compare cell sizes and get a good idea of coverage. It’s also a way for us to understand the antenna gain, because 60 dB of extra antenna gain will always double the usable distance of an RF signal. Now, how could this become even more relevant?

And here’s a hint about another office building. In many implementations of wireless, we will purposely lower the amount of power or gain on an access point. And, as I mentioned, we may have another access point, and we do want some overlapping and possibly another access point.

And I won’t draw too many of these, but we purposely don’t use the full power because the hope is that, let’s say that one of the access points goes down, then we can automatically increase the power. The six DBs of power are needed so that we can try to COVID an area that lost coverage because its access point went down. And we do that through a variety of different tools. When you get into the different equipment, often people talk about having some sort of controller that controls the access points, can boost coverage when needed, etc. And again, that’s just part of our design.

1. RF Mathematics

So I’m sure that you’re all thinking, “Ken, we didn’t come here to become mathematicians or physicists.” and I get that. And the logarithmic functions do look a little bit scary. So rather than going through understanding or reviewing your math skills, there’s a simple set of rules that we can use that you’re going to see in just a minute. And here’s how much mathematical skill you need to have. The question is, can you add and subtract using the numbers three and ten? And can you do multiplication and division using the numbers two and ten? If you can do that, then you can get this information very close to an accurate scale. It is more of an approximation, but it’s close enough for you to be able to do the calculations that we were just talking about. So it’s not technically accurate, but it’ll be close enough to help you understand where, again, you would put those access points. So we’re going to take a look at some examples of what we’re going to eventually call the rules of three and ten.

1. Rule of 10s and 3s Part2

So before I show you the math and take you through some story problems, if you would, let’s just talk about the rules of three and ten. So right now, let’s say you have an access point, and that access point is configured to transmit 100 milliwatts, as you see over here.

So it’s going to transmit its power at 100 milliwatts. And the antenna is rated for three DBI of passive gain. So what does that mean? That means that I’m looking at this directional antenna, right? The antenna will passively add three DBS. Now, that just means that if I’m going to add three DBS plus three DBS, what do we say if we do that with three DBS? The milliwatts will then be multiplied by two.

So because the antenna added to the power, we would multiply that by two, and then we would be talking about 200 milliwatts for the power. Now, with this rule, as we said before, if we increase by three, we double. We have it if we subtract three. So, consider my access point. Now, let’s make a new one. And this one here says that the transmitter, which is the AC power, is sending 100 milliwatts to the antenna. I should have just drawn that as an antenna. However, for whatever reason, the cable is losing power as it transmits electricity, resulting in three DBs of loss. So even though we said, “Okay, okay,” we’re going to send out 100 milliwatts, but the cable is reducing the DBS. So what’s actually going to be sent out is one-half or 50 milliwatts of power.

1. Math Examples (eNotes) Part1

Alright, I’m going to take you through a couple of examples of using the rules of tens and threes. And so what I’m going to do is start off with two columns, one of which is going to be DBMS and the other of which is going to be milliwatts.

And next to the DBMS, we’re going to talk about adding or subtracting the DBS. That’s kind of what we’ve already talked about. And we know that when we add or subtract, it will either double or subtract by half, depending on whether we are adding or subtracting by tens or by twos.

So it’s supposed to be a division sign. Just keep track of which side you do the multiplication and division on and which side you just add or subtract from the DBS. All right? So now what we’re going to do is write down the numbers that we use over here, the gains of three or ten DBMS. The rule of three and ten applies once more. And over here, we’re either multiplying by two or dividing by two, or multiplying by ten or dividing by ten. So now I’ve got this little chart that helps me remember what the mathematics are.

So, if you were doing anything, say, a test question, or just doing this calculation out on the road, which most of us wouldn’t because we’ll have vendor information already done for us, we’ll have other tools that can collect this information, and we won’t have to do this. But it’s useful, I guess, to understand what happens when we set that up.

So anyway, now that we have a table, what we’re going to do is know that if we add or subtract a three on the left, or a ten, but we’ll just talk about the three, that then we’re going to be doubling over here. That’s why I’ve got the three at the top and the two at the top. We’ll be doubling up. If we subtract three, we’re going to divide by two. But, as you can see, the idea is to connect the three to the two over here. And if we add ten DBMS, then we’re either adding or subtracting ten DBMS, and then we’re either doing multiplication or division by ten. So the idea here is to have a table to help you remember what it is that you want to do. And remember, we started with zero DBMS equaling one milliwatt.

So that’s where we started. All right? So now what we’re going to do is start at one milliwatt and double the power three times in what we’re going to look at. So in addition to calculating the new power level in milliwatts, I should also be able to calculate the DBMS because this, like any math equation, can go in both directions. So if I decide to multiply the milliwatts by two, my new answer is that I now have two milliwatts. So in this particular case, I said, “What’s going to happen if I double the milliwatts?” What’s it going to do for me on the DBMS? that I would calculate. So now that I’ve done that, we know that if I’m doubling the milliwatts and adding more power, then I’m adding three to it.

So I’d be adding a plus three, and that would give me a total of three DBMS. I hope that seems simple enough. If I double it again, going from two to four, then I’m going to double or add, in this case, three again. So I would have six DBMS. So we could keep doing that calculation. What if I said it the other way? What if I said, “Let’s add three DBMS”? Right now, I’m at nine. Adding three makes me multiply by two. So then I would be at eight milliwatts. And so that, I hope, seems fairly easy, but unfortunately, it doesn’t always get that easy. But I’m trying to give you some examples of how this would happen for us. So, let’s say we have a wireless device that generates 100 milliwatts of signal, and the bridge, in this case a wireless bridge, connects to an antenna. So a wireless bridge, again, is just an access point that is helping us bridge the gap, say, from one building to another building, right?

So we’re not actually accepting users as much as we’re just having our wired network connect to another wired network. But that connection is going to be wireless all the way through. So anyway, that bridge is going to generate 100 milliwatts. I’m going to have to make another column here pretty soon in another set of columns to do this. And that bridge is connected to an antenna through a cable that creates a 3-DB loss. So, obviously, connecting to that cable introduces a minus three DB. All right? So I know how many milliwatts I’m sending. I’m already out three DBS due to the cable absorbing some of that energy.

So there’s that loss. So, what happens if we divide by three? When we decrease by three, then we’re going to divide by two, which is a normal thing to consider, and that’s something you have to look at. But at that point, I’d be able to tell you that the power is 50 milliwatts. But now let’s say that this bridge, the antenna, is adding ten DBS because of the way in which it’s concentrating that signal. So I have a net of seven, but the cable to the antenna has a three-dB loss. Furthermore, the antenna is passively adding ten DBS. So in this case, what you want to do is calculate what the IR in the EIRP is going to be. Maybe I could have done that picture a little bit better. Let me see if I can kind of recreate that without connecting the buildings, like I was talking about with the bridge. So the alternating current is basically sending 100 milliwatts.

The cable is doing minus three DB. And when it arrives at that antenna, it adds ten DBS. Okay, hopefully you’re all with me here, right? So we’re talking about this device being a little more focused or directional with its antenna. So the first step is to determine if we’re going to be using tens or twos and multiplication or division, and then you could again figure out what it would take. So let me put up my new table. So here are my milliwatts.

And remember, we started at one milliwatt compared to the DBMS, which is zero. And you can still see the other chart with the threes and tens and the pluses and minuses versus the rest of it. Maybe it’s just a good idea to get into the habit of making these charts so you know where to start. So that is where we began. Now we have to start off with the fact that we need to know if we’re doing things by tens or twos and by multiplication or division, and we’ll start with the milliwatts. What I do know is that we’re starting with 100 milliwatts. So that means I would have to multiply this by ten and then multiply it by ten again to be able to get 100 milliwatts. All right? So when we’re multiplying by ten, that means that we’re going to be adding by ten. So I’m going to add plus ten, followed by another plus ten.

And so now I know that I’m at 20 DBMS, because we started off with that when we looked at the number of milliwatts. Maybe I’ll put 100 milliwatts here so you can forget that’s over there. Now, if the cable is subtracting three DBS, I’m going to do minus three over here. That leaves me with 17 DBS. And when I subtract by three, I then have to do what? I have to divide by two. So now I do the division by two, and I’m left with 50 milliwatts. All right, that’s pretty drastic. I realise that what’s happening sounds very drastic, I realize, of what’s happening. So, now that we’ve gotten to that point, we know that the antenna adds ten DBS. So, if I multiply by ten, I get 27 DBMS DBM. There we go. And if I’m adding by ten, then I’m multiplying by ten. So by multiplying by ten, I’m now at 500 milliwatts. So, based on all of the information about the components that make up this wireless unit, I’ve been able to predict what the effective strength of that signal coming out of that antenna will be.

1. Math Examples (eNotes) Part2

All right, in our next setup, we’re going to go a little more complicated than you’ve seen so far. And so let’s draw the diagram here. So I’ve got my transmitter that’s sending out 50 milliwatts of power. And again, the signal loss from the cable to the antenna—we call it the IR, but I just keep calling it the antenna—is doing a minor DB loss coming through.

And from there, we can deduce that the access point is employing an antenna that will add plus five DBS. Okay? So I see effectively what the DBS are going to be, so we can get a sense of what we’re doing. And so the first thing we have to do is try to convert our channel. So let’s remember what we had. We had that column of DBS, and we had the columns of milliwatts, multiplication, and division. Then there’s addition and subtraction over here.

And it was about the three and ten to the two and ten at this point. And we know when we start, zero DB is equal to one milliwatt. So, now we’re going to try to figure out when the last time we gave you numbers was. By the way, that worked out really easily mathematically. So we have the signal losses and the signal gains from the antenna. And so I’m going to start off, as you saw here first, by just trying to draw this example here. And what I’m looking at here is that in the DBM column, well, first of all, we start off by multiplying or figuring out what the 50 milliwatts is going to be.

So what can I do to be able to figure it out because, you know, last time we went from one to 100, it was easy because what do we do? We multiply by ten. So let’s just say we multiply it by ten. So then, if I did that, I’d be at ten milliwatts. And when I multiply it by ten, then the DVS are going to become ten, right? because I’m just adding, in this case, ten. And then what if I multiply that by ten again? Now I’m at 100 milliwatts. Well, being at 100 milliwatts, I’ve got a little bit of a problem because I’m only sending 50. But if I did that, then I’d be adding ten, and I’d be at 20 DB’s. The good news is that I can divide this by two. That gives me 50 milliwatts. Cool. I’m at the number that’s been provided. If I divide by 2, then I have to subtract by 3. So now I’m at 17 milliwatts, or, I’m sorry, DBS. Let me get the right column and the right name. So now I’m at the starting point here, right? Call that step number one. I’ve made it there. So it was basically an easy way to get to that initial setup.

Again, I have another problem. I’m subtracting my DB loss and adding my DB loss, and they’re not using the nice, easy numbers that we had from the previous example. So, how do I get rid of just one DB? I mean, I know I could say, “Oh, let’s just do minus one.” But if I subtract one, I’m then at 16. And I don’t have any rule of three and ten that helps me with that, do I? So I have to figure out how to get to page 16. And so what I’m going to do is basically go do some more math genius work. I’m going to subtract ten DBS, leaving me at seven. If I subtract, then I have to divide by ten. So it leaves me at five milliwatts. Okay, neither one of those is the number we want. We want to just subtract one. But what’s really cool is that I can add three many times, and nine plus seven will get me to that number, 16 DB, from which I wanted to subtract one. So if I add three times, then I multiply this by two, so it becomes ten. Another multiplication, which becomes 20.

Another two-digit multiplication yields 40 milliwatts. I hope you saw the example of how I’m trying to set that up here. Okay, now we have the problem of adding five DBS. So again, we could do a similar type of step, knowing what it would take to add five. I want to get to the number 21 DBS. And so, if you can think about it, we could add ten. Add ten, and we would be right there, equal to 36. And then we need to subtract enough so that we get to 21. Let me do a little quick math here. -21, so I need to subtract 21 or 15. I’m sorry, I have to subtract 15 decibels to get to that number. And fortunately, three times five would be 15.

So I subtract three times. You’ll notice I’m running out of room. I should have planned this a little bit better. So what do I do if I start off here plus ten? So plus ten means that I’m multiplying this by ten. So now I’m at 400 milliwatts. The next plus ten is another multiplication of ten. So I’m at 4000. Now that I’m at 4000, I’m going to subtract three. Subtracting three means I’m going to divide by two. So I’d be at the year 2000. Subtract another three again, and I’ll be at 1000. Subtract three again, and I’ll be at 500. Hey, we’re almost done. Another one, right? Another three. I have it again. 250. Make one more subtraction, one more having. Finally, a response of 125 milliwatts, for a total of 21 DB. Okay, remember, it’s not the most accurate way of doing this mathematics, but it’s certainly something that’s important for us in trying to determine things like the coverage area again.

1. Math Examples (eNotes) Part3

All right, I promise I’m going to torch you with only one more example, and let’s see if I can make better use of my board here. So I’ve got this transmitter sending out 30 milliwatts of power. And in this particular case, what we’re doing is getting an access point that is providing coverage, let’s say, to an area of a warehouse through a directional antenna. So that means we’re going to have a little bit more or a lot more passive gain from that antenna. So in that case, the cable itself is going to subtract three DBS of power. And when we get to that antenna, I’ll make it look a little more like a dish. How’s that? because it’s going to be directional and add, in this case, 20 dB.

So we’re getting off to a pretty good start. Now, what we’re looking for here is trying again to calculate the IR and EIRP values that are going to be out there. And one of the things that’s really kind of sad, and I hate to say this, is that it’s sometimes hard to do the calculations by using tens and threes. You saw how tricky it was last time by figuring out how many tens to add and how many threes to subtract. And so sometimes you just can’t do this by using ten or two. and this is one of those cases. So you’re not going to be able to set the milliwatts and DBM values to be equal, but you can still calculate the milliwatt values by using the information that we had before. So again, I’m going to go back to my tables, which are the DBMS and the milliwatts. Again, we have the times and divide two and ten, as well as the plus and minus three and ten. And I mean, we could basically start with the idea.

I mean, we’ve always started with zero DBMS equaling one milliwatt. So instead of creating that kind of template, we’re going to start off by saying, “Look, we know we’re starting with 30 milliwatts, all right?” So why couldn’t I do this in a way that made sense? I mean, how many tens would I have to add, multiply by, or increase to be able to do this type of math? It just gets a little tricky. So here we’re just going to say in the DBM column, “unknown.” So even though we’re still not going to know what the actual DBM value is, we can still do some of the necessary mathematics that we’d have to do. So one of the first ones is that we know we are going to subtract three DBS from the unknown. So that will become essentially unknown minus three. And I know that if I’m subtracting three, I’m still going to divide by two.

So I’m down to 15 milliwatts. Now, the next thing is that we’re adding 20 DBS. So now if I think about that, if I add ten, then what I’m going to be left with is the unknown at seven. But because I added ten, I know that I’m going to multiply by ten over here and come up to 150. And, well, I have 20. So then I’m going to add ten more to the unknown, which makes whatever I started with in DBMS still unknown. But I know that it’s going to be basically a plus 17 when I’m done with it, because we’re at plus seven. Plus seven. And again, I’m going to multiply by ten. And so there, I’m seeing what my milliwatts are going to be. Oh, not 15,000! I didn’t multiply by ten very well. We know what that’s going to be. We just don’t really know what the starting DBS were. But you see, that was still a solution that made things work. I mean, if I had started with zero DB and one milliwatt, I might have had a harder time getting from one milliwatt to zero DB and one milliwatt.

I mean, you can imagine if I were to start at one milliwatt, which is equal to zero DBS, then I would have to figure out how to get from one to 30 using the rules that we’ve seen. I could add a bunch of threes, but I would still not get the right mill wattage. I could add a bunch of tens, because that’d be 21, but 31 is still not enough, right? I can’t then subtract from that point. And so that’s why we started off with an unknown DBM, because there was no easy way with this rule to get to that number. 30 milliwatts. I mean, imagine we got somewhere close along the way, but we only have ten thousand threes to work with over there. So even though I said it may be a little more complex, in reality, it wasn’t really that bad, was it?

1. Noise Floor

Now, let’s talk about this concept of what we call the noise floor. The noise floor is the ambient or background level of radio energy on a specific channel. Now, it could be because another transmitter is using the same channel, or it could be caused by those devices that emit radio frequency but not for a purpose, like a no transmitter, like a microwave oven, or some other form of noise.

The reason this is important to us is because we have to have a measurement of what that noise floor is to see if it’s going to be basically a distraction from the actual transmitter sending its signal. Maybe distraction is not the right word. An interferer. And we have to ask the question: Is there more in the noise floor than the strength of the signal I’m sending? And if that’s the case, chances are the signal will never reach the receiver.

1. SNR

You’ve probably heard of this concept, signal to noise ratio. And what we do is we look at that ratio to come up with how good a quality we have of an actual transmission, if you will. Or the radio frequency.

So as An Example we Say if A Radio Receives A signal of -85 DBMS so there’s that WiFi signal Right Up There and It’s -85 and I Know That Sounds Bad to Say -85 but you’ll Learn More About that as we get into some of the Other parts of Radio frequency and the Noise Floor Is Measured at-100 Of The DBMS what we do is We Look At The Difference between The Received Signal and The Background Noise and the Difference between those Is what -15 DBM if I Did that right in Math yes I Think so if I Subtract another 15 from 85I Get To -100 and so what We Would say then is that the signal to Noise ratio is 15 decibels which gives us an idea of how it’s going To Affect the Overall quality Of The WiFi signal.

Many of you understood this idea of RSSI before you ever got into this business of WiFi because that was something you were always seeing, right? The received signal strength indicator really is talking about the sensitivity or the received sensitivity to the power level of the RF signal that we need, at a minimum, to be able to successfully hear and receive the transmission. Perhaps another way to put it is if you were at a concert, say a rock concert or something similar, and it was extremely loud, as we expect them to be. I think that’s part of what we pay for: hearing loss at these concerts. But I would have to say, at what volume of speech would you have to speak for me to be able to hear you over the noise floor of the rock concert? In other words, whatever that is, whatever that minimum amount of yelling is, tells me everything I need to know about the signal, your speech.

And that’s what we’re doing with RSSI. We’re trying to figure out what the minimum power level is that the receiver can have to be able to process the actual information. And so that’s what the RSSI is: a measurement. I mean, you may be on your computer, whatever it is, and you go to connect to a hotspot somewhere, and you notice that the one you’re trying to connect to has like one little bar. Remember, those bars are really just telling you the bare minimum that needs to be present in order to use that data stream coming from the antenna or the transmitter. And so we look at those bars as a comparison. Again, it’s another ratio. It’s another comparison of your computer saying, “This is the minimum I need to be able to hear.” I go to a lot of places, including businesses that have hotspots and all the different offices, and there are some that show up on my list of access points. They have no bars, but they’re still there. That means my computer is hearing enough to identify that as an access point, but its signal isn’t anywhere close to the minimum that it needs.

When we look at the example of the RSSI and we’re talking about an antenna, remember that distance is an important factor for us, right. The strength of that signal is going to get worse and worse as distance goes by or goes away. So, when we look at some of the original access points or frequencies that we’re giving the US, such as 800 and 211 A or G, we might not always get 54 megabits per second. Because I need to do that, the bare minimum is 79 DBMS.

And that means I might have to be really close to the antenna to be able to get that kind of strength. If I’m further away, so far away, let’s say that I’m way over here, at -91, DBMS, I might be lucky to get nine to six megabits per second. So what’s happening is that it’s harder to receive because I’m not at my maximum level. And so your throughput actually goes down as you increase your distance away.

Now, suppose you add some sort of interference to that, say, my microwave oven. Well, when I first grew up with them, they were called radar ranges, and they had knobs instead of push buttons, so that’s what I’m drawing. You could also think of it as a TV, but because it’s a microwave, it’s providing some of that interference, right, that noise floor stuff.

And that noise floor is also going to take away from the DBMS that I receive. So I could be very close enough to get, let’s say, 48 megabits per second. But because of that ground floor or that noise floor coming at me, I might actually only be able to get 36 megabits per second. I hope you can see how the mathematics we’ve been doing helps us understand where we should place the antennas to get the best signal out to the most people while maintaining high-quality communications. You.

1. Section Review

Alright, so in this module, we talked about the components of RF communications. We looked at the units of power and comparison, took you through a lot of RF mathematics, and showed you how some of it can be very easy to do. Although not completely accurate, the rule of tens and threes can still get you close.

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