 Our general model of any wireless system is that we have a transmitter. We take some electrical current from, say, a computer, just want to transmit some data, and the antenna converts that electrical current into a wave, an electromagnetic wave. The signal that we're sending from A to B, and receive antenna takes that waveform and converts it back to electricity, which is then received by our receiving computer. So we care about the antennas, how they are designed, what are their characteristics, and another thing we'll go through today is look out the relationship between the antennas, the power of transmitting and receiving, and the distance. How far apart can we place our antennas, our transmitter and receiver, so that they can still communicate? The antennas. We said yesterday an ideal antenna is an isotropic antenna, where if we transmit our signal out of an isotropic antenna, it disperses equally in all directions. So we can say that we start with a power level that we transmit, and that power energy disperses in all directions. How do we measure power? What are the units? Watts, okay? Watts, remember? When we talk, we can talk about volts, but when we talk about communication systems, we'll usually talk about, use the units of watts. One watt, one megawatt, one microwatt, and so on, okay? So when I talk about a signal strength, the signal magnitude, the signal power, I mean measured in watts. So with an isotropic antenna, I transmit some power out of the antenna, and we say that we start with the transmit power, say Pt, some power we start with, and that energy disperses. And one factor that we know about is attenuation. As that signal travels across a distance, it will get weaker and weaker. And today we'll cover and see how much weaker. So if this is my transmitter, I transmit with some power level, say one watt. The energy comes out. If this is an isotropic antenna, the energy goes in all directions. And at some distance ahead, if I measure the power at that point, it will be less than one watt, because if it comes out at one watt, it gets weaker across distance, so it's going to be less than one watt. We want to see the relationship between what impact the antenna shapes have on the dispersion of the energy and the power, and also eventually how much weaker does the power get across some distance. We'll do that today. Isotropic, think of some ideal theoretical antenna. The antennas that we use actually concentrate some power in a particular direction. So they don't disperse the power equally. There may be some concentration of energy in one direction, so strong in one direction, but weak in some other direction. And we said there's omnidirectional antenna, which tries to be equal power dispersion in one horizontal plane, for example, but up and down in the vertical plane, it may be weaker. And more generally, a directional antenna, which tries to send the energy all in one direction and very little in the other directions, so that the signal goes much stronger in that one direction. Now, the first important thing we want to introduce today is how do we measure these directional antennas, an omnidirectional antenna, and how can we talk about how much greater or how strong the signal is? Well, everything is done relative to this ideal isotropic antenna. And the handout will use this extra handout. If you don't have one, there's a few copies lying around. Just a few pictures to try and demonstrate this concept of real antennas, which have some directionality versus the isotropic antenna. Of course, I cannot draw very well in 3D, so I'm just going to draw a 2D picture of our antenna. So imagine just looking at one plane, say a horizontal plane. Let's say I've got an isotropic antenna at this black dot and I transmit a signal with some power level called Pt. And let's write down and give it a number. In this handout, we just use variables, but on the board, let's say, for example, I just make up a value, I transmit a signal with some power level Pt equal to 4 watts as an example. So I think that's the power that I start with, 4 watts. If I use an isotropic antenna from all directions around that antenna, the signal goes and disperses equally. So if I had a device that could measure the power level, say, 1 meter away, I walked 1 meter away from the transmit antenna and I measure the received power, is it going to be greater or less than 4 watts? That's the first question. Greater, same or less than 4 watts? I measure at this point 1 meter away from the transmitter. It's going to be less than 4 watts, okay? Because we know, because of attenuation, if we start with 4 watts across some distance, the signal gets weaker. So remember that, it always will be less than 4 watts. How much? We don't know, but it will be less. Now, if I measure the received power 1 meter away in this direction, and let's make up a number, I measure it to be, say, PR to be 1 watt, okay? I measure it to be 1 watt. And then I go and measure 1 meter away in the opposite direction. What's the power level? It will also be 1 watt. In all of these positions, 1 meter away from our isotropic antenna, because an isotropic antenna disperses the power equally in all directions, if it's 1 watt, 1 meter away here, then 1 meter away here will also be 1 watt, and 1 watt here and so on. So if we take this distance of 1 meter away from the transmitter and measure, it will always be 1 watt. In this example, I'm not saying that in all cases, 1 meter away goes from 4 to 1. I'm just using these numbers as an example. If I measured the power 2 meters away, will it be less than equal to or greater than 1 watt? It'll be less than, okay? The further we go away, the weaker it gets. That's just attenuation. So isotropic equally in all directions. Let's say now I have a real antenna, which is not isotropic. It focuses the energy in one particular direction, and I buy this antenna, the blue one, and I put it in the same position as my isotropic antenna, the blue dot here. What this blue shape or the line shows us is that, or go back, what the circle shows us, if we take the received power and if it's 1 watt, then we plot a point on the circle. We get a point of the circle. What the blue one shows us is that if I measured at this point, I get a received power of 1 watt. If I measure, which may be, I don't know, 3 meters or 2 meters away, if I measure at this point on the blue line, I'm saying the received power is also 1 watt, and at this point 1 watt, and at all points that I measure the signal on that blue line, let's say we measure it to be 1 watt. The same with the circle. I'm saying at all points on that circle, if I measure the signal, if I get 1 watt, 1 watt received power. With isotropic, we get the circle. With my directional antenna, we notice that the power is concentrated in one direction, and in fact in the opposite direction, this way, it's in fact weaker. So let's analyze that a bit more. So we're saying that say at this point, the received power would be 1 watt. The same as if we use an isotropic antenna and measured at this point. What if using my blue antenna, I measure the power here? What's its value? Anyone want to guess or say something about the value? If I measure at this red dot, the received power from my blue directional antenna, what can you say about the power level? Not 1 watt. Let's make notes. This was my isotropic, isotropic. In both cases, we start with the same transmit power, 4 watts. I'm saying 1 meter away with isotropic in any direction. We measure to be 1 watt. With my directional antenna, my example antenna, the transmit power again is 4 watts. I just made up that number. And what we're saying this blue line represents that every position on that blue line, the received power is again 1 watt. And of course this is on a geographical map that is the distance between the transmitter and this point is greater than from this point to here. So what can we say about Px? It's less than 4 watts and it's more than 1 watt. We cannot say any more the exact value. We don't know yet. But of course it will be less than the transmit power because again our signal attenuates across distance. It's got to be less than 4 watts. But in this direction, we notice if we start at 4, we've said that this point further away, we have 1 watt. That means if we measure Px because it goes down, it must be greater than 1 watt. Px is greater than 1 watt and less than 4 watts. Somewhere in between. I don't know the value. Let's give it a number. Let's say we did measure the value and found Px to be 2 watts. Now compare from that point, if I use an isotropic antenna and measure the signal at this point, what power level? 1 watt. From our isotropic, if I measure the signal at this point, I get 1 watt. If I use my new blue directional antenna, what power level at this same point? I've said Px is 2 watts. How much stronger? Twice as strong. So we can say using my directional antenna, the signal strength some distance away is twice as strong. We've got 2 watts divided by the original 1 watt. So this was for isotropic 1 meter away and this was for my directional antenna. 1 meter away. The 2 power levels measured. We can say the gain of using my isotropic antenna relative to using an... Sorry, wrong. The gain of using my directional antenna relative to using ideal isotropic antenna is 2. Our signal is 2 times stronger. In that direction only, only in this direction, if I looked at the opposite direction, it would be different. This is antenna gain and it's common characteristic when you see an antenna or purchase an antenna, one of the properties in the specification will be the gain, which says that a gain of 2 says that this specific directional antenna in this one direction will have a power 2 times as strong as if you used an isotropic antenna. What if using my directional antenna, I measure the power here? What can we say about say the PX at this point? Any observations? If we measure with the blue one at this point, what would the power level be? It would be less than 1. That's the thing we observe because this blue line says if we transmit here at 4, at this point we'd get 1 watt. That's the definition of this blue line. Therefore further away, it would be less than 1 watt. So if we took at this point, then with the directional antenna, let's say it was less than 1, it was half a watt, 0.5. Then the gain would be 0.5 divided by 1. That would be 0.5. In fact, it's not a gain, it's a loss. A gain of 0.5 is a loss by a factor of 2 with halved the power. That is with a directional antenna in one specific direction we may have a high gain but in other directions we may have low gains which is always the case. With antennas when you look at the details of them you'll often see plots, some pictures that look like this that try and illustrate that in one direction the gain is high but in other directions it's low. They're drawn slightly different than this but try and capture the same information. And another characteristic we often are interested just in the largest gain. So with this blue antenna think of it, if I point it in this direction I get high gain, a gain of 2. But if I point it, point it in this direction and measure in that direction I get a low gain. So behind it it's not good but in front it's good. A common property that you will see with antennas is what is the highest gain that this antenna can achieve which is in the direction where we get the highest value in this example in this direction. So with our blue antenna I can calculate with this example the gain is 2. Times stronger than an isotropic antenna. We can also express gain not just as a factor but using decibels. Remember decibels? Decibels is 10 log one power level divided by another power level. Well, we have one power level divided by the other. The other is the power for an isotropic antenna. So in decibels we get 10 log base 10 of 2 which is log of 2 is 0.3 times 10 is 3 dB. And the notation we use with antenna gains is that my directional antenna is two times stronger than using an ideal isotropic antenna. Or in decibels 3 dB and to indicate this 3 dB is relative to an isotropic antenna we add an i, lowercase i here, and we get dbi. What it means is so 3 dbi means 3 dB greater than using an isotropic antenna. And that's a common characteristic of antennas. Be equal to Px? No. Px the one that we calculated which gave us a gain of 2 2 watts was only for this specific direction. Because this blue antenna is designed to focus the energy in one direction. So you can imagine that most of the energy goes in this direction. Some of it goes in this direction. Very little goes in this direction. That's what this blue shape is showing. We have a high gain in this direction. Slightly lower gain in this direction and then gets lower and lower and it's quite a small gain in this direction. Like less than one. So it will vary depending upon the location. But often we care just about what is the highest? What's the best we can do? From this website and I didn't get to show you yesterday the internet wasn't working on this page eventually and I've scrolled down a lot but just quickly it lists some product that this company sells, some antennas. So this is one of those antennas like on the access point these small dipole antennas. There's a mount here and it's just that stick style antenna. It shows where's my pointer? It captures based on the design of this antenna information about the gain in different directions. That's what these two plots do. We're not explaining how they are interpreted but similar to mine but in a slightly different style it looks at the azimuth and elevations. So in one plane the horizontal plane and in the vertical plane how much gain in particular directions. So it's equal or approximately equal in all directions on the horizontal plane but if you go up and down these are angles we see that it's strong say in this area but as you go higher it gets very weak. So this is some way to capture the gain of this specific antenna. The greatest gain is given here as part of the spec. 2.2 dBi So if you buy this antenna the best you can achieve is 2.2 dBi if you point it in the right direction which means 2.2 dB better than using an isotropic antenna. A bit less than the one we used in our example and there are other antennas just scroll through. Similar let's find a 5 dBi sector antenna. 5 dBi is the maximum gain of this antenna so you mount it on a wall for example and it points out in one specific direction so you can think on the horizontal plane if the antenna is here it's strong in this direction but weak in the reverse direction. So that's what these diagrams try to capture. But maximum 5.5 dBi and just quickly a ceiling mount antenna a wall mount antenna 6 dBi slightly different patterns so depending on what area you want to cover you choose the antenna which will give the signal strongest in that area. If you want to cover I don't know why but if you want a wireless access point to cover this straight down here but not in the corners so if you use your laptop in this area you can access but here the signal is very weak then you'd buy an antenna and mount it here and you'd choose one which has a pattern such that the signal goes strongest in these areas and it's weak in these areas so depending on what coverage you want choose the antenna pattern 8 dBi 10 dBi so different style antennas 13 dBi and so on so they list some of their products so each antenna we can characterize and calculate or determine its gain let's ignore the physics of parabolic antennas we'll come back to them in a moment well how can we calculate the gain alright we can do measurements that is if I have an isotropic antenna and measure one meter away and then take my real antenna and measure one meter away then I can calculate the gain so we can do that can we calculate it some way without measuring well yes here's a general formula the gain G of an antenna is 4 times pi times by the effective area of that antenna divided by the lambda the wavelength squared so first the wavelength the gain depends upon the signal that we're sending what's the equation for wavelength very important one lambda wavelength speed of light divided by the frequency so remember the relationship the speed of light fixed 3 by 10 to the 8 meters per second divided by a frequency of our signal so if I know the frequency of the signal that I'm using let's say 5 GHz is the signal I'm using I can determine the wavelength lambda and use that in this equation so the gain of an antenna depends upon the signal we're transmitting with that antenna the frequency or the wavelength of that signal and it also depends upon the effective area what is the effective area that's related to the physical size generally the bigger the antenna the bigger the effective area but it differs amongst different antenna designs whether it's a dipole antenna whether it's a a sector or patch antenna or whether it's a parabolic dish antenna they have different effective areas for this course we will not explain or look any more details about the effective area some questions I may say the effective area of this antenna is X I would give that to you or I would say that the effective area of a parabolic antenna is half of its physical area as an example what's a parabolic antenna one of those dish shaped antennas like in here if we look at a sidecar of it like if you have satellite TV the receiving antenna is a parabolic dish antenna what's the approximate area of a parabolic antenna how would you determine it approximately if you look you know the antennas I'm talking about the dish shaped antennas if you look at one looking down on it what's it look like so here's my dish antenna it's curved like that if you look looking down on it what shape is it it's a circle from that dimension it looks like a circle so what's the size or the area of that parabolic dish it's about the size or the area of a circle so if we know the size of the antenna let's say it has a radius of one meter which is quite big radius of one meter then we can calculate the area approximate area of the antenna pi r squared and then we'd say okay once we know the physical area well the effective area is say half of the physical area what is this multiplier in fact differs in some cases but as an example a half of the physical area once we know the effective area we know AE if we know the wavelength and we're sending with this antenna lambda we can calculate the gain of that antenna G where the gain is in is the absolute value it's not in DBI if we want it in DBI we need to then convert this equation gives us this value not the value in DBI think of different units or different scales a quick example and we'll use this example later so let's say we have a parabolic a dish antenna so I have a dish and it's one meter diameter what's the area of that dish approximately how would I calculate the area of this parabolic dish antenna what is it calculate area of a circle hmm no not 2 pi pi r squared what's the radius well our diameter is 1 meter the radius is half a meter a half squared so there's our approximate area of this parabolic dish antenna a 1 meter which is what about this size antenna a dish shaped pi square meters and let's make an assumption and say that the effective area is half of that I'd have to give you that in an exam this assumption but let's say the effective area A E is a half of the real area and then we get you do the maths pi on 8 meters squared so with this 1 meter the effective area is about pi on 8 square meters pi 3.14 divided by 8 so a bit less than half a square meter now we send a signal using this antenna let's say we know the frequency of that signal it's 5 gigahertz find the gain of our antenna quickly try and find the answer some very simple maths we know the frequency of the effective area find the gain of course using this equation 4 times pi times the effective area divided by lambda squared what's our wavelength anyone calculated the wavelength yet remember frequency of 5 gigahertz speed of light 300 million meters per second 3 by 10 to the 8 giga 10 to the power of 9 and you can calculate 0.06 meters our wavelength and now just plug in the values into our gain equation we know the effective area we know the wavelength find g and so we can move along because I calculated in the previous class I'll give the answer it's about 1371 1370 point something you can use your calculator to solve that it's 4 times pi times our effective area of pi over 8 divided by 0.06 squared so as long as you get the units correct meters meters squared for our area then you get the right answer there no units what that tells us is that my dish antenna of a parabolic dish of 1 meter in diameter if I measure the signal when I use this dish antenna and then measure it again at the same distance away using an isotropic antenna using my dish antenna the power is 1371 times stronger than if using isotropic antenna so that's the gain 1371 times stronger convert it to dbi so this is the absolute value not in decibels, now convert it to dbi and with a calculator I've done it before and it is about 31 dbi simply log of log of our gain multiplied by 10 most antennas in practice you will see the gain expressed in dbi but we can convert it back to the absolute value if needed remember decibels is not a unit it's a logarithmic scale that is it compares one power level to another the general formula 10 log power 1 divided by power 2 a ratio of two power levels well in our case our ratio is 1371 1371 times larger than using isotropic so 31 dbi larger than isotropic to indicate that we mean larger than an isotropic antenna we include the I meaning isotropic any questions before we move on to the next concept so when you go out next to buy antenna you'll look on the spec and you'll see and notice which one's stronger based upon the gain and it will be a part of the spec saying 2 dbi, 5 dbi or whatever to get more details about where is the signal strong for that particular antenna you need to look at those plots that show is it strong in elevation in azimuth or which direction are the antennas and how strong they are or how we can measure their strength particularly the gain let's now look at how signals propagate through the air we know that they attenuate we know that when we transmit they get weaker across distance shortly we'll see an equation to determine in some conditions how to calculate how much weaker they get because it's it's important to know if I start with a transmit power of 4 watts and I transmit for 1 meter what's the received power going to be is it going to be 1 watt or something else we'll see a way to determine that shortly but first let's look at some general characteristics of different frequency signals how do signals propagate while the signals well it depends upon the frequency that we use the first classification we see we divide into three different types of propagation if we're sending signals with frequencies below 2 megahertz we talk about what's called ground wave propagation the signal follows the contour of the earth these plots show those concepts better if we go together those two slides the top plot shows of course the earth, it's curved if we look at the entire earth if we have a transmitter and receiver if we're sending signals less than 2 megahertz then the signal follows the contour of the earth so it can go around the earth in theory I cannot remember the physics of why that happens but if you go to high school physics and read the textbook and talk about what causes both ground wave and the second one sky wave propagation of how signals of different frequencies bounce off things reflection refraction and so on how they are affected by different molecules water and so on that's the direction that they take it's interesting to read but we're not going to cover it we just need to understand well, given different frequencies what are the characteristics of the propagation ground wave propagation follow around the earth sky wave propagation if we're using between 2 and 30 megahertz effectively bounces off the ionosphere and the earth so we send a signal up it bounces back down to earth and we can use this technique to send the signal around the earth from Thailand to somewhere in Europe we don't have a direct line between them a line of sight we'll see in the last one but using the first two techniques if we use the right frequencies we can have that signal go around the curvature of the earth the last set is anything above around 30 megahertz we have what's called line of sight LOS propagation the signal goes straight which means to be able to receive it we need no obstructions between it if we're using line of sight propagation if I have an antenna here in Thailand and a receiver in Europe they will not be able to communicate because there's not line of sight between them there's the curvature of the earth in that case but with the first two approaches we would be able to communicate turns out most of the systems we deal with today use line of sight propagation greater than 30 megahertz there's some special cases that use these you think of what's called short wave radio you can get radio receivers that will pick up radio stations from anywhere in the world so from Europe from the US they use short wave radio which follows the contour of the earth to be received by your radio it's one case that you may have come across so depending upon the frequency of our signal the signal propagates in different manners this table captures a more detailed range of frequencies and some typical uses of signals at those frequencies some example applications and the propagation characteristics and it's divided by these bands that we introduced yesterday like low frequency, ultra high frequency infrared and visible light let's just look at a few selected examples infrared your remote control for your TV you are sitting in your lounge room TV is in your lounge room you're sitting in your bedroom you want to change the channel can you? TV is in one room, you're in another room can you change the channel with your remote control? unlikely because your remote control uses infrared most normal ones do frequencies ranging as listed here up to terahertz and the characteristics of signals at these frequencies is that A, they use line of sight propagation they need to be direct and B, that the signal comes out of your remote control and it hits a wall and the wall has materials that obstruct that signal it doesn't pass through the wall the light does not pass through walls as a result the signal cannot be received at someone on the other side of the wall you have your laptop in your bedroom at home and you have the wireless access pointer router in another room can you use the wireless internet? yes, I think some of you would have done it I have an access point here maybe I'm out in the corridor there's a wall separating me my wireless transmitter, the laptop and the wireless receiver can they communicate? in many cases yes because wireless LAN uses a different frequency range it's in the order of 2.4 GHz which falls in here ultra high frequency again uses line of sight propagation but the characteristics of those lower frequencies is such that the signal will go through the wall it hits the materials in the wall and is attenuated by the wall it gets weaker but some of the energy passes through so depending upon the frequencies we can pass through obstacles in different manners and that makes the selection of the frequency important depending upon your application satellite TV going back to your dish antenna at home you receive a signal from a satellite up in space the signal most likely will not go through the building you usually need your antenna you receive antenna to be pointed at the satellite if you're on the wrong side of the building and you do not have a line of sight to that satellite you probably will not be able to receive satellite TV in some cases in some systems with satellite TV which uses frequencies in the order of super high frequency range or band in the order of 10 gigahertz frequencies in this range are attenuated by the atmosphere and water vapor for example so when it's raining the signal from the satellite comes down to your home and the receiver the signal needs to go through the rain the water in the atmosphere but when it hits that water the signal gets weaker it attenuates so if it's raining a lot and the signal goes through it may be that the signal received is very very weak and on your TV you may see some disruption or some poor quality signal poor quality image because the satellite signal at those frequencies is attenuated by water vapor in that case so depending upon the frequency we need to consider the environment where we need to send the signal and how far we want to send to determine what's a good frequency to use so this just gives a set of examples of different systems the last thing we want to do today the main thing is come back to this issue I transmit a signal we know it attenuates the question is how much weaker I had an example at the start that said I transmitted with 4 watts across a distance of 1 meter I received with 1 watt well I made that number up I'd like to be able to determine over a distance of 1 meter how much weaker is the received signal compared to the transmit signal we know our signal loses power across distance how much power does it lose well there are models mathematical models to determine that it's called path loss across some path I lose power and the one we'll cover is called free space loss or free space path loss so it talks about it gives us a model for determining how much power we lose across some distance the signal attenuates over distance it gets weaker there is one impairment and the only one we will cover in this course there are other impairments like I mentioned with satellite if the signal passes through water it attenuates or it passes through tries to pass through a wall the signal gets much weaker and we may or may not be able to receive on the other side depends upon the frequencies and the materials that it needs to pass through and multiple copies of that signal arrive at the receiver that creates problems we're not going to explain or go into any detail of these three let's focus on how much power do we lose between transmitter and receiver and let's give a mathematical model for determining how much power we lose it's called the free space loss model or a free space path loss model there's another name the free space part assumes that we're operating out in space in free space well maybe more accurately in a vacuum there is no other transmissions assuming there's no other transmissions there's no obstructions between transmitter and receiver if I start with some power level how much power do I lose across some distance D this equation gives us that relationship so it's an ideal model it's not true inside this building and in most practical cases but it's a good approximation or a good way to start with determining path loss let's look at the different variables we start with some power level we transmit with some power level Pt we transmit a signal across some distance D and the signal has some wavelength lambda and from that some frequency there are two antennas involved in the transmission the transmit antenna and the receive antenna and both have some gain Gt and Gr and we receive some power so the signal receive has power Pr so all these factors come together if we know all but one we can determine that one so this assumes there are no obstacles between transmitter and receiver and we're operating in a vacuum no other transmissions and perfect antennas so just determined by their gain let's go through an example to illustrate how we can use this mathematical model of path loss let's try and first illustrate a scenario we have a transmitter and receiver and we want to determine some characteristics of the system what if we start with we have our transmitter an antenna and we have our receiver an antenna and they're separated by some distance D so let's note D the distance between transmit and receive is D meters we're going to send a signal which has some wavelength and frequency so the wavelength lambda will need to know or the frequency from the frequency we can determine the wavelength the free space free space loss model tells us the relationship between these two factors and if we start we transmit a signal at the power level PT if our transmit antenna has some gain GT our signal comes out of the transmit antenna we start with PT the transmit antenna introduces some gain increases the signal the signal comes out of the transmit antenna and it gets weaker as it goes across the D meters then it's received by the receive antenna which also has some gain I'll write that in a moment which increases the antenna the resulting power level is the receive power PR so this equation relates all those factors together so receive antenna has a gain GR and we receive with the power PR let's give some numbers so we can do a quick calculation let's say I have a system of one kilometer we have a transmit power of one watt the gains of our two antennas are the same as what we calculated in the previous example what do we get so that one meter parabolic dish antenna we calculated a gain of 1371 GT and in this example only let's say both antennas are the same one can be a big antenna one can be very small but in this example they are the same antennas and therefore the same gain GT GR 1371 and we had in the previous example a wavelength of 0.06 meters meters that is there's our scenario if I want a transmitter signal across one kilometer using these two antennas and the gains of those two antennas using a wavelength of that signal of 0.06 meters a frequency of 5 GHz if I transmit with power one watt my signal comes out it gets weaker at what power is it received with what is PR find the answer find PR and you use the free space loss model equation and this is the example in the handouts that has used this equation to solve this question it's very easy because you have the equation you just need to rearrange it so you can calculate PR because all the other variables are known if you rearrange if you could look at the slide you get PR is the transmit power PT times by the two gains GT GR times by lambda squared divide by what do we get at the end 4 pi D all squared all I've done I take this equation and rearrange it to find PR and a quick rearrangement gives us this transmit power times by the two gains times by the wavelength squared divided by 4 times pi times the distance all squared anyone have an answer the hardest thing now is just to make sure that you use the right units in our case PT is in watts this is one watt GT is 1371 just substitute GR is also 1371 lambda is 0.06 meters 4 times pi times what's D it's 1000 meters because if we're using the units of meters here with everything else then we need to make sure D is in meters so don't use D equal to 1 do D equal to 1000 and with a calculator solve that anyone have the answer yet it's about 42.8 microwatts what it tells us you don't have to do the calculation now in an exam you'll have your calculator you can solve that easily what it tells us is that if I start with a power of 1 watt I start with if this is the magnitude of my signal 1 watt with these two antennas and this 5 gigahertz signal I transmit a signal out of well I start with 1 watt the antenna introduces some gain so I think that magnifies the amplitude of my signal then when it comes out of the transmit antenna the signal attenuates across distance across the distance getting weaker and weaker it's received by the receive antenna which introduces some gain which multiplies it by 1371 the received the resulting value is the receive power and in this case the received power is quite small compared to the transmit power 42.8 microwatts so across this one kilometer we ended up with 42 microwatts how can we use this this tells us if I need to buy a receive receiver, the receiving equipment usually a characteristic of every receiver is the minimum power at which it can successfully receive same as your ears what's the minimum audio signal that your ears can make sense of well we had an example a couple of weeks ago where if I talk very quietly you cannot hear me because the signal you receive is very weak it's too low for your ears to make sense of same as our receiver electronics at our receiver device we can use this knowledge to work out well what's the minimum power that that receiver needs to be able to receive because we know how much power is lost across this distance of one kilometer so the example was a simple application of this free space path loss model which tells us how much power do we lose if we're operating in free space in a vacuum no obstacles perfect antennas in real life there are obstacles there is noise we don't have perfect antennas, perfect devices there are other models that people have developed to model how much power we lose in different scenarios for example inside a city or for TV transmission across the city or inside a building so there are different mathematical models to determine approximately how much power you lose if you start with some transmit power and transmit a signal across some distance with particular antennas and frequency of the signal but those mathematical models the ones that I list but don't give the equations are more complex than this and they make more assumptions so we will not go through them but just be aware that there are other models but using this we can predict approximately how far we can send our signals if I knew the gain of my antenna in my laptop the transmit gain and the gain of the antenna on this access point GR if I knew those values and I can find them out I think when you buy this access point it gives you the specification of the gain it's about 2.2 DBI for those antennas for the laptop I think you could find out the gain of the antennas so if I know GT and GR I know the length I use with wireless LAN because I know the frequency is 2.4 GHz therefore for Wi-Fi I can determine the wavelength so I can determine lambda for this access point I can determine the transmit power it's again a part of the specification of the device I can look it up and I think from memory it's normally one of them is 100 milliwatts the transmit power of my access point 100 milliwatts so if I know GT, GR, lambda transmit power of my access point is 100 milliwatts and another characteristic of devices is the minimum receive power I can look up and find the receive power needed for my laptop to successfully receive a signal so if I know PR then in theory what I can use this equation for is to say okay I know PR, the PR needed I know GT, GR, lambda and PT I can find the maximum distance I can separate the laptop and the access point by such that they still communicate that is I can rearrange and find D the distance which tells me I don't know if the value is 1000 meters then it tells me if I separate the access point and laptop by 1000 meters in free space not inside a building but outside with absolutely no obstacles no interference then they should be able to communicate so we can use that for such calculations it doesn't apply inside a building because there are obstacles and there's other interference questions on the free space loss model we need to apply it in different scenarios I will not ask you to remember the model the equation in an exam I give you that equation but you'll often see questions like here's the scenario and you need to understand this is PT, this is GT, GR this is lambda and I know the distance I need to find PR for example usually I give you a question which is here's the equation here's some description from that description you can find all but one of the variables then you just rearrange to solve for that one missing variable last 10 minutes it's finished with something slightly different some notation some new notation remember our general equation for gain the gain in dB we calculated as 10 log base 10 of one power level divided by another when we spoke about gain we said P out divided by P in let's just write it as one power level P1 generally divided by P2 when we have a ratio between two power levels P1 divided by P2 in dB by taking the logarithm in base 10 and multiplying by 10 for example here we had the ratio of two power levels two watts relative to one watt gives us a ratio of two or expressed in dB three dB but in this case the lower the power level of two watts was relative to the power level if we used isotropic antenna so the notation we used in the end was saying that if I have two watts with my directional antenna gives a gain of two which is equivalent to a gain of three dBi relative to the isotropic antenna this last letter here the I means three decibels relative to using isotropic antenna we can use that same concept with other factors let's say for example P2 sorry is one watt and P1 is 100 watts what's the gain from P1 to P2 it's a factor of 100 or in dB the absolute factor is 100 100 divided by 1 easy in dB it is 20 dB log of 100 is 2 times by 10 is 20 dB that's our normal we say P1 is 20 dB larger than P2 another way to write P1 20 dB it's 20 dB so we get this new notation dBW P1 is 20 dB larger than one watt the ratio between P1 and P2 or P1 and one watt so think of this as the reference power level is 100 or 20 dB so another way to write 100 watts is simply 20 dBW where the W means the other power level is one watt so now we're using dB to express an actual power level my input power is 100 watts is the same as saying my input power is 20 dBW so now we're using dBW as a different notation what if I had a power level P1 of 10 kilowatts what is its value in dBW I have a power level of 10 kilowatts compared to one watt how many dB 40 dBW 10 kilowatts remember is 10,000 watts 10,000 watts relative to one watt and that's what this W means in dBW is a factor of 10,000 log of 10,000 is 4 times by 10 40 dBW so 10 kilowatts is equal to 40 dBW so this new notation is relative to some reference power level in this case the reference is one watt and it's commonly used in communication systems and other systems another reference, which is commonly used is not one watt but one milliwatt what if P2 was one milliwatt and P1 was for example 100 milliwatts relative to one milliwatt how many dB is P1 larger relative to one milliwatt let's make it simple how many times larger is P1 than P2 100 times that is relative to one milliwatt a power level of 100 milliwatts this is an M is 100 times expressed in dB is 100 is a factor 100 is 20 dB log of 100 times 10 so we can also write here 100 milliwatts is 20 dBMW 20 dB relative to one milliwatt and in fact it's common not to write dBMW but to omit the W and just write dBM so when you see dBMW don't think of dB relative to one meter think of dB relative to one milliwatt that's the more common notation okay this will test you if I have a power level of 60 dBM how many watts so I say that my system takes an input power of 60 dBM how many watts if you can solve it and tell me the answer try and find the answer one megawatt no someone said one megawatt someone's had one watt 1000 watts correct remember dBM is a power level relative to one milliwatt so 60 dBM I'm not trying to do the calculations here but 60 dBM 60 dBM was 10 log something 60 dB anyone 10 log of one million is 6 times by 10 is 60 so 60 dB is equal to a factor of one million which means that 60 dBM is a power level which is one million times larger than one milliwatt that's how we interpret that 60 dB relative to one milliwatt 60 dBM is a factor of one million because log of one million is 6 times by 10 is 60 so watt is one million times larger than one milliwatt in watts is 1000 watts because there are 1000 milliwatts in one watt and therefore one million milliwatts in 1000 watts going to get confusing 60 dBM is the same as saying 1000 watts which is the same as saying how many dBW 30 dBW because dBW is relative to one watt 1000 watts relative to one watt is a factor of 1000 convert to dB log of 1000 is 3 times by 10 is 30 so these three values are exactly the same 1000 watts equals 30 dBW equals 60 dBM in communication systems we often you see all of those units used dBM for decibels relative to a milliwatt dBW and simply watts or milliwatts or whatever prefix we want so be aware that be aware of what they mean especially dBM and dBW and how to convert between them because often in questions and in devices when you buy a device it will be expressed in dBM not in watts or milliwatts if you look up the specifications of wireless LAN access point or your laptop or even your mobile phone the receiving transmit power will most likely be expressed in dBM in one of the handouts at the front of your notes the handout title definitions and concepts on that last page there's the definition of dBM and dBW so at the start of your handouts you'll see that written down