 In the previous lecture we introduced a model for wireless transmission, in fact if we go back that we have a signal that we want to transmit from transmitter to receiver and a simple model is we transmit an electrical signal with some power level, some strength. If you think of the sine wave as our signal, then the amplitude of that sine wave is the power. So that's the signal strength, how large it is, that's Pt, we denote that power as. But we use antennas to convert that electrical signal to radio waves or electromagnetic waves that propagate through the air. And we're talking about antennas and we arrived at some description of the antenna gain. We have the basic or the reference antenna called an isotropic antenna that when we transmit the energy comes out of that antenna and goes in all directions equally. Let's think of that as the perfect antenna. But in practice we use directional antennas even though we may be very close to an isotropic antenna and the power is concentrated in a particular direction. So instead of spreading equally in all directions the power will be strong in one direction, weaker in another direction. And we talked about that if we measure in a particular direction our directional antenna versus the isotropic antenna we can compare them and we can say that the directional antenna has some gain compared to the isotropic antenna. So we talked about that concept and it's a key characteristic of antennas. The antenna gain usually specified in the direction where it's strongest. So the gain changes in different locations for a particular antenna but in that direction where the signal is strongest we'll see a speck of that antenna is the antenna gain. Measured in dB usually decibels. Decibels and the I indicates the decibels of our antenna relative to using an isotropic antenna. That's why we write it as DBI. We say we're comparing ours relative to some reference isotropic antenna. And we went through an example where we looked at two different points for our blue directional antenna and this was a made up example for an antenna where we set up the red point, point X if we used our black isotropic antenna the signal strength received would be 10 milliwatts anywhere on the black circle 10 milliwatts. If I use my blue directional antenna the signal strength received let's say we measure to be 70 milliwatts. So at that one point our directional antenna is 7 times stronger than the isotropic antenna and that gives us the gain. A gain of 7 or in dB 8.45 dBi. Just the conversion of logarithm times by 10. And we could think for my blue directional antenna this is a part of the speck for that antenna. When I go looking to buy one I see this antenna has a gain of 8.45 dBi. We'll see how we'll use that later. But in fact the antenna in different directions has different gains. So we looked at the point behind the antenna at point Y. On the black circle the measured received power would be 10 milliwatts for the isotropic antenna but with our blue directional antenna on that same point PY let's say we measured it to be 2 milliwatts then our gain is 0.2. It's in fact a loss. The signal strength of our antenna compared to an isotropic antenna is less than the isotropic antenna 2 divided by 10 0.2 or minus 7 dBi. And if we measure to other points 1 meter away we could determine the gain. So usually for an antenna we list at least the maximum gain like in the direction with the maximum signal strength and sometimes we'll see pictures that show the gain in different directions called antenna patterns. And I'll show you a few examples of them where Cisco is a company that makes computer networking equipment and they make and sell some antennas and the reason I'm going to their web page is they have a nice web page that describes what are antennas especially related to Wi-Fi. So they have this guide on antennas and of importance for us they list the specs of their antennas. So I'll just show you some examples and I've just scrolled down to the actual specs maybe I'm at the wrong point. So they show some of the antennas that they sell and some of the specifications for them. So this first one is called a dipole antenna. Antennas have different shapes, shapes and sizes and the shape and size impacts upon the maximum gain and also the direction where the gain is strongest. So this dipole antenna is one of the stick antennas stuck on the access point on the wall. It has two dipole antennas. It has a maximum gain of 2.2 dBi. So that's typical for those access point antennas and if we scroll down a bit we see that that antenna the maximum gain is 2.2 dBi but in different directions it would have a different gain and the way that the specs capture that is via these two plots here. It's hard to draw in 3D so we draw two different plots one for each of the different planes. So the azimuth plane is the direction if we go on the horizontal plane around us. Elevation plane is up and down. So I think that if we have this antenna and we look in front of it to the left to the right behind and we measure the gain at points around it then this red plot shows us approximately in all directions going around that antenna the signal strength or the gain is about the same. We'll see some different ones later. So the gain we're not going to ask you to read these in an exam or a quiz but just to explain antenna gain this is showing that the gain in all directions all 360 degrees around that antenna is about the same. But if you look up and down from that antenna if you have the antenna here and you look direct in front versus up the way to interpret this blue plot is that direct in front is this 0 degrees here as we go up to maybe 30 degrees the antenna gain directly in front is about the same as 30 degrees up. But as we go up to say 60 degrees at this point if you measure at the same distance away the gain will be less the way that it's coming in. And if you measure directly above that antenna the gain will be very small. That's what this plot shows. So directly below the antenna at this point indicates that the gain is very small. This shows the gain in two dimensions on two different plots if you combine it what sort of shape do you get if you try and draw this as three dimensions and maybe you have it on your slides. A donut. You can imagine that in all directions around it's the same but up in that direction is about the same but if you go directly above it it's very weak so it sort of creates a hole just above it and just below it and it sort of becomes a donut type shape if you combine them. So that's the characteristics of a typical antenna on an access point. Most antennas are designed to work at a specific range of frequencies so this one is for 2.4 GHz. The typical Wi-Fi frequencies it's a Wi-Fi antenna and there may be other characteristics. Let's look at some more. Just another dipole antenna let's find some different ones different shape antenna, a monopole different design same gain, maximum gain of 2.2 dBi but the shape and it's hard to see they've superimposed the red and the blue on the one plot but the shape is slightly different in terms of the radiation pattern it's not necessarily a donut type shape it's in one particular direction it's a bit stronger than behind that one's hard to see with a single plot we'll find another one a 5 dBi sector antenna larger maximum gain so the shape of this antenna the sector antenna implies that it's you stick it in a location and it tries to cover a particular sector say of a circle rather than covering all 360 degrees maybe it covers 60 or 120 degrees of that circle with a strong signal and the other parts of weak signal and if we look at the antenna pattern on the azimuth plane we can think directly in front strong signal, high gain and maybe across these 120 degrees the signal is strong but if you measure behind the antenna here the gain is much lower so behind the signal will be weak designed to concentrate the power in a particular sector of our circle and the elevation is slightly different in front sorry, in front and then if you follow up and around you will get weak as you go up and down similar to our dipole so antennas have different shapes different designs to try to cover different areas a sector antenna is commonly used in mobile phone base stations there's an antenna that points and covering these 120 degrees of the city and then another sector antenna for another 120 degrees for example a couple more, that's a different shape let's go down a 6 DBI wall mount antenna similarly you stick it on the wall and it tries to cover a particular direction again tries to concentrate narrowly in one direction so if we stick this wall mount antenna on the wall here we could select the antenna such that it will try and cover where everyone is sitting it doesn't need to propagate a signal out that direction because no one sits over there in the room so we could choose an antenna to cover the area we want to cover and if we go up at a larger antenna 8.5 DBI different type 10 DBI antenna and I think one 12 DBI antenna essentially all directions around about the same gain but very focused in this direction that is if you go up a little bit the signal will be very weak if you go down a little bit the signal will be weak maybe 15-20 degrees the signal will be very strong there's a very high gain and you can use such antennas to cover a large distance you point this antenna at the similar antenna at the other location and as long as they are aligned then they should be able to communicate across a large distance they need to be aligned because if they're not aligned they're not pointing at each other the signal strength may not be large enough to be able to communicate so the more concentrated their energy is the higher the directionality of that antenna the more you need to align it to point to the receiver so that they can communicate and I think that's all a couple of others 14 DBI and I just scroll down to a couple more back to a dipole this is 3.5 DBI the only difference mainly this is designed for a frequency of about 5 GHz 5.1 to 5.8 GHz what is that frequency range commonly used for? about 5 GHz anyone? what do you use it for? we use it some of you may use it sometimes maybe not so often but maybe your device supports it it's another Wi-Fi frequency Wi-Fi is commonly very common in the 2.4 GHz range but there's another frequency band of about 5 GHz so if you've got a new phone or especially an access point this one doesn't but a newer access point that will allow you to support either 2.4 or 5 it has different characteristics maybe the practical benefits of 5 GHz is there's less people using that frequency and less interference but sometimes less range it depends on your wireless device it will support both so just some examples of antenna patterns and real antennas and a few more on the slides just the 3D and also the antenna pattern plots any questions on antennas? so we looked at the gain and we calculated in our example the gain it was say 70 mW divided by 10 mW the problem with this approach is for me to know the gain of my blue antenna I need to use my antenna and also use an isotropic antenna and measure the signal strength at the same location what we would like is to be able to predict the gain before I build it this requires measurements to know the gain a designer of the antenna wants to be able to design one and predict what would the gain be especially in different directions so this approach is not practical to find the gain when someone designs an antenna because it involves it being built and compared to an isotropic antenna it turns out there is a mathematical relationship between the gain and the effective area of an antenna and that's given by this equation we'll explain effective area in the moment but it's related to the physical area of the antenna so the gain is equal to 4 pi times by the effective area of the antenna something to do with the size of the antenna divided by the wavelength squared so the gain depends upon the size of the antenna and the frequency that we use in the signal being transmitted by that antenna if you increase the size does the gain go up or down with all other conditions the same increase the size of the antenna put your hands up if the gain goes up increase the size does the gain go up or down hands up for up hands up for down if the size goes up the area is going to go up so the effective area we'll explain a little bit more in a moment but the effective area is related to the how much area that antenna component covers so it depends upon the size so generally a good rule to remember if the antenna size goes up and G will go up the bigger the antenna the bigger the gain what if the frequency goes up we transmit a signal with a higher frequency what happens to the gain for example we saw with Wi-Fi there's 2.4 GHz and 5 GHz if we change from 2.4 up to 5 GHz with the same sized antenna will the gain go up or down frequency up what happens to the gain hands up for up frequency up gain some uncertain hands anyone have an answer remember frequency and wavelength are inversely proportional wavelength lambda equals the speed of light divided by the frequency so if frequency goes up wavelength goes down if wavelength lambda goes down we divide by a smaller number G will go up higher frequency higher gain if all the other conditions are the same lambda is the signal wavelength so if we know the signal frequency we can find the wavelength what about the effective area what does that mean for me is what we denote as the effective area it's related to the physical size but antennas we saw have many different shapes so sometimes it's hard to measure the physical size of the actual antenna component so we don't have an easy equation to calculate the effective area it differs so we need to know something about the internals of the antenna design to know the effective area but we can approximate for some antennas a parabolic dish antenna I think we showed in a previous lecture those like satellite receiving antennas they're a dish shaped maybe if you have satellite TV or satellite internet or you have seen the receivers the big dish shaped receivers the shape is a parabolic antenna if you look at that dish then the area is about it's approximately the area of a circle it's circular shaped but it dips in the middle but if you look front on the area is about that of a circle so the physical area of a parabolic antenna is approximately pi r squared if we have a dish which is one meter in diameter the radius is 50 centimetres the area is about pi times 50 or 0.5 squared in terms of meter squared that's the physical area the effective area it depends actually on the design the components and how it's built as to what the effective area is but commonly it's about half of the physical area in an exam I may tell you I may say assume the effective area is 0.5 times the physical area but I need to tell you that so it may differ on different antennas we may use that in an example shortly so if we know the physical area we can often determine the effective area and then from that if we know the signal frequency we can determine the gain of that antenna and that's useful to know in our subsequent analysis we will do a couple of calculations towards the end today so that's about antennas the next thing is about how does our signal travel between transmit antenna and receive antenna how does it propagate and then how much power do we lose we'll talk about those two things how does a signal propagate if I transmit a signal let's say I turned off the microphone and I talk we can think the signal goes it spreads out and propagates almost directly but in different directions towards your ears well it turns out there are different ways at which signals propagate especially when we transmit across long distances at some of the lower frequencies some which we which we may not see so often in this course but are important to mention the way that a signal moves depends upon the frequency of the signals and it depends upon the obstacles in the way or nearby whether it will pass through different obstacles and the way that it reflects off different obstacles so there are three main propagation models two on this slide ground waves, sky wave and on the next slide we'll see line of sight and the first two we'll mention quickly but we'll not see very common in this course are especially relevant when we're transmitting a long distance thousands of kilometres a wireless signal if we're sending a signal with a frequency below 2 MHz so under 2 MHz it turns out when we transmit the signal the signal due to the magnetic field of the earth changes speed there's some pressure on the signal that changes the speed and also the impacts of the atmosphere or ionosphere causes that signal to effectively bend around the curvature of the earth what that means or what this picture is trying to show the black line is the earth we have two antennas that transmit and receive antenna let's say several thousand kilometres away from each other normally if we try to send a signal straight through from one to another it would be obstructed by the earth we cannot go through the earth the signal will not propagate very well but if we use below 2 MHz the signal bends around the earth it follows the curvature of the earth meaning that even if there are obstacles in the way such as the earth itself the signal can still be propagated to the receiver ground wave propagation allows us to communicate it across long distances and used in AM radio similar but for frequencies from 2 up to 30 MHz is sky wave propagation it allows us to cover long distances but there's different characteristics here the signal is really transmitted up and it hits the ionosphere and the nature of the ionosphere is that the frequency of those 2 to 30 MHz the signals bounce off, they reflect and they come down to earth and bounce back up and keep going and again allows us to transmit across a very long distance really covering around the earth and this is commonly used in international radio stations short wave radio sometimes it's called you can pick up radio stations from Europe maybe from America because the signal propagates around in this reflection type mode in our data communications like Wi-Fi mobile phone systems and others we'll see with data links usually we use higher frequencies than 30 MHz so these 2 don't apply mainly for radio communications like AM or short wave radio so what does apply for higher than 30 MHz what we call line of sight the transmit and receive antenna must be able to see each other by seeing imagine you stand at the transmit antenna and if you had perfect eyesight you should be able to see the receive antenna in particular the antennas cannot be spread so far such that the curvature of the earth means that the earth is an obstacle in between them if we bring the antennas around they'll be obstructed by the earth so line of sight is the common model that we will use it doesn't mean that we can't have no obstructions it just means that the signal effectively goes straight line of sight communications it doesn't curve around the earth so with Wi-Fi we consider it line of sight in this mode even though we don't have to physically see the receiver there can be a wall but the signal goes straight and that's the mode we will see commonly there are other aspects on how the signal propagates whether it's obstructed by water by different temperatures and so on so some signals cannot be successfully received at different times of the day at night or during the day because they are impacted by temperature by the atmosphere what we want to concentrate on now is when we transmit a signal how much power is lost between the transmitter and receiver how much is the signal attenuated so let's analyse that first we'll talk about a general model for how we can compare signal strength at the transmitter and receiver in terms of a wireless transmission we transmit a signal with some power, PT the transmit antenna has a gain and we think of that gain as like in any gain it multiplies the signal strengths if I transmit at 100 milliwatts and the gain is a factor of 2 then you can think what comes out of the antenna is 200 milliwatts it's a gain, it's a multiplier as the signal comes out of the transmitting antenna the signal gets weaker we said attenuation means the signal as it travels some distance always gets weaker by how much we care about and at this stage we'll denote by how much is the loss L or the path loss to be specific L means in this equation means if L is 50 it means from the transmitter to the receiver the received signal will be 50 times weaker than the transmitted signal so the loss is by how much do we lose the power so we can think we transmit a strong signal it gets weaker as it travels some distance it's received by the received antenna and then that received antenna also has a gain it effectively amplifies the signal and the result after that received antenna is what we receive the power as PR mathematically we can think we transmit a power at power level PT the transmit antenna introduces a gain of GT a multiplier the receive antenna also introduces a gain of GR another multiplier and the path loss is captured by the parameter L that reduces the signal strength so we divide by L the result is the receive power PR a quick example transmit one watt we know the antenna characteristics let's say the gain not in dB the absolute values let's just make some easy numbers is 100 and the receive antenna has a gain of 50 that is the transmit antenna compared to an isotropic antenna gives a signal which is 100 times stronger the receive antenna has a signal which is 50 times stronger let's say we know the loss is a factor of 1000 so we can think we transmit a signal and I cannot draw it to scale we start with a transmitted signal the transmitting antenna introduces a gain so it increases the signal strength then there's a loss so that as the signal propagates it gets weaker and weaker by a factor of 1000 so this is the gain of the transmit antenna this is the loss we start with the transmit power there's a gain according to the transmit antenna the signal loses power across distance then it's received and the receiving antenna introduces a gain which amplifies again and what we receive here is the receive power PR whatever we end up with is the receive power strength what is the receive power strength? what is PR in this example? these are absolute values so PR is our transmit power 1 watt times by the gains no units divided by the loss I didn't choose very good numbers normally the loss will be much larger let me fix that let's add a zero here so I just made up some numbers typically the loss in many wireless systems will see is very high compared to the other factors but not always so we transmit at 1 watt the antenna is as 100 times 50 or 5,000 the total signal strength lost as it propagates through the air is a factor of 10,000 so we end up at the receiver with half a watt in this case I assumed I knew the transmit power I knew the characteristics of the antenna gains and let's say I measured the loss how much power was lost 10,000 then I could calculate the receive power we'll go through another example in a moment these values, the gains are in the absolute values not db don't use the db value here for the antenna gain for example but we can easily convert to db remember db, logarithm in base 10 multiply by 10 and if you do that on this equation on both sides you take the logarithm and then multiply by 10 then really because the logarithm of two numbers multiplied together is the same as the adding of the log of those two numbers together and dividing by becomes subtraction what we get is that the receive power measured in db is the transmit power measured in db plus the gains in db minus the loss in db so if our values are expressed on the decibel scale we can use this approach sometimes easier so let's go through another example that uses some different values and also combine back to the loss and distance in a moment maybe first new example let's consider an example of using wifi the scenario is I've got my I've got two endpoints so I want to connect together I've got two wireless devices wifi devices I'm going to use 2.4 gigahertz is the frequency what I'd like to know is how far apart can I separate those devices such that they can still communicate let's say I put one wifi device here at sit or on the roof then I'd like to know well how far away can I go such that my other device the receiver can still communicate with my transmitter what's the distance that we can achieve let's try and consider that by using some realistic examples for wifi the scenario maybe you're living out in the country and you want to connect your house to your friend's house and to connect them you're going to use an access point like the one on the wall you have one at your friend's house one at your house and you set them up in a mode so that they talk to each other we'd like to know well how far apart could they be such they can still communicate here's an access point that we'll use we have a few of these downstairs in the network lab actually in the other building just some newer access points than the ones on the wall so let's look at the specs somewhere where are they here they are alright the specs of the data rates actually the wired data rates up to 1000 megabits per second on the wired ports let's focus on the wireless features this access point supports the two different frequency bands available for wifi 2.4 gigahertz and the 5 gigahertz sometimes you'll see the precise names like IEEE 802.11 B, G, N, A, C, A they refer to different standards for how wifi works data rates here denoted as signal rate for 2.4 gigahertz goes up to 450 megabits per second 1.3 gigabits per second if you use 5 gigahertz for our example what's important is first we'll go to transmit power when we transmit a signal what's the power of that signal well it says if you transmit a signal with this access point if you're in Europe so the standard in Europe CE and other regions is if you're using the 2.4 gigahertz frequency range you can go up to 20 dBm 20 dBm is 100 milliwatts you convert back to milliwatts which you know from your quiz is 100 milliwatts if you use 5 gigahertz you can go slightly higher 200 milliwatts if you're in the US the US standards they control how much you can transmit at maximum power levels goes up to what 1,000 milliwatts or 1 watt let's use the 20 dBm value as the transmit power we'll use that in our example our device can transmit at 20 dBm what the other thing we need to know is when we receive a signal what is the weaker signal that that device can understand and that's often referred to as the receiver sensitivity reception sensitivity here let's focus on 2.4 gigahertz we'll use that in the example if I transmit a signal from one of these access points to another then the receiver is designed such that if the signal received is greater than minus 77 dBm if we're using this particular standard at 54 megawatt per second if the received power is greater than this my device receives successfully if the received power is less than minus 77 dBm you think it cannot hear it you cannot receive and it differs depending upon the standards and the frequencies as to what this received sensitivity is think of it as the lowest power we can successfully receive let's remember this one, minus 77 dBm we'll need it to work out how much loss we can tolerate between transmitter and receiver let's write down those values we've got our access point at one location think of that as the transmitter and some other location we want to have the receiver same access point and we know the characteristics this one has a transmit power let's set it to 20 dBm and this one when it receives a signal the smallest signal it can successfully receive we don't notice PR the minimum value of PR we can tolerate is minus 77 dBm what we would like to know is how much loss can we have between the two devices how much power can we lose such that the signal strength will still be greater than minus 77 dBm so we'll try and determine the loss the frequency we're assuming is 2.4 GHz the next thing we need to know is about the antennas what's the gain of the antennas on these devices I'm not sure if it's specified on the web page sometimes it says, sometimes not I think in this case it doesn't show us the antenna gain but we may guess I've got one of these devices the antennas are slightly bigger than those dipoles on the access point but let's assume that they're still about the 2.2 dBi I think they may be a little bit larger but let's give it a number the antennas it doesn't matter that there are three we just focus on the gain of a single antenna let's set it to be about the same as the one on the wall which I know is 2.2 dBi and at the transmitter and receiver they are the same same device so we can say the gain of the transmit antenna like that first Cisco antenna 2.2 dBi and the gain of the receiver antenna is the same they don't have to be the same you can have different antennas at the transmitter and receiver and they can have different gains just in this case they turn out to be the same what is the maximum loss that we can tolerate such that these two devices can still communicate find the maximum loss in dB if we transmit at 20 dBm there's a gain of 2.2 dBi then we lose some power then there's a gain of 2.2 dBi at the receiver antenna and we must receive at a power of at least minus 77 dBm so how much power can we lose such that the received power is minus 77 dBm what's L note that all of the values we saw in the spec transmit and receive power also if the antenna gains are in the dB scale decibels so use this equation don't convert them to milliwatts absolute values that's too hard just use the equation here which will give you the same answer but faster I will not write the notation or the subscript of dB we just PR measured in dB is Pt plus Gt plus Gr minus L but be careful all of these values must be expressed in the decibel form so we want to find L rearrange if we rearrange we can calculate the loss and we know those four values Pt is 20 dBm Gt is 2.2 dBi so is Gr minus minus 77 dBm this is why it's sometimes useful to use the values in dB most of the specs for equipment will be expressed in dB and then just adding and subtracting is quite easily 22.2 24.2 plus 77 is a 101.2 dBm 101.4 dB not dBm just add them up let people catch up and write that down and then we'll answer some questions about it the common question that comes up now how did you add up these numbers when you've got dBm dBi and how did you end up with dB that's strange the important point to remember is dB is not our normal unit it's a measure of the scale that we use if you think about the units what are the units for power? watts power transmit power receive watts or with a prefix of milliwatts the units for loss and the gains there are no units they're dimensionless they're ratios or factors so even though we write dBi and dBm we can still add them up in this because in dB scale we can add the factor in the i just means relative to isotropic so don't be confused and think that we somehow need to change dBm into dBi no the transmit power measures watts receive power measures watts in this case it's milliwatts and milliwatts the others are just factors or ratios and because we're on a logarithmic scale we can add them together if you don't understand that then convert them all to the absolute values convert to milliwatts and back to the absolute values and do the multiplication and division and you'll see you'll get the same answer loss, gain really measured in dB if we convert back to the absolute value there are no units in them so what does this number tell us it means if I transmit a signal from my access point if there's a loss of 101.4 dB or we can convert that back to the normal value the absolute value is 10 to the power of 10.14 not in dB remember the we divide by 10 10 to the power of or take the logarithm of this value and then times by 10 to get dB so this is the inverse operation what does it tell us the signal coming out of the transmit antenna if it loses its power by a factor of 10 to the power of 10.14 it is what about 10 billion if it loses the power such that the signal going into the receive antenna is 10 billion times smaller than the one coming out of the transmit antenna then with the gain of the receiver we will receive a power of minus 77 dBm and the spec of my equipment said if I can receive minus 77 dBm it will work okay if it was less it would not work so we've determined what's the maximum loss we can tolerate such that these two devices can communicate questions on this so far why do we care about loss what do we want to know I want to know how far apart I can put them distance can I separate them by such that they all communicate well it turns out if we know the loss there are some relationships between loss and distance so we can use some models to find out well if the loss is 101.4 dB what distance does that correspond to let's go to that now so we'll continue that example and convert it to distance and there are different ways to relate loss and distance it depends it depends upon the obstacles between the transmitter and receiver the walls whether the signals bounce off walls whether there are people in between trees and many other factors but we'll start with a very simple model in the ideal case assuming there are no obstacles we're operating in perfect conditions we say in free space imagine we're out in space nothing in between transmitter and receiver then the ideal model is referred to this free space path loss equation which says the loss is equal to 4 times pi times the distance divided by the wavelength all squared we know what the loss we can tolerate we know L we can find the wavelength because we know the frequency therefore we can find D the distance that our two devices can separate by let's do that now use this equation to find D the free space path loss model tells us loss not in dB be careful L here is not measured in dB it's the absolute value equals 4 pi D divided by lambda all squared what's lambda? we'll need that what was our frequency? 2.4 GHz so we can calculate the wavelength let's do it here lambda equals the speed of light divided by frequency what's the speed of light? 300 million meters per second 3 by 10 to the 8 meters per second the speed of light is about 300 million meters per second nice one to remember the frequency is 2.4 GHz so 2.4 by 10 to the power of 9 hertz or times per second calculator time effectively 3 divided by 24 300 million divided by 2.4 billion is 0.125 meters that's our wavelength we know L it's 10 to the power of 10.14 we know lambda it's 0.125 let's find D and it's just a matter of rearranging this if you rearrange what do you get? D the distance is the square root of L square root of it let's try that bit better the square root of the loss times by lambda divided by 4p 4pi I will not write down the numbers we'll calculate direct the square root of do we have 10 to the power of 10.14 that was a loss not in dB but in the absolute value times by the wavelength 0.125 divided by 4 and divided by pi 1,168 meters is the distance 1,169 if we round up to an integer so what does this number tell us now? we've got two of these TP-link access points the one on the web page one at your home one at your friend's home we know the specs of the transmit power and the minimum receive power PT and PR we assume the antennas had a gain of 2.2 dBi that's a good assumption when we transmit a signal with a frequency of 2.4 GHz we've used our mathematical models in particular the free space path loss assuming there are no obstacles in a perfect environment we've determined that we can separate them by 1,169 meters if we separated them by say 1,200 meters we would transmit a signal the gains of the antenna and the loss across that distance would be such that the receive power would be less than our minus 77 dBm so greater than this distance if the distance goes up the loss goes up and it means the receive power will go down and the threshold for our receive power was the minus 77 dBm so your friend can be 1,169 meters away if you want to communicate with these two access points any questions? okay it's not finished time yet yes the lambda is the speed of light divided by the frequency 3 by 10 to the power of 8 divided by 2.4 by 10 to the power of 9 the gigahertz you need to learn some of my writing especially the number of 9 is this realistic? this says not just if we're going to our friend's house but if you have your wireless device this access point and your laptop if it had a similar antenna and similar characteristics you could separate them by about 1 kilometer and still have Wi-Fi access do you think it's realistic? or another way? do you think you can communicate with this access point in this room if you're 1 kilometer away? most likely not in reality we have many obstacles between the transmitter and receiver even if there were no walls we're out in an open field the atmosphere has some impact upon the attenuation and it's not as good as this this is the best case result if we're out in space with no obstacles so we call it the free space path loss model in reality it's going to be less than this but this gives us an approximate value if we're say in an open field but not very good if we're indoors walls cause big problems there are other models other equations that try to approximate if we're inside in this course I think we will not see them but the free space path loss model is quite easy this equation there are others there's some for inside a city with different obstructions and different reflections there's some for TV broadcasts say from a TV station to your home and there's some for indoor modelling that is when there are walls and ceilings and so on to try to accurately model how far can we transmit to produce a particular path loss? let's stick with free space path loss for now I have a problem my friend is 20 kilometres away from me not one kilometre his house is a long way away how can I communicate with him using the same access points we've bought the access points we went out and bought them we want to set up a link between our two homes but they are 20 kilometres away from each other what do we do? what could we do? to still communicate I can't move my home what could I do? I need to communicate with my friend via Wi-Fi I must have a solution what do you propose? do you get a job as an IT specialist and you set up Wi-Fi networks what do you tell me? what do you sell me as a solution? move closer? remember our calculations was that so one thing that we can change quite easily usually is the antennas the antennas introduce a gain a bigger antenna, a bigger gain bigger gain means that under the same conditions the received power will be greater if we amplify more the received power will be larger and in fact most of these access points the antennas screw off so you can take them off and you can attach a bigger antenna and you can buy bigger antennas let's try a calculation to finish today let's keep everything the same same transmit power same frequency, same receive threshold but let's change the antennas and let's say now we use a big dish antenna let's see if it works both the transmit and receive antenna let's remove the dipole antennas and attach a dish antenna which is a 50 centimeter diameter antenna we buy parabolic dish so we need to point it at the dish at the receiving end we set them up we want to know can we make the distance of 20 kilometers if we buy these two antennas let's assume just for simplicity the antennas are the same as the transmit and receiver so we only have to do one calculation so if I know my dish is a diameter of 50 centimeters what do I do next? what's the gain of that dish? we have a way to relate the antenna size the frequency or wavelength and the gain let's assume that we have our parabolic antenna we know the radius is 25 centimeters the diameter is 50 centimeters let's assume that the it's a circle it's not quite a circle the area it's not a flat circle but let's assume it's a circle so the area is pi r squared and let's assume just for this calculation the effective area is half of pi r squared that would depend upon the actual design of the antenna but it's a good assumption given that we'll use this equation to find our antenna gain the area is pi r squared what's the radius in meters? 0.25 note that we use meters here, convert the meters everything will be in the standard units that's the area and let's say that the effective area is half of that in the equation the area of our dish is pi times 0.25 squared the effective area for the antenna calculation is half of that our antenna gain 4 pi Ae divided by lambda squared we know lambda, we calculated before it's 0.125 we can plug in the value for Ae to get the gain g of our antenna Ae is a half of A Ae is pi times 0.25 squared I'll plug them in into the calculator and find the value 4 times pi the effective area is a half times Ae Ae is pi times 0.25 squared so let's just times it twice divided by the wavelength squared wavelength from before was 0.125 2 just plug in the values 79 about we get a gain of about 79 we'll write that down in a moment and if we want to express in DBI we can log that times by 10 or about 19 DBI 79 as the absolute value as the multiplier or 19 DBI is our parabolic dish antenna which is the same as 19 approximately DBI our dipole antennas were 2.2 we've changed the antennas we're up to 19 DBI for simplicity let's say the antennas are the same at the transmitter and receiver we need to calculate the gain separately what's our loss now the transmit power 20 DBM plus the gain of the transmit antenna 19 DBI plus the gain of the receive antenna also 19 DBI minus our minus 77 DBM anyone can calculate for me 135 dB convert to the absolute value 10 to the power of 13.5 we know the loss now what's the distance from before we're just using the same equations but different values this time square root of 10 to the power of 13.5 our loss times by our wave length 125 divided by 4 divided by pi did I get that right 55,000 56,000 meters our distance is about 56 kilometers by increasing the antenna gain using different antennas in this case they have a larger gain we can tolerate a larger loss to receive at the same power or in other words we can transmit across a larger distance to still receive at minus 77 dBm so we achieve our link between our two friends check the calculations of those we will summarize in the next lecture and finish on this wireless transmission so you should be able to do some calculations of path loss antenna gains and similar we'll continue tomorrow