 We've spent some time looking at different aspects of wireless transmission and after some examples we have arrived at some model for how the signal is transmitted or how we can relate the transmit and receive power. We think we transmit a signal with some power, PT, the antenna compared to an isotropic antenna introduces some gain, denoted as GT at the transmitter and GR of the receiver. We can find out in the same way the transmit and receive antenna and importantly between the antennas as the signal propagates there's attenuation. Across the path between transmitter and receiver we lose some power. We denote that as the path loss or L. So if we start with a transmit power of PT the antennas introduce some gain effectively amplify the signal. We multiply by GT and GR and the loss is how much we reduce the signal strength by so that we divide by the loss factor L in that case. So we get a relationship between those factors which is useful for answering some practical questions in wireless transmission or design of wireless networks like how far can I transmit under certain conditions. One of our examples from yesterday was could we transmit using our wireless access points from my house to my friend's house. If we know something about the characteristics of the transmitter such that the transmit power, the characteristics of the receiver such as the minimum power it can successfully receive. If we know the antennas and the gains of those antennas then we can find how much loss we can tolerate between two points and the next things of value is that there are some models that determine for a given amount of loss what distance does that correspond to and we used what's called the free space path loss model. Out in space no obstacles no impacts from the atmosphere if we transmit a signal wirelessly how far will it travel or what's the relationship between the distance and the loss well it's given by this equation. If we transmit a signal D meters and the signal has a wavelength of lambda then we can calculate the loss L from this equation. So that gives us some relationship that we can use in the previous equation if we know PT and PR we know GT and GR if we know the distance we can calculate the loss or given the loss find the distance is what we did in one of the previous examples. We can do it in the the absolute values which is this equation and the free space path loss model or we can convert everything to DB why convert everything to DB because it allows us to do addition and subtraction as opposed to multiplication and division sometimes it's easier and if you look up the specs of equipment often the values are expressed in DB so sometimes it's easier to convert. The other thing that we've seen is that we also have an equation that allows us to calculate antenna gain if we go back a few slides antenna gain if we know the effective area this one if we know the effective area of the antenna and the wavelength of the signal we're transmitting we can calculate the gain of that antenna and the effective area is related to the physical area and we'll see a couple more examples of that today so let's summarize on the remaining slides and then just go through one more example relating antenna gain path loss together we are going to use so we have in one example and we will again today use this free space path loss model it assumes perfect conditions it doesn't apply if we're transmitting a signal indoors for example if we have an access point at the back of the room and I have my laptop in another room then if we try and determine the amount of loss between those two points we shouldn't use this model it's not accurate it's only accurate if we're out in space with no other effects which is not never the case but this is an easy one to calculate it's a good starting point there are more complex models that try to relate distance with loss in different environments we will not present them but some of their names are listed here for example there are mathematical models that say if you transmit a signal through a city over D meters how much path loss are you going to have or if you're a TV station and you transmit from your TV station tower to the TVs at people's homes there are models to determine how much path loss occurs across different distances and even there are models for indoor indoor we have a problem with walls and other obstacles so especially walls if we have an access point at the back and my laptops in the next room the signal propagates through the air but then it hits the wall what happens then is that the signal attenuates by a lot more than when it was propagating through the air you think it's propagating through the air it's getting weaker it hits a wall and it jumps right down it gets very weak it goes through the wall but very weak and propagates a bit more until it gets to the receiver so this free space path loss model doesn't capture how much power we lose due to walls and other obstacles there are other mathematical models that try to do that we will not see them today I'm not sure if we'll see them in this course we've gone through one example yes yesterday about the Wi-Fi path loss we'll see another one shortly the remaining slides are just a few examples of different wireless technologies but I think you know them already we've mentioned some of them you use some of them satellite communications satellite TV you may have a receiver at home a dish that picks up the TV broadcast from a satellite where the TV station sends us the TV signal up to the satellite and the satellite sends down everyone who has a receiver within the footprint of that satellite can receive that signal so that's a point a moldy point one transmits moldable receive so that's one application of satellite communications another one is positioning what's the acronym for positioning that we use for satellites how do you find your position GPS global positioning system so that uses a series of satellites in space and they send signals and your phone picks up the signal and from multiple signals you can triangulate and calculate where you are the coordinates so that's another application some companies may have a private network say you have your office in Bangkok and another office in LA in the US you want a link between those two offices well you can access the internet and use the the submarine cables and so on or you can have a dedicated link by renting access to a satellite you send from an antenna on the roof of your office here in Bangkok up to a satellite and that sends your data down to the office in the US so that's like a private link using satellite communications and you can subscribe to internet satellite internet access via satellites in different cases especially if you're in remote areas maybe there's no ADSL there's not good mobile phone coverage so maybe your only option is to use satellite internet access one of the companies that is is quite popular in the Asian region Southeast Asia Australia the Pacific is IP star so well that's the service it's a tie run by a Thai company what Thai com have several satellites and they provide internet access so IP star is the service that they provide on the website I think there are a few slides that give the specs of the satellites but we'll not cover them today we'll return a little bit to satellite and space communications in our example today there are many other types of wireless technologies terrestrial wireless means the two points one is not in space they're both on the ground so an example is that on at this campus on the other building we have some antennas at the top of the building and one of them is pointing to one of our buildings at the rung sit campus that's a terrestrial wireless link between our two campuses so covering that 12 or 15 kilometers we have a wireless link that we use to send data between our two campuses there are different technologies available to do that and you get different speeds Ymax is one of them there are others you know about mobile phones they use different frequencies how do they work you use a a base station or a cell phone tower and you send wirelessly from your phone to that cell phone tower and then via wires from the cell phone tower out to the rest of the network the range or the distance that the transmissions occur typically in the order of hundreds of meters to kilometers so one cell phone tower covers say about a circular area of maybe a kilometer a radius of a kilometer that differs in different cases and then that's why you see many cell phone towers to cover the entire city of Bangkok you need to have many cell phone towers to cover all the little pockets all the little areas maybe several kilometers in some cases and I think you know about the data rates you can achieve with internet access via mobile phones and Wi-Fi is another example of wireless technology and we had a recently detailed example yesterday about Wi-Fi and we may see some more as we go through this course so that's the end of the slides let's just have one more example on antenna gain path loss and relating those factors together just to give you some practice and the example we use is a example of space communications an example of communicating from Earth to Mars okay so NASA has some some spacecraft on Mars and also orbiting around Mars this is a selfie that the Mars Curiosity rover took it's a vehicle on Mars it's there now and it has some cameras on it and I think this is a picture it's taken multiple times of itself there's no one else to take a photo of it on Mars so this rover is on Mars and it sends the photos back to Earth so we can see them so we would like to look at a little bit about well the communications between Earth and Mars how does it work especially with respect to path loss sorry by light the in fact there are different ways it just uses normal electromagnetic waves we'll see frequencies of around 8 gigahertz is one but there's different options so this Mars rover just a vehicle on Mars needs to go for several years it's been there I think for two years already it can't plug into a charger to charge its batteries so it must conserve power and to transmit signals back a common way that it transmits signals back is not sending it all the way back to Earth but NASA has another spacecraft orbiting around Mars has several in fact one of them is this it's hard to see there but there's a spacecraft that orbits around Mars called the Mars Reconnaissance Orbiter and one role of this spacecraft is that the rover on Mars sends a signal up to the spacecraft and that relays it back to Earth this spacecraft have has bigger antennas and can transmit better than the rover so in fact what we will look at in our example is how do we communicate between Earth and this orbiter that spacecrafts orbiting around Mars so this one sends a signal back to Earth where do we receive it and where do we transmit from there are some big dishes at different locations that NASA has one in I think in California one in Spain one in Australia I have several dishes like this large parabolic antennas remember larger the antenna larger the gain further we can transmit this one I think is this one or another one is a diameter of 34 meters one we will use is a diameter of 34 meters same shape as your satellite TV antenna but just bigger so we want to look at a scenario if we want to transmit from Earth using such an antenna transmit up to the orbiter or to the orbiter going around Mars how much power do we need to transmit with that's what we'd like to know so to analyze that we need to know some of the specs of the transmitter and the receiver and I'll give you them and the details I'll write down but if you want to read about them and find the specs and pictures of this equipment I have on a website linked from our course that talks about how we communicate from Earth to the rover on Mars and it goes through some of the technical details of the distance between Earth and Mars the different spacecraft near Mars or have been used and for the different spacecraft the antennas the transmit power receive power and other characteristics but to save some time today I'll just I've grabbed some numbers from there already and we'll use them in our example how far between Earth and Mars it varies the orbits of the two planets mean that they the distance between them changes over over the year or over time we would not need all of these details so if it's it's a bit hard to read don't worry don't try and copy it down I'll show you what we need in a moment but if Earth is here and we have our ground station our big 34 meter parabolic dish sending to the orbiter MRO here and that's about several hundred kilometers above Mars and then our rover that vehicle was on Mars and they communicate using UHF usually we're going to focus on the link transmitting from our ground station on Earth to the orbiter near Mars what's the distance it ranges between a hundred million kilometers to 400 million kilometers so it depends upon the time of the year as to how far apart they are let's put a number to that let's assume some value let's assume it's about 250 million kilometers so the numbers I write down we will need for our example but let's say the distance is 250 million kilometers that's the one we'll use we're focusing on this part from the ground station on Earth to the orbiter in Mars or around Mars that that's the link that we're interested in I'll give you some specs of the equipment the transmitter and receiver first how do they communicate they send a signal over with a particular center frequency the band of frequencies is called the X band in space or satellite communications there are different range of frequencies available there's L band C band X band KA KU and a few others I've looked up the details for X band and in particular for transmitting to the the orbiter and the frequency used is about 7 gigahertz remember Wi-Fi is 2.4 gigahertz or 5 gigahertz this transmits sort of frequency of to be more precise 7.183 gigahertz that's our signal frequency when we transmit in fact transmitting up is this frequency transmitting down is closer to 8 gigahertz they use different frequencies in each direction why am I writing them down we need to know something about distance to work out path loss and also path loss depends upon the the wavelength or frequencies so we'll need those values shortly how big is the antenna on Earth the radius alright it's a 34 meter diameter dish so the radius is 17 meters so the radius of the dish is 17 meters we know something about based upon the size of an antenna we can calculate the gain of that antenna if we go back one of our equations we had this one the gain of an antenna depends upon the wavelength well we know the frequency and also depends upon the effective area and this is something that differs depending upon the construction of the of the antenna the effective area is usually smaller than the actual or the physical area for a dish we can think the physical area is about that of a circle if you look front on it's a circle so the physical area is about pi r squared we know the radius is 17 meters so we can find the physical area the effective area is some fraction of the physical area and I looked up the specs for this antenna that in the the NASA system and in this case it's about 0.8 times the physical area that is the effective area AE is 0.8 not 0.5 like in the previous example times the physical area A and the physical area is simply pi r squared so we can find that we know are the radius so here's a hint you can use these values to find the gain of the transmitting antenna what about the receiving antenna on the spacecraft orbiting around Mars it has a 3 meter antenna and I again I looked up the specs about the the efficiency and in fact to make it a bit easier for us I looked up the gain and it tells us the gain was 45.2 dbi the receiving antenna has a gain of 45.2 dbi the transmitting antenna has a gain that you need to calculate in a moment from the values given so we know something about the gains of the both antennas we know something about GT and GR we know the distance we need to cover given the distance we can calculate the loss in free space how using this model if we know the distance and the wavelength we can find the loss L another characteristic of the receiver is what's the minimum power it can successfully receive it's called the receiver sensitivity PR or the minimum PR and I looked up and it varies for different data rates as different values but the one we'll use PR minus 100 dbm what that means is if from earth we transmit a signal and it's received eventually after the gain of the receive antenna if the receive power is greater than minus 100 dbm we can successfully receive if it's less than minus 100 dbm then we cannot receive and we can't talk to our orbiter and we can't control or talk to our curiosity rover so that's the what we call the receive sensitivity it's the cutoff above there's okay below it's not okay so we want to find out at what power should we transmit at such that we receive at this level what's PT how much power do we need to transmit such that we can receive a signal at minus 100 dbm there's your challenge for the next 10 minutes or so try and do those calculations and find PT and the hints find the gain of the transmitter antenna first and for that you'll actually need the wavelength and then you can use your equations to find PT and another hint note that some values are in db some you'll get in the absolute values I suggest convert them all to db where possible it'll be easier at the end try that for the next 10 minutes try and calculate on your own ask any questions and then we'll go through the answer we need the gain of the transmit antenna to be able to find eventually at the transmit power we know the radius of the antenna is 17 meters so we can find the physical area is pi r squared and then we said the effective area is 0.8 times the physical area not 0.5 in this case it differs in different antennas 0.8 times pi r squared will give us AE if we know AE if we can find the wavelength the speed of light divided by the frequency then we can find G let's do that we need the wavelength the speed of light 3 by 10 to the power of 8 meters per second frequency 7.183 gigahertz by 10 to the power of 9 we could leave it like that and calculate later but let's find the wavelength 3 by 10 to the power of 8 divided by 7.183 times 10 to the power of 9.04176 now we need we should be careful when we calculate steps and then round the numbers or approximate we should actually save this actual number I shouldn't write it as 0.04 or even 0.041 I should save the actual number so we are a little bit more accurate but sometimes we can let's say let's say it's 0.0418 just so it's easy for me to write meters the wavelength the area of that sat at that transmitting dish pi r squared we said the radius was 17 meters pi times 17 squared the effective area is 0.8 times that where 0.8 was given I will not calculate yet because we use that in the gain of cap equation the gain of our transmit antenna for pi AE divided by lambda squared AE is 0.8 pi times 17 squared divided by our lambda squared now we need our calculator four times pi times 0.8 times pi times 17 squared divided by 0.0418 squared there's our gain of our transmit antenna about 5.2 million that is our big 34-meter dish parabolic antenna compared to our standard isotropic antenna this one is 5.2 million times stronger if we measure the receive power the same distance from those two antennas if it was one watt for an isotropic antenna it will be 5.2 million watts if we use our actual parabolic dish antenna now it's going to be easier if we do the last calculations in db so let's convert it to dbi simply take the logarithm times by 10 I will not write that down but instead log of that times by 10 67 dbi we should be accurate here in fact again I shouldn't round too much because especially on db a small difference is quite significant because it's a long on a logarithmic scale so I'll write it down a 67.18 dbi 67.18 that's the gain of our transmit antenna I've given you the gain of the receive antenna 45.2 dbi what's next the loss we know GT we know GR we know PR we want to find PT so there's another thing missing at the moment L if we can find L we can find PT how do we find the loss well we have another equation here the loss in free space and sending a signal out to Mars is as close as we'll get in real life to free space the loss is four times pi times the distance the distance in meters divided by the wavelength all squared so we can calculate that easily the distance is the 250 million kilometers four times pi times the distance 250 million kilometers which is 250 times 10 to the power of what how many meters 250 by 10 to the power of six kilometers or 250 by 10 to the power of nine meters that's a nine divided by our wavelength well we have that and square all of it so be careful when the distance is given in kilometers convert it back to meters if you want to use it in this free space path loss equation four times pi times 250 times 10 to the power of nine divided by point oh four one eight to the power of two or squared we transmit a signal you can think if the signal comes out of the big dish antenna comes out at this level then it travels 250 million kilometers when it comes into the receive antenna at the orbiter near Mars it is this many times weaker five by 10 to the power of 27 times weaker than what was start we started with signal attenuates by this factor over that distance that very long distance convert to db take the logarithm times by 10 it'll be easier in the next step and again using db is easier because instead of thinking of 5.64 by 10 to the power of 27 logarithm times 10 we get 277.52 db that's the loss in this case we know from this equation in the db form the receive power equals the transmit power plus the gain of the transmit antenna plus the gain of the receive antenna minus the loss across the path where all those are expressed in their db form well that's what we have we know gt we just calculated to be was 67 we know gr I told it was 45.2 dbi we just calculated the loss to be 277 db and I also said that the receive sensitivity was minus 100 dbm so we know four of the five variables the one we want is pt so we can rearrange to find pt take that equation and rearrange to find pt I will not write the subscript of db they're all in db form if you rearrange it becomes pr minus gt minus gr plus the loss pr we said pr was minus 100 dbm gt I gave you as 45.2 dbi we calculated gt to be what 67.18 so we know those three and we also found the loss across this long distance we lose by a factor of 277 point whatever it was 51 db so plug those four values into our equation minus 100 dbm minus I was at 67 point what was the value I'll look up if no one will tell me 67.18 dbi minus 45.2 dbi for the receiver and the loss 277.52 I wrote 51 here 52 plus what do you get minus 100 minus 67.18 minus 45.2 plus 277.52 is 65.14 think of gt gr and l as having no units well the units is db but they are dimensionless pr is measuring power level milliwatts in this case so pt we have the same units as pr dbm if pr was in dbw pt would be in dbw but it's in dbm and if we want to convert back to the absolute values 65.14 dbm how many milliwatts or 10 to the power of that number divided by 10 remember to go in the opposite direction we don't we had 10 log 10 times log the power or the ratio so to go backwards we have the ratio divided by 10 and then 10 to the power of is that many milliwatts dbm said milliwatts convert to watts divide by a thousand three thousand two hundred and sixty six watts so what we've arrived at at the end is how much power we must transmit at on earth such that the signal with the two antennas we're using and that very large amount of loss across the 250 million kilometers the signal received is at least or is equal to our threshold or our received sensitivity of minus 100 dbm so if we transmit at this then we should receive at minus 100 dbm and our receiver can understand if we transmit it larger than this three thousand three hundred four thousand watts then the received power will also be larger than the sensitivity and they'll receive the signal but if we transmit it at lower at three thousand watts so the received power would be less than minus 100 dbm it would be lower than the sensitivity and the receiver at the Mars orbiter would not be able to understand the signal so we need at least this many watts to transmit at three thousand volts three thousand two hundred and sixty six luckily i've looked up the specs of the ground station and it goes up to the maximum transmit power is 20 kilowatts kilowatts so our calculation says we require to transmit at 3.2 kilowatts but that ground station can go up to 20 kilowatts so it's okay it's within the limits of the the transmitter the transmitter can usually change the power so we can communicate from earth to our orbiter going around Mars