hello and welcome to lecture seven where we're going to talk about angle modulation that means frequency and phase modulation so just as a reminder last week we finished talking about amplitude modulation and in particular we spoke about the demodulation of double sideband suppressed carrier modulation we introduced something called the coherent detector also known as a synchronous detector and we said that a coherent detector looks very much like a dsb modulator consisting of a local oscillator in common with the modulator a multiplier the same as in the modulator and this added box or this added block of a low pass filter to block the high frequency components and recover the message so the idea is that our recovered message would be similar to the original message we spoke about the possibility of having frequency or phase errors in the local oscillator at the receiver we spoke about how these errors might affect the quality of the recovered audio so today we're going to talk about angle modulation so rather than talking about how the amplitude of our message can affect the amplitude of a high frequency carrier we're going to have the frequency of your high frequency carrier modulated by your signal so your signal amplitude will modulate the frequency or the phase of your high frequency carrier we're going to learn how frequency and phase are closely related so one is the derivative of the other we're going to introduce the idea of instantaneous frequency so whereas in the past a signal would have a frequency and a phase now we're going to have something called the instantaneous frequency and phase later in the week so on wednesday night i will record lecture eight for you where we'll be talking about the demodulation of fm and pm that will be available for you on thursday because on wednesday you will be completing the first class test now remember that's worth 15 of the module and there's no repeat opportunity for this test so make sure you're available for that test if you can't make it at 10 o'clock on wednesday the 17th of march make sure you get in touch with me before the test okay let me know if you're unable to make it at this time before the test okay so just as a reminder what's included in the test is lectures one through six so everything up to and including the demodulation of dsb is included in the test today's lecture lecture seven is not included in the test okay so seven and eight we'll be talking about fm these will come before the easter break then there'll be a break then we'll talk about digitization and all of these will be included in the second class test okay so we are currently here in week six your test is on wednesday this is lecture seven lecture eight later this week and this is the easter break and then we'll be back on the 14th of april okay we'll start with a problem class okay and our second class test will be here on the 12th of may and that will be the last week before your exams so really your best opportunity to revise for the exam will be during the easter break this is your best opportunity to prepare yourself for those exams so what i'll make sure is that before the easter break you will have lectures seven and eight available to you so by the time we meet on wednesday you will have already hopefully seen that and on the monday i'll even provide lecture nine for you in anticipation of the following wednesday's problem class okay so on to today's class angle modulation so we've spoken about how we can encode the message in the amplitude of a high frequency carrier so that's given us all the different variants of amplitude modulation so am which is just the shorthand for dsb lc we've done dsb sc which is sometimes sometimes just called dsp we've talked about ssb single sideband and vlc vestigial sideband so today we're going to look at what happens if we encode the message into the angle of the carrier so here's our message instead of encoding this message into the amplitude or the envelope of our carrier what we're going to do is embed it or encode it into the frequency so you can see the instantaneous frequency here is high then it's low high and then it's low almost corresponding to high and low high and low and as you'll see frequency modulation and phase modulation are almost indistinguishable so looking at this it wouldn't be possible to tell whether that's frequency or phase modulation unless we had the message alongside it so when we talk about angle modulation we're talking about both frequency and phase or either because both of these contribute to the angle and as you'll see in a second one is a derivative of the other so before we start what do you think which is more susceptible to noise am or fm and by susceptible we mean vulnerable so which is more affected or more influenced so which is more affected by noise vulnerable to noise or susceptible to noise so am where you have your carrier amplitude that varies with the amplitude of your message or fm where you have a a constant amplitude but you have a frequency which varies so which of these two signals do you think is more affected by noise now remember if noise is going to affect a signal it will add itself to the signal so this is what we term additive noise it adds itself to the signal so it'll affect the amplitude of your signal so you can probably guess that when it's the amplitude of the carrier that actually contains the message information that's going to be more affected because here when the amplitude changes so even if this amplitude became so high and then so low as long as the frequency doesn't change the information is relatively safe so where is it we look for the frequency the frequency is here isn't it so let me just um show you this is where we actually note the frequencies the amplitude doesn't really matter so it doesn't really matter if this goes up or down because of the noise all right so this dark blue there this is your additive noise so which is more affected by noise i think it's clear am is more affected by noise so it doesn't make it better it makes it more vulnerable makes it less good in terms of quality of the recovered message but we'll look at um how these two compare in a second so angle modulation remember when we say angle modulation you might look at the a and look at the m and think oh that's am but no that's not am am is for amplitude modulation so angle modulation doesn't stand for am or am doesn't stand for angle modulation so what we're actually comparing whenever you see am i want you to think fm even though it includes fm and pm just think fm just so you don't get confused so what's an advantage of fm compared to am so we've already just spoken about signal quality and that's because of the noise we've spoken about that but it's also a more effective use of power why do you think that is now we already know about the carrier term so we've already looked at dsb lc and dsb sc and we've established that the carrier term is inefficient but why why is fm even better than dsb lc in terms of power well look at that you you i want you to think about these reasons but we will look at that now fm has some disadvantages or maybe it's better to say am has some advantages over fm these two are bandwidth and range so the bandwidth of fm the bandwidth of fm is often larger than the bandwidth of am now this won't be an accurate statement unless we specify which type of am and which type of fm but generally for broadcast fm and for broadcast am if we're talking about audio or radio stations then this is the case okay we'll look at exactly how much or you can calculate how much later but these will be in megahertz and this will be in the kilohertz region another um okay so uh the fact that it uses more bandwidth that is a disadvantage of fm so having a large bandwidth isn't a good thing remember we said properties of a good communication system are that the bandwidth should be as small as possible but fm also has a shorter range so you can probably tune into your local fm radio station but you probably couldn't tune into an fm station more than a few hundred miles away why is that because off the way fm waves propagate so there is a limited distance between a transmitter and a receiver for an fm signal whereas for am signals especially at night the signal can actually bounce off the ionosphere which is the layer of the atmosphere and therefore travel much greater distances so you have a much larger range so with your am radio you can tune into stations you know hundreds you know even a thousand kilometers away whereas with fm you're lucky if you can pick up something you know even even 200 kilometers away you know you're often limited just to your local um your local neighborhood up to 50 50 to 100 kilometers okay so um there's two main advantages and two main disadvantages of fm there are more and you will you will be able to to express these further by the end of lecture eight so now we look at some of the mathematical representations so i want to introduce something called the instantaneous frequency okay the instantaneous frequency is a function of time okay so f i is a function of time that's why we call it instantaneous so the frequency isn't just the carrier frequency we also add something which is a multiple of the message so if this is your message and this is the message amplitude okay m of t is the amplitude of our base band message all right so this is our base band low frequency now we multiply that by some constant call it the modulation sensitivity and that will give you your instantaneous frequency so your instantaneous frequency will be will vary from something slightly above or slightly below because mft can be negative the carrier frequency but notice that the amplitude is constant that amplitude is constant we'll write the mathematical expression in a second but if you just remember that what we're modulating we're modulating the frequency and not the amplitude so the amplitude is constant so it's less prone to noise so we've just introduced another word so pro less prone to noise means less susceptible to noise less susceptible to noise means less vulnerable to noise it means it's less affected by noise okay a question for you before we move on we're talking about radio we're talking about am and fm so when we talk about fm transmitters and fm receivers in particular do you know whether your smartphone contains an fm receiver so the way you interact with your smartphone on a daily basis you probably don't use an fm radio regularly but do you know whether your phone has an fm receiver some phones do some phones don't now i'm not talking about a radio app i'm talking about a radio receiver so can you listen to the radio on your mobile phone without being connected to the internet i.e without using a 4g 3g 5g or wi-fi signal so without these are you able to listen to the radio so if you don't know pick up your phone and find out okay you might be um you might be interested to hear to see the results okay so most korean and chinese phones do have fm radio receivers until a few years ago iphones had fm receivers i think they still have the fm receiver hardware built into the phone but they've been disabled in software and you can ask yourself why that is okay but find out if your phone has an fm receiver now phones have had fm receivers for a long time so since since the late 90s phones had fm receivers even before phones had color screens they still had radio receivers so why do you think in 2021 phones some of the flagship smartphones still don't have um fm receivers or they used to and they've been disabled why do you think that is so there are there are several reasons and these are not technological reasons they're not hardware reasons they're not engineering reasons they're often commercial reasons there's a little a very short two minute video clip i wanted to share with you so bear with me well smartphone makers are under pressure tonight to activate the hidden fm radios inside our smartphones u.s senator bill nelson tells nbc 2's dave elias he is pushing for the government to require the activation and dave is live in our newsroom with the latest developments there yeah you know almost every day we hear about new smartphone apps that make life easier yet these modern day mobile miracles can't even perform a function offered by a 1980s walkman senator bill nelson wants to change that i haven't had owned a radio in so long the only radio that i have is my vehicle for many radios have become a thing of the past i know a lot of people were running around trying to find you know battery powered radios and everything last minute in case hurricane irma knocked out power as well as cell and internet service rendering our phones useless i don't think my children have ever owned radios now this tiny chip buried inside of your smartphone basically does the same thing all of these radios do to be able to have an fm radio in their hands would have been really helpful that shocks me i mean if it's in there already why aren't they doing it the same question u.s senator bill nelson once answered you dog going right he wants the fcc to get involved then there's got to be a way that we can activate that chip so these are the actual logic boards that sit inside the iphone jeremy azinger fixes smartphones after showing us the hidden fm radio chip he says activating it would be an easy task i could easily imagine there being a a setting on your phone that you could just turn on or off at your leisure to have accessibility to a radio giving people like jessie kasem peace of mind cell phones are an emergency device their utility at this point and there if there's a way that it can be used in emergencies for free information then they should make that available now for the fm to work it has to be activated and companies like apple are fighting it however some android phones have the feature unknown though to most users companies like samsung at t and t-mobile are also on board fema calling and saying they support it they say it's a communication device that certainly comes in handy during a crisis live in the newsroom dave elias nbc2 okay so that that i hope you found um interesting um so when we're talking about fm radio we're not just talking about technology from 50 years ago we're talking about radio which millions of people rely on every day for news for entertainment for music vital traffic information and in emergencies it could provide a lifeline for people who don't have access to the internet okay remember i said frequency and phase one is the derivative of the other so which is the derivative of which is frequency the derivative of phase or a phase the derivative of frequency okay so think about that for a second because that's almost 50 of today's lecture so is frequency the derivative of phase or is phase the derivative of frequency okay frequency is the derivative of phase and we'll look at why that's important in a second so let's talk about fm now remember we said f i is the instantaneous frequency now just like we have the instantaneous frequency we also have the instantaneous phase so phi is your phase or your instantaneous phase now your instantaneous phase can be can be simply some function multiplied by your message or it can be the integral of your message so where does that come from remember if frequency is the derivative of your phase then your phase is the integral of the frequency and that's where this integral comes from now we're often very interested in something called the maximum frequency deviation sometimes often just called the frequency deviation now this frequency deviation delta f sometimes or delta f max more formally that frequency deviation is how far your instantaneous frequency will deviate from the carrier frequency so your instantaneous frequency is equal to your carrier frequency plus the derivative of your instantaneous phase so that maximum deviation that's what we call the frequency deviation and just like in amplitude modulation we had the modulation index or the depth of modulation and that was in amplitude here too we have something called the modulation index it's also a depth of modulation but it's modulation and frequency so instead of saying it's a ratio of max remember we had e max plus e min e max minus e min we had this for am and that was a ratio of amplitudes here we have a ratio of frequencies so also unitless but this is our new modulation index for fm so it's the ratio of the frequency deviation delta f to your baseband bandwidth so this is what we used to call fm so delta f over fm that's your modulation index okay so this is the second thing we really need to know today the first thing was that um the frequency is the derivative of the phase and the phase is the integral of the frequency the second thing is that the modulation index is the ratio of delta f to w or to fm so the modulation index is proportional to the frequency deviation or the maximum frequency deviation and inversely proportional to the baseband bandwidth so if you think about it a big modulation index is where you have a great deviation in frequency just like in amplitude modulation a big modulation index is where you'd have a big variation in amplitude so that was fm for pm it's similar but now if you write out the whole band pass signal representation x of t we have some constant amplitude and we have cosine of some phase now that phase that instantaneous phase has a carrier component and it has this component which um uh well i should have called this the angle and this the phase so the angle consists of a carrier component and this additional phase component and as we just said in the previous slide this for pm is just the product of some constant times m of t and for fm is the integral of the message multiplied by some constant so just like we had delta f max in frequency modulation we have delta phi max in phase modulation and delta phi max is the same thing it's just the maximum deviation of this phase or the angle from the carrier so your modulation index for pm you don't use this often but it's simply that maximum phase deviation so beta for fm was delta f max over fm and for pm it's delta phi max but we don't divide it by anything so we're not going to talk about demodulation in this lecture that'll be in lecture eight i want to talk about a few quick things i want to talk um about the power in am sorry in fm and pm and note that the power doesn't vary with modulation or modulation index whereas the power of amplitude modulation signals did vary with modulation index also note that fm and fm and pm they don't have an envelope because the amplitude is constant now we've said before the frequency deviation of the carrier is proportional to the amplitude of the modulating message so whether it's you know k p times m of t or k f times the integral of m so one is a phase and one is a frequency but the frequency is proportional to the amplitude so m here represents the amplitude so in practice we would use a vco so that's a voltage controlled oscillator where the frequency of the output is proportional to the input amplitude so that satisfies exactly what we just described there okay so here you'd have your audio signal it'll be amplified and that would drive a vco and that would drive the output so this is a it's not an electronic um circuit but this is how you can imagine fm being generated by using some device where the output or the frequency of the output is proportional to the amplitude of the input okay quick question really easy say we have an am signal sorry an fm signal that looks like this it's a cosine and inside the cosine we have two things we have the carrier and we have this now that it's either the message or the integral of the message it's actually kf times the integral of your message m the question is what's the average power of the signal so we're interested in the power of our fm signal so where should you be looking to find the power remember this is a cosine so it's a sinusoid should you be looking here here here or here now remember the amplitude of this fm signal is constant the amplitude here is constant how much is the amplitude well that amplitude is simply six times two isn't it so peak to peak is six times two because you've got the six there so what's the power of this signal the power is the mean square value and even though the frequency varies we're not interested in that we're interested only in this amplitude here so your amplitude defines the power so it's a squared over two or if you like think of it as your rms value squared so that'll give you 6 squared over 2 18. that's your power okay similar signal similar signal it's fm we have the same amplitude there that's your carrier but now we have a little bit more going on here so it's a slightly strange signal you're not you don't normally see a cosine with a sine and another sign inside the argument so inside the angle here and that's because it's fm isn't it so by definition you're modulating the frequency and the question is what's the maximum phase deviation so how far will the phase deviate from the phase of the carrier how far will the phase deviate from the phase of the carrier so to answer this question we need to find the phase the instantaneous phase so you need to find the instantaneous phase or find the angle and subtract this carrier component and then ask yourself what's the maximum value what's what's the maximum value of that okay i think there's a detailed solution on the next slide but basically you you you will find a value of t such that these two sign sinusoids will be in phase and the 2 will add up with the 10 and you'll end up with 12 radians as your maximum phase deviation so this is the solution to the first question first example and here we have the solution to the second so when it asks for the maximum phase deviation what we want to do is subtract the instantaneous phase from the carrier phase or vice versa and find the maximum value of that so what's the maximum value of that so again if there is some value of t for which these sine waves will be in phase and i think it's always safe to assume that's the case even if these are not so you know you have a pi here which is irrational so there might not be a point in time where these actually add up exactly to make 12 but it's still a safe assumption to assume that these can be added so even if we don't get exactly 12 we'll get something close enough to 12 for that to be a valid um answer for the maximum phase deviation so sometimes we sometimes we just drop the word maximum we say that's the phase deviation but what it means is it's the maximum phase deviation so quick recap what have we covered today we're talking about variations in frequency of phase your modulated signal is in there so the message is encoded somehow in there how does that happen by some some function of the message that function can be an integral if we're talking about fm because the phase is the integral of the frequency or it can just be a direct product so phase is the integral of frequency that's something important we've learned today we'll look at this in more detail in lecture eight so in summary fm and am we've studied about so fm and pm we've studied how they're different to ankle amplitude modulation some of the advantages and disadvantages where fm is used how we generate it in simple terms mathematically what we mean by the modulation index and this idea of instantaneous frequency and instantaneous phase so we'll go into more detail in the next lecture but that's enough for a quick introduction to angle modulation next on wednesday or wednesday night i will release lecture eight where we'll talk about demodulation but you probably won't actually receive that online until thursday in any case on wednesday you should be busy with your class test again if you can't make it for 10 o'clock i need to know so you need to tell me if you can't make it for 10 o'clock for that test okay so there may be some way to rearrange or reschedule your test but you need to tell me before the test okay also don't forget there is a progress check um this week so before sunday make sure you complete that i hope you found that helpful just as a reminder this is where we are now next week we have the easter break for two weeks so you have a two-week break i call it a break but really it's a good chance for you to prepare yourself for the final exam okay so even though you will have completed your first class test i think it's still a good chance opportunity for you to prepare yourself for your final exam because you won't get a break after your final lecture so your final lecture so um this is lecture 7 8 9 10 11 12 and immediately here you have your exams okay so you won't get a break and it's an 11 week semester so really the time to prepare for your final exam is now so as soon as you have that break make a start rereading all this content okay so until we meet again stay stay and stay home