LCR frequency response & quality

if a lot of people speak together we can't make out anything but a radio cam even though it continuously receives hundreds of different radio signals we can make it listen to any particular channel how does it do that well radios have something that we don't lcr circuit so let's see how it uses resonance to tune into specific channels we've already seen before that even if you keep the voltage or the values of inductance or capacitance or the resistance all of them are constant and just change the frequency the current will change dramatically if the frequency is very low or very high we saw that the current is very tiny the pink arrows over here are the current but if the supply frequency equals a magic number given by 1 by 2 pi square root of lc we saw resonance this is when the impedance in the circuit becomes minimum and the current goes haywire now if you need a refresher on this then we have a dedicated video called lcr resonance and resonant frequency feel free to go back and check that out but what i want to do here is to understand this relationship between the frequency and the current a little bit better and one of the ways to do that is to draw a graph so what i want to do is i want to go ahead and plot a graph of the current i naught versus the frequency okay what will happen to i naught i'm basically want to plot the same thing that you're seeing over here but on a graph so that i don't have to keep watching this animation now before i draw it i want you to take a shot at this one clue is that we know that at resonant frequency the current is maximum so let's assume that that resonant frequency is somewhere over here so given that can you make a guess as to what this graph would look like go ahead give it a shot all right if you're giving it a shot let's see here's how i'm thinking i know that at this point my current has to be maximum which means if i go away from here on either sides the current should decrease so with that if we plot the graph here's the maximum and on either sides the current decreases decreases and that's what the graph would look like again notice it's telling us the same story at resonant frequency the current is maximum but if you go away from it with too low or too high frequency then notice the current becomes minimum so we can get rid of this animation we can now just focus on this graph okay now with this graph let's see if we can decipher the mysteries of radio the important thing to understand is that different different radio stations get broadcasted at different frequencies for example i'll just name a couple of famous radio stations that i am aware of i know one radio station called radio mirchi and all the messages over here gets broadcasted at 98.3 and that's why you may have heard this number a lot 98.3 megahertz of frequency so whenever you're listening to radio mirchi or if you want to then that is that frequency of 98.3 megahertz similarly let me just let me just show one more another one which i remember is big fm and again they have that punchline 92.7 big fm and that basically means they are broadcasting all their messages at 92.7 megahertz now let's imagine that in our radio currently the lc values are such that if you calculate the resonant frequency it happens to be exactly 98.3 megahertz let's assume that what's going to happen well here's our radio and here are both the radio waves i've shown there are multiple radios due to lots of channels but let's assume just two they're both hitting our antenna and as a result antenna vibrates with both the frequencies and what an antenna does is basically converts radio signals into electrical signals so because of these two the antenna is trying to drive our lcr circuit at both of these frequencies but look at what look from from the graph we can see that whatever messages are coming at 98.3 it's able to generate a much larger current let me show you that it's able to generate a much larger current the current that that is generating is over here due to the radio mirchi signals and the current that is generated due to the big fm look at that that current generated is very tiny and as a result this very high current goes through the speaker and this current well it can hardly drive the speaker and as a result you will only hear the messages from this particular channel now imagine you want to switch to big fm what should you do i think you can now guess well now we need to reduce the resonant frequency of our lcr circuit how do we do that well you have to either now since you want to reduce this we need to increase this so you either increase the inductance or you increase the capacitance and there are ways in which it can be done different radios do different ways for example in some radios when you turn the knob the distance between the plates of the capacitor changes and you might know as that distance changes the capacitance changes interesting isn't it and so just by turning the knob one of them will change and in this particular case all we have to do is increase the value of capacitor and as you increase the value of capacitance the resonant frequency will start shifting towards the left so the graph will start shifting towards the left and so your new graph as you increase the value of that capacitance your new graph will eventually come to this now the opposite happens now it's the big fm it's these messages that start exciting your radio because your radio's resident frequency has changed and as a result your radio will start picking up those signals and this is how by using resonant frequency concept resonance concept you can tune into any station that you want beautiful isn't it all right now let's make things a little bit more interesting imagine your friend also has her own radio and let's assume for the sake of simplicity that in her radio the value of inductor and the capacitor as of now is exactly the same so it's resonating at 98.3 megahertz but there's one difference let's say that the resistor the resistance of her lcr circuit is higher than your lcr circuits resistance so the value of resistance is higher i want you to predict what that new graph of this new radio is going to look like same resonant frequency but higher resistance again can you pause the video and give this a shot all right because it has the same resonating frequency it will peak at the same frequency however at the peak value the current would be smaller because the resistance is higher and so the graph that we could expect is somewhat like this you immediately see the graph is much flatter than before and that has consequences for example if you just concentrate on this graph so let me just get rid of the other one and now look at what's going to happen to the radio just like before this frequency is going to generate the maximum current but notice because the graph is so flat the current generated by the big fm frequency is considerable it is smaller but it's considerable which means in this particular case your radio might be giving some amount of message from this as well there will be some mixed messages that you'll be getting you'll be able to hear this as well as a little bit of this as well compare that with what we got before before the difference was so huge it was able to select this frequency very nicely and reject everything else but now notice it's not all that great so you can pretty much agree and let me get both the graphs okay we agree that this curve has a higher quality of selecting the frequency and rejecting everything else which is off resonance higher quality but this one has lower quality so not all lcr circuits have equal quality if you want a very high quality ability to select very specific frequency and reject everything else you need the graph to be very very sharp and so such sharp graphs are what we call high quality lcr circuit now of course the engineer inside you might actually be more curious and be wondering okay can we give a number to it how do i calculate this quality and that's something we'll talk about in a future video there's a number called quality factor but let's not worry about that right now but i'm pretty sure one thing you can immediately get is that quality is inversely related to the resistance notice if you have lower resistance you end up with a higher quality circuit with a higher resistance you end up with a lower quality circuit and so although we don't use radios as much today it's a perfect reminder of how lcr resonant circuits can be used to tune into very specific frequencies sometimes i wish i too had this ability to listen to just what i want and filter everything out