0:05 hello everyone how's it going my name is Dan the Tudor and today we are going to be talking about low-pass versus high pass filters so before we start talking about the filter side of things I want to talk more about the behavior of reactants in an inductor and reactants in a capacitor in an AC circuit because if you don't understand this then there's no point in explaining low pass and high pass filters it's going to go right over your head so if you're a member we have an equation for reactants in an inductor it's 2 pi F times L and if you remember the reactants in a capacitor it's 1 over 2 pi f c where f is the frequency L is the inductance and C is the capacitance and when do you use
0:52 these equations you use them whenever you have an AC circuit and you want to find the resistance in the circuit except you don't have resistance again this is called reactants but as far as you're concerned reactants resistance impedance they're all funny words for the same thing really it's just resistance at the end of the day and there's something you should know about resistance it affects the current and let me show you how so basically the relationship is pretty simple the higher the resistance or the higher the reactants it means that you have a lower current and vice versa if you have a low reactant or a low resistance then you're going to have a high current and they are inversely proportional and this makes sense if you want to think about
1:38 cars on a highway for instance if you have a high resistance think about like a short road like a one or two lane road and you've got all these cars on here well the cars are not going to be moving very fast because you had a high resistance you have a lot of traffic there's only a small current moving right there compare that if you have a big Highway with like four lane and there's only a few cars on the highway and those cars are going to be zooming there's a very high current because you had a low resistance so that makes sense intuitively I think and so here's why it matters back with these equations here it's because the frequency is going to affect your reactants for the inductor and capacitor so let's just focus on the inductor
2:24 first XL equals 2 pi f l if you have a high frequency then you are going to have a high reactants and the reason why is because that's in the numerator you plug in a bigger and bigger number you're going to increase your reactants conversely if you have a low frequency then you're going to have a low reactance and that of course means that you're going to have a low current for the first case and a high current for the second case and then that's all for the inductor and so basically what that means is that if you imagine an inductor in a circuit it normally looks like this this is
3:10 we'll say normal conditions well if you have a high frequency again high frequency means High reactants it's like you're going to have an open circuit which is going to look like this it's going to be we call an open circuit and then on the other hand when you have a low frequency we call it a short circuit and it's as if the inductor is not even there as far as the human eye can tell it looks like a straight portion of wire because there's such a low resistance or reactants and we call that a short circuit this is going to be very important when we talk about the filters low pass and high pass because this is what's going on and then now if I talk about the capacitor it's going to be the
3:55 exact opposite everything I said will be flipped basically if you have a high frequency that means you are going to have a low reactants because it's in the denominator and the fraction is becoming smaller and smaller which means you're going to have a higher and higher current similarly if I have a low frequency you're going to have a high reactants and you're going to have a very low current and finally let's draw the picture of that again so this is what a capacitor looks like normally if we have a very high frequency like we just said it's going to look like the opposite of the
4:42 inductor which is going to be a short circuit at high frequency short circuit basically the capacitor is not even there and then we compare that to low frequency where the capacitor looks like an open circuit it literally looks like there's a gap in the circuit and we call that an open circuit okay now with all that information we can now start talking about the filter side of things what the heck is a low pass and a high pass filter so first let me draw the graphs and then I'll explain them so this is going to be a graph of amplitude you can think of amplitude as a voltage it's not exactly voltage but you can think of it like that versus the
5:27 frequency and this is going to be my high pass filter this is what the high pass filter looks like the word high pass means high frequencies are allowed to pass and every other frequency is going to be cut out so basically I have only the high frequencies have amplitude so low frequency zero zero zero zero and then eventually at some point we reach a Max amplitude of whatever and then it stays there this is what the graph looks like roughly and that's supposed to be a straight line up top maybe I can draw maybe I can draw that part better supposed to be flat like that okay perfect and again this is the high pass filter because it allows high frequencies to pass through and then on
6:13 the opposite side of things we have the low pass filter which is going to look like this it's just the opposite of the high pass filter and it is going to allow low frequencies to pass through but then we are going to cut off the high frequencies and it goes to zero amplitude like this and so that's it for High versus low pass filters but the question becomes how would I build a circuit that acts like a high pass or a low pass filter it's going to look like this imagine that I have an AC power source right here connected to a resistor like this and an inductor like this and let's say I want to have vs where s stands for source so
7:01 it's your Source voltage and then we have V out right here it's the voltage at the output which we're going to measure right here okay this is a high or a low pass filter it's one of the two we don't know which one yet but to find out let's consider what's going on at high and low frequencies so at a high frequency your inductor like we said is going to have a high reactance which means a low current it's going to look like an open circuit let me draw this again so that it looks like an open circuit for again high this is high frequency it's going to look like this for high frequency now at your first guess you may say that well the voltage is zero
7:46 because it's like literally there's a hole in the graph there but actually as it turns out it's not zero voltage as a matter of fact the voltage is equal to vs and the reason why is because if you want to find the voltage of anything in this class then it's just going to be the voltage I'll say VA and the voltage VB it's the voltage between these two points is your voltage now since there's no current in this circuit and why is there no current like we said before high reactants no current because there's no current it's like there's no voltage drop across the resistor and so what that basically means is that the voltage everywhere in red is the same the voltage everywhere at the red is vs and the voltage
8:33 everywhere in green on the lower side is going to be zero like our ground and so therefore VA minus VB vs minus zero your voltage is just vs now if you don't understand that explanation that's fine let me tell you the shortcut that you should memorize basically all I'm saying is that if you have an open circuit like this then the voltage is the source and so what that means is I can already tell this is going to be the high pass filter because your voltage was high for a high frequency so this is definitely going to be a high pass filter in this configuration and if you don't believe me well then we can also look at the low frequency side of things at low
9:18 frequency it's going to be the opposite it's going to be the short circuit it's like that wire is not even there and I'm just going to tell you for short circuits and this is true always not sometimes it is true always for short circuits the voltage is zero automatically and the reason why is because all the voltage is basically going across the resistor so that resistor is now vs for its voltage but I don't want the voltage at the resistor I want the voltage at the inductor for this example so the voltage is zero volts meaning that at low frequencies no voltage and that further conforms and that further confirms it's a high pass filter so once again this shape right here was a high pass filter and now I'm
10:03 going to switch the positions of the inductor and the resistor and let's see what happens so again I want to find the voltage here across this circuit element on the right it's not always the inductor it's whatever I choose to be and this time I want to look at the resistor for that voltage so again this is vs if I consider high frequencies again for the inductor that's going to be the open circuit like we said before so therefore your graph is going to look like this well not graph circuit but you know what I mean and so since you have the open circuit that means this voltage right here is equal to the source voltage it's got all the voltage but again I don't care about that voltage I want the voltage right here across the
10:50 resistor and that voltage is zero because the open circuit stole all the voltage so it looks like at high frequencies no voltage looks like we have a low pass filter because all the high frequencies are going to be cut out and only the low ones are going to pass through now technically we haven't looked at the low frequencies yet but I'll tell you if you do look at it it's going to be the opposite it's going to be a short circuit for the inductor and the resistor stays the same again for the short circuit that voltage is zero which means all the voltage is going across the resistor now so that confirms it's a low pass filter and now let's just look at the last two configurations you can have which is the
11:35 capacitor if you have a capacitor circuit that looks like this again we are going to consider the high frequency case first at high frequencies if you remember that's a low reactance which means a high current it's going to be a short circuit which basically means the capacitor it's like it's not even there so if I were to redraw the circuit I have a resistor here short circuit here for the capacitor and once again Short Circuit the voltage is automatically zero it looks like for high frequencies it was Zero that means I already know it's going to be a low pass filter but just to confirm we can look at when the frequency is low for a low frequency
12:22 again low frequency means High reactants which means low current which finally means an open circuit and obviously I have all this stuff memorized it's actually not true I don't have it exactly memorized but I can just think my way through it in the same way I've been saying out loud and the only reason I know that is because I practice and if you practice then you too can be good at circuits but I have very little faith in you for practicing because I know my students and then for the open circuit scenario we're going to look like this where it's disconnected that means all the voltage is going across your open circuit and since all the voltage is going across at the low frequency that confirms that this is a low pass filter and then maybe you can try the last one
13:07 on your own AC circuit capacitor connected to a resistor like this again I want to know the voltage V out right here and this is V Source this time you tell me will it be a high pass or a low pass filter and why and I want you to think about what the circuit looks like at high frequencies and low frequencies just like I've been doing so go ahead and pause the video and try that on your own okay I'm going to explain now so first I would look at the high frequency case for high frequencies for a capacitor the capacitor is going to be a short circuit again and so that's going to look like this with the short circuit and the resistor here now it looks like V out
13:54 since you had a short circuit all the voltage is going across the resistor so immediately I know it's going to be high pass filter because at high frequencies the resistor got all the voltage then just to confirm our answer what you don't actually have to do once you're on the test but you know if you have extra time you can I suppose if you consider the low frequency case again the capacitor is going to act like an open circuit and so basically what I would say is open circuit here at the top resistor still here this time all the voltage is going across the open circuit that means there's none left for the resistor and so therefore the V out would be zero
14:40 it's definitely a high pass filter for this one and so one more time when you have the low pass versus the high pass this is what the graphs look like this is the graph for a low pass filter only low frequencies are allowed to pass high frequencies can stay and then the opposite is true for the for the high pass filter high frequency stay low frequencies are cut out and that's going to do it for today thank you all for watching I hope you have a great rest of your day and I'll see you in the next video bye-bye [Music]
