01 - The Non-Inverting Op-Amp (Amplifier) Circuit

hello welcome back to engineering the circuit analysis we're talking about op amps up until now we've talked a great length about the basic principles of an op amp we've talked about the inverting op amp configuration which is really really common the summing amplifier configuration now we're going to talk about the non inverting amplifier circuits so in this case we're going to talk about an op amp configuration where the output is not an inverted version of the input now I could just give you the equations right now I could write it down tell you here's what the circuit looks like here's the gain equation here's the output here's the saturation region and say go have fun and most of you would probably do just fine but I kind of see my job to sort of you know explain what I've learned and kind of how these things come about so that you get a little bit deeper understanding than just using equation slang like a monkey or something like that so we're not trying to do that here we're trying to understand so before we actually get into actually giving you the punchline and deriving everything I want to show you what I'm actually talking about by in a non-inverting amplifier circuit so we already talked about the concept of the inverting amplifier now and all of the circuits that we've done they've all been DC inputs but still I've been trying to kind of give you the ideas we've been going along that you can hook up alternating current we haven't talked much about alternating current this class yet but you got to know what we're going we're going to be having an alternating plus or minus current that might look like let's say this let's draw a sinusoid or something like this right so the inverting amplifier if you take this to the input right it's going to give you an output signal on the output side that's going to be a look exactly like the input except every point that's positive is going to be mapped to be negative and every point that's negative is going to be mapped to be positive so if the input signal looks like this the output signal is basically going to look something like this right so you see every point that's positive becomes negative and every point that's negative becomes positive so that's why in all of the circuits when I flows DC sources when I sent positive one volt in you get a negative whatever volt out whenever we had the inverting configurations before or if I send a negative half a million you always got a positive value out because it was inverting it now you can also make the signal bigger or smaller you can amplify it in the larger sense or in the smaller sense but always in those inverting configurations the sign of the end the output was always opposite of what the input was just like I'm kind of drawing for you here now in most applications inverting an output like this is not a problem right but in some cases maybe it is maybe you don't want an inverting version maybe you want to be able to amplify this thing but not have it be inverted like this so we're gonna talk about how could you accomplish that now you could accomplish it you could hack it together by putting two inverting amplifier configurations in series of one another so for instance you could get an inverted the kind of signal you're looking for if you're in the first stage of the amplifier you place signal in like this and then the next stage in right what are you gonna get you're gonna get after the amplification of the first time you're gonna get something that looks like this is exactly what we're drawing on the board here well you can take the output of this and feed it into yet another stage of the amplifier which would take the previous stage here and invert it again so you see then you start with something like this and you end with something like this so you could have amplification going on and different into different stages maybe make it a little bit bigger here and a little bit bigger yet here and then you would have a signal that would look like this here and also like this now I'm not gonna draw a detailed drawing of this but between this guy to make this happen you would have an op-amp that would look something like this you would have some output like this you would have this is an inverting I'm saying weak how could we do this with inverting configuration is what I'm trying to say then we have something like this we have an input resistance here in a voltage source like this right and then we have a feedback resistance right this is what we've been doing all the time this is inverting amplifier configuration that's going to take something with a positive input and give it a negative output if we tap it off of here so this would be V naught the V output right but then if we take this output this V out here and run it through another inverting op-amp which let's say we stick it in between these these stages like this so I'll change colors and we'll draw this one something crazy like pink right so we have exactly the same thing we have another amp fire here we have another output root resistor we call this one V out again this would be plus minus so it's an inverting configuration this is tied straight to ground and then here we have an input resistance like this and we're sending the signal in like this and we also have a feedback resistance would you agree that this is also an inverting amplifier configuration right you have the inverting terminal where the input signal is driven in you have a feedback resistance source resistance this is grounded this is through an output the only difference is you see basically you're gonna take the output of this one V out and you'll connect it right over here to drive the second stage again so you inverted here and you invert it again that's how you could do all of this stuff with in other words if you really cared about the input signal not being out of phase or not being an opposite signs of the input signal you could hack it together by just putting two inverting amplifiers in series with one another and adjust the games correctly and you could do it all just fine but then you have to have two stages you have to have two op amps so it increases the complexity of the circuit a little bit honestly as far as a fast way to do it that's probably the fastest way to do it because you have a lot of experience with making these inverting configurations but in this state in this lesson we're gonna talk about how to make a non inverting this is called a non-inverting amplifier because the input is not inverted with the output we're gonna learn how to make a non-inverting amplifier circuit without using two separate stages and connecting them together like it like this kind of hacked way to do it we're gonna do it with one op-amp and a different configuration of resistors and we're gonna go through the proof to show you why the output is not an inverted version of the input and it's going to have a different gain equation than the ones that we've used in the past for the inverting configuration so I wanted to show you in a big picture you know how it would be done and now we're gonna go over here and show you or how you could do it with inverting amplifiers now I want to go and show you how to build this thing with one op-amp and we call it the non-inverting and/or the non-inverting op-amp right so we have one amplifier right like this and of course we have VCC and we have negative VCC as we always have but other than that it completely differs from what we've done before so let me go ahead and draw this here this is gonna be Plus this is gonna be - okay and what we're gonna have is over here we're gonna drive over we're not we're going to drive we're gonna have a resistor here I want to tie that to ground we're gonna have a feedback resistor okay we're gonna call this resistor R sub s we're gonna call this resistor R sub F because it's the feedback resistor now the interesting thing here is notice that in all of these other configurations like down here the inverting amplifier we always drove the input signal into the inverting terminal so that's why you know when you go through the math you figure out the reason that we're getting an inverted output is because we drove the signal through the inverting terminal here there is no source here I'm not driving the input signal into the inverting terminal anymore I'm actually going to drive it do the other terminal through another resistor that I'm gonna label here a second for you like this so this is gonna be plus or minus we're gonna call it V sub G it's just the source voltage I'm just calling it V sub G right now and this is R sub G alright this is basically the this is basically what we call the non-inverting amplifier configuration so let's label a few more things we'll talk about it and then what we're gonna do is derive the gain equation that comes about from this configuration and you'll see that it makes sense that it's non-inverting and so on you'll learn how to use it so when you see something configured like this you'll know how to handle a problem like this first of all the output is tapped right here we call it V out that's not terribly terribly unusual it's coming off the output like this it could be a resistor that is across as well all right and then we're gonna call this remember way back when we introduced op amps we said the current the voltage here we called v1 and we call this one v2 the current going into this terminal was v1 the current going into this terminal is v2 so right now I'm just going to write this as V and right this is v2 and I'm basically going to put a little negative here we'll do it like do something like this put a plus here and a plus here to kind of remind you basically what I'm saying is that the voltage at this terminal of this op-amp relative to ground is called positive e1 and the voltage here from this terminal to ground is called v2 and the way you can remember that this is the convention anyway is notice the v1 is a line here the number one is a line well that kind of goes with the inverting terminal that's our convention and two goes with the positive terminal so this is basically what it is so we have a resistor here we have ground we have a feedback resistor and we have a the resistor that comes after the source here in this derivation we're calling VG the source doesn't matter it's gonna be an actual voltage source in a real circuit it might be one or two volts or whatever this is gonna be so many ohms so many ohms so many ohms and so on and when you drive a signal through this and when you measure this on the outside over here you're gonna be able to amplify it amplify the signal and you're also gonna be able to see that the output is always it's not inverted with the input in other words it's not gonna be the negative sign of the input it's always gonna have the same sign so if I Drive one volt in here positive one volt I'll get positive some voltage over there if I Drive this with negative 2 and I have millivolts I'm gonna get some negative voltage over here and I'll be able to amplify it accordingly so we need to just jump into it it's not hard it's not a complicated derivation but we're gonna do it step by step so that you understand so I want you to recall a few things I want you to recall that this voltage at this terminal and this voltage of this terminal I've label them v1 and v2 but because of the ideal op amp and the virtual-short condition that exists there v1 is always equal to v2 now for a real op amp they're really close within a few millivolts but for an ideal op amp we're saying that they're actually equal and also recall that I sub 1 is equal to I sub 2 is equal to zero I haven't labeled them here but I sub 1 is the current flowing into this op amp I sub 2 is the current flowing into that op amp but because real ideal op amps have an infinite input resistance and no current can go into there so we basically know that there's no there's no current there so we're just writing this down okay because all of these things are true which should come as no surprise to you because we've been talking about it forever then the following is also true v2 has got to be equal to this v2 has got to be equal to VG whatever that is and we've done a problem like this very similar a few several lessons ago when you have a voltage source here connect it through a resistor into the into the input of an op-amp like this you know that no current is flowing into this op-amp it isn't because there this is an open circuit here so it's almost like you cover it up and it's just open air this thing the other side of this resistor is just connected to nothing it's connected to it a hundred billion ohms or something crazy like that so there's no current flowing through it so whatever voltage is on this side has got to be the same exact voltage on the other side because there's no voltage drop across that resistor so if this were for instance one volt on this side then it would be one volt here if it were negative three volt it would be negative three volts here because there's no current going through that resistor so what I'm saying is the voltage v2 is the same as the source voltage VG on both sides of that resistor that's all I'm saying okay and this is because of the fact that I sub two the current going into the op-amp is equal to zero so because this is true and because of the virtual-short then I also know that v1 must be equal to v2 which must be equal to VG so all I've done is a lot of complicated looking math which basically says that since these guys are the same voltage and because this voltage is the same as this one you know what the voltage up here is v1 it's equal to the source voltage that's the punchline that's all you need to know because of the Vote virtual-short and because there's no current in the op amp if this were five volts then this would be five volts which would also mean this were five volts if this were negative two volts then this is negative two volts this is also negative two volts all of that stuff doesn't require analysis because it comes from the ideal op-amp assumptions so you don't have to as long as you know what those are which the virtual-short condition between the terminals is always true and there's no current going in the op amp then this falls out straight away from that all right so that's important because you know that this is now equal to VG so what this means when you really look at it if you turn your head sideways then and kind of ignore the bottom of this op-amp ignore the source ignore this ignore the triangle even and you look at this voltage and kind of see that it goes across this resistor and then you have kind of a tap off point we call it v1 and then it goes through this to ground if you turn your head sideways this kind of becomes a voltage divider right when you look at it this voltage is kind of across the whole thing because this is tied to the same thing as here the V knot is across the entire set of resistors but in the middle you have a tap off point we call it V sub 1 so it becomes a voltage divider like that and I'm gonna show you I'm trying to decide if it's better to show you here or on the other board hmmm I think we're going to show you on the other word let's just slide right over again turn your head sideways you'll see this as a voltage divider I'm going to draw it for you so it's a little bit clearer for you to see okay so this becomes a voltage divider or you can model it as a voltage divider and what I mean by that is the following thing you have this resistance and then you have another resistance and they're connected to ground and this one is called R sub s and this one's called R sub F and then here you have plus minus V out and then here you have a tap off and this one's called V sub one so you need to be able to look at these two things and see that they're the same thing if you look sideways the voltage at the far end of the RF is called V naught that goes all the way to ground which means it connects across both resistors that's why V naught goes from here all the way to the bottom and across both resistors the only thing is right in the middle between these two resistors is something we're calling V sub one like this okay so when you look sideways you should see that now because it's a voltage divider the rest of the analysis is kind of incredibly simple because then you know what's the point of a gain equation what are you trying to find you're trying to figure out what the output of of the op-amp is as a function of its input when you know the output is a function of the input you know the multiplicative thing in there the multiplicative thing that when you multiply the input times that to give you the output that's what we call the game right so you need a relation that relates the output to the input and we'll see how we get there in a second so what we can do is we can say then the following is true V sub one just looking at this diagram straight as it is is going to be equal to this voltage drop v naught times what well it's a voltage divider it's this RF over the sum of them right or actually I have it have it wrong it's not going to be x this is going to be times this guy so two BRS over RF you know what let me write it it's the same either way but I'm going to write it as R s plus RF make sure you understand that basically you have a voltage from here all the way down what you're saying is that this tiny little fraction of the voltage v1 from here to the ground is equal to the total voltage times the fraction of this resistance divided by the sum of the total this is a simple voltage divider from basic basic circuits right and that's what it is right there but we also have another constraint we know but we know that v1 is equal to VG and that we wrote a long time ago here v1 this guy is equal to the source voltage because of the virtual-short condition and everything else we talked about so basically even though I wrote it in terms of v1 I'm gonna rewrite the whole thing again it's kind of a waste of ink but I'm gonna rewrite the whole thing again we're gonna say that V sub G is equal to V naught times R s over R plus R F now look at what we have the input voltage the output voltage these are kind of variables you can change one and the other one changes but these resistors are functions of the circuit right there just resistors you can change them and change everything else so what we want is an out if we want the output of the circuit as a function of the input here we have the input as a function of the output so we're gonna solve we're gonna rearrange and solve for V naught so basically if we flip this around again what we're gonna get is V naught is going to be equal to the G when we divide by this mega fraction on the other side it's gonna flip that fraction over so you're gonna get R s plus r f over R s let me double check them right so now we have the output of this circuit as a function of the input and this is the multiplicative asset that basically changes the input multiplied by this to give us the output so this quantity right here is what we call the gain of this amplifier okay that's the bottom line okay now there's a couple of different ways to write this but this is the simplest way to write it you have the input times the game gives you the output now notice this game is very different than the game for the inverting configuration the inverting configuration was simply a negative sign in front feedback resistance divided by sorcerer's this is very simple simple fraction with a negative sign in front first of all I want you to notice there's no negative sign here all of these resistors are positive numbers resistors can't be negative right not in circuits and on the basic circuits anyway so since all of these are positive numbers there's no negative sign in front that means that the output signal is always going to be the same sign is the input signal that's the proof of what I've been telling you this is the what we call the non-inverting configuration does not invert the signal because there's no negative signs here whereas the gain equation for the other one it actually had a negative sign there now what we're gonna do is rewrite this a little bit further this is fine to use but I want to you know I want to I want to make it a little bit clearer so make sure I have this correct what we can do is we can rewrite this we can say actually I'm going to change colors we can take this relation and make it a slightly simpler we can say v naught is equal to VG and on the inside notice what we have a big fraction right divided by this so we could rewrite that as RS over RS plus our F over Rs make sure I understand this if you add these fractions together you have a common denominator and you'll add the numerators all you're doing splitting the fraction up but RS are over RS this is just a fraction equal to 1 so we can say that V naught is equal to VG 1 plus RF RS this is a very common way that you can write it neither of these is totally fine but you could also say that this is the game alright this is the game so let me go ahead and just on the next board let me go ahead and write the game down again and then we're going to talk about some interesting facts that come about because of this so all I'm gonna do is rewrite these two equations exactly as they sit I shouldn't say I'm gonna rewrite them exactly as they said this is this is the output as a function of the input I'm gonna write the gains on the next board so we have a nice clean board to talk about and then we'll draw some conclusions and then we'll be done with this lesson basically here's what we call the gain of the non-inverting op-amp right there's two ways to write it depending on your book you'll see it two different ways the game can be written as one plus the feedback resistance over the source resistance or the gain can be written as R s plus R F over s so this by far is the most important thing to write down and it's exactly the same thing here we have RS plus RF over RS 1 plus this fraction all I've done is take those out and write them down ok so this is the most important thing here and those of you that look carefully at this top version of it this is why it's very nice to write it like this what do you see from this these resistors have always they always have to be positive I mean whether or not they're big or small they're always going to be positive and so this fraction is always going to be something bigger than 1 right it's always it may be really tiny point 0:01 whatever it's not gonna be I shouldn't say bigger than 1 I'm saying it's gonna be a positive number something it's gonna be a positive number when you add this to the number 1 what you're gonna find is the gain of this configuration is always greater than 1 always and that's really important so I'm gonna write that down the game is always greater than 1 there are no resistors that you can hook up into this configuration to get a gain less than 1 even if I put one on the top and 100,000 ohms on the bottom I'm still gonna have a positive number it'll be small but it'll be positive and I'll be adding the number 1 to it so the game will be 1.000000 1 it'll be slightly bigger than 1 that means that and this is incredibly important you always have a positive gain greater than 1 when you build this amplifier configuration like this so if you think back to the inverting amplifier when the I know it's drawn a little weird but when the game was this / this with the negative sign you could choose those resistors so sometimes you had to gain bigger than one sometimes you had to gain less than one that means you take your signal and you make it smaller right the game is less than one you're multiplying the input signal by a fraction negative sign but with by a fraction to make the output smaller in the inverting configuration you had that flexibility to make a gain smaller than one to actually make your output signal smaller here you don't have that flexibility you cannot create a game smaller than one so the best you can do if you choose these resistors to be equal to one another is you have a game well even if you choose them where one is very big and one is very small you're always going to have the closest you can get to one is gonna be super super close to one 1.000 something and then all the other games are going to be higher than that so basically don't use this configuration if you actually want to attenuate your signal that's what we call it when you make the signal smaller we attenuator we make it smaller do you want to make the game bigger then power a loud speaker or something great the games always gonna be bigger than one but don't ever try to make the signal smaller than then then the input signal because you can't do it it's the minimum value is going to be a gain equal to one which means it'll be the same size as the amplitude as the input also these resistors in the gain equation are f + RS these are these resistors these are the resistors that aren't even connected to your source this we called our G remember and believe it or not our G didn't actually come out in the gain equation at all our G the input resistance that comes out of the source that you're driving is irrelevant to the gain of this amplifier right the amplifier is only dependent on the other guys and we went gone through all the math you know as to why and in the past but basically these resistors the resistors govern the game ok just as before it's just you can't make a gain less than 1 ok so the final thing I want to write down you'll probably see in a book I just want to explain it to you for linear operation remember what does linear operation mean it means that the output of the amplifier V out has to be between these power supply signals that we have so something you're going to see in your book probably at some point is gonna be an equation that looks like this it's not terribly useful but you'll see it so I'm gonna explain it to you you'll see something like this 1 plus RF over RS this is the gain has got to be less than the absolute value of VCC over VG a lot of students look at this and say what does this mean for linear operation what does this mean all it means is that the game has to be smaller than this fraction right because if you make the gain too big then you're gonna blow out and saturate the output it's gonna be too big so another way to look at this to kind of make it more have it make a little more sense multiply both sides by VG and what you'll see in other words this is I like to write in other words if you multiply both sides by VG you have 1 plus RF over RS times VG has got to be less than VCC and I'm taking away the absolute value signs and assuming positive values to make it easier to understand basically if you take an input signal this is the input you're driving the thing that you're amplifying and you multiply by the game then this value after you multiply by the game times the input has got to be less than VCC it means the output which is what this is this is the output right the gain times the inputs got to be the output it must be less than VCC it's the constraint on linearity because by definition linear means the output has to be less than VCC if you're talking about positives and of course you have the negative side too that's why we have the absolute value here but basically if you take the input as a positive value times this positive game it better be less than or equal to I guess in the probably less than safer then VCC another way to write that is this basically the gain has to be less than this fraction and that just comes straight from multiple multiplication it's a little easier to start looking at this one and back up and realize that this must be true so basically if you know what VCC is you know what the input signal is then you can calculate the maximum gain that you can allow this thing to get to have in order to not saturate that's basically it for this for this lesson basically what we talked about just a quick quick recap is we had this idea of an inverting amplifier that's what we were studying all the time we take the input signal and it inver to make an output signal how could you then create an output signal that was non inverted well you could sandwich these guys together and put two amplifier stages together so you invert it here and you invert it again here but then you have two amplifiers it makes things complicated so we say without proof that this is what we call a non-inverting amplifier configuration and basically to prove that it's true that it is non-inverting we realize that this voltage because of the constraints in the op-amp must be the same as v2 which then must be the same as this at this point right here so then we go and look and say well this looks an awful lot like a voltage divider so the output voltage whatever it is falls across those resistors and we write an equation showing that but since we know that v1 is equal to the source voltage we can replace it and now we have an equation that relates the output to the input voltage so we flip it around and get you get the output voltage as a function of the input voltage this is what we then call the game so we then write the gain of this configuration down in two ways you might see it different ways in your books but there give you the exact same thing but then you have to realize that you always have a gain greater than one right so you do have the simplicity of a non-inverting op-amp but you can't attenuate your signal it always is going to be 1 or greater there and then we had some discussion about the linearity there so make sure you understand this we're gonna do some problems in the next few lessons so that you will understand how to use these concepts and so once you understand these ideas follow me on to the next section we'll do it right now

Channel: Math and Science

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Keywords: non-inverting op-amp, non inverting op amp, op-amp, non-inverting amplifier, amplifier, circuit, electrical engineering, engineering, circuit analysis, circuit theory, circuits course, inverting, op, amp, non, operational amplifier, op amp, non-inverting, current, voltage, electronics, operational, circuits, opamp, non-inverting op amp, tutorial, gain, non inverting op amp gain, non inverting op amp example, non-inverting op-amp circuit, non inverting op amp examples

Id: UD-6JOY1BWo

Length: 28min 34sec (1714 seconds)

Published: Mon Feb 19 2018