Transistor as a voltage amplifier

let's explore in this video how a transistor can behave as a voltage amplifier now be even before we begin drawing the circuit for a transistor let's first understand what does it mean mathematically for the output voltage or output signal to be amplified version of the input voltage or input signal so so let's take an example imagine we have our input voltage like this which swings from zero two units it could be world's millivolts whatever let's not worry about the units say zero two two units quickly and then slowly dies out back to zero and suppose we want our output voltage to be I don't know maybe ten times more magnified what why what could we expect oh we might expect our output voltage to be something like this itself the pattern should look exactly the same but it would swing from zero to twenty now ten times more magnified right zero to twenty and then go back to zero so here's my question what what do you think is the mathematical relationship between the output voltage and the input voltage well we might say hmm also say this 10 times more than this we might write o V naught to be equal to as an example 10 times 10 times VI and so we could say yeah this is the necessary condition for output to be the amplified version of the input right oh not necessarily this is not a necessary condition I'll tell you why this is one example one condition but let me give another example in which the output will be the magnified version of the input so let's say the output doesn't swing from 0 to 20 instead the output is something like this let's say I push this whole graph up by 10 units by 10 units this is still the amplified version of this right because it still resembles that and it's still you know bigger than that 10 times bigger than that but notice now since I pushed the whole thing up by 10 units this is 10 and this is now 30 because it was 20 before I push it up so this is not 30 now this relationship is not satisfying you see V naught is not it's not 10 times VI right it's not but what is the relationship over here can you see what's the relationship notice over here the change is magnified see the input changed by 2 the output changed by 2010 2 that is 20 see the input decreased again by two the output also decreased by twenty so you know notice what's really important this need not be satisfied but what is important is that the change in the output voltage so let's write that now the change in the output voltage has to be some number times the change in the input voltage if we get this then we could say that our circuit is behaving like an amplifier all right let's bring in our transition circuit now this is the same circuit that we've been using for quite a while it's an NPN transistor notice that the emitter base is forward biased by grounding the emitter and connecting base to a positive 0.72 turn on the transistor and the collector base is reverse bias the collector being n-type is connected to a positive more positive than the base and if you need more clarity on this it would be a great idea to go back and watch previous videos will be spoken about a lot in that and then come back over here the only change we might see over here is I put the NPN so that'd be some it will be more clear and one more thing is this is usually called the VCE right because it's the collector voltage with respect to the emitter emitter is grounded but since that that's the point we're gonna take as the output voltage we'll just call it as V naught in this video now we have to add one more element to this circuit because naught is we don't have an input voltage we only have an input current that's what we've been doing so far but in reality to get this current we might require we need a voltage source right so attach a voltage source over here but not directly through a resistor just like how we did over here so attach a voltage source through a resistor so VI is the voltage that we want to amplify notice VI is a fluctuating voltage that I've given over here and we would expect an exact copy of that but an amplified version over here so let's see if you get that in this circuit so let's start with what we already know we already know that when the transistor is in the active State and we're going to assume it's in the active State don't worry how but when it is in the active State we already know that the output current IC output current IC can be written as some number we call as beta which is the current gain times the input current IB beta is say 200 it means the output current is 200 times the but current we've already seen that but now let's convert this equation into changes in the current because that's what we eventually want changes in the voltage how do we get to changes in the current so this is what we'll do we'll assume that at some time T 1 the input current IB is IB 1 and as a result the corresponding output current is IC 1 then we'll wait for some time to pass and let's say now at new time T 2 IB 2 is the new car input current IC two would be the corresponding output current to calculate the change we have just subtract the 2 so if we subtract we get this you just subtract the 2 so this is the change in IC and therefore we will write this as Delta IC and similarly if you take beta is beta as a constant but it doesn't change with time so you can take meet a common and inside will get IB 2 minus IB 1 and so that can be written as Delta IB and this is how we can take any equation and convert into changes that's what we'll do for all the equations that is going to follow alright alright so this is telling us that the output current is the amplified version of the input current excellent but how do we how do we get the output and the input voltages into the picture well what we can do is we can connect the output voltage to the output current build one equation there connect the input voltage to input current build another equation there and maybe maybe just put them together using this relationship let's do that let's first build an equation connecting the output voltage and the output current we can just use Ohm's law for this if we call this resistor as let's say RC because this is the resistor connected to the output wire then Ohm's law tells us that the potential difference here the potential difference would be this voltage that is 3 minus this voltage that is V naught so 3 minus V naught that's the potential difference over here that should be equal to IR Ohm's law so that should be equal to I C times RC and why am i doing 3 minus V naught well we always do higher voltage minus lower voltage since the current is flowing downwards we can assume this is the higher voltage and this is the lower voltage that's the whole idea but I wonder I want this equation in terms of changes in the voltage right so we'll do the same thing now like what we did over here but mentally we'll do it mental you assume that a time t1 these values are 1 and then time to do their to and then we'll subtract them what will happen when you subtract so let's take that change directly so if you take change of this entire equation but notice 3 is not changing right this 3 doesn't change with time it's a supply voltage that's what I remain fixed so the change in that would be 0 when you subtract that will be give us 0 minus the change in this well that's going to be just Delta V naught that will be equal to whatever the change in this number well that is our C is not changing and therefore we can pull that our C out let's use the same color so we pull the our C out and we can write delta i-c just like how we did that we pull the a beta out in video delta i-b same thing so that's going to be our C times Delta IC and let's get rid of the 0 we can also get rid of that minus sign we can multiply the whole equation with minus sign and put that minus sign over here I just want to keep this thing positive and so there we have it we have now connection between the output voltage change and the output current change let's call it as equation 1 now next thing we'll do is connect VI and IP and I want you to pause the video and just see if you can do this yourself all right let's do it a little bit this exact same thing will apply Ohm's law over here let's call this resistance as our B and so the voltage difference over here is VI it's the higher voltage because current is flowing down minus 0.7 so voltage difference is VI minus minus 0.7 that's equal to the I times R Ohm's law this should be equal to I that's the current times our R is are we here and again we have to take changes in this so let's take the changes in that again if you have not tried please try now just pause the video and just see if you can do this yourself when you take the two equations are two different times and subtract it this will be Delta VI but this number is pretty much a constant we've seen this before once you hit that point seven volt forward bias to the base emitter Junction then even for you know why'd were wide range of the current the voltage here pretty much remains a constant and as a result we can say when you're subtracting these just cancel out so he's gonna say minus zero because that is not changing with time that's equal to the change in this value RB is not changing so just like what we did before we can just say it's RB times delta i-b because IB is the one that's changing again we get rid of that zero and there we have it that's our equation number two so what do we do with these two equations oh I want to relate these two right well we can just divide them let's do that so let's make some room over here we don't need a circuit anymore we just have four divide the two equations alright so if we divide them we'll get Delta V naught divided by Delta VI that equals let's see what is that equals is a negative sign it's a minus RC divided by RB divided by RB times Delta IC divided by Delta V or what's Delta a by Delta IB oh that's beta that's beta and there we have it we found it all we have to do now is multiply the whole equation with Delta VI that time this goes over here and Delta VI gets multiplied over here and voila notice this now number over here is going to represents the amplification factor so our alpha voltage is this many times amplified compared to the input voltage and that number we're gonna call that as AV and that's usually called as the voltage gain voltage gain just like our beta is the current gain that tells us how much the current is being amplified this is telling us how much the voltage is being amplified and so you can clearly see that our transistor behaves as a voltage amplifier so that's pretty much it we just have to understand what this minus sign is telling us what is that minus sign telling us what is it even mean alright what the minus sign is just telling us that if Delta VI is positive this would be negative on Delta VI is negative this is positive which means if the input voltage increases by some factor the output voltage will decrease by an amplified factor so that's the whole that's that's what's happening and why is that happening well the only reason that's happening again this is something that we've seen before is because notice when you increase this voltage the mark more current flows here and as a result more current flows here because of this but as more current flows you notice there is a higher potential drop here and as a result there's a lower potential drop here so if you bring back our graph then we're pretty much getting a graph like this notice the changes in the output voltage is an amplified version of changes in neutral Church but the negative sign just means that this this thing will be flipped so when the input is increasing by some amount the output is decreasing by an amplified amount and in most cases where we use this like for example speakers that won't bother us because all we care about is how much the changes it doesn't even matter whether it is increasing or decreasing the change is all that matters to us and as long as the change in the voltage is amplified version of the changing input this circuit behaves like a voltage amplifier and so you notice that the amount by which it amplifies the voltage gain depends on beta and the resistance is the output resistance you can call this and the input resistance