Transistor current and parameters

let's name the different currents through our transistor find out what's the connection between these different currents and also see what makes a transistor a good transistor we'll explore some specifications of a transistor so let's look at an NPN transistor the same one that we have been working with for quite a while now we've seen the different parts of these transistors the heavily doped one is called the emitter this lightly doped thin region is called the base and the biggest region is called the collector and we've also seen in order to make it work as an amplifier the connections that we do we usually connect the emitter to the ground then we supply a positive over here forward biasing this Junction and as a result let's quickly recap what happens due to this forward bias the depletion region here vanishes and the charge carriers can diffuse into each other so the electrons over here that diffuse into the base region and since base region has a very tiny amount of holes only few of them recombine with the holes over here and as a result only a small fraction of these electrons can turn come out from the base terminals and what happens with the remaining electrons well because of the positive that is supplied over here that that positive starts pulling these electrons you see the collector base is reverse biased because the n-type over here is connected to more positive than the p-type over here and as a result the remaining electrons will be swept across due to this reverse bias and they will be collected over here and they come out from this terminal of course the electrons don't come out like this they come out through the hole higher but you get the idea so what we'll do is we'll look at the different currents to the different parts of this transistor let's try with the current that we get over here you see because the electrons are flowing out of the base terminal the direction of the current is in the opposite direction so over here we would say the current would be in this direction and we'll call that as the base current the base current because it's coming out of the base terminal similarly over here not is because of the electrons coming out from here we get a current downwards you see that electrons are going upwards so the conventional direction of the current is downwards so we get a current downwards and we call that current as the collector current this is the collector current and now if you put some numbers let's say about five electrons five electrons came out from here and let's say about ninety five electrons came out from here from the from this wire the notice as the final Ektron come out over here they push these electrons because there's a there's a connection over here there's a surrogate over here and as a result five electrons get injected into the into the emitter from the external wire and similarly as 95 electrons come out over here these ninety-five electrons get injected back and as a result total hundred electrons are getting injected at the same time and as a result there is a current downwards over here and we'll call that as the emitter current emitter current so these are the three currents that we have in a transistor and if you look at these numbers carefully we can even identify the connection between these three currents so I want you to pause the video and just see if you can find out what's the connection between IC IB and ie well one way you can see is that hundred electrons are going in out of which fire are going here and ninety five are going here which means if you add these two currents you get this current so let's write that down the connection between the three currents is that ie the emitter current will be equal to the base current which we'll show using green plus plus the collector current the collector current over here and you can also see directly by looking at the direction of the currents you can see that IC and IB are entering the transistor and that total current entering the transition should be equal to the current that's exiting the transistor ie the one that's exiting how are we going to do this is the connection between the currents and we can find more connections between the currents for example if you look over here out of hundred electrons that got injected about ninety five electrons went through over here and so we could say the collector current is 95% of the emitter current right so you can write that over here for our example we could say the collector current collector current IC is 95% which means 0.9 five times the emitter current and this number is usually represented as alpha so in more general terms we could say IC IC equals alpha that number is called alpha times ie in our example this alpha is about point nine five and that number is pretty much a constant for a given transistor it only depends upon the doping levels of the emitter maybe depends upon how thin the base is how few holes though how many holes the base has and all these design specification is what decides the value of alpha higher the value of alpha for example if alpha is 0.99 that means 99% of electrons get through and only one person of electrons come out over here that means the amplification is very high so higher the value of alpha better amplification you would get out of the transistor and say if alpha was I don't know maybe 0.4 that would be a horrible transistor because that would mean only forty percent get through and about sixty percent comes out that's pathetic you wouldn't buy a transistor which has alpha value of 0.4 so alpha value is ideally very very close to one very close like 0.99 or 0.999 or something like that all right another connection that we would like to do is between the collector current and the base current and the reason for that the collector card is usually the output because that's the amplified current let me call it this is usually the output let me use the same color so this is usually the output in any application and this base current is usually the input this is usually the input so we also like to have a connection between these two and we can see that connection again from these numbers you see in our example we could see that IC is equal to well how many times more compared to IB well I see is 95 IB is 5 so 95 divided by 5 is 19 so we see that IC is 19 times more than I be because 19 times 5 is 95 right so we could say IC is let's use this color 19 times more than IB more than IB and in general this number is called beta so usually you will see for writing it is IC equals beta beta times IB and if you look carefully if you know what alpha is you can calculate beta right because if you know alpha then you get this how much fraction go through and as a result you can calculate how much fraction comes out over here and you can calculate what beta is so chic the speaking you only need to know one of these numbers you can calculate the other and this beta is often called current game it's called gain because it's literally telling us how much is the output current gaining compared to the input in our example it is 19 but in a practical transistor that number can go up to 200 or 300 and one last thing we'll do is find the connection between this alpha and beta because you've seen that if you know 1 we can find the other so before I do that I really encourage you to pause this video and see if you can do it yourself alright there are a couple of ways in which you can do that one way maybe you can just substitute these equations somehow into this equation and do that but I had to do it more intuitively than that so I don't think think of it this way let's say about 1 million electrons 1 million get injected from emitter to base or you can think of it as 1 billion whatever you want so let's take some large number so let's say over 1 million I'm just gonna write the 1 over here then we know that only alpha fraction of it get through that means alpha million will get through over here make sense right we've alpha is 0.95 only 0.95 million will get through and the remaining will be collected over here how much is that remaining one well out of one if alpha goes through remaining would be 1 minus alpha 1 minus alpha will come out from here and so from this we can find what beta is beta it is the current gain is the ratio of the collector current and the base current can you see that so it is the collector current in our case is d alpha divided by the base current that's going to be 1 minus alpha and there we have it that's the connection between beta and alpha and I don't remember this equation whenever I need this I will always derive it this way in my head and of course you can also in this equation and get alpha is equal to something in terms of beta I leave that to you so to quickly summarize I'll find beta are two numbers that tell us how good or bad our transistors are and they're not two independent numbers if you know one if you fix one the other one also gets fixed for a good transistor alpha value is very very close to one like 0.95 or 0.99 or something and beta value is much larger than one could be something like 200 or 300 or 500 and their value largely depends on the width and the doping concentration of this base region