Yesterday’s post covered common mode rejection, how it works what it is and what benefits it has for us. This feature of op amps is courtesy of a key central design element of the op amp, the differential pair. This will be the toughest to comprehend and get through – the rest will be easy – so this is the one I think you should read until you get it. You’ll be rewarded by grasping this essential element.
I really struggled with how to write this one – first because it’s posting on Monday morning – but mainly because on the one hand I want to have some measure of true understanding on the simplest overview level but I also want to go a little deeper into the core because if you can head there with me you’ll actually understand the fundamentals of how this works – should that be interesting to you.
I think I am going to err on the side of depth because of an experience I had years ago with my former partner Arnie when he came over one evening to help my boys learn math ( a subject I am weak in). Their high school teacher had given them some sort of problem that touched on calculus with some algebra sprinkled in and I could be of no help to them. Arnie, a nuclear physicist by training, knew it quite well and agreed to help. When he was presented the problem he couldn’t remember some of the necessary formulas to solve it – which of course delighted the boys that they might have stumped Arnie with their high school math. Arnie stunned them by announcing “since I can’t remember the formulas, let’s just work it backwards from the core and then figure it out. When this type of math was invented there were no formulas so we’ll just do the same and recreate those formulas from scratch.” And that’s exactly what happened and to this day my boys can figure out just about anything math related without having memorized anything. They simply understood at a fundamental level how the math worked. Let’s get started learning the same about diff pairs.
Here’s a picture of a simple differential pair of transistors. Remember, this type of circuit is not exclusive to transistors and can be made with tubes, FETS, bipolars, anything that can amplify. Also, note that there are two transistors – labeled Q1 and Q2 – thus forming “the pair”. Vcc is the power supply and the little rake symbol on the bottom is ground. The R’s are resistors.
Now remembering from our series on Tubes vs. Transistors that transistors (like tubes and FET’s) always have three elements to them: collector, base and emitter, I am going to tear the diff pair down to its simplest form, a single transistor. At this point you might ask how a single transistor can form a pair, and that would be a fair question – so read on.
Here is a picture of a traditional single transistor amplifier.
As you may remember from our former series on tubes and transistors, this amplifier is really quite simple. When you put a voltage into the input a current begins to flow through the transistor from where it says V+. Depending on the size of the resistor connected to where it says “output” you get a voltage that is a copy of the input – only larger and in the opposite direction.
But whenever we talk about a transistor as an amplifier we usually think of its input as the base and the output for amplification gain as the collector and the output for current as the emitter. So if you want voltage gain (bigger signal out than in) you put a small signal into the base and you get a bigger signal out of the collector. If you want to drive something that needs power rather than voltage gain (like a headphone or a loudspeaker) then you use the emitter as the output – you get no voltage gain but you do get more power gain. Make sense? Here’s a picture of the transistor we’re talking about. For voltage gain (little voltage in, bigger voltage out) use what is in the picture. For power gain (little power in, bigger power out), move the Vout and the resistor in the picture from the collector to the emitter and you’re good to go. Here are two diagrams showing how easy it is to change things up a bit (Vcc is the + battery input, the little three line symbol on the emitter in the first picture is ground – the minus of the battery – Vin is the signal input and Vout is the amplified signal output).
But this isn’t the only way you can use an amplifying device like a transistor (or a tube). You can also use the emitter as an input by moving things around once again! That’s right and here’s what’s cool about that:if you use the emitter as an input, the amplified signal you get at the collector is in phase. If you use the base as an input the larger signal you get at the collector is out of phase. Put the same size signal in both the emitter and the base at the same time and you get …… wait for it ……. nothing at the output. Yup, zero. Remember yesterday’s post about common mode rejection? The op amp refused to amplify anything that was the same (common) for both its inputs. OK, that’s how that works on the inside.
Here’s a picture of what a transistor with its emitter as an input looks like (known as a common base amplifier).
And next is a picture of what a single transistor “diff pair” looks like.
Notice in this drawing each of the two inputs has the signal going into it reversed – one in phase and the other out of phase. When you do that you get an amplified signal at the output – but when they are the same phase you get nothing. Nothing, of course is a good thing as you’ll remember, because signals in common are usually something we don’t want like noise – thus we are happy when we have common mode rejection. Ok, we’re on the home stretch, I promise.
So if we can do everything with a single transistor, why do diff pairs have two? Because there is a penalty to pay when you use the emitter as an input: it’s hard to drive. The impedance at the emitter is 100, perhaps 1000 times lower than that of the base and that means you need 100 to 1000 times more power to send the signal through the emitter than you do through the base.
Remember I just explained that if you move the output of the transistor from its collector to its emitter you get power gain instead of voltage gain? Yup, and that’s called a buffer or an emitter follower when you do that. It is an impedance matching technique when you need more power – and here we have a perfect situation where we need more power to drive the emitter of our single transistor differential amplifier. So, we add another transistor and voila! We now have a pair!
Take a look at this drawing of a single transistor and then a pair.
Figure A shows our classic single transistor amp with a small signal going into the base and a bigger signal coming out of its collector. (The one with the little arrow is always the emitter – and if the arrow points down it likes positive voltage and if it points up it likes negative voltage).
Figure B shows exactly the same thing only with another transistor added. Note that the first transistor’s emitter is powering the second transistor’s emitter. Since there is no voltage gain on a transistor’s emitter (like there is on its collector), the size of the signal on its emitter is exactly the same size as it is on the base (input). Only there is more power to drive something like a headphone pair or – in this case – the emitter of a second transistor.
Here’s another picture showing the output size at the emitter of the first transistor.
And look what appears at the output of the collector on the second transistor! Another, identically sized larger signal appears out of phase from the first. Simple really – once you know how it works.
Now let’s go back to the beginning of our post and look once again at a classic diff pair.
Now that you’re an expert in diff pairs it should be easy to see that if you put a signal into Q1 you will get a larger signal out at both collectors of Q1 and Q2 – and the same is true if you put a signal into the base of Q2 – or the same signal on both and get nothing.
The rest of understanding op amps has to do with the next stage which makes more gain, feedback – which typically is the final output going into the input shown here as Q1 – and lots more stuff.
Nothing is more important to understanding how these work, IMHO, then the core of the device, the input differential pair.
If you’ve managed to stay awake through all this you’re a stud! If you have questions as follow up feel free to write or comment and ask.
Tomorrow we’ll get to the easy parts which are the last two remaining micro elements in the op amp functional block: the gain stage and the current stage.