How Does The Transistor Amplify?

We've been talking about transistors recently, particularly the BJT, on What Can You Do With Two Transistors? Part 1 to 3. And  perhaps before we continue with more installments on the topic, more discussion about the transistor as an amplifier would be very helpful.

These tiny devices have been a game changer since they were introduced more than 50 years ago, and still don't fail to mesmerize people. From amplifiers, band gap references, current sources, to trans-linear amplifiers, they are absolutely phenomenal devices with a host of utility. We would dwell on the concept and  idea of the amplification on this blog, perhaps not the same as many of us have been taught about transistors in school. The concept we will be discussing here is equally applicable to the MOSFETs.

Many of us were taught that the BJT gets its amplification property from its Beta, the ratio of the collector  current to  its base current, and that it mainly is a current amplifier because of that. There is nothing wrong with that, except that we typically deal with a voltage input, not current, when we talk about amplification. We see that when we have a voltage input, the idea of current amplification when we start to look at the circuit below  easily falls apart, or at the least causes confusion to many that are uninitiated.

The figure above is an amplifier. We might ask, with everything in the figure given, including the 1V being  the DC bias point at the output, what is its AC voltage gain? It would be a good exercise at this point perhaps to get a piece of paper and work out what the gain of the circuit is.  Then if we're ready, we may continue to read on and see if we got the right answer. But wait, aren't we supposed to know what the Beta of the transistor is? The answer is no, the Beta ain't  got nothing to do with the gain of the circuit. Pretty shocking, isn't it?

The most intuitive way to look at the circuit as an amplifier is by considering that the output current of the transistor is a function of VBE, by Ebers Moll Equation, where IC is the collector current, and IS the transistor scale current, and VT Thermal Voltage which has a value of 26mV at room temperature.

We're not going into the details of the equation, but one can check the link from Wikipedia to find out more about the equation. From the equation above, we see that the collector current will change when the VBE changes. If we get the change in the output current, IC, to the change in VBE, we should be able to know or calculate what the change in the output voltage will be. So, by the taking the derivative of IC  with respect to VBE, we have:

It's very interesting, really astounding, to find out that the small change in the VBE, which in fact is the input, would simply result to IC, the collector DC bias, divided by VT which is given at room temperature to be 26mV. We call the equation above the transistor transconductance, or gm. So with the given values in the circuit, the voltage gain would be:

The voltage gain is 154. So that's how we're able to work the gain out of the circuit. So the next time we come across a transistor we'll probably have a different outlook in life, I mean, in the way these transistors work. I hope everyone has got a good start of the weekend.