This one is similar to what I did with the gain, except that this time I kept the base current constant and measured the collector current in relation to the collector-emitter voltage. I reworked the original test circuit, which is how this blog follows the last one so quickly. As before, I'm looking at an NPN bipolar junction transistor (a 2N3904) and the situation where the emitter is the common terminal between input and output.

Here's the circuit (minus decoupling caps):

I've moved the constant-current source to the base and chosen a resistor that will give me base currents in the area of a few tens of microamps. The collector I'm driving with a follower so that I can set the voltage without having to account for the voltage drop of the ammeter. All the measuring I'm doing is with meters, so there's no need for great precision and accuracy - as long as it holds everything steady, that's enough.

Here are the curves I get for various base currents.

If the transistor output was a perfect current sink, the output curves would be horizontal lines, each at a single value of collector current. As it is, whilst approximating a current sink, the lines slope and the transistor doesn't operate all the way down to a Vce of 0V. The situation at the bottom end is due to saturation - when the collector voltage gets down to the base voltage, the base-collector diode is no longer reverse biased and the increasing forward bias as the collector is moved lower starts to affect the way the transistor operates. The slope higher up is due to base width modulation (Early effect) - here's the Wikipedia entry if you want to read more:

https://en.wikipedia.org/wiki/Early_effect

For a fixed collector voltage, the proportionality between the base and collector currents is reasonably good. However, in a practical circuit, when a simple resistor is used to convert from the output current to an output voltage, there will be some distortion because of the variation in gain as the collector voltage varies. That distortion will be higher for a large signal than a small one.