Hi Edo,
A transistor is a highly intuitive device; a current injected or extracted into the base (depending on whether it is NPN or PNP) will control a current in the collector/emitter circuit according to a relationship called the beta, which you've worked out already.
The three configurations Nelson refers to determine how you will use the transistor - and the outcome. A common emitter, the most frequently used configuration, gives current and voltage gain, and makes the transistor work pretty hard, revealing, incidentally, all it's faults. A base current controls the collector current, which, if passed through a resistor at its collector - the load - gives a voltage gain in the same way as a tube. This voltage gain is given by the ratio of the collector impedance to the emitter impedance. If the emitter is grounded, then the emitter impedance is given typically by 26/mA, where mA is the current flowing through the collector/emitter (almost the same for most transistors since one is generally at least 99% of the other). When the collector load is in fact a constant current source, with very high impedance in the megohms range, then the ratio of these two is typically around 2000, or 66dB. This is a very high voltage gain, and must be throttled back for most practical applications. This leads naturally to global negative feedback, which serves precisely this purpose.
The next most common configuration is the common collector, sometimes (indeed often!) called the emitter follower. Here the collector is connected to a power rail, and the signal injected at the base from a high impedance source. The output is taken from the emitter, current (but not voltage) amplified. This is effectively an impedance transformer, and a fully complementary double emitter follower (two acting in cascade) is frequently used for current amplification in the output stage of an audio amplifier - and is roughly analogous to the differential on the wheels of an automobile.
The least used configuration is the common base, where signal is injected into the emitter at low impedance and taken from the collector, much amplified in voltage, but with no current amplification. This is of lesser use in audio, though still seen in the cascode, but has great advantages in bandwidth and is commonly used in radio frequency applications.
The way in which the base is driven in common collector and common emitter is difficult to describe, since a combination of both current and voltage is involved. That is, the base is not strictly driven by a current generator or a voltage source; it is driven by a combination of the two. By this I mean that the current drive to a common emitter amplifier - a voltage amp with current gain - varies, and with it varies the voltage drive between base and emitter, though not by very much, typically 0.6 volts to 0.75 volts. It is the mathematical combination of these two which gives us the transfer function of the transistor; a thing of some complexity, but not something you need to understand intimately in order to design with these elements.
You should know that beta, the ratio of collector to base current, varies with a number of factors; collector current, temperature, collector/emitter voltage, and even frequency. Because the resulting relationships are so complex, and so non-linear, we usually finish up loading the device with a very high impedance, such as a constant current source, and then fixing the overall gain by use of a negative feedback network, which absorbs all these non-linearities into a couple of fixed, accurate resistors which establish the overall gain of the circuit on a global basis, removing all the quirks of the transfer function. This works well enough, but care must be taken to bring overall gain below unity at a frequency where the negative feedback abruptly swings to positive feedback. We have to do this because positive feedback creates ever larger outputs from tiny inputs, creating oscillation, which can destroy our creation, and particularly our loudspeakers.
This is a complex area, but the basic rules rely simply on Ohms Law and a bit of common sense. It's a fascinating hobby, full of unexpected discoveries, and I do hope this is helpful!
Cheers,
Hugh
www.aksaonline.com