At end of this posting, you'll know how to compute voltage gain of a bipolar.
Lets examine a table of Vbe versus Collector Current, for an imaginary bipolar:
0.458 10uA Notice 58mV more Vbe gives exactly 10X more current.
0.690 100mA [transistor is HOT, so the current may runaway and
melt the transistor (a known risk with bipolars
biased with constant base voltage)]
0.748 1AMP transistor is HOT
0.806 10Amps transistor is HOT
Can we actually operate a bipolar transistor over 1uA to 10Amps collector current? Yes, if its a power transistor. And at higher currents, this fine table -- showing 58 milliVolts more Vbe produces 10X more current --- loses accuracy because the bulk silicon has a linear resistance and curve tracers will show that.
How about smaller than 58mV changes?
0.2 volts 1nanoAmp (approx. 3 factors of 58mV below 1uA at 0.4v)
0.226 2.718 nanoAmp (the 0.026v of physics gives E^1 more I)
0.218 2.000 nanoAmp
0.236 4.000 nanoAmp
0.254 8.000 nanoAmp (you'll find N*18mV in voltage references)
OK, enough tables. Lets view the bipolar transistor similar to vacuum tubes or MOSFETS...............as transconductors, where changes in Input Voltage cause changes in Output Current.
Bipolars are fun to use, because we know EXACTLY the transconductance for any bipolar, if we know the DC collector current (that is, with no input AC signal).
For shorthand, we lable this the 'gM' or 'gm', because vacuum tube databooks used the variable "mutual transconductance" to explain how the Grid voltage controlled Plate current. We can honor Lee deForest by using gm for this.
The gm of a bipolar, at 25 degrees Centigrade, and knowing kt/q is 0.026 volts,
is -------> Ic/0.026
and if the Collector current is 0.026 amps (26 milliAmps), the gm is 1 amp per volt.
Thus 1 millivolt PP on the base causes 1milliAmp PP collector AC current.
Ignoring some distortion, which you can predict using Taylor Series. Or Barry Gilbert's writings on IP2 and IP3 for bipolars.
Suppose we have 1Kohm resistor from collector to +30 volt, carrying 26mA. The Vce is 30 - 1K*26ma = 30 - 26 = 4 volts, so the bipolar is in "linear" region.
What is our gain?
Gain is gm*Rcollector or 1amp/volt * 1,000 ohms or Av=1,000x.