In a Grounded-emitter Amplifier Circuit below
When we ignore the existence of AC signal, we have
so we can have the static working point Q as
based on the output curve, at the working point Q, we can have a small-signal model ONLY FOR AC as
If you find it hard to remember, just remember that base and emitter serves as a resistor and will always be linked with a , and collecter and emitter serves as a current-controlled source and will be always linked with a power source. As and sometimes even near , we can totally ignore it.
Based on the working Q point and the signal source, we can easily have all the other component aside from , and is accually the slope of the output curve(), with what we know about BJTs, we have
so that with KCL we have
let's take a look at the equivalent resistence in a BJT
as the dosage concentration is a lot higher at collecter than emmiter, . Also, when we don't take heat loss into account, can be ignored.
As a result, the for shold be written as
we know for it is a constant for every BJT, so we only need to get , which is the slope for ,As we know what the form of the current on a PN node is, we can have
based on the fact that is small compared ro , we can simplify as
derivate on both sides, we have
so that we can have
we can have
and totally simplify it into a small-signal model.
We can also know the parameters for perfermance, which the input resistence is ,the output resistence is , and the amplification is