is the forward transit time which is equal to the average time an electron spends in the Base and is

Where is the physical base width, is the Fudge factor and is the electron diffusion constant.

In practice we can make

Ist order model of BJT (CE-forward active)

Now we can define a frequency at which short circuit current gain is

Where is finite base current

And emitted base current

So we have the collector current as

being the low frequency current gain

The first order model is given in Fig 15.4

Current gain is modeled as

In case of electrons diffusing across base,

The transit time is given by

And the cut-off frequency is given by

where is the time required to change the by charging up the capacitances through base- junction resistance.

Space charge transit time is time required to drift through depletion region in BC junction.

being the Base-Collector depletion region width.

Collector charging time

Where and are emitter and collector resistances.

A more detailed BJT model is the Gummel-Poon model, shown in Fig 15.5, in this model we have

The Early effect is depicted in Fig 15.5