[ENGN2211 Home]

   
AC Model and Parameters

  We will also need an AC model for the transistor. There are AC parameters $\beta$ and $\alpha$, which are in general slightly different from their DC counterparts. However, we will assume them to be the same in this course. The equations for the AC currents are

$$i_c = \beta i_b .$$ (88)

and

$$i_c = \alpha i_e .$$ (89)

Of course we also have

 

i_e = i_b + i_c . (90)

The AC model we use takes two equivalent forms, Figures 101 and 102.

  

Figure 101: AC equivalent circuit model for an npn transistor.

The small resistance r_e takes into account Ohmic effects in the BE current path, and can be calculated from

$$r_e = \frac{0.025}{I_E} \ \Omega$$ (91)

where I_E is the DC emitter current (in amps). (This equation is easy to derive from the diode equation (74) and the definition

$$r_e = \frac{1}{di_{BE}/dv_{BE}} .)$$

We also need

$$r_\pi = (\beta + 1) r_e$$ (92)

 

  

Figure: AC hybrid-$\pi$ model for an npn transistor.

These AC models are only valid when the transistor is operating in its active region.

Exercise. Show that the two AC models are equivalent.

[ENGN2211 Home]