7.5. HIGH-FREQUENCY BEHAVIOR OF A BJT 333
n+ - E p - B n- - C n+
wB wd,BC
iB
iE iC
iω( 0 ) iω(wB)
VCE
VBE (t)
Figure 7.14: Current components in a bipolar transistor when a small signalvinis applied. The
direction of the arrows shows the direction of the electron flux.
7.5.1 Bipolar Transistor Small-Signal Equivalent Circuit ............
In figure 7.14, we show a schematic diagram of various current components in a bipolar tran-
sistor when a small signalvin(t)is applied. The total base-emitter voltageVBE(t)is given
by
VBE(t)=Vdc+vin(t) (7.5.27)
where we assumevin(t)to be of the form
vin(t)=vωejωt (7.5.28)This generates a small-signal currentiEat the emitter. The current entering the base is denoted as
iω(0). In general,iω(0)differs fromiEbecause of the delay in the emitter-base depletion region.
Electrons then continue through the base, where they undergo a transit delayτB, resulting in a
fluxiω(wB)leaving the base. Finally, the delay in the base-collector region results in an output
currentiCat the collector. We are interested in determining the output currentiCas a function
of the input voltagevin.
We continue to make the assumption that the current in the base is purely diffusive and is
therefore given by
iω(x)=eAEDn∂nω(x)
∂x(7.5.29)
whereiω(x)andnω(x)are the position-dependent amplitudes of the ac current and charge. Thus
to determineiω(x), we must first calculatenω(x). In order to do this, it is necessary to solve the
time-dependent continuity equation for electrons, which in the case of zero recombination takes
the form
∂n(x, t)
∂t
=−
∂
∂x(
Ie(x, t)
−eAE)
=Dn∂^2 n(x, t)
∂x^2