326 CHAPTER 7. TEMPORAL RESPONSE OF DIODES AND BIPOLAR TRANSISTORS
applied at the base terminal, resulting in an output voltagevoutat the collector terminal. The
device remains in forward active mode at all times, so the charge control framework developed
for this mode is sufficient to derive the small-signal response.
When the emitter current in the device is modulated by an amountΔiE, the collector current
does not respond immediately. The delay in establishing the change in collector currentΔiCis
a result of the finite time required to modulate the various stored charge elements in the device.
The total emitter to collector delayτECis given by
τEC=τBE+τB+τBC (7.5.1)whereτBEis the EBJ capacitance charging time,τBis the total delay in the quasi-neutral base
region, andτBCis the delay associated with the base-collector capacitance (which includes the
contribution due to change in mobile charge in the collector, which is equivalent to the collector
transit delay). It will be shown later in section 7.5.3 that the current gain cutoff frequencyfτof
the device is given by
fτ=1
2 πτEC(7.5.2)
This is the maximum frequency at which it is possible to achieve current gain in the device.
To calculate the delays in the device, we apply the following rule. The ratio of the change in
stored charge to the change in current is the delay associated with the element. We are interested
in the delay in setting the output current. We can write the ac portions of equation 7.4.11 as
|ΔiE| =ΔQF
τB+
ΔQBE
τBE|ΔiC| =ΔQBC
τBC(7.5.3)
The delay elementτBEcan be written asτBE=ΔQBE
ΔIE
=CBE
(
ΔVBE
ΔIE
)
∼=CBE
(
ΔVBE
ΔIC
)
(7.5.4)
where (
ΔVBE
ΔIC
)− 1
=gm 0 =(re)−^1 ∼=eIC
kBT(7.5.5)
is the transconductance of the device.τBEis therefore given by
τBE=reCBE=(
kBT
eIC)
CBE (7.5.6)
The base delayτBis the time required to supply the additional chargeΔQFto the quasi-
neutral base region. If we assume Shockley boundary conditions(np(wB)=0),thenτBcan be
written as
τB=w^2 B
2 DnB