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53
4 Bipolar transistors
voltage with respect to emitter current:
re ≡
∂ VE
.
∂ IE
(4.5)
The dynamic resistance tells us how, for fixed base voltage, the emitter
voltage would change in response to a change in emitter current – for
example, how the emitter voltage would differ if the emitter were driving
a small load resistance as opposed to a large one. To determine re , we
differentiate Eq. 4.3 at fixed base voltage, giving
re =
kT 1
.
e IC
(4.6)
(In addition there is the ohmic resistance of the emitter, which is typically
a few ohms.)
Dynamic resistance of base
On the other hand, if we fix the emitter voltage, we can find from Eqs. 4.3
and 4.4 the dynamic resistance rBE to the emitter as seen at the base:
rBE =
∂ VB
kT 1
=β
.
∂ IB
e IC
(4.7)
This tells us how the base loads the circuit that is driving it. We see that
the base–emitter junction appears to have a low resistance when viewed
from the emitter end, but appears to have a higher resistance (by a factor
β) when viewed from the base end.
Some useful approximations
Since at room temperature, e/kT = 39 V−1 , in practice a reasonable approximation is
25 mV
,
IC
25 mV
=β
.
IC
re =
(4.8)
rBE
(4.9)
Since the emitter acts as a low impedance (only a few ohms for typical
collector-current values), its voltage hardly depends on the current flowing
through it. But the base acts as a high impedance, so it is easy to apply a signal voltage to the base. This comes about because the base current is smaller
than the emitter current by the factor β, which is of order 100. Although
rBE is only a few hundred ohms, the factor β applies also to any resistor