the transistor given this collector current. We assume that base current remains relatively the same
as for the active mode:
We call this gain
, and it is strictly lower than the gain of the transistor would be if it were in
active mode:
. This represents the idea that the transistor is trying to
‘
pull
’
its collector as
close in potential to the emitter as possible (to draw more collector current, as determined by its
‘goal’ of
). However, it is limited by this lower limit of
. We define a new
factor based on this adjusted gain:
We now have a choice. Our first option is to model the C
E circuit with something like the piecewise
linear model for the diode. In this case, we define
, which is a series resistance:
This model will work in most cases, but we do not know
without further information, much
like with the diode. Some common values are known for all transistors, though. For example, with an
overdrive factor of 2 (i.e.,
), most transistors will have
. This process suffers
from the same problem that we were trying to solve, though, so it is rarely used. Mostly, we go
directly to the complete formula for
, which is much like the exponential model for the diode:


[
]
This will give a direct relation for
in saturation mode to any value of
and incoming base current
(through calculating
). In general, though, the additional accuracy of this method (and the
previous PWL option) is rarely needed, unless extremely high currents are in use.
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227
BJT Switch Example
Consider the following circuit, where an NPN BJT is used to switch an
load on and off.
Estimate the efficiency of the switch and the power dissipated by the BJT from C
E when the BJT
is conducting, given
. Assume that
. Compare this to a similar type of
MOSFET which has
.
Solution
Since we are told the circuit is switching a load on and off, and we are analyzing a case where
current is conducted through the load, when guessing the transistor mode we can try one of the two
conducting modes first. In particular, since the transistor is used as a switch, then it is a good idea to
guess saturation mode. In this case,
is fixed at the given
:
(1)
We can calculate the current through the load (and collector) directly by assuming that from
there is a constant drop of
:
(2)
𝑅
𝐿
228
This gives us the final power dissipation, as we know
and
. Efficiency can be found by also
calculating the useful power delivered to the load.
(3)
To compare this figure with the MOSFET, we assume triode mode and replace the MOSFET with
:
(4)
We can see that the MOSFET is more efficient, but only slightly. For most low to mediumcurrent
applications, the BJT and MOSFET are relatively comparable. Here, we only have a load current of a
few amps in both cases. However, the MOSFET quickly supersedes the BJT in efficiency at high
currents (i.e., greater than 10A).
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 Spring '17