Download 5 Dynamic Characteristics I

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Dynamic Characteristics I
5.1 Switching Times
In practice, changes in the state of conduction of the transistor take
time to occur. These cause delays in the response of the output to
changes at the input. Consider the circuit in Fig. 5.1.
VCC
RC
IC
IB
RB
VO
Vi
Fig. 5.1
Non-Instantaneous Switching in the Transistor Inverter
Fig. 5.2 shows the sequence of events during turn-on and turn-off of
the transistor. The following characteristic switching times can be
identified.
Delay Time, td
This is the delay between switching on the input base current to the
transistor and the point at which the transistor reaches cut-in and
enters the forward active mode. During this time, the transistor is not
truly conducting but ionization currents are flowing which essentially
charge up the base-emitter and base-collector junction capacitances.
The length of this duration is usually quite small compared with the
other switching times and can be neglected.
Fall-Time, tf
Note that the fall-time for the output voltage is, in fact, the rise time of
the collector current. During this time, the transistor is operating in
the forward active mode, passing between cut-off and saturation. Note
that the collector current reaches its maximum value at the edge of
saturation, even though the charge stored in the base of the transistor
continues to rise as the transistor is overdriven into heavy saturation.
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The fall-time is usually estimated between the 90 and 10 points on
the output voltage profile.
Storage-Time, ts
This is the time between the point at which the input voltage is
brought low and that at which the output voltage begins to rise, or
correspondingly, the point at which the collector current begins to fall.
During this time, the transistor is still in the saturation region. Hence
the collector current remains at its maximum saturation value, IC MAX,
during this time. In effect what is happening is that the volume of
excess minority charge stored in the base, which has been put in by
overdriving the transistor, is being removed through the base resistor
until the transistor reaches the edge of saturation and enters the
forward active region again. Very often, the storage time is the largest
of the switching times and may be the principal limiting factor in the
speed of operation of the transistor in digital circuits.
Rise-Time, tr
Note that the rise-time for the output voltage is, in fact, the fall-time
of the collector current. During this time, the transistor is again
operating in the forward active mode passing between the edge of
saturation and cut-off. The collector current falls from its maximum
value towards zero. Note, also, that during this time, the base current
is negative as excess minority charge carriers are being removed from
the base region. The rise-time is usually measured between 10 and
90 points on the output voltage profile.
The Ebers Moll model is a good large-signal, steady-state transistor
model. However, it does not deal with the transient conditions of
changing charge carrier profiles during changes of mode of operation
of the transistor when it is turning on or off. A better model is needed
to take account of these dynamic conditions.
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VCC
Vi (t)
t
IB
FOR
iB(t)
t
IB
REV
Q’B(t)
Q ' SAT
Q' EOS
IC
t
MAX
iC(t)
t
VCC
VO(t)
t
Saturation
Forward
Active
Cut-off
Forward
ts
tf
tr
Active
td
Fig. 5.2
The Sequence of Events During Transistor Switching
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5.2 BJT Charge Control Model
Recall the minority carrier concentration profile in the base region of a
bipolar npn transistor operating in the forward active mode as shown
in Fig. 5.3 below.
B
Linear
approximation
E
C
Including
recombination
0
Fig. 5.3
Wb
Minority Carrier Charge Profile in Base Region of the BJT
Collector Current
The profile of the charge distribution can be approximated as linear,
which means that the slope of the distribution is taken as constant.
This is equivalent to neglecting recombination in the base region and
assuming that all electrons diffuse through the base into the collector
region. If the hole component of the collector current is neglected, it
can then be said that the collector current is directly dependent on the
volume of charge in the base region in the forward active mode, QF,
and the forward transit time, F, for electrons passing through this
region
Then under steady-state conditions:
IC 
QF
F
which is equivalent to taking F = 1
If the linear approximation is assumed to extend to dynamic
conditions where the volume of charge in the base is changing, then
for the instantaneous collector current:
iC (t) 
QF (t)
F
diC (t) 1 dQF (t)

dt
F
dt
and
That is to say that, changes in the collector current will directly follow
changes in the excess minority charge stored in the base when the
transistor is operating in the forward active mode.
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Base Current
The base current is composed under steady-state conditions of a
recombination component and the hole currents across the junctions.
The recombination component can be estimated as the volume of
charge in the base divided by the minority carrier lifetime:
IBR 
QF
B
The hole currents can be accounted for by taking a modified equivalent
carrier lifetime BF
 F F
to give a simplified steady-state base current
of:
IB 
QF
BF
If the base terminal is used as an input or controlling terminal, as in
the case of the single transistor inverter, then any change in the base
charge will be due to a change in the base current. Including a time
varying component for dynamic conditions then gives the
instantaneous base current as…
iB (t) 
QF (t) dQF (t)

BF
dt
Emitter Current
Finally, for the emitter current,
iE (t) 
iE  iB  iC , so that:
QF (t) QF (t) dQF (t)


F
BF
dt
The complete model of charge control must also account for the charge
stored in the junction capacitances and changes in these charges as
shown in Fig. 5.4. These are designated QBC and QBE for base-collector
and base-emitter junctions respectively. Dynamic changes in these
charges will give rise to additional components of currents as dQBC/dt
and dQBE/dt.
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dQ BC
dt
CBC
+
-
+
-
iC
iB
dQ BE
dt
CBE
Fig. 5.4
iE
Currents due to Changing Charges in the Junctions of the BJT
The final complete set of Charge Control Equations for the Forward
Active mode of operation of the Bipolar Junction Transistor is then
given as:
iC 
QF (t) dQBC (t)

F
dt
iB 
QF (t) dQF (t) dQBC (t) dQBE (t)



BF
dt
dt
dt
iE 
QF (t) QF (t) dQF (t) dQBE (t)



F
BF
dt
dt
In a more complete charge control model, these equations can be
extended to include the reverse mode of operation of the transistor
also, but this is not necessary for our purposes.
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