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TRANSISTOR SWITCHING
Introduction
Electronic circuits inevitably involve reactive elements, in some cases intentionally but
always at least as parasitic elements. Although their influence on circuit performance may
be subordinate for a particular circuit reactive elements always introduce an ultimate
limitation on frequency response/switching speed. Reactive elements introduce ‘past
history’ into the analysis of a circuit. The voltage across a capacitor, for example, is
proportional to the capacitor charge, and that charge is the cumulative result of past current
into and out of the capacitor. To change the voltage across a capacitor the stored charge
must change, i.e., there must be a current to transport charge into (increase voltage) or out
of (reduce voltage) the capacitor. There is therefore inevitably a delay in changing capacitor
voltage since a finite current requires a finite time to transport a finite charge.
A similar historical dependency is associated with an inductance. Energy is stored
magnetically by the current flowing in an inductor. A current change requires a change in
stored energy, and for a finite power capability a finite time is required for an energy
change.
This note examines switching delays associated with circuit capacitance and inductance.
There are related delays associated with the internal device phenomena, generally
significant only for very fast changes. These device-specific contributions are considered
elsewhere; ordinarily they are of little import for significant time intervals less than
(roughly) 10 to 100 nanoseconds. Switching is examined here in the context of a bipolar
junction transistor circuit.
Switching a Capacitative Load
The circuit on the right is that of a simplified CE amplifier with an external
capacitor load; the capacitor may represent an inevitable circuit parasitic or it
might approximate the capacitance that would be added by an additional stage of
amplification. A voltage pulse is applied, increasing the base input voltage from
an initial zero level for which the transistor is cut-off, to a level at which the
emitter junction is turned ON.
Qualitative Evaluation
Consider the circuit performance qualitatively at first; this is done with reference to the figure below. A
single representative constant base-current BJT collector characteristic is shown, and superimposed on the
graph is the load line for the circuit. Initially (base voltage zero) the transistor is cut-off and there is no
collector current; the collector voltage then is VCC. This is the abscissa point labeled 'cutoff' on the figure,
and is the quiescent point so long as no base voltage is applied.
Note particularly that energy is stored in the capacitor, i.e., the
capacitor is charged so that the voltage across it is VCC.
Now suppose an abrupt base voltage change occurs
corresponding to the leading edge of the base voltage pulse.
(As a practical matter ‘abrupt’ means the change occurs within a
time interval much shorter that that within which the circuit can
respond; the analysis will indicate how small this interval need
be.) Base current rises abruptly to a finite value, approximately
equal to (pulse height - 0.7 volt)/ base resistance. The collector
voltage however remains at VCC initially, since the capacitor
charge cannot change instantaneously. Hence the operating
point jumps abruptly, as shown, to the collector characteristic
corresponding to the base current. Note that the transistor is
not saturated initially whatever the base current because the collector voltage is constrained by the
Introductory Electronics Notes
42-1
Copyright © M H Miller: 2000
The University of Michigan-Dearborn
revised
capacitor. Note also that initially there is no current through so and no voltage drop across the collector
resistor. It is the capacitor that supplies the BJT collector current, and so to the extent that the collector
current remains constant the collector voltage drops linearly.]
As the capacitor discharges, lowering the collector voltage, current through the collector resistor increases
and the current from the capacitor decreases. Roughly equal magnitudes of change are involved, at least to
the extent that the transistor collector current for a fixed base current remains constant. As the collector
voltage decreases the operating point moves down the constant base current characteristic until the
intersection with the load line is reached. At this point the collector current is provided entirely through the
collector resistor. There is no current drawn from the capacitor, and so no further decrease in collector
voltage.
This is the steady-state condition that persists until the base voltage pulse level changes. The transistor
may or may not be saturated in steady state; this depends on the circuit element values fixing the
intersection of the load line and the collector characteristic. In general the turn-on will be fairly rapid,
because the transistor provides a relatively high-current discharge path for the capacitor.
Assume now the steady state has been reached, and after that the base voltage is brought back to zero
voltage, once again cutting off the transistor; this is at the trailing edge of the base pulse. The collector
current immediately (ideally) drops to zero. However the capacitor once again does not permit the
collector voltage to change abruptly. Hence the operating point drops abruptly to intersect the abscissa;
zero current, same voltage. Current now flows through the collector resistor to charge the capacitor, and
the operating point moves along the abscissa to return to steady state at VCC.
Quantitative Evaluation
A PSpice analysis of the switching circuit considered was performed, using a 2N3904 transistor model
and circuit element values as shown in the netlist below
.*BJT CapSwitch
VBB 1 0
+ PULSE (0 5 20u .01u `
+.01u 150u 10)
RB 1 2
220K
Q1 3 2
0
Q2N3904
RC 4 3
2.2K
VCC 4 0
CL 3 0
.TRAN .1u 500U
.PROBE
.END
10
.01u
The following figure shows the computed turn-on and turn-off locus for the circuit.
Introductory Electronics Notes
The University of Michigan-Dearborn
42-2
Copyright © M H Miller: 2000
revised
It is left as an exercise to verify (use the idealized diode model)
VCE = VCC - IRC e -t/RC)
where I = ß(VB-0.7)/R B is the collector current corresponding to a pulse
amplitude VB.
The computed currents as a function of time are shown in the next figure
below. The transistor collector current (which should be distinguished
from the current provided by the power supply) jumps immediately on
turn-on to a magnitude determined by the collector characteristic
corresponding to the base current; the transistor is not saturated at this
point and there is no current-limiting because of saturation. A turn-on current spike of this sort can cause
damage if the current is not limited to a safe value by one means or another. In this example the base
resistor provides that limiting, but the point really is that it should not be left to chance.
The supply current, on the other hand, initially is zero; the capacitor holds the voltage drop across the
collector resister to zero. As the supply current increases (the capacitor is discharging through the
transistor and consequently the collector voltage is decaying) the collector current decreases in this
illustration. As is not uncommon in such switching; the base current magnitude used generally is intended
to saturate the transistor. Because the capacitor at first prevents the transistor from saturating an initially
larger current speeds the capacitor discharge,
Eventually steady state is reached; there is no current contributed by the capacitor, and the power supply
provides the collector current. When the transistor is cutoff on the trailing edge of the base voltage pulse
the collector current drops to zero immediately, The supply current, however, continues to flow,
recharging the capacitor.
Switching an Inductive Load
Because of a fundamental conflict between the physical laws associated with
the inductive effect and the practical and economic constraints of monolithic
construction the phrase integrated circuit inductor is by and large an
oxymoron. On the other hand discrete inductors are important in a number
of applications; high-current mechanical relay switches are an example. A
simplified transistor-actuated switch circuit is shown below, left; the dotted
rectangle represents a switch having a winding resistance RL and an
inductance L; associated switch contacts are not shown since they are not
involved in the discussion.
As was done in the capacitor switching illustration a pulse is applied which
Introductory Electronics Notes
The University of Michigan-Dearborn
42-3
Copyright © M H Miller: 2000
revised
temporarily switches the transistor from a cutoff state to a conducting state. And, also as in that earlier
illustration, we first examine the circuit behavior during the pulse qualitatively.
Qualitative Evaluation
The inductance is a more sinister circuit element than a capacitor in the sense that it stores energy
dynamically, i.e., via a current flow through the inductor. For capacitor loading turning off a power
supply is a relatively benign operation, although there are some hazards. Capacitors discharge their stored
energy if there is a current path, but if not they remain dormant in an energized state. An inductor, on the
other hand, stores its energy in a current flow, and in general turning off the power supply means turning
off that current flow. An inductor responds to a changing current by generating a voltage which attempts to
mitigate the change; the faster the change the larger the generated voltage magnitude. Unfortunately the
result, particularly where care is not taken, quite often is to produce a destructive release of the stored
energy.
A sketch of a representative pulse trajectory on the IC-VCE plane is drawn below. Initially the transistor is
cutoff and the operating point is at (VCC , 0). When the base drive turns the transistor ON the operating
point must lie on the transistor characteristic which corresponds to the base current.
On the other hand the inductance prevents the collector current from changing immediately. To
accommodate both requirements the collector voltage drops immediately and moves to the zero-current
intersection of the collector characteristic; the collector voltage change is provided by the inductive reaction
to an attempt to change the current. Note however that the current is in the process of increasing.
Operation moves up the saturation part of the collector characteristic and over until the load line is
intersected.
This corresponds to the steady-state operating point. In most instances the operating point will be selected
to saturate the transistor so that the collector dissipation will be relatively small.
Quantitative Evaluation
A PSpice computation of the turn-on transient follows ( the source specification for the turn-off transient,
considered below, is included.
*BJT Inductive Switching
VBB
1
0
* Leading edge
+ PWL(0 0 10u 0 10.005u 2 50u 2)
* Trailing edge
*+ PWL(0 2 10u 2 10.005u 0 50u 0)
RB
1
2
47K
Q1
3
2
0
Q2N3904
Introductory Electronics Notes
The University of Michigan-Dearborn
RC
4
3
LC
5
4
VCC
5
0
D1
3
6
RD
6
5
.TRAN .001u 50U
.PROBE
.END
42-4
2.2K
10m
10v
D1N4004
2.2K
Copyright © M H Miller: 2000
revised
The turn-on transient response is drawn below (input step starts at 10µs). Note that the collector current
remains zero initially and then rises approximately exponentially ( along the collector characteristic) into
steady-state (with a small overshoot) Similarly the collector voltage initially drops rapidly towards zero
(through saturation), and remains low as the current rises (along the saturation portion of the collector
characteristic). As the operating point moves to the intersection of the load line and the collector
characteristic the voltage and current increase to their steady-state values.
While a similar calculation can be made for the turn-off transient this is not done here. The reason is that
circuit operation is quite erratic and in practice generally destructive. On the trailing edge of the base pulse
the transistor is suddenly cut-off. However the energy stored in the inductor can not simply disappear
(conservation of energy), i.e., the current through the inductor cannot immediately drop to zero. The
faster the current attempts to decrease the higher the inductive voltage generated (E= LdI/dt), and as noted
before operation becomes erratic and more often than not destructive. The inductive increase in collector
voltage at first tends to increase the collector current (because of the Early effect ). Unfortunately a fast
current change causes a very large induced voltage, ordinarily increasing the reverse bias of the collector
junction to a point where junction breakdown begins. This new current flow mechanism leads into
unstable operation with the usual consequence being destruction of the transistor. While we do not
consider this operation further we do consider a modification of the circuit to avoid this problem.
Actually the general nature of a solution is fairly straightforward;
simply provide a current path to replace conduction through the
transistor which enables the stored inductive energy to be dissipated
harmlessly. This added current path should be activated only when the
transistor is turned off, since energy is supposed to be stored when the
transistor is turned ON. One method to accomplish the objective,
illustrated in the circuit to the right, is to add a resistor and diode as
shown. When the transistor is turned ON the diode blocks current
flow through the added branch and the turn-on operation is as
described before. On turn-off however the inductive voltage generated
increases the collector voltage to the point where the diode is turned
ON and what was collector current now flows through R.
In fact if the steady-state collector current is I then the collector voltage jumps by an amount IR + diode
drop and thereafter decays exponentially with time constant L/(R+RL). The amount of the voltage drop
can be controlled by the choice of R, but there is a trade-off between rapid decay (L/R small) and a limited
voltage jump (IR small).
The netlist already includes the diode branch; the diode is reverse-biased during turn-on and is not
involved in the preceding discussion. The figure following is a sketch illustrating the turn-off transient;
the turn-on transient also is shown to present a coordinated picture of events. On turn-off the collector
Introductory Electronics Notes
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Copyright © M H Miller: 2000
The University of Michigan-Dearborn
revised
current drops immediately the base drive is removed. However the inductor current is diverted through the
diode branch, which is turned on by the inductive voltage generated. However the collector voltage rise is
limited to a value (see note in figure) sufficient to maintain (initially) the current that was carried by the
collector.
The computed transient response for the circuit parameters described in the netlist (above) is shown below.
(There is a small post-transient, not shown, associated with the diode turning OFF after the inductive
voltage has decayed).
Integrated circuits are available commercially designed specifically to include inductive ‘kick’ protection.
The mechanism used is the same in principle but different in detail. A Zener diode is connected between
base and collector of the switching transistor designed to break down when the collector voltages rises on
turn-off. Current through the diode then drives the base, enabling the transistor to continue conduction as
the current decays. This ‘bootstrap’ operation uses the inductive energy to support its own release.
The next figure illustrates the trajectory of the turn-off transient on the IC-VCE plane. The voltage rises
very rapidly to ≈ 16 volts, during which time the collector current decays towards zero, and then decays
exponentially to the steady-state value of 10 volts.
Introductory Electronics Notes
The University of Michigan-Dearborn
42-6
Copyright © M H Miller: 2000
revised
Introductory Electronics Notes
The University of Michigan-Dearborn
42-7
Copyright © M H Miller: 2000
revised
PROBLEMS
1)
Use the simplified capacitatively loaded PWL transistor model to
verify the theoretical expression for the turn-on transient
where I is the collector current ß(VB-0.7)/R B corresponding to a base
voltage pulse amplitude VB.
2)
In the netlist used to analyse the capacitively loaded transistor
replace the 2N3904 transistor model by the PWL model used above; use ß
= 120 and VBE = 0.7 volts for nominal parameter values. Plot the turn-on
and turn-off transients on the IC-VCE plane. Compare the PWL computation to the 2N3904 model
computation, and compare these to the theoretical expectation. Estimate the turn-off transient by
approximating saturation by a line whose slope is (roughly) 1ma/0.3v , i.e., the transistor is approximated
as a 300Ω resistor.
3)
Modify the netlist for the inductively loaded PWL transistor
model by replacing the 2N3904 model by a PWL model as shown.
Include the turnoff protection diode. Compare the computed response
for the PWL model with that computed for the 2N3904 model.
Compare these with expectations.
4)
Use a 5-volt peak base voltage pulse, VCC = 10 volts, R E = 2.2
KΩ, R B = 220KΩ, C = 0.01µF, and a 2N3904 transistor; compute the
emitter voltage as a function of time. Compare the computed response to
theoretical expectations using a simplified PWL transistor model.
5)
Use a 5-volt peak base voltage pulse, VCC = 10 volts, R C = 2.2
KΩ, R B = 220KΩ, C = 0.01µF, and a 2N3904 transistor; compute the
base and collector voltages as a function of time. Compare the computed
response to theoretical expectations using a simplified PWL transistor
model.
Introductory Electronics Notes
The University of Michigan-Dearborn
42-8
Copyright © M H Miller: 2000
revised