Active mode operation
When a transistor is in the fully-off
state (like an open switch), it is said to be cutoff. Conversely,
when it is fully conductive between emitter and collector (passing as
much current through the collector as the collector power supply and
load will allow), it is said to be saturated. These are the two
modes of operation explored thus far in using the transistor as a
switch.
However, bipolar transistors don't have
to be restricted to these two extreme modes of operation. As we learned
in the previous section, base current "opens a gate" for a limited
amount of current through the collector. If this limit for the
controlled current is greater than zero but less than the maximum
allowed by the power supply and load circuit, the transistor will
"throttle" the collector current in a mode somewhere between cutoff and
saturation. This mode of operation is called the active mode.
An automotive analogy for transistor
operation is as follows: cutoff is the condition where there is
no motive force generated by the mechanical parts of the car to make it
move. In cutoff mode, the brake is engaged (zero base current),
preventing motion (collector current). Active mode is when the
automobile is cruising at a constant, controlled speed (constant,
controlled collector current) as dictated by the driver. Saturation
is when the automobile is driving up a steep hill that prevents it from
going as fast as the driver would wish. In other words, a "saturated"
automobile is one where the accelerator pedal is pushed all the way down
(base current calling for more collector current than can be provided by
the power supply/load circuit).
I'll set up a circuit for SPICE
simulation to demonstrate what happens when a transistor is in its
active mode of operation:
"Q" is the standard letter designation
for a transistor in a schematic diagram, just as "R" is for resistor and
"C" is for capacitor. In this circuit, we have an NPN transistor powered
by a battery (V1) and controlled by current through a
current source (I1). A current source is a device that
outputs a specific amount of current, generating as much or as little
voltage as necessary across its terminals to ensure that exact amount of
current through it. Current sources are notoriously difficult to find in
nature (unlike voltage sources, which by contrast attempt to maintain a
constant voltage, outputting as much or as little current in the
fulfillment of that task), but can be simulated with a small collection
of electronic components. As we are about to see, transistors themselves
tend to mimic the constant-current behavior of a current source in their
ability to regulate current at a fixed value.
In the SPICE simulation, I'll set the
current source at a constant value of 20 µA, then vary the voltage
source (V1) over a range of 0 to 2 volts and monitor how much
current goes through it. The "dummy" battery (Vammeter) with
its output of 0 volts serves merely to provide SPICE with a circuit
element for current measurement.
bipolar transistor simulation
i1 0 1 dc 20u
q1 2 1 0 mod1
vammeter 3 2 dc 0
v1 3 0 dc
.model mod1 npn
.dc v1 0 2 0.05
.plot dc i(vammeter)
.end
type npn
is 1.00E-16
bf 100.000
nf 1.000
br 1.000
nr 1.000
v1 i(ammeter) -1.000E-03 0.000E+00 1.000E-03 2.000E-03
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
0.000E+00 -1.980E-05 . * . .
5.000E-02 9.188E-05 . .* . .
1.000E-01 6.195E-04 . . * . .
1.500E-01 1.526E-03 . . . * .
2.000E-01 1.914E-03 . . . *.
2.500E-01 1.987E-03 . . . *
3.000E-01 1.998E-03 . . . *
3.500E-01 2.000E-03 . . . *
4.000E-01 2.000E-03 . . . *
4.500E-01 2.000E-03 . . . *
5.000E-01 2.000E-03 . . . *
5.500E-01 2.000E-03 . . . *
6.000E-01 2.000E-03 . . . *
6.500E-01 2.000E-03 . . . *
7.000E-01 2.000E-03 . . . *
7.500E-01 2.000E-03 . . . *
8.000E-01 2.000E-03 . . . *
8.500E-01 2.000E-03 . . . *
9.000E-01 2.000E-03 . . . *
9.500E-01 2.000E-03 . . . *
1.000E+00 2.000E-03 . . . *
1.050E+00 2.000E-03 . . . *
1.100E+00 2.000E-03 . . . *
1.150E+00 2.000E-03 . . . *
1.200E+00 2.000E-03 . . . *
1.250E+00 2.000E-03 . . . *
1.300E+00 2.000E-03 . . . *
1.350E+00 2.000E-03 . . . *
1.400E+00 2.000E-03 . . . *
1.450E+00 2.000E-03 . . . *
1.500E+00 2.000E-03 . . . *
1.550E+00 2.000E-03 . . . *
1.600E+00 2.000E-03 . . . *
1.650E+00 2.000E-03 . . . *
1.700E+00 2.000E-03 . . . *
1.750E+00 2.000E-03 . . . *
1.800E+00 2.000E-03 . . . *
1.850E+00 2.000E-03 . . . *
1.900E+00 2.000E-03 . . . *
1.950E+00 2.000E-03 . . . *
2.000E+00 2.000E-03 . . . *
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
The constant base current of 20 µA sets a
collector current limit of 2 mA, exactly 100 times as much. Notice how
flat the curve is for collector current over the range of battery
voltage from 0 to 2 volts. The only exception to this featureless plot
is at the very beginning, where the battery increases from 0 volts to
0.25 volts. There, the collector current increases rapidly from 0 amps
to its limit of 2 mA.
Let's see what happens if we vary the
battery voltage over a wider range, this time from 0 to 50 volts. We'll
keep the base current steady at 20 µA:
bipolar transistor simulation
i1 0 1 dc 20u
q1 2 1 0 mod1
vammeter 3 2 dc 0
v1 3 0 dc
.model mod1 npn
.dc v1 0 50 2
.plot dc i(vammeter)
.end
type npn
is 1.00E-16
bf 100.000
nf 1.000
br 1.000
nr 1.000
v1 i(ammeter) -1.000E-03 0.000E+00 1.000E-03 2.000E-03
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
0.000E+00 -1.980E-05 . * . .
2.000E+00 2.000E-03 . . . *
4.000E+00 2.000E-03 . . . *
6.000E+00 2.000E-03 . . . *
8.000E+00 2.000E-03 . . . *
1.000E+01 2.000E-03 . . . *
1.200E+01 2.000E-03 . . . *
1.400E+01 2.000E-03 . . . *
1.600E+01 2.000E-03 . . . *
1.800E+01 2.000E-03 . . . *
2.000E+01 2.000E-03 . . . *
2.200E+01 2.000E-03 . . . *
2.400E+01 2.000E-03 . . . *
2.600E+01 2.000E-03 . . . *
2.800E+01 2.000E-03 . . . *
3.000E+01 2.000E-03 . . . *
3.200E+01 2.000E-03 . . . *
3.400E+01 2.000E-03 . . . *
3.600E+01 2.000E-03 . . . *
3.800E+01 2.000E-03 . . . *
4.000E+01 2.000E-03 . . . *
4.200E+01 2.000E-03 . . . *
4.400E+01 2.000E-03 . . . *
4.600E+01 2.000E-03 . . . *
4.800E+01 2.000E-03 . . . *
5.000E+01 2.000E-03 . . . *
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Same result! The collector current holds
absolutely steady at 2 mA despite the fact that the battery (v1) voltage
varies all the way from 0 to 50 volts. It would appear from our
simulation that collector-to-emitter voltage has little effect over
collector current, except at very low levels (just above 0 volts). The
transistor is acting as a current regulator, allowing exactly 2 mA
through the collector and no more.
Now let's see what happens if we increase
the controlling (I1) current from 20 µA to 75 µA, once again
sweeping the battery (V1) voltage from 0 to 50 volts and
graphing the collector current:
bipolar transistor simulation
i1 0 1 dc 75u
q1 2 1 0 mod1
vammeter 3 2 dc 0
v1 3 0 dc
.model mod1 npn
.dc v1 0 50 2
.plot dc i(vammeter)
.end
type npn
is 1.00E-16
bf 100.000
nf 1.000
br 1.000
nr 1.000
v1 i(ammeter) -5.000E-03 0.000E+00 5.000E-03 1.000E-02
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
0.000E+00 -7.426E-05 . * . .
2.000E+00 7.500E-03 . . . * .
4.000E+00 7.500E-03 . . . * .
6.000E+00 7.500E-03 . . . * .
8.000E+00 7.500E-03 . . . * .
1.000E+01 7.500E-03 . . . * .
1.200E+01 7.500E-03 . . . * .
1.400E+01 7.500E-03 . . . * .
1.600E+01 7.500E-03 . . . * .
1.800E+01 7.500E-03 . . . * .
2.000E+01 7.500E-03 . . . * .
2.200E+01 7.500E-03 . . . * .
2.400E+01 7.500E-03 . . . * .
2.600E+01 7.500E-03 . . . * .
2.800E+01 7.500E-03 . . . * .
3.000E+01 7.500E-03 . . . * .
3.200E+01 7.500E-03 . . . * .
3.400E+01 7.500E-03 . . . * .
3.600E+01 7.500E-03 . . . * .
3.800E+01 7.500E-03 . . . * .
4.000E+01 7.500E-03 . . . * .
4.200E+01 7.500E-03 . . . * .
4.400E+01 7.500E-03 . . . * .
4.600E+01 7.500E-03 . . . * .
4.800E+01 7.500E-03 . . . * .
5.000E+01 7.500E-03 . . . * .
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Not surprisingly, SPICE gives us a
similar plot: a flat line, holding steady this time at 7.5 mA -- exactly
100 times the base current -- over the range of battery voltages from
just above 0 volts to 50 volts. It appears that the base current is the
deciding factor for collector current, the V1 battery voltage
being irrelevant so long as it's above a certain minimum level.
This voltage/current relationship is
entirely different from what we're used to seeing across a resistor.
With a resistor, current increases linearly as the voltage across it
increases. Here, with a transistor, current from emitter to collector
stays limited at a fixed, maximum value no matter how high the voltage
across emitter and collector increases.
Often it is useful to superimpose several
collector current/voltage graphs for different base currents on the same
graph. A collection of curves like this -- one curve plotted for each
distinct level of base current -- for a particular transistor is called
the transistor's characteristic curves:
Each curve on the graph reflects the
collector current of the transistor, plotted over a range of
collector-to-emitter voltages, for a given amount of base current. Since
a transistor tends to act as a current regulator, limiting collector
current to a proportion set by the base current, it is useful to express
this proportion as a standard transistor performance measure.
Specifically, the ratio of collector current to base current is known as
the Beta ratio (symbolized by the Greek letter β):
Sometimes the β ratio is designated as "hfe,"
a label used in a branch of mathematical semiconductor analysis known as
"hybrid parameters" which strives to achieve very precise predictions of
transistor performance with detailed equations. Hybrid parameter
variables are many, but they are all labeled with the general letter "h"
and a specific subscript. The variable "hfe" is just another
(standardized) way of expressing the ratio of collector current to base
current, and is interchangeable with "β." Like all ratios, β is unitless.
β for any transistor is determined by its
design: it cannot be altered after manufacture. However, there are so
many physical variables impacting β that it is rare to have two
transistors of the same design exactly match. If a circuit design relies
on equal β ratios between multiple transistors, "matched sets" of
transistors may be purchased at extra cost. However, it is generally
considered bad design practice to engineer circuits with such
dependencies.
It would be nice if the β of a transistor
remained stable for all operating conditions, but this is not true in
real life. For an actual transistor, the β ratio may vary by a factor of
over 3 within its operating current limits. For example, a transistor
with advertised β of 50 may actually test with Ic/Ib
ratios as low as 30 and as high as 100, depending on the amount of
collector current, the transistor's temperature, and frequency of
amplified signal, among other factors. For tutorial purposes it is
adequate to assume a constant β for any given transistor (which is what
SPICE tends to do in a simulation), but just realize that real life is
not that simple!
Sometimes it is helpful for comprehension
to "model" complex electronic components with a collection of simpler,
better-understood components. The following is a popular model shown in
many introductory electronics texts:
This model casts the transistor as a
combination of diode and rheostat (variable resistor). Current through
the base-emitter diode controls the resistance of the collector-emitter
rheostat (as implied by the dashed line connecting the two components),
thus controlling collector current. An NPN transistor is modeled in the
figure shown, but a PNP transistor would be only slightly different
(only the base-emitter diode would be reversed). This model succeeds in
illustrating the basic concept of transistor amplification: how the base
current signal can exert control over the collector current. However, I
personally don't like this model because it tends to miscommunicate the
notion of a set amount of collector-emitter resistance for a given
amount of base current. If this were true, the transistor wouldn't
regulate collector current at all like the characteristic curves
show. Instead of the collector current curves flattening out after their
brief rise as the collector-emitter voltage increases, the collector
current would be directly proportional to collector-emitter voltage,
rising steadily in a straight line on the graph.
A better transistor model, often seen in
more advanced textbooks, is this:
It casts the transistor as a combination
of diode and current source, the output of the current source being set
at a multiple (β ratio) of the base current. This model is far more
accurate in depicting the true input/output characteristics of a
transistor: base current establishes a certain amount of collector
current, rather than a certain amount of collector-emitter
resistance as the first model implies. Also, this model is favored
when performing network analysis on transistor circuits, the current
source being a well-understood theoretical component. Unfortunately,
using a current source to model the transistor's current-controlling
behavior can be misleading: in no way will the transistor ever act as a
source of electrical energy, which the current source symbol
implies is a possibility.
My own personal suggestion for a
transistor model substitutes a constant-current diode for the current
source:
Since no diode ever acts as a source
of electrical energy, this analogy escapes the false implication of the
current source model as a source of power, while depicting the
transistor's constant-current behavior better than the rheostat model.
Another way to describe the constant-current diode's action would be to
refer to it as a current regulator, so this transistor
illustration of mine might also be described as a diode-current
regulator model. The greatest disadvantage I see to this model is
the relative obscurity of constant-current diodes. Many people may be
unfamiliar with their symbology or even of their existence, unlike
either rheostats or current sources, which are commonly known.
- REVIEW:
- A transistor is said to be in its
active mode if it is operating somewhere between fully on
(saturated) and fully off (cutoff).
- Base current tends to regulate
collector current. By regulate, we mean that no more collector
current may exist than what is allowed by the base current.
- The ratio between collector current
and base current is called "Beta" (β) or "hfe".
- β ratios are different for every
transistor, and they tend to change for different operating
conditions.
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