Jonathan Roderick
Hakan Durmas
Scott Kilpatrick Burgess
Experiment #5
BJT Transistors
Introduction:
Transistors are at the heart of integrated circuit design. As active elements, they are capable of
implementing gain stages (impossible with purely passive networks), buffers, electrically-operable
switches, op-amps (yes, that is what is inside those circuits from labs 2 and 3!) and a host of other
applications that require active elements. The word active refers to the fact that transistors require static
power in the form of bias current and/or voltage to operate correctly. The static power provided by the bias
is consumed so that the input signals may be amplified. Thus, when one says that transistors provide gain,
it is signals that experience gain, at the expense of static power consumption.
In this first transistor lab, Bipolar Junction Transistor (BJT) theory, biasing and their use as current sources
will be explored. In the next lab, gain and other dynamic aspects of transistors will be explored.
Bipolar Junction Transistor Theory:
Bipolar transistors consist of two back-to-back pn junctions, as shown in Fig. 5.1.
n
collector
p
n
base
(a)
emitter
p
n
p
collector
base
(b)
emitter
collector
base
emitter
base
emitter
(a)
collector
(b)
Fig. 5.1 Device-level representations of (a) npn & (b) pnp bipolar transistors, along with corresponding
schematic symbols.
The discussion that follows pertains to npn transistors; the same discussion applies to pnp transistors
provided every instance of is “n” be replaced by “p”. In forward-active operation, which is the most
common for bipolar transistors, the base-emitter junction is forward biased, the base-collector junction
reverse biased. As the emitter is highly-doped n+ material (i.e., low impedance), electrons are injected quite
easily into the base under forward bias. The base is doped moderately relative to the emitter, implying that
the base-emitter depletion region lies almost entirely on the base side of the junction. Furthermore, the base
is a very narrow region, thus the associated electric field is quite large, sweeping the injected electrons right
through to the collector (actually, due to the finite base width, and associated finite transit time, a few
electrons recombine with available holes in the base before diffusing to the base-collector depletion region,
but this is not a dominant effect in modern processes). These electrons are the minority charge necessary to
supply the reverse current through the reverse-biased base-collector junction. It is the forward bias across
the base-emitter junction that supplies this charge, thus the current through the base-collector junction is
not limited to the negligible reverse saturation current. In fact, neglecting recombination of the electrons in
transit with available holes in the base, the current through the collector is practically identical to the
current through the emitter.
The really nice thing about the transistor becomes apparent if one explores what happens if the current
injected into the collector is then allowed to flow into a resistive load, as shown in Fig. 2.
Vcc
Rload
Vbe
Fig. 2
NPN transistor with forward bias across base-emitter junction and resistive load attached between
collector and power supply.
As the base and power supply voltages are fixed, it follows that varying the load resistance causes a
different collector node voltage to develop. Thus, the base-collector reverse bias changes. However, recall
from the diode labs that the magnitude of the reverse bias voltage has very little effect on the reverse
current (i.e., it approaches the reverse saturation current in the limit), and thus it is the electrons injected by
the forward-biased base-emitter junction that control the collector current. The significance is that the
transistor approximates an ideal controlled current source, where the controlling variable is the base current
(which is in turn controlled by the base voltage, so you can think of that as the controlling variable if you
prefer) and the controlled variable is the collector current. In comparison to the controlling variable, the
load has relatively little effect on the transistor current!
Now that the emitter and collector currents have been discussed in some detail, one must consider what
base current (if any) exists before writing down the key bipolar transistor equations. First, recall that most
of the emitter current flows through the collector, with some of the emitter electrons being lost to
recombination with available holes in the base region. While this effect can be minimized by making a
small base, there are always some holes in the base region, and these holes have to be supplied as base
current. A second phenomenon is reverse current through the forward-biased base-emitter junction. Again,
this effect can be minimized by heavily doping the emitter, but nonetheless, some reverse current exists,
and must be supplied through the base contact.
Now that the basic principles of bipolar transistors have been discussed, we can go ahead and write the
three key equations for bipolar transistors, one relating collector current to the base-emitter voltage (i.e., the
controlling variable), one accounting for the base current, and the third satisfying KCL:
 VVbe
 V
I c  I s  e t  11  ce

 V a


Ic  p


Ib  t
Ie  Ic  Ib 



(1)
 1
Ic

The second parenthesized quantity in the collector current equation accounts for the slight variation of
collector current with collector voltage. Though ideally the collector current is influenced solely by the
base-emitter voltage, the base-collector reverse bias does influence things a bit. Since the effect is not
dominant, people usually model it with a simple linear dependence on collector voltage, with the slope
determined by the Early voltage factor, named in honor of J. M. Early. This is a secondary effect, and for
much of what is presented will be ignored.
Biasing the common-emitter amplifier
Consider the following common-emitter amplifier:
Vcc
Fig. 3
Rb1
Rc
Rb2
Ree
Common-emitter amplifier.
The question is how to achieve the resistors such that a certain bias condition is achieved. The easiest way
to see how to do this is with an example, so consider the following requirements: the base-emitter junction
be forward-biased, the collector-base junction be reverse biased, the base voltage be approximately 1V and
the transistor current be 1mA (assume the supply is 5V). Assuming the transistor beta is large (as it should
be), one can assume for all design calculations that the collector and emitter currents are essentially equal.
Since the forward-bias voltage of a p-n junction is somewhere around 700 mV, it follows that
approximately 300 mV drops across Ree. Thus, for a 1 mA current, the emitter resistor should be
approximately 300. We want to ensure that the base-collector junction is reverse-biased, so we choose
(arbitrarily) a collector voltage of 3.5V. For a 3.5V output voltage, the voltage dropped across the collector
resistor is 1.5V, which for a 1mA current implies a 1.5k resistor. Assuming that the base current is
negligible, Rb1 and Rb2 form a voltage divider at the base, so to achieve a base voltage of 1V requires the
resistors be in a 4:1 ratio. Resistors of 1k and 3.9k will work fine.
Note that in biasing the transistor, the equations developed earlier were unnecessary; only the qualitative
ideas of small base current and forward-bias voltages being around 700 mV were used. This may seem odd
(after all, why did we develop the equations if we don’t use them?), but it is actually good practice to have
as few circuit performance metrics as possible depend on transistor parameters, as these parameters vary
wildly from one transistor to another. As an example,  for a good transistor is large (say, 100 or better) but
not at all predictable. One transistor might have a =83, while another has a =137. If your design was
highly sensitive to , it would not have repeatable performance (i.e., if you built your circuit, measured it,
and then replaced only the transistor, you would get different results). Thus, while the above equations are
important, particularly for analysis and understanding basic transistor mechanisms, they are not always
used in design. However, there are exceptions to every rule, which the next section demonstrates.
A bipolar current mirror:
When you build the common-emitter amplifier in the lab, you will probably notice that the measured
current is not exactly 1mA; in fact, it may be off a great deal. The main reason for this is the rather arbitrary
assumption of a base-emitter voltage of 700 mV. It is a simple matter then to adjust the emitter resistor to
achieve the correct current. However, what if you had, say, 4 or 5 transistors, each requiring different bias
currents? It would not be efficient to fine-tune each one by tweaking resistors; a better approach would be
to fine-tune the current of one transistor, and then somehow force all of the other transistor currents to be a
fixed multiple of this current. Thus, achieving the correct current in several transistors would rest on one
the accuracy of only one current!
Vcc
R
Iref
Iout
Q1
Q2
R1
R2
Fig. 4 Simple bipolar current mirror.
Assume transistor Q1 has been biased appropriately to achieve exactly the right reference current. Applying
KVL (and ignoring the Early voltage), one gets:
I 1 R1  Vbe1  I 2 R 2  Vbe2
I 
I
I 1 R1  Vt ln  c1   I 2 R 2  Vt ln  c 2
 I s1 
 I s2
I 2  I1
R1 Vt  I c1 I s 2

ln 
R 2 R 2  I c 2 I s1



(2)



Beearing in mind that we want the current through Q2 to be a fixed multiple of that through Q1, largely
independent of transistor parameters, it would be nice to make the logarithmic term (error term) disappear.
If that happens, the currents through transistors are determined by simple resistor ratios! To make the error
term vanish, the reverse saturation currents must have the same ratio as the collector currents. If the
collector currents are to be given by a resistor ratio, the reverse saturation currents must be in the same
ratio, which requires that the transistor areas be in the same ratio. This is routinely done in IC design, where
ratios can be very accurate. However, using discrete components in the lab, the only way to make a
transistor with bigger area is to parallel multiple transistors, which has the following drawbacks: 1) it takes
a lot of space, 2) it limits you to integer multiples of the area of your reference transistor and 3) with
discrete components, there is wide variation in the saturation current from one transistor to the next, so
paralleling, say, 3 devices does not mean that the effective reverse saturation current is 3 times that of the
reference transistor.
However, note that the error term decreases inversely with R2; this means that using large reference
resistors reduces the error term significantly. Secondly, note that the error incurred due to mismatched
reverse saturation currents increases only logarithmically, so the error is not that substantial anyway. In the
prelab, you will design a current mirror and investigate numerically the percentage error arising from the
logarithmic term.
Regulators again
In previous labs, some simple regulators were explored. We return to this topic once more, now armed with
some knowledge of transistors. Consider the circuit below:
Vcc
R
Vcc
+
Vz
_
Vout
R2
Fig. 5
Voltage regulator employing BJT.
This circuit is identical to one previously explored, except that now a BJT is inserted between the op-amp
output and the output of the circuit. The idea is that realistically, op-amps can only source a few tens of
milliamps of current, and this may not be enough for most applications. The BJT has the nice property that
the emitter current is (+1) times the base current, so the op-amp can now get away with supplying a very
tiny current to the base of the transistor, with the burden of driving the load resting on the transistor.
An improvement to the above circuit, similar to what is used in actual power supplies, employs a technique
called current limiting, as shown below:
Vcc
R
Vcc
+
Vz
Q1
_
Q2
Rf
R2
Vout
R1
Fig. 6
Voltage regulator with current-limiting capability.
The idea here is that under normal operation, no current flows through Q 2, and thus the circuit operates
identically to the previous voltage regulator. However, should the load start to source so much current that
the voltage drop across Rf is enough to turn on Q2, then the collector of Q2 draws current from the op-amp,
leaving less for the base of Q1, resulting in a lower voltage drop across Rf. Thus, Q1, Q2 and Rf form a
negative feedback loop that tends to keep the output current at a desirable level.
Thermal dependence of BJT’s
Equation (1) indicates that the collector current of a BJT depends on the temperature of the device. In
commercial circuits, lots of care is given to designing circuits that are independent of temperature. The
resulting circuits can get quite complicated, but it is possible to explore the thermal dependence of BJT’s
and make a (admittedly crude) thermometer without making life too unbearable. Consider rewriting (1) as
follows:
I 
Vbe  Vt ln  c 
 Is 
(3)
Looking at this equation, and recalling that Vt is proportional to temperature, one might deduce that V be is
proportional to temperature. Experimental results indicate this is not the case; in fact, V be decreases with
temperature. The key is the Is term. It turns out that Is has a temperature dependence as well, which
experiments show fit the following equation reasonably well:
I s  Ioe

Vg o
Vt
(4)
Combing the above relationships with the empirical result that Io >> Ic gives:
Vbe  V go  Vt ln I o   ln I c 
(5)
This correctly predicts that Vbe decreases with increasing temperature. Now, consider the following circuit:
R
Vd4
Vbat
Fig. 7
Thermometer circuit.
The BJT’s are hooked together as diodes (realize that by shorting the base-collectors terminals together, the
result is a single p-n junction), and the battery and resistor set up a current for the diode string. If one has
good SPICE models for the transistors, this circuit can be simulated over a range of temperatures, and from
this data, Vgo and ln(Io) determined empirically. Again, though, this is more amenable to IC design, where
the four transistors are well-matched (and, in case you are wondering, diodes in IC design are implemented
most easily as diode-connected transistors). Using discrete components in the lab, there will likely be wide
variation in the transistor parameters. In this case, one may use two different bias voltages at room
temperature (use a standard mercury thermometer to determine room temperature), measure the resulting
Vd4 and current, and thus extract an effective V go and ln(Io). After this initial calibration, one may heat the
circuit with a heat gun and estimate how hot the circuit becomes by measuring the lower Vd4 and higher
current. This measurement can be compared with a thermometer reading to assess the accuracy of this
method.
Prelab Exercises
1)
Reconsider the design of the common-emitter amplifier of Fig. 3. With all design parameters
remaining the same, how large may the collector resistor be such that the collector-base junction
remains reverse-biased (assume that this reverse bias must be at least 200 mV)?
2)
Reconsider the design of the common-emitter amplifier of Fig. 3, this time assuming finite  (i.e.,
collector and emitter currents are not equal, and base current is not zero) and that the 1mA
specification refers to the collector, not emitter, current. Determine expressions for the four
resistors in terms of . Evaluate these expressions for  = 50, 100, 200 and infinity, and comment
qualitatively as to the sensitivity of these values on .
3)
Reconsider the design of the common-emitter amplifier of Fig. 3, this time assuming arbitrary V be
(i.e., in your equations, use the symbol Vbe rather than 700 mV). Determine expressions for the
four resistors in terms of Vbe. Evaluate these expressions for Vbe = 600 mV, 700 mV and 800 mV,
and comment qualitatively as to the sensitivity of these values on V be. What causes greater
changes in resistor values, Vbe or ?
4)
5)
6)
Consider the current mirror of
Fig. 4. Assume you desire the current in Q 2 to be 2.4 times that of the reference transistor. What is
the required emitter resistor for Q2 (assuming R1 = 1k)? To get a feel for the error involved in
this design, assume that the reverse saturation current for Q 2 is 25% smaller than that of Q1 and
that T = 300K (i.e., room temperature). Evaluate the error term as a percentage of the desired
current. Is this acceptable assuming you want less than 1% error? To reduce the error by a factor
of 5, what new resistor values are required?
Lab Exercises
1)
Build the common emitter amplifier of Fig. 3. Measure Vbe in the lab. Using your equations from
prelab exercise 3, adjust your resistor values based on the measured V be. Is the collector current
now 1 mA? Measure the voltage across the collector and emitter resistors as well as the resistors
themselves, and from this deduce the  of the transistor.
2)
Build a current mirror that is supposed to deliver a current of 2.4 mA (append a load resistance up
to the supply). Measure the emitter resistors carefully and try to implement the correct ratio as
close as possible. Measure the output current, and determine the percentage by which it is off from
the ideal value. Increase each of the emitter resistors by a factor of 5, and measure the currents
through both transistors. Is the ratio closer to 2.4 than before (that is, did the error get smaller)?
Did the error go down by a factor of 5 roughly?
3)
Build the voltage regulator of Fig. 5. Append a load resistance, and measure the output voltage as
you vary the load resistance from 100 to 100k.
4)
Build the thermometer circuit. Use a battery of 3.5V and 4.5V along with a mercury thermometer
reading of room temperature to determine empirical values for V go and ln(Io). Now that you have
calibrated your thermometer circuit, apply a heat gun to the circuit, and measure V d4 and the
current (you may need to wait a while for the circuit to reach thermal steady-state, since the
temperature doesn’t change instantaneously). Once the voltage and current have settled, determine
the temperature of the circuit from the equation you derived in the prelab. Does the voltage across
the diodes display a negative temperature coefficient, i.e., does the voltage go down with increased
temperature? Compare the temperature calculated with that measured with a mercury
thermometer.