Chapter 5L
Lab 5: Transistors II, Differential Amp
Contents
5L Lab 5: Transistors II, Differential Amp
5L.1 “Difference” or “Differential” Amplifier . . . . . . . . . . . . . . . . .
5L.2 Setting up the Test Signals . . . . . . . . . . . . . . . . . . . . . . . .
5L.2.1 Setup I: Using a Function Generator that can “Float” . . . . . . .
5L.2.2 Setup II: Using a Function Generator that Cannot “Float” . . . .
5L.2.3 A mediocre differential amp: resistor in ‘Tail’ . . . . . . . . . .
5L.2.4 Improving Common-mode Rejection: Current source in ‘Tail’ . .
5L.3 A Home-made Operational Amplifier . . . . . . . . . . . . . . . . .
5L.3.1 Stage One: Increase the Gain of the Bipolar Differential Amplifier
5L.3.2 Stage Two: Gain stage: common emitter amplifier . . . . . . . .
5L.3.3 Stage Three: Output stage: push-pull . . . . . . . . . . . . . . .
5L.4 Trying Feedback . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5L.4.1 A X11 Amplifier? . . . . . . . . . . . . . . . . . . . . . . . .
5L.4.2 A follower? (optional: risky business) . . . . . . . . . . . . . .
5L.5 Appendix on CMRR degradation as frequency climbs . . . . . . . . . .
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REV 21 ; August 23, 2015
Overview of the Lab
To do all of today’s lab is a challenge: the circuit is the most complex that you’ve built, so far, and if some
stage holds you up, you’re likely to run out of time. But that shouldn’t worry you. Only the differential
amp—not its conversion into op amp—is fundamental: only section 1. We hope you’ll get at least partway
into the op amp construction, because that experience will make you feel more at home with the op amps that
enter next time; but you need not finish the exercise.
1 Revisions: add alternative way to provide diff and cm signals, using Xformer (5/15); insert a couple of Ray redraws (10/14); add
headerfile, add index (6/14); add photo of CA3096 & carrier; add note re substrate of CA3096 (10/12); cut reading (8/12); add CA3096
insertion detail, after spring 12 distribution (2/12); diminish repetition of Paul’s point ’Q’s are hard.’ May need further cutting.(9/09).
1
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1
2
3
3
4
5
6
7
7
8
9
10
10
12
12
Lab 5: Transistors II, Differential Amp
2
5L.1 “Difference” or “Differential” Amplifier
45 min.
Predict differential and common-mode gains for this amplifier (don’t neglect re ). Note that you will build
this using an IC array of transistors, not our usual 2N3904’s.
Figure 1: First stage: differential amplifier, made from transistor array
5L.1.0.1 Transistor Array
We would like you to build the circuit on an array of bipolar transistors, the CA3096 or HFA3096. These
transistors are fairly well matched,2 and will track one another’s temperatures; such tracking helps assure
temperature stability, as you know.
Here’s the pinout:
Figure 2: CA3096/HFA3096 Array of bipolar transistors
The “substrate,” connected to pin 16 on the CA3096 version, is the P-doped material on which the transistors are built.
Since we don’t ever want that implicit set of diodes to conduct, we should connect substrate to the most negative point in
the circuit. Here, that is -15V. The HFA3096 offers no such substrate connection.
If you have the HFA3096, which comes in a surface-mount package (SOIC), you (or someone) will need to solder it to an
adapter, so that you can plug it into the breadboard.a Fig. 3 shows the DIP and surface mount versions of the ’3096.
Figure 3: ’3096 in two versions: CA3096 and HFA3096 mounted on DIP carrier
a As
you will see in this book’s parts list, we use a company named Proto-Advantage to do this service for us.
2 HFA3096 NPN
transistors show VBE matching typically within 1.5mV, max 5mV (at IC = 10mA).
Lab 5: Transistors II, Differential Amp
3
Here is the way its pins are numbered, and the way it goes into the breadboard.
Figure 4: DIP package pin numbering and insertion in breadboard
It straddles the trench so that its 16 pins are independently accessible.
5L.2 Setting up the Test Signals
Now you will use two function generators to generate a mixture of common-mode and differential signals.
there is more than one way to do this.
5L.2.1
Setup I: Using a Function Generator that can “Float”
The signal setup is easy if you have a function generator that permits you to “float” its common lead—the
one tied to the BNC cable’s surrounding shield, a lead that until we now we have always left tied to ground.
“Float,” here, means simply “disconnect from world ground.” Not all function generators, however, permit
such floating, and for these we suggest an alternative method, in § 5L.2.2 on the next page.
5L.2.1.1 Preliminaries
One generator will drive the other. Doing this requires that one “float” the driven generator. Find the switch
or metal strap on the lab function generator that lets you disconnect the function generator’s local ground
from absolute or “world” ground. You will find such a switch or strap on the back of some generators.
Figure 5: “Float” the external Function Generator
As you connect the two function generators to your amplifier, you will have to use care to avoid defeating
the “floating” of the external function generator: recall that BNC cables and connectors can make implicit
connections to absolute ground. You must avoid tying the external generator to ground through such inadvertent use of a cable and connector. So, you must avoid use of the BNC jacks on your breadboard; you
must also avoid linking function generator to scope with a BNC for external trigger. You may find “BNC-tomini-grabber” connectors useful to link function generator to circuit: these connectors do not oblige you to
connect their shield lead to ground.
Lab 5: Transistors II, Differential Amp
4
5L.2.1.2 Composite Signal to Differential Amplifier
Now let the breadboard’s function generator (which cannot be “floated”) drive the external function generator’s local ground or “common” terminal. Use the output of the external function generator to feed your
differential amplifier. That output can carry pure common-mode, pure differential, or a mixture of the two,
and you will exploit this versatility in the coming sections, § 5L.2.3 on the facing page.
Figure 6: Common-mode and Differential Signal Summing Circuit
5L.2.2
Setup II: Using a Function Generator that Cannot “Float”
If your main function generator lacks a switch that can float it, then you can use a transformer to provide the
required separate control of difference and shared signals (usually called “differential” and “common-mode”
signals).
Fig.7 shows the arrangement, using a 6.3V transformer—the same type that you used in Lab 3. Note that
this transformer is NOT to be plugged into the 120V wall socket! We will, instead, use the external function
generator to drive the transformer’s power-input plug. Thus the external generator drives the primary of the
transformer.
Figure 7: Transformer allows two function generators to provide separate differential and common-mode signal sources
The breadboard function generator, driving the center-tap of the transformer secondary, provides equal signals to the two inputs of the amplifier.
Fig. 8 shows the signals that this arrangement can generate at the amplifier’s inputs. These are the pure cases:
only difference, or only common-mode.
Lab 5: Transistors II, Differential Amp
5
A
CT
B
difference signals (no common mode)
common-mode signal (no difference)
Figure 8: Transformer use allows pure difference or pure common signals
5L.2.3
A mediocre differential amp: resistor in ‘Tail’
Suggestion: measuring common-mode and differential gain:
Common-Mode Gain (first try)
• Measure common-mode gain:
– Shut off the differential signal (external function generator)3 while driving the amplifier with a
signal of a few volts’ amplitude. Does the common-mode gain match your prediction? If it
is too high, the probable cause is the sneaking-in of a difference between the diff amp’s two
inputs, so that the output you see includes some differential gain as well as common-mode. You
can discover whether this is happening by simply shorting the diff amp’s two inputs together
(parallel the series-pair of 27Ω resistors with a length of wire). That piece of wire assures that
the applied signal is true common-mode. If you do insert this wire, be sure to remove it after you
measure GCM . The two inputs must be permitted to diverge in the next step, where you measure
differential gain.
Differential Gain
• Measure differential gain:
– Turn on the external function generator while cutting common-mode amplitude to a minimum
(there is no Off switch on the breadboard function generator).
– Apply a small differential signal. Does the differential gain match your prediction? If the differential gain appears to be high by about a factor of two, recall that when you watch a wiggle
at a single input, you are looking at about one-half the difference signal you are applying to the
amplifier. If you doubt this, try watching both inputs, on the scope’s two channels. You should
find approximately equal and opposite (180-shifted) waveforms on the two inputs.
– Now turn on both generators and compare the amplifier’s output with the composite input. To
help yourself distinguish the two signals, you may want to use two frequencies rather far apart;
but do not let this experimental convenience obscure the point that this differential amp needs no
such difference. The method you used in Lab 2 to pick out a signal while rejecting noise did, of
course, require such a difference.
3 You
may prefer to cut amplitude to a minimum, rather than shut off power to the generator.
Lab 5: Transistors II, Differential Amp
6
This experiment should give you a sense of what “common mode rejection ratio” means: the small amplification of the common signal, and relatively large amplification of the difference signal.
Nevertheless, this circuit still lets a large common-mode signal produce noticeable effects at the output. The
improvement in the next step should make common-mode effects much smaller.
Common-Mode Gain (second try)
5L.2.4
Improving Common-mode Rejection: Current source in ‘Tail’
Replace the 10k “tail” resistor with a 1.5 mA current source. You may build this current source as you choose.
The laziest way is to use a pair of field-effect transistors (JFET’s: devices we will not discuss in this course)
that serve as current-limiting diodes. These are a part called 1N5294, rated at 0.75 mA ±10%. Two in parallel
provide the desired 1.5 mA:
Figure 9: JFET Current-limiting diodes can provide the tail current source
If this trick is too shabby and black-box for your taste, you know, of course, how to build current sources
using bipolar transistors. Here are two possible circuits:
Figure 10: ...or two alternative bipolar-transistor current sinks
Replacing the “tail” resistor with a current source should reduce the common-mode gain a great deal. (What
is common-mode gain if the output impedance of the current source is around 1M?)4
You should see very good CMRR at low frequencies: say, 100Hz. As frequency climbs, however, you’ll see
the output grow. This apparently results from capacitive coupling between input and output, as we argue in
an appendix to these lab notes (below, § 5L.5 on page 12).
4 Common mode gain is
approximately RC /(2 × Rtail ) ≈ 10k/2M = 0.5 × 10−2 .
Lab 5: Transistors II, Differential Amp
7
Common-mode and Difference Signals Mixed See how this improved circuit treats a signal that combines
common-mode and differential signals. Leave this circuit set up. You will be adding to it.
5L.3 A Home-made Operational Amplifier
Time: 1 1/2 hour
Here, we’ll ask you to string together the three stages of the device that make up a standard operational
amplifier. The op amp is a just a good high-gain differential amplifier, so you can see that at this point in the
lab you are partway to your destination.
An op amp typically is a three-stage amplifier: a differential stage, a gain stage, and a push-pull output. Here,
we ask you to add the two additional stages—a common emitter gain stage and a push-pull output stage—to
the diff amp you have built. These additions will convert this diff amp into a modest operational amplifier
(“op amp”). That device is, as you know, the building-block that you’ll rely on in most of your analog designs,
from Lab 6 onward. The op amp you build today won’t work as well as the IC version you meet in Lab 6,
but it should help you to gain some insight into what an op amp is, and how it achieves its borderline-magical
results.
Here’s a block diagram that restates graphically the point we just made: an op amp is a high-gain diff amp
with low output impedance:
Figure 11: Generic 3-stage operational amplifier
We will ask you to modify your diff amp somewhat, so as to achieve higher gain, and so as to prepare it to
drive the second stage conveniently. You’ll test that; then the first two stages together; then the 3-stage amp.
Finally, toward the end of this exercise, we’ll ask you to apply overall feedback—a topic we have not yet
discussed at any length. Perhaps you’ll find the subject puzzling; we hope you won’t mind this preview, even
if the topic does come clear only later.
5L.3.1
Stage One: Increase the Gain of the Bipolar Differential Amplifier
Two Circuit Changes:
Lab 5: Transistors II, Differential Amp
8
5L.3.1.1 Maximize Gain
Remove the 100Ω emitter resistors. Do you expect the circuit to lose temperature stability, with these gone?
What happens to the constancy of gain?5
Test your views:
• to test temperature stability, watch VOUT (with scope or DVM) as you try heating the CA3096 with
your finger.
• to test constancy of gain, use a small triangle as input, and see whether you notice “barn-roof” distortion
like what you saw in Lab 4.
5L.3.1.2 Move Output Quiescent Point Up
To get ready for addition of the next stage, change the collector resistor, RC , from 10k to 1.5k. This will
violate our usual rule that calls for centering the output in the available range (here, 0 to 15V). This change
will also lower the circuit gain. But your circuit’s modest gain is not so sad as it may seem: we hope CMRR
will remain respectable. Calculate your circuit’s new differential and common-mode gains—or, if you are
energetic, measure these gains.
Figure 12: Stage one diff amp: preparing it to drive later stages
5L.3.2
Stage Two: Gain stage: common emitter amplifier
When you reduced the RC to 1.5k, you placed the diff amp’s output quiescent voltage close to the positive
supply. Ordinarily, that would be a mistake. It’s not a mistake this time, because we want this output to drive
a common-emitter amplifier made with a PNP. This second stage will provide most of the voltage gain in the
circuit.
Fig. 13 on the facing page shows the amplifier circuit that we propose. It’s a conventional common-emitter
amp (except that it probably looks annoyingly upside-down, to the NPN-centric among us). The amplifier’s
input impedance is high enough not to load the preceding stage appreciably, as usual.
5 The circuit is temperature-stable without emitter resistors, because the two transistors run at equal temperatures.
Though their VBE ’s
will change with temperature changes, their sharing of Itail will not; so, the quiescent output voltage will not change as temperature
changes.
Constancy of gain, in contrast, will suffer: you will see distortion. Gain changes as Vout swings, for much the same reasons that cause
“barn roof” distortion in a common-emitter amp, as noted in Classnotes 5. The diff amp’s distortion is shaped differently; supplementary
note S51 explains this shape, in case you are curious.
Lab 5: Transistors II, Differential Amp
9
When you have made this addition, the circuit looks like this:
Figure 13: Two-stage Amplifier: differential and common-emitter
5L.3.2.1 Measure Gain
Watch input and output of the CE amplifier stage, and measure this stage’s gain. Then measure the overall
differential gain, circuit input to circuit output (simply ground pin 1, applying a “pseudo-differential” input
at pin 5).
You may need to tinker with the function generator’s DC offset as you watch this high-gain amplifier, in order
to make sure that neither first nor second stage clips.
5L.3.3
Stage Three: Output stage: push-pull
In order to give the circuit low output impedance, we’ll give it a push-pull output stage. We won’t bother to
fix cross-over distortion, because we want to keep the circuit simple. In a minute, we’ll let feedback try to
undo this distortion. Here’s a push-pull voltage follower, made with two more transistors in the CA3096 IC
that’s holding the two-stage amplifier you have built to this point:
Figure 14: Push-pull output stage (bipolar)
Lab 5: Transistors II, Differential Amp
10
With this stage added, the baby op amp is complete. The circuit—driven still with a pseudo-differential input,
and still running “open-loop” rather than with overall feedback—looks like this:
Figure 15: Home-made op amp: complete 3-stage circuit; still running open loop
Feed a small sine wave differential signal to the input, at a low frequency: 1kHz or under; watch input and
output of this push-pull stage. You should notice cross-over distortion: dead sections in the output, while the
input is too close to zero to turn on either the PNP or the NPN transistor. To show this crossover distortion,
the circuit output must cross zero. You may need to adjust the DC-offset of the input signal, in order to center
the output waveform.
5L.4 Trying Feedback
Op amps almost always use overall feedback. Let’s try it with your circuit.
5L.4.1
A X11 Amplifier?
Now we’ll try the op amp in the configuration that is normal for such devices: we feed back circuit output to
circuit input (more precisely, we’ll feed back a fraction of the circuit output). This arrangement is shown in
fig. 16. We must keep the sense of feedback “negative:” output tending to diminish the input.
Connect the input at pin (1) to an attenuated version of the circuit output, marked “X” in fig.15: 1/11 of the
amplifier output that appears at pins 7 and 13. This connection, shown in fig. 16, will force the amplifier to
try to drive this input, (1), to the voltage applied at the other input, pin (5). As a consequence, we will trick
your circuit into amplifying by about 11X (11X is the nominal gain, because we are feeding back one part in
11). Try it:
Lab 5: Transistors II, Differential Amp
11
Figure 16: X11 Amp?
Gain is likely to be below the hoped-for X11, because our circuit gain is so modest.6
What’s valuable and interesting about this feedback circuit is not, of course, that it delivers lower gain. As
the British patent office reminded Mr. Black, reduced gain is not one’s ultimate goal, in amplifier design.7
Instead, one sacrifices gain for other desirable characteristics. In the present example, we hope you’ll see two
improvements in your amplifier’s performance, now that you’ve applied negative feedback:
• Perhaps the most interesting difference from the open-loop case that you tried one stage back is the
disappearance of cross-over distortion from the circuit output—at least at modest frequencies.
Feed a small sine, and continue to watch input and output of the last stage. We hope you’ll find the
output of the op amp looking sinusoidal, while the input to the push-pull (pins 8, 14) looks strange—
because feedback is forcing that point to do something to cancel the cross-over distortion. Pretty
magical?
• A less striking virtue: the amplifier should not show the inconstant gain that causes “barn-roof” distortion in a triangular waveform. Such distortion somewhat troubled the pre-feedback design.
If your circuit begins to oscillate on its own, you’ll need to reduce its high-frequency gain. The best way
to do this is to place a small capacitor (try 100pF) between collector and base of the common-emitter gainstage transistor (pins 11, 12). This exploits Miller effect, forming a low-pass filter whose apparent C is
enlarged by the gain of this stage. Such reduction of high-frequency gain in order to achieve stability is
called “compensation” and is routinely applied within op amps.
330
(11)
(10)
(12)
100pF
Figure 17: “compensation” capacitor can stabilize a feedback circuit, by killing high-frequency gain
6 If you want to compare your circuit’s gain against a theoretical estimate, see AoE §2.5.2. The circuit gain ought to be A/(1 + AB),
where “A” is your circuit’s “open loop gain” (the differential gain you measured earlier, in § 5L.3.2.1 on page 9), and “B” is the “fraction
fed back” (here, 1/11).
7 See AoE §2.5.1 and Overview notes at Day 6 of this book. Of course, the point of that story is that Black had the last laugh!
Lab 5: Transistors II, Differential Amp
12
5L.4.2
A follower? (optional: risky business)
Oddly enough, the simpler circuit below—the voltage follower—is more difficult to stabilize than the “X 11
amplifier”; that is, the follower is more likely to show those nasty parasitic oscillations. If your circuit is very
tidily built, you may be able to see a stable follower; some of these home-made op amps, however, cannot be
stabilized at unity gain, even with the compensation effort described above.
Figure 18: Overall feedback imposed: a voltage follower
(end Lab 5: Appendix follows)
5L.5 Appendix on CMRR degradation as frequency climbs
Here’s a fine point we referred to back in § 5L.2.4: an explanation for the observation that CMRR degrades
as frequency of the common-mode input grows.
The waveform’s phase and frequency-response provides a clue that what we’re seeing does not result from
any failure of the current source in the tail. Here are a couple of scope images, showing output for commonmode inputs. The first, below, shows outputs for sinusoids at two input frequencies: 1kHz and 10kHz. The
amplitude is much larger at the higher frequency.
common-mode input
(applied to both inputs)
common-mode output @1kHz:
very small (10mV/div)
common-mode output @10kHz:
(about 10X amplitude @1kHz)
Figure 19: Common-mode rejection diminishes at higher frequency: sinusoid inputs at 1kHz vs 10kHz
That sounds like high-pass behavior, certainly. The scope image below says the same thing in another way,
showing the output looking like a differentiation of the input:
Lab 5: Transistors II, Differential Amp
13
Figure 20: Common-mode output acts like a differentiator: shows slope of triangle input
Does your circuit behave the same way? If so, what you’re seeing is capacitive feedthrough, from input (base
of the input transistor) to output (collector resistor). A cascode could minimize this effect (see Miller Effect
discussion in AoE §2.4.4). But let’s not pause for such perfectionism, now.
(lab5 diff amp headerfile june14.tex; August 23, 2015)
Index
1N5294 current-limiting diode (lab), 6
CA3096 array (lab), 2
CMRR, op amp from array (lab), 12
common-mode gain
measuring (lab), 5
compensation capacitor
op amp (lab), 11
differential amplifier (lab), 2–7
differential gain
measuring (lab), 5
DIP package
breadboarding, 3
float
function generator common (lab), 3
HFA3096 array (lab), 2
operational amplifier
made from transistor array (lab), 7–13
14