**Lab
12: Op Amps: Characteristics and Applications**

In this lab you will build 6 different op amp circuits.

In order to do this lab you need to understand the characteristics of operational amplifiers (op amps).

**Reading**
Ch **8**.0-4 + lecture notes.

**Components:
**

The following circuits use the 741 op amp in the 8-pin DIP package.

** Op Amp
Golden Rules** (memorize these rules)

**1) **The
op amp has infinite open-loop gain.

**2) **The
input impedance of the +/− inputs is infinite. (The inputs are ideal
voltmeters). The output impedance is zero. (The output is an ideal voltage
source.)

**3) **No
current flows into the +/− inputs of the op amp. This is really a restatement
of golden rule **2**.

**4) **In
a circuit with negative feedback, the output of the op amp will try to adjust
its output so that the voltage difference between the + and − inputs is zero (*V*_{+} = *V*_{−}).

**Throughout this lab you will
measure the input and output waveforms using the oscilloscope with your scope
probes. **

** PART
1) The Voltage Follower.** We have already made voltage followers in the
BJT and FET labs. Op amps can also be used as a voltage follower. It is a very
simple circuit, which requires no resistors, only the op amp and power!

Construct
the circuit above. Drive it with a 100 mV_{p-p} amplitude 1 kHz sine
from your function generator. Use two scope probes to measure both the input
and output waveforms simultaneously.

**Q 1) 2pts.**
Measure V_{out}, V_{in}, and calculate V_{out}/V_{in}.
It should be very close to unity. Is there a noticeable phase shift?

**Q 2)
2pts.** Vary the input frequency. As you increase the frequency V_{out}
will begin to deviate from V_{in} both in magnitude and in phase.

At what frequency does ÷V_{out}ç=÷V_{in}ç/Ö2
?

**Q 3) 2pts.**
As you decrease the frequency, does V_{out} continue to track V_{in}?
Adjust the DC offset of the function generator. Does V_{out} also track
the DC offset?

Now with **50
kHz** sine wave input, increase the amplitude. Does the output waveform
change? You are seeing an effect called *slew rate limiting*, because
there is a maximum rate that the output voltage can change. This is a large
signal behavior of real op amps. We will largely ignore it in this lab, but it
is important to be aware of it so you can recognize the effect. Later in the
lab, if you see this effect, you will need to reduce the input amplitude.

**Q 4) 4pts.**
As you vary the amplitude if V_{in}, you will see that the slope of the
V_{out} waveform is roughly constant. Measure the slope of the linear
part of the waveform. Calculate the slew rate and report it in V/μsec.

** PART 2)
Inverting Amplifier.** The op amp is a very useful device. Op amp
circuits are very predictable—that is they work the way you expect without tinkering.
The inverting amplifier is one of the most common op amp circuits. Construct
the inverting amplifier shown below. You will use four different values for R

**Table 1) 10pts.** Complete the
calculated columns in your notebook. Compare the measured gains to the
theoretical gains based on the measured resistor values. What is the average
percent deviation from the theoretical gain?

**Q 5) 4pts.**
Now with your op amp configured for the highest gain, set the input for a 1 kHz
sine wave input. Increase the amplitude. Does V_{out} get clipped? (See
the diagram below.) What are the minimum and maximum clipping voltages? What is
the difference between the clipping voltages and the supply voltages?

**Sketch 1) 5pts.** Using the same set up as in Q5,
clip a second scope probe to the node of the inverting op amp input V_{–}.
According to the op amp golden rules, what should the V_{–} be in this
circuit? Adjust V_{in} for the lowest input amplitude. What do you see?
Sketch the V_{–} and V_{out} waveforms labeling their approximate
amplitudes. These are effects of real op amps. If the op amp had infinite loop
gain, V_{–} = V_{+} would be correct. For finite loop gain,
some finite difference between V_{–} and V_{+} is required to drive
the op amp output to change.

**Sketch 2)
5pts.** Increase V_{in} until V_{out} is clipping. Sketch the
waveform again showing approximate amplitudes. What can you say about V_{–}
and the op amp golden rules when the output is clipping? Construct the non-inverting amplifier
shown below. The non-inverting amplifier has the advantage that the input
impedance is very high. You will use four different values for R

PART 3) Non-inverting Amplifier.

**Table 2) 10pts.** Complete the
calculated columns in your notebook. Compare the measured gains to the
theoretical gains based on the measured resistor values. What is the average
percent deviation from the theoretical gain?

** PART 4)
Differential Amplifier.** You have seen many examples in the class where
we wanted to measure the voltage between two points in the circuit, but
instruments like the oscilloscope can only measure the voltage to ground. The
differential amplifier can be used in this case. Its output is the difference
between the two input voltages. Furthermore the output is referenced to ground,
so it is easily measured with oscilloscopes, etc. There are many other
applications of differential amplifiers.

Build the
following differential amplifier. Select the resistors for a gain of ~4. Choose
R_{1} no smaller than 1K so that the input impedance is at least 1K. You
will need two of each resistor. Record the nominal resistances of R_{1},
and R_{2}, in the table in your lab notebook, you do not need to
measure them. Construct two simple voltage divider voltage sources from 100K
potentiometers connected to the +15V and –15V power supplies. (You will use
these voltage sources in the next part too.) Measure V_{in–}, V_{in+},
and V_{out} for 6 different combinations of V_{in–} and V_{in+}.
At least half of your input voltages should be >+5V or <–5V to illustrate
that this is truly a differential measurement. __You can use your DMM for
the measurements in part 4.__

**Q 6) 2pts.** You should observe
that changing V_{in+} will change V_{in–}, but the reverse is
not true. Why is this? Explain using the characteristics for the op amp and
your voltage sources.

**Table 3) 15pts.** Complete the
calculated columns in your notebook. Compare the measured gains to the
theoretical gains based on the nominal resistor values. What is the average
percent deviation from the theoretical gain?

** PART 5) Summing Amplifier.**
The inverting amplifier has special properties. Multiple inputs can be added,
which then sum together in the output. Each input has a gain defined by R

Build the
following summing amplifier. Select three different input resistors. The
minimum gain should be unity. The maximum gain should be 10. No R_{in}
should be less than 1K so that the input impedance is at least 1K. Construct three
simple voltage divider voltage sources from 100K potentiometers connected to
the +15V and –15V power supplies. Measure V_{in–}, V_{in+}, and
V_{out} for 6 different combinations of V_{in1}, V_{in2},
and V_{in3}.

Connect all three input voltages and make sure the V_{out} is
not clipping. You can do this by testing that V_{out} is within the
clipping limits you have already observed and that it is responsive to the
change of each input voltage. Make six measurements so that you have three
pairs of measurements where only one V_{in} is changed. V_{out}
should change by at least 1V. For example, measure V_{out} with two
different V_{in1} and the same V_{in2} and V_{in3}. Although
it is possible to do this experiment with a minimum of four measurements, that
requires you to accurately return the changed input to its initial value—a task
that can take longer than simply making a new set of measurements! __You
can use your DMM for the measurements in part 5.__

**Table 4) 15pts.** Complete the
calculated columns in your notebook. You will compare the measured gain for
each input to the theoretical gain based on the measured resistor values. Because
you have designed the experiment so that you make two different sets of measurements
while holding the other two constant; the gain for each input is easily
calculated. The fancy mathematical notation of that statement is below.

**Q 7) 2pts.**
In this experiment we used DC voltages to measure the gain. Propose another
simple method to separately measure the gain of each input using equipment you
have used in Elab.

** PART 6)
Transimpedance Amplifier.** In this experiment we will use the
oscilloscope to graph and to measure the I-V characteristic of a few
components—the device under test (DUT)—e.g. resistors, diodes, capacitors, etc.
The DUT is anything you want to stick in!

A common way
to measure current is to insert a “measuring” resistor, R_{m}, into the
circuit and then measure the voltage drop across it. The resistor in this case
functions as a current-to-voltage converter. Its advantage is its simplicity. Its
disadvantage is that one of the voltages we need to measure in order to
construct the I-V graph is not referenced to ground (see circuit below).

In this experiment
we place the measuring resistor in the feedback loop of an op amp to hold the
DUT-R_{m} junction at ground. This construct is called a *transimpedance
amplifier* or *current-to-voltage converter.* The only current path is
the series-connected DUT and R_{m}. A current flowing through the DUT,
as shown, creates a voltage drop across R_{m}. The op amp feedback
makes its output swing negative forcing the DUT-R_{m} junction to
ground. So V_{DUT} is now referenced to ground! V_{Rm} is also
referenced to ground, but inverted. Measurements of V_{Rm} is easily
converted to current. This amplifier has transimpedance gain, which has units
of volts per amp. The resistor, R, is present to limit the current. Because its
voltage drop is outside the measurement area, it will not disturb your results.

Build the
circuit above. Use 1K for both resistors, and a 10K resistor for your initial
DUT. Initially drive your circuit with a 10 V_{p-p} 100–1000 Hz
triangle wave with zero DC offset. You can then adjust it as needed.

**Oscilloscope
set up.** So far in this lab the x axis of the scope has been provided by
scope’s time base. We can also use it to graph one voltage (y axis) against
another (x axis). To do this, on the horizontal menu, select: time base = X-Y. Channel
1 becomes the x input and channel 2 the y input. Initially set x=0V and y=0V to
the center of the screen. Set the channel 1 input to ground, then center the
spot in x using the vertical offset on channel 1. Next, set the channel 2 input
to ground, then center the spot in y, using the channel 2 vertical offset
adjustment. In this experiment, we use the triangle waveform driving the
circuit to provide a linear sweep in voltage on the x axis. With the 10K
resistor as the DUT, set channel 2 to invert (CH2 menu: invert = on) so that
the current is positive for positive voltage. This will set the I-V graph
display in the conventional way. A resistor should have a positive slope and
exist only in quadrants I and III.

**Sketch 3)
5pts.** Make a sketch of the I-V graph of the 10K resistor from the scope. Measure
the current at 2 V using the scope. *(Hint: convert the measured voltage from
the current-to-voltage converter back to its input current.)* Calculate the
resistance of the 10K resistor. Compare this to the resistance you measure with
the DMM.

**Sketch 4)
5pts.** Make a sketch of the I-V graph of the 1N4148 diode from the scope. Measure
the forward voltage drop at 1 mA from the oscilloscope. Compare this to the V_{f}
= 0.6V we have been using as a rule of thumb.

**Sketch 5-6)
10pts (5pts ea).** Make a sketch of the I-V graph of two different color
LEDs. Measure the forward voltage drop at 1mA from the oscilloscope. Reduce the
frequency of the triangle wave to less than 1 Hz so you can see when the LED
turns on. Indicate on your sketch, when the LED is illuminated. Which LED has
the larger voltage drop, the one with the larger or smaller photon energy?

**Q 8) 2pts.**
In this experiment we used the op amp current amplifier to make both V_{DUT}
and V_{R} referenced to ground. This is not the only op amp solution. Propose
another op amp circuit that would have the same function, with V_{DUT}
and V_{R} outputs referenced to ground. Draw the schematic, showing the
op amp, resistor(s), DUT, etc.

This work by L.A. Bumm is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.