E-mail: mcdonc4@unlv.nevada.edu
This lab contains:
Part 1: Calculation of Bandwidths Using a Datasheet
Part 2: Verification of GBP with a Non-inverting Op-Amp Topology
Part 3: Verification of GBP with an Inverting Op-Amp Topology
Part 4: Measuring Slew Rate
Pre-lab work
- Watch the video op_amps_II, review op_amps_II.pdf (associated
notes), and simulate the circuits in op_amps_II.zip.
- Read the write-up seen below before
coming to lab.
Part 1: Calculation of
Bandwidths Using a Datasheet
Again, this lab will utilize the LM324 op-amp (LM324.pdf).
For the following questions
and experiments assume VCC+ = +5V and VCC- = 0V.
Estimate, using the datasheet, the bandwidths for
non-inverting op-amp topologies having gains of 1, 5, and 10.
Table 1:Gain Bandwidth Product for
LM324
Here are my
calculations for the bandwidth at gains 1,5, and 10 respectively:
Part 2: Verification
of GBP with a Non-inverting
Op-Amp Topology
Experimentally verify these estimates assuming a
common-mode voltage of 2.5 V.
We must experimentally
verify the above results by measuring the frequencies as the output of a
non-inverting op-amp as it approaches approximately 70% of the expected output.
We will find that the theoretical frequency (3dB bandwidth) should resemble the
experimental frequencies bandwidth that we calculated in part 1.
We will be inputting a
2.5v DC offset with a sinusoidal signal of 100mVpp. The expected gains should
resemble 1 times the input, 5 times at 500mVpp, and 10
times at 1Vpp.
The gain in a
non-inverting op-amp gain be generated through the manipulation of the two
resistors connected to the negative terminal of the op-amp. The equation for
gain in this schematic is 
. We can see, however, that for a gain of 1 we just shorted the
negative terminal with the output. We weren’t asked to simulate the schematics,
however I felt it would aid in observation of the various bandwidths.
Gain of 1:
Figure 1:Non-inverting Op-Amp topology with a gain of 1
and simulated result at 70% at 1.04MHz
Figure 2:Input and output at 1kHz
Figure 3:Output measured at 70% for a freq reading of 897.7kHz
Gain of 5:
Figure 4: Non-inverting Op-Amp schematic Gain of 5 along with simulation results. Y axis is measured in hundreds of millivolts.
Figure 5: Oscilloscope Measurements for gain of 5. Left measurement is the input and output at gain of 5 and the measurement to right indicates the output at 70% of desired output. Freq reads 90.01kHz
Gain of 10:
Figure 6: Non-inverting Op-Amp schematic Gain of 10 along
with simulation result.
Figure 7: Oscilloscope Measurements for gain of 10. Left measurement is the input and output at 10 and the measurement to right indicates the output at 70% of desired output. Freq reads 43.9kHz
Summarized data table:
|
Closed-Loop Gain |
Theoretical Bandwidth |
Experimental Bandwidth |
Simulated Bandwidth |
|
1 |
1.3 MHz |
900kHz |
1.04Mhz |
|
5 |
260 MHz |
90kHz |
210kHz |
|
10 |
130 kHz |
44kHz |
99kHz |
We can observe that
some of our experimental values and simulated values are a bit off from our
theoretical values. LTSpice can observe certain
op-amp models with varying parameters that would lead to imperfect evaluations just
as we observed. Regardless the simulated results remain in the ballpark. This
will reign true in part 3 as well as we observe the same experiment with an
inverting op-amp topology. We can also see that as we try higher gains we have larger deviations in our experimental and
theoretical results. This may be due to the fact that the
manufacturer used far different parameters than we did when conducting the same
experiment. The manufacturer lists a Vcc of 30V which
is much larger than what we used for this experiment.
Part 3: Verification
of GBP with an Inverting
Op-Amp Topology
Repeat these steps using the inverting op-amp topology
having gains of -1, -5, and -10.
We will repeat the
procedures with the same results from above, however we will be basing our
resistor values based on the gain for an inverting op-amp topology. However, we
will have to recalculate the theoretical values for the bandwidth given the different
topology. Below are my calculations:
Gain of 1:
Figure 8: Oscilloscope Measurements for gain of 1. Left measurement is the input and output at gain of 1 and the measurement to right indicates the output at 70% of desired output at a freq of 504.9kHz
Figure 9: the left measurement is our input and output at 1kHz. The right measurement shows our output at 70% of our expected gain, which reads a frequency of 648.1kHz
Gain of 5:
Figure 10: Oscilloscope Measurements for gain of 5. Left measurement is the input and output at 5 and the measurement to right indicates the output at 70% of desired output and a frequency of 167kHz
Figure 11: the left measurement is our input
and output at 1kHz. The right measurement shows our output at 70% of our
expected gain, which reads a frequency of 121.4kHz
Gain of 10:
Figure 12: Oscilloscope Measurements for gain of 10. Left measurement is the input and output at 10 and the measurement to right indicates the output at 70% of desired output and a frequency of 90.8kHz
Figure 13 the left measurement is our input
and output at 1kHz. The right measurement shows our output at 70% of our
expected gain, which reads a frequency of 43.88kHz
Summarized Data Results:
|
Closed-Loop Gain |
Theoretical Bandwidth |
Experimental Bandwidth |
Simulated Bandwidth |
|
-1 |
650kHz |
650kHz |
500kHz |
|
-5 |
217kHz |
120kHz |
167kHz |
|
-10 |
118kHz |
44kHz |
90kHz |
Similarly to part 2, we notice
that our some of our experimental bandwidths aren’t precisely on target. Again this may be the results of the manufacturer experiment
parameters being far different from ours, or this could be a result of our
circuit picking up ambient noise from the surrounding electronics in the lab.
Part 4: Measuring Slew
Rate
Design two circuits for measuring the slew-rate of the
LM324. One circuit should use a pulse input while the other should use a
sinewave input.
Here is the circuit we
used to measure the slew rate:
Figure 14: Slew rate circuit schematic
of a voltage follower
We were able to
implement the above circuit for both observations of the slew rate by inputting
both a pulse input and a sinusoidal input to serve as our two circuit designs.
We can also see from figure 15 that the above circuit, which is called a
circuit follower, was used by the manufacturer to conduct the same experiment.
This was a wise choice as the gain for this circuit is 1 and will lead to a
simpler analysis. We can measure the slew rate of the LM324 op-amp by observing
the time it takes the output signal to reach 10% and 90% of it’s
peak output and determining the time difference between the two measurements.
Figure 15: Data obtained from the datasheet, which indicates the use of voltage follower
Figure 16: Our measurements for the sinusoidal wave(left) and pulse wave(right). Note that our cursors are set to read the difference in time between the output at 10% and 90%. They read 5us and 1.2us respectively.
Pulse Calculation:
Sinusoidal
Calculation:
Both of these results we
obtained are slightly off from what the manufacturer measured, however this may
also be due to the fact that the experimenter used a Vcc
of 15v in their experiment, whereas we used a Vcc of
5v.