Experiment #1:
Operational Amplifiers
Friday Group
Dr. Somnath
Ari Mahpour
9-4-09 and 9-11-09
Teddy Ariyatham
Due 9-18-09
Jayson dela Cruz
Table of Contents
Objective: ........................................................................................................................................ 3
Tools: .............................................................................................................................................. 3
Theory: ............................................................................................................................................ 3
Discussion and Results ................................................................................................................... 6
Part 1: Measuring Offset Voltage ............................................................................................... 6
Part 2: Inverting Gain Amplifier ................................................................................................. 6
Part 3: Non-Inverting Gain Amplifier....................................................................................... 10
Conclusion .................................................................................................................................... 10
Appendixes ....................................................................................Error! Bookmark not defined.
Objective:
The purpose of this experiment is to learn how to measure the offset voltage on an
amplifier along with manipulating and analyzing the gains on an inverting and non-inverting
amplifier. From the analysis there are steps to calculate dB roll-off and also to find and compare
phase shift between Vi and Vo.
Tools:
-
Oscilloscope
-
Functional generator
-
Power supply
-
LM741 operational amplifier
-
Resistors
Theory:
For the first part of the experiment it is required to contruct the circuits pictured in
figures 1.4, 1.5, and 1.10. Before doing so, some preliminary calculations using the theory
learned in the corresponding ECE 340 lecture class, were to be made.
Figure 1.5
Figure 2.4
𝑅
𝑅
For Inverting Amplifier: 𝐴𝐶𝐿 = − 𝑅𝑓 = − 𝑅2
1
1
2a. In order to achieve a gain of -10, two resistors of the values 𝑅1 = 10𝑘Ω and 𝑅2 = 100𝑘Ω.
2b. In order to achieve a gain of -100, two resistors of the values 𝑅1 = 1𝑘Ω and 𝑅2 = 100𝑘Ω.
Figure 3.10
For Non-Inverting Amplifier: 𝐴𝐶𝐿 =
𝑅2 +𝑅1
𝑅1
.
3a. In order to achieve a gain of 1, two resistors of the values 𝑅1 = 100𝑘Ω and 𝑅2 = 1Ω.
3b. In order to achieve a gain of 100, two resistors of the values 𝑅1 = 1𝑘Ω and 𝑅2 = 100𝑘Ω.
Discussion and Results
Part 1: Measuring Offset Voltage
The measured output voltage was 1mV. This, in turn, became our – 𝑉𝑂𝐹𝐹 value.
Theoretical
Experimental
0.101
% Error
0.686 5.792079
The experimental error was incredibly high due to a broken amplifier that was only detected
later on to have fried. This was corrected later on before performing the rest of the remaining
steps.
Part 2: Inverting Gain Amplifier
Resistors
Vin (V)
Vout (V)
Av = Vout/Vin
Phase Shift (µs)
100kΩ and 10kΩ
0.104
-0.976
-9.38
20
For the first part of part 2, it was required
to calculate the input and output voltage of
the circuit designed. Once the voltages
were found the total gain could be found.
After observing the outform waveform the
phase shift was approxuimated at 20 micro
seconds (see attached paper labeled “Part
2: #2 in top left corner).
The table to the right shows where the gain
dropped by 3 dB. It required a minimum
frequency input of 125 kHz in order to
achieve that drop.
The effect on the power supply was as follows:
As the amplitude was raised the voltage it was
found that it must be at a precise point to
prevent sine wave cutoffs. The value of 7.31 V
for the amplifier voltage input allowed the
achievement of a 10 V peak-to-peak value in
the output sine wave. When using a 1 kHz input
the full sine wave can only be achieved with 5
volts peak-to-peak. After that point the wave
starts to cap.
Frequency (kHz)
1
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
105
110
115
120
125
130
135
140
Vo Amplitude (V)
1.020
1.000
0.992
0.992
0.992
0.992
0.992
0.984
0.976
0.960
0.952
0.928
0.912
0.912
0.904
0.880
0.864
0.848
0.840
0.832
0.816
0.792
0.784
0.768
0.752
0.720
0.704
0.692
0.672
Av (dB)
19.83134
19.65933
19.58957
19.58957
19.58957
19.58957
19.58957
19.51924
19.44833
19.30476
19.23207
19.01029
18.85923
18.85923
18.7827
18.54899
18.38961
18.22725
18.14492
18.0618
17.89314
17.63384
17.54565
17.36656
17.18369
16.80598
16.61079
16.46146
16.20672
Resistors
Vin (V)
Vout (V)
Av = Vout/Vin
Phase Shift (µs)
100kΩ and 1kΩ
0.104
-10.1
-97.12
15
Just like the previous first portion to part 2, it was required to find the Vin, Vout, gain,
and phase shifts in the similar fashion. Considering the gain, the 3 dB drop came dramatically
sooner than its counterpart’s circuit. The phase shift visual calculation can be seen in the
attached paper labeled “Part 2: #5.”
Frequency (kHz)
1
5
10
15
20
25
30
35
40
45
50
55
60
65
Vo Amplitude
(V)
10.100
9.520
7.780
6.040
6.660
5.020
4.400
3.690
3.280
1.230
1.130
0.819
0.614
0.614
Av (dB)
39.746
39.232
37.479
35.280
36.129
33.673
32.528
31.000
29.977
21.457
20.721
17.925
15.423
15.423
This function worked in a slightly inverted manner. The lower the voltage went, the
more potential there was for a cap. The output voltage stayed constant at around 10V but once
the amplifier's voltage input was changed to 6.5V or lower, the sine wave started to cap out. In
the previous amplifier’s setup there were opposite results.
Both output waveforms were superimposed onto one another which show that the
second evaluated circuit was significantly larger than the first one. See the attached graph
labeled as “Part 2: #6a” for more details.
The Frequency vs. Gain plot can be seen in the attached document labeled “Part 2:
#6b.” The 𝐹𝑏 , 𝐹𝐶1 , 𝐹𝐶2 , 𝑎𝑛𝑑 𝐹𝑇 values were extracted from the graph (see attachment for details).
It is also important to note that this part of the experiment must be hand drawn (rather than
including it as an excel graph) due to the nature of the lines’ behaviors.
120mV
80mV
40mV
0V
-40mV
-80mV
-120mV
0s
1ms
2ms
V(R3:1,R3:2)
V(R1:1,R1:2)
3ms
4ms
5ms
6ms
7ms
8ms
9ms
10ms
Time
Figure 2.7a: PSPICE Gain Comparison
The 6th step of part 2 required that PSPICE be used to simulate the input and output voltages to
find the AV gains of the inverting amplifier. Those values were then to be placed onto the same
graph. The attached graph, “Part 2: #6a”, is very similar to the PSPICE waves shown above. This
shows that the experimental results were in accordance with the theoretical PSPICE simulation.
Figure 2.7b: PSPICE Implemented Circuit
1.0V
0.8V
0.6V
0.4V
0.2V
0V
1.0KHz
V(R3:1,R3:2)
3.0KHz
V(R1:1,R1:2)
10KHz
30KHz
100KHz
300KHz
1.0MHz
Frequency
Figure 2.8: PSPICE Frequency Response Analysis
It was difficult to compare the experimental (see attached “Part 2: #6b”) to the
theoretical (Figure 2.8, above), since they did not match up properly. There are many factors to
consider why this would occur. Factors such as hardware discrepancies, which cause small
percentage errors, can be amplified on a circuit such as this. One should note that the PSPICE
amplifier that was built and simulated is significantly more efficient and modeled a perfect
behavior whereas this not being the case with our circuit. The nature of both their behavior,
however, was very similar therefore one can conclude that the error was insignificant.
Part 3: Non-Inverting Gain Amplifier
In this part of the experiment it was required to find the gains and phase shifts of the
two circuits that were to be implemented and built.
Resistors
Vin (V)
Vout (V)
Av = Vout/Vin
Phase Shift (µs)
15kΩ and 100kΩ
0.101
0.101
1
5
The actual required gain was to be a value of 1. Short circuiting the R2 resistor is
avoided because it creates a unity gain amp. Instead a 15Ω resistor is used because it creates a
small enough value where the gain will be 1.00015. Though this isn’t exactly what was required,
it was the closest possible experimental value that could be achieved.
Resistors
Vin (V)
Vout (V)
Av = Vout/Vin
Phase Shift (µs)
1kΩ and 100kΩ
0.104
10
96.154
30
Similar to the gain above, the two resistor values of 1kΩ and 100kΩ were the closest
possible experimental values to achieve a gain near 100. Though 96.154 is close to the 100
value its percentage error of 4.41% made it seem that there were resistor values that could
have achieved a greater closeness. For both of these circuits the phase shifts were calculated in
a visual manner. They can be found in as the attached documents entitled “Part 3: #3” and
“Part 3: #4.”
Conclusion
Operational Amplifiers have many real world applications such as radio transmitters and
receivers. Data that needs to be transmitted over large distances are incapable of being
transmitted via the circuit voltage alone. Therefore, it requires an operational amplifier to
magnify that voltage so it can travel over long distances. A broad way of using operational
amplifiers would be in a scenario where you need this amount of voltage based off of this input
at this point. In the future, to ensure that fewer errors are made, it is important to perform an
exhaustive test on all of the chips and equipment prior to embarking on the laboratory
experiment.