Table of Contents
I. ​INTRODUCTION
II. EQUIPMENT
2​-4
4
III. RESULTS
5
IV. DISCUSSION
5-9
V. CONCLUSION
VI. SOURCES
9
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I. INTRODUCTION
An operational amplifier (op-amp), is a voltage amplifying device that is used with external
feedback components such as a resistor or a capacitor. An ideal amplifier may have an infinite
gain when used in an open loop that has a DC gain of 100 dB or more.
A typical op-amp consists of three terminals, two of which are high impedance inputs. One of the
input terminals is known as the inverting input which is indicated by a negative sign, whereas the
positive sign indicates the non inverting input terminal. The third terminal is therefore known as
the output terminal.
As mentioned above, the primary purpose of an op amp is to be used as a signal amplifier.
Therefore, by drawing little to no input current in the input terminals, the input impedance is
considered to be very high, while the input impedance is approximately zero. The output voltage
of the op-amp is equivalent to the negative value of the input voltage. As the op-amp senses the
difference between the input and the output voltage value, it boosts the value of the signal
generated significantly through multiplying it by a gain value.
Generally, an op amp consists of two uniques configurations:
1. Inverting configuration
2. Non-inverting configuration
In the inverting configuration, the op-amp is connected with a feedback which results in a closed
loop operation.
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The gain value of the op-amp is determined through making the following necessary
assumptions:
1. No current is enters the input terminals
2. The difference between the voltage values across both the input terminals to zero which
is represented mathematically below:
V1 − V2 = 0
Where:
●
V 1 = Voltage across the non-inverting terminal (V)
●
V 2 = Voltage across the inverting terminal (V)
Using this assumption above, the gain of the op-amp be determined through the following
relationships:
R
Gain (Av ) = − ( R f ) =
in
V out
V in
Where:
●
Av = represents the gain (no units)
●
Rf = represents the input resistance (Ω)
●
Rin = represents the input resistance (Ω)
●
V out = represents the output voltage (V)
●
V in = represents the input voltage (V)
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Figure 1: Circuit represented in Multisim
II. EQUIPMENT
Following equipment was used in the experiment:
● 741 Operational Amplifier
● Breadboard
● Alligator clips
●
1.2 Ω and 18.0 Ω resistors
● Oscilloscope
● Function generator
● AC power supply
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III. RESULTS
Index
Power Source
Voltage Input
Voltage Output
Phase Difference
1
14 Vp
2.09 Vpp
12.1 Vpp
176.85​°
2
12 Vp
2.09 Vpp
11.3 Vpp
179.48​°
3
10 Vp
2.09 Vpp
10.3 Vpp
167.93​°
4
8 Vp
2.09 Vpp
8.6 Vpp
141.64​°
5
6 Vp
2.09 Vpp
6.6 Vpp
125.07​°
6
4 Vp
2.09 Vpp
3.8 Vpp
82.8​°
7
2 Vp
2.13 Vpp
2.0 Vpp
15.31​°
Table 1: Variable power source voltage at 100 Hz input
Index
Frequency Input
Phase Difference
Voltage Input
Voltage Output
1
100 Hz
-205.12​°
2.09 Vpp
10.7 Vpp
2
200 Hz
176.6°
2.09 Vpp
11.5 Vpp
3
400 Hz
179.8°
2.09 Vpp
9.2 Vpp
4
800 Hz
-179.2°
2.09 Vpp
8.6 Vpp
Table 2: Variable input frequency at 14 Vp to amplifier
IV. DISCUSSION
Calculating theoretical gain:
A​V​ = -R​f​ / R​in
A​V​ = 18 k​Ω​ / 1.2 k​Ω
A​V​ = 15
This gain value can be used to calculate the theoretical V​outt​ from the measured V​in​.
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A​V​ = V​out​ / V​in
V​out​ = A​V​ V​in
V​out​ = (15) (2.09 V)
V​outt​ = 31.35 Vpp
Given that input voltage and both resistors remained constant for the duration of this experiment,
and assuming V​out​ / V​in​ = R​f​ / R​in​, this means the output voltage should have remained constant as
well, as long as it is not limited by the voltage source to the amplifier.​ Input voltage during these
trials was kept constant at 2.09 Vpp (measured by the oscilloscope), but one trial yielded a
measured input voltage of 2.13 Vpp. This discrepancy may be attributed to equipment error in
either the oscilloscope or waveform generator.
Effect of Power to Amplifier:
Varying power to the amplifier showed a variation in voltage output of the circuit. In theory,
given the power to the amplifier is sufficient, the gain should be equal to R​f​ / R​in​. The theoretical
gain, given the resistors used in the experiment, was calculated to be 15. Given the input voltage
for the duration of the experiment was 2.09 Vpp, the output voltage theoretically should have
been 31.35 Vpp assuming the power source in the amplifier was sufficient to allow maximum
output voltage. The experimental values collected for output voltage are drastically lower than
expected. To reach maximum output voltage, the power source would have to be equal to or
greater than 15.675 Vp. The highest power given to the amplifier during the experiment was 14
V, which means theoretically the AC wave of the output voltage should become flat once it
reaches +/- 14 V, giving a maximum output voltage of 14 Vp, or 28 Vpp. Experimentally this
expected output voltage was measured as only 12.1 Vpp. As the power source to the amplifier
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was decreased in intervals of 2 V, output voltage was consistently below the theoretical value.
On average, experimental values for output voltage were 48.8% less than the corresponding
theoretical value determined by the voltage supplied to the amplifier. This major error is likely
due to the amplifier not functioning as it should because of extensive use previous to this
experiment. It is also notable that the experimental gain at best was only 5.8, which was far less
than the theoretical gain of 15, which could be attributed to the same source of error. Despite
this error, the trials still showed that output voltage changes proportionally with voltage applied
to the amplifier.
Figure 2: Multisim circuit
with 100 Hz input
frequency and 16 Vp
supplied to the amplifier.
Figure 3: Multisim circuit
with 200 Hz input
frequency and 14 Vp
supplied to the amplifier.
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If the experiment were done again, trials would be conducted were a voltage of at least 15.675
Vp and greater would be supplied to the applifier, to demonstrate the behaviour of the circuit
when sufficient power is applied to the amplifier to allow the maximum amplitude of the output
sinusoidal wave, without the peaks being flattened (as in Figure 2). Another observation which
can be made is that the phase difference between the input voltage and output voltage changed
dramatically as voltage to the amplifier decreased. With 14 Vp applied to the amplifier, the
phase difference was nearly 180​°, as expected. But as the voltage supplied to the amplifier
decreased, the phase difference also decreased consistently to as low as ​15.31​° with 2 Vp
supplied to the amplifier. It appears that as the voltage supplied to the amplifier approaches zero,
the phase difference also approaches zero.
Effect of Input Frequency:
Observing the variable frequency trials, the experiment showed that changing the frequency of
the input voltage causes a roughly proportional change in frequency of the output voltage,
maintaining the rule that the output voltage is always roughly 180​° out of phase with the input
voltage. The oscilloscope did not measure the phase difference as exactly ​180​°, and values
changed slightly between trials. Trials at 200 Hz, 400 Hz, and 800 Hz all yielded a phase
difference of 180° +/- 4°. The trail at 100 Hz yielded a phase difference of ​-205.12​°, which is not
accurate to the theoretical 180°. Error in phase differences may be attributed to equipment error,
specifically the amplifier and the oscilloscope. In the four trials with variable input frequency,
the output voltages in each trial were not consistent. The average output voltage for these trials
was 10.0 Vp. There is no clear relationship between input frequency and output voltage, and
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these deviations are expected to be due to equipment error in the amplifier, wiring, or
oscilloscope.
V. Conclusion
This experiment demonstrated the fundamental behaviours of an operational amplifier circuit, in
particular the effects of varying input frequency and varying voltage supplied to the amplifier.
The experiment showed the operational amplifier does multiply output voltage with respect to
input voltage, but in practice, the experimental gain was dramatically less than the theoretical
gain determined by the ratio of ​R​f​ / R​in​. ​Trials were conducted at constant input frequency and
varying voltage to the amplifier, and it was observed that there is a proportional relationship
between voltage supplied to the amplifier and output voltage, given the voltage supplied is below
the theoretical output voltage at maximum gain. Comparing experimental output voltage from
these trials with theoretical output voltage, it was observed that the experimental values were
48.8% less than the expected values. This is likely a result of error in the amplifier itself. The
trials with varying frequency showed that input frequency is always roughly proportional to
output voltage, but the phase difference between the waves is always 180°, since the amplifier is
inverting. There is assumed to be significant error in the data collected, which may be attributed
to the amplifier, wiring, the oscilloscope, the wave generator, and/or the power supply to the
amplifier.
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VI. SOURCES
“Inverting Operational Amplifier - The Inverting Op-Amp.” ​Basic Electronics Tutorials,​ 24 Feb.
2018, https://www.electronics-tutorials.ws/opamp/opamp_2.html.
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