A. Basic Theory
Op-amps, or operational amplifiers, are essential components in electronic circuits due
to their high gain, low noise, and ability to amplify and process signals. They are widely used in
applications such as amplifiers, filters, oscillators, and signal-processing circuits. In this lab, we
will explore six different op-amp configurations: inverting, non-inverting, buffer, summing,
integrator, and differentiator. Op-amps can basically perform the mathematical operation from
4 basic operations (adding, subtracting, multiplying, and dividing) to integral and differential
also logarithmic, inverse logarithmic, squaring, and square root. Each of these configurations
has a unique set of characteristics and applications, and understanding their operation is critical
for designing and analyzing electronic circuits.
The inverting configuration is a basic op-amp circuit that provides a negative voltage
gain. It is commonly used in applications where the input signal needs to be inverted or when a
precise voltage gain is required. (see Figure 2. Inverting op-amp)
The non-inverting configuration, on the other hand, provides a positive voltage gain and
is often used when a high input impedance and low output impedance are needed. (see Figure
3. Non-inverting op-amp)
The buffer configuration, also known as a voltage follower or unity-gain amplifier, is
used to isolate the output from the input and to provide a high-impedance input to the load. It
is commonly used in applications where the input signal source has a high output impedance or
when the load requires a low input impedance. The buffer configuration is also useful for
preventing loading effects, signal degradation, and noise interference in electronic circuits. (see
Figure 4. Unity-gain )
The summing configuration combines multiple input signals and produces a single
output signal which is the weighted sum of the input signals. It is commonly used in audio
mixers, analog signal processing, and instrumentation amplifiers. The summing configuration
allows multiple signals to be combined and processed in a single circuit, simplifying the overall
circuit design and reducing the number of components needed. (see Figure 5. Summing opamp)
The integrator and differentiator configurations are used to perform mathematical
operations on the input signal. The integrator produces an output signal that is the integral of
the input signal, while the differentiator produces an output signal that is the derivative of the
input signal. These configurations are commonly used in control systems, signal processing, and
communication systems. The integrator and differentiator configurations allow complex
mathematical operations to be performed on the input signal in a single circuit, simplifying the
overall circuit design and reducing the need for additional components. (see Figure 6.
Differentiator op-amp and figure 7. Integrator op-amp)
Furthermore, it is important to consider the transient response of an op-amp circuit.
The transient response refers to how the circuit responds to changes in input, such as sudden
spikes or dips in voltage. This is important in many applications, such as in control systems or
audio amplifiers where sudden changes in the input signal can cause distortion or even damage
to the circuit.
Op amps can also have other important characteristics, such as noise level, gain
bandwidth product, and slew rate. Noise level refers to the amount of random electrical noise
present in the output signal of the op-amp, which can be a concern in low-level signal
applications. The gain bandwidth product is the maximum frequency at which the op-amp can
amplify a signal without significant distortion. The slew rate is the maximum rate at which the
op-amp can output voltage changes, and it is important in applications where fast voltage
changes are required.
In summary, op-amps are versatile and essential components in many electronic
circuits. Understanding the different op-amp configurations and their characteristics can help
engineers and hobbyists design and optimize circuits for a wide range of applications.
B. Objectives
1. To be familiarized with the different configurations of the Practical Operational
amplifier
2. Calculate and measure the gain of the different configurations of the Practical
Operational Amplifier
3. To Observe the Characteristics of the output signal of the amplifier when there is an
AC input signal.
4. To Observe what happened to the output signal if we change the characteristic of the
input signal specifically the frequency.
5. To Compare the calculated value and the measured value.
C. Schematic diagram
Figure 1. LM324 Circuit Diagram
51 K Ohm
Figure 2. Inverting- Constant gain
51 K Ohm
Figure 3. Non-inverting Constant gain
Figure 4. Buffer/Unity Follower
Figure 6. Differentiator
Figure 5. Summing Operation
Figure 7. Integrator
D. MATERIALS/EQUIPMENT/INSTRUMENTS AND COMPONENTS
Components:
1pc. LM324 (practical-op-amp IC)
3pc. 10 kΩ Resistor
1pc. 52 kΩ Resistor
Connecting Wires
Breadboard
Equipment and Instruments:
1 unit of Digital Multimeter
1 unit of Computer with Electronics
Simulation Software, Scilab and Waveforms
1 pair of Function Generator Probe
1 Pair of Oscilloscope Probe
1 unit of Digilent Discovery 2
E. Procedure
E.1 Inverting Op-Amp
1. Set up the circuit in Figure 2 on the breadboard supply the positive terminal with 5 V
and the negative terminal with -5V.
2. Measure the offset voltage by first connecting the input terminal to the ground and
measure the voltage output using a Digital Multimeter.
3. Record the value.
4. Apply a 0.5 Vdc to the input terminal measure the voltage output and calculate and
compare the results.
5. Using the same circuit (Figure. 2) apply an input signal with a 1V peak and 1KHz
frequency at the input terminal.
6. Connect the oscilloscope to the output and input side of the Amplifier and observe the
output wave and the input wave.
E.2 Non-inverting Op-amp
1. Follow the steps in E.1 Inverting Op-amp but use Figure. 3.
E.3 Buffer
1. Follow the steps in E.1 Inverting Op-amp but use Figure. 4
E.4 Summing
1. Follow the steps in E.1 Inverting Op-amp but use Figure. 5
E.5 Differentiator
1. Set up the circuit in Figure 6 on the breadboard supply the positive terminal with 5 V
and the negative terminal with -5V.
2. Apply an input signal with a 1V peak and 1KHz frequency at the input terminal.
3. Connect the Oscilloscope probe to the output of the Op-Amp in figure 6.
4. Change the waveform of the input signal by varying the frequency. Use the frequency
from 10 Hz to 1K Hz
5. Observe what happened to the output.
E.6 Integrator
1. Follow the steps in E.5 Differentiator Op-amp but use Figure 7. (Integrator Op-amp)
2. Use the frequency from 1K Hz to 100K Hz
F. Results and Discussion
F.1 Inverting Op-Amp
Offset Voltage
10 mV
Vi(dc)
0.5 V
Vo
2.57 V
VO = −
𝑅𝐹
51K
Vi = −
× 0.5V = − 2.55 V
𝑅1
10 K
Figure 8. Constant Gain Inverting Operation
Figure 8 shows the input and output waveform of a constant gain inverting operation of
an Op-Amp, we can see that the output signal (orange line) is out of phase by a 180 degree and
amplified 5 times the original signal, which means that the input voltage of 0.5 V results to a
2.57 V at the voltage with an offset Voltage of 20 mV in which if we subtract the offset voltage
the voltage out is equal to 2.55 V which is also equal to the calculated value of Vo. The gain for
the constant gain inverting operation is just the ratio of the feedback transistor over the
resistor that is in series to the input signal.
F.2 Non-inverting Op-amp
Offset Voltage
17 mV
Vi(dc)
0.5 V
Vo
3.072 V
VO = (1 +
𝑅𝐹
51K
) Vi = (1 +
) × 0.5 = 3.05V
𝑅1
10K
Figure 9. Constant Gain Non-Inverting Operation
Figure 9 is the graph of the input and output waveform of a non-inverting constant gain
operation of an Op-amp. Just like the inverting operation, the non-Inverting is also a constant
gain with the same ratio but with plus 1 gain. Since the input signal is applied on the noninverting input the output signal is in phase with the input signal. Applying a 0.5V in Figure 3 will
results in a 3.072 V at the output with an offset voltage of 17 mV, subtracting the offset voltage
will give us a gain of 3.055 V at the output which is approximately equal to the calculated value
of voltage output which is 3.05 V.
F.3 Buffer or Unity Gain Follower
Offset Voltage
Vi(dc)
Vo
17 mV
1.0 V
1.02 V
VO = Vi = 1V
Figure 10. Unity Gain Follower
Figure 10 shows the output and input waveform of a unity gain follower. We can
observe and see that the input and output in the unity gain follower are the same. Applying 1V
at the input also results in approximately 1.02 V with 17 mV offset voltage without the offset
voltage, Vo is equal to 1.003 V which is the same as 1.0 V. Unity gain follower has and will only
have a gain of 1 and will only produce an output that is exactly the same as the input provided
that it will not be saturated.
F.4 Summing
Offset Voltage
20 mV
Vi(dc)
0.5 V
Vo
1.03 V
VO = −(V1 + V2 ) = −(0.5V + 0.5V) = − 1V
Figure 11. Summing Operation
Figure 11. shows the graph of the input and output waveform of the signals during the
Summing operation, basically in summing it all adds up the input signals applied at the noninverting input, considering that the feedback resistor and the resistor connected to the input
signal are with the same value. And if not, we can always solve the voltage at the end of every
resistor with respect to the ground then that will be the input voltage and just add with the
other input voltages. With the same value of the resistor and applying 0.5 V in Figure 5 results
in a 1.03V voltage output with a 20-mV offset voltage. Considering the offset voltage, the gain
of the op-amp is only 1.01 V which is approximately equal to 1.0V it proves that the two-input
signal was added to produce a 1.0 V at the voltage output. Since it is in non-inverting input, we
can expect that the output signal will also have a 180-degree phase angle difference from the
input signal.
F.5 Differentiator
𝑓𝑐 =
1
1
=
= 159 Hz
2πRC 2𝜋 × 10K × 0.1𝑢F
𝑓 > 10𝑓𝑐
→ 𝑓 > 1590 Hz
Inverting amplifier
𝜏 = 𝑅𝐶 = 10K × 0.1𝜇F = 0.001
H(s) =
R𝑓 𝜏𝑠
0.001𝑆
=
R1 𝜏𝑠 + 1 0.001𝑆 + 1
Table 1. Differentiator Op-Amps With different waves at different frequencies
Input Signal = 0.5 V
500 Hz
Sine
Wave
1000 Hz
5000 Hz
Output signal
500 Hz
Square
Wave
1000 Hz
5000 Hz
500 Hz
Triangular
1000 Hz
Wave
5000 Hz
Table 1 shows the different output signals given by different waveforms at different
frequencies produced by a differentiator circuit. Differentiator circuits have some conditions for
them to function as a differentiator otherwise if not met it is just an inverter circuit. The
frequency of the input signal must be lesser than ten times the cut-off frequency, if this met
sine wave will turn into a cosine wave, square wave will turn to impulse or spikes, and
triangular waves will transform into square waves. As we increase the input frequency and
move closer to the cut-off frequency the magnitude of the output signal also increases until it
reaches the maximum gain of 1 in this state the magnitude of the output signal is the same as
the input signal but the peak is cut-off or the signal is rejected therefore it turns into just an
inverter circuit. We can prove that the magnitude of the output will be equal to the input as we
1
increase the frequency by the formula of the magnitude that is equal to |H(s)| =
, if
𝑓𝑐
√1+( 𝑓 )2
the frequency of the input signal is 10 times of the cut-off the gain will be equal to one or closer
to one.
Figure 12. Bode Plot of the Differentiator Circuit
Figure 12 shows the bode plot for the circuits in Figure 6, as shown it displays the
characteristics of a high pass filter. Those frequency that is below the cut-off are the
differentiating range which means that those are the frequency which will make the circuits as
a differentiator. And as we increase the frequency towards the cut-off the magnitude also
increases but the phase angle decreases.
F.6 Integrator
𝑓𝑐 =
1
1
=
= 159 Hz
2πRC 2𝜋 × 10K × 0.1𝑢F
𝑓 < 𝑓𝑐
→ 𝑓 < 159 Hz
Inverting amplifier
𝜏 = 𝑅𝐶 = 10K × 0.1𝜇F = 0.001
H(s) =
R𝑓 1
1
=
R1 𝜏𝑠 + 1 0.001𝑆 + 1
Table 2. Integrator Op-Amps With different waves at different frequencies
Input Signal = 0.5 V
100 Hz
Sine Wave
200Hz
500 Hz
100 Hz
Square
Wave
200 Hz
500 Hz
Output signal
100 Hz
Triangular
Wave
200 Hz
500 Hz
Table 2 shows the different output waveform if we applied a different waveform and
frequencies at the input of an integrating circuit. Just like the differentiator the integrator also
has some conditions for it to be an integrator otherwise it will be just an inverting circuit. If the
input signal has a frequency below the cut-off, it will be an inverting amplifier to avoid this
situation the frequency must be greater than ten times of the cut-off frequency. We can also
notice that as the frequency of the input signal increase the magnitude of the output becomes
closer to zero and we can prove that by the formula of the magnitude of the gain which is
1
|H(s)| =
. For the integrator circuit if met with the right conditions the sine wave will
𝑓
√1+(𝑓𝑐)2
turn into cosine wave, the triangular wave will turn into sine wave, the square wave will turn
into triangular wave, so it does the opposite of the differentiator circuit.
Figure 13. Bode Plot of the Integrator Circuit
Figure 13 shows the bode plot for the integrator circuits in Figure 7, it displays the
characteristics of a low pass filter, but for the integrator circuits, we do not need those
frequencies that will be accepted by the circuit but those frequencies which are above the cutoff and those are the integrating frequencies which our integrator circuits will operate. And as
we increase the frequency of the input signals from the cut-off value the magnitude will
eventually become zero as shown in the graph and the phase angle will decrease as we
decrease the frequency.
G. Observation
In this lab experiment, we were able to explore the behavior of different operations and
configurations of the operating amplifier such as inverting and non-inverting with constant gain,
buffer, summing, integrator, and differentiator circuits using LM324 which is an Op-Amp IC with
four independent high-gain operational amplifiers.
We observe that the inverting and non-inverting amplifiers both amplified the input
signal by a constant gain but in different ways. The inverting amplifier produced an inverted
output signal with a phase difference of 180 degrees while the non-inverting, input and output
signals are in phase. The gain of the inverting amplifier is determined by the ratio of the
feedback resistor and the resistor connected in series with the signal while the gain for noninverting is determined by the same ratio but plus 1. The buffer or unity gain follower
configuration as the name suggests, has a gain of 1 or unity gain. The input and output signals
were identical, indicating that this configuration is useful for isolating stages of a circuit or for
preventing loading effects on the input signal. In Summing Operation, the Op-Amps combined
or sum up all input signals applied in the input of the circuit. We observed that the output
waveform depended on the individual input waveforms and the amplitude of each input signal.
When the input signals were all the same frequency, the output waveform exhibited
constructive and destructive interference patterns that varied with the amplitudes and phases
of the input signals.
We then explored the integrator and differentiator configurations and observed that it
produces continuous, smooth output waveforms that represented the integral and derivative of
the input signal, respectively, but it must meet some conditions for it to be an integrator or
differentiator circuit. In integrator, the frequency of the applied signal must be greater than 10
times of the cut-off frequency while for the differentiator the applied frequency must be lower
than 1-tenth of the cut-off frequency. Depending on the frequency of the input signal the gain
on the integrator and differentiator circuit also varies.
Lastly, we observed that the frequency response of each configuration varied and that
high-frequency signals were often attenuated or distorted due to the op amp's limitations.
H. Conclusion
Through this experiment, we were able to gain a better understanding of the behavior
of op-amp circuits and their various operations. And we conclude that Operating Amplifier can
do basic operations such as addition, subtraction, multiplication, and division but it does not
limit to those basic operations it can even perform higher operations such as integration and
differentiation. It can also solve logarithmic and exponential operations.
Each configuration had unique characteristics and could be used for specific purposes.
The inverting and non-inverting amplifiers provided a constant gain to the input signal, the
buffer configuration isolated and prevented loading effects, the summing amplifier combined
multiple input signals, and the integrator and differentiator configurations provided the integral
and derivative of the input signal, respectively considering that it met the conditions. The
integrator and differentiator can convert or transform the waveform to another form like
transforming a triangular wave to a square wave using a differentiator circuit considering it met
the required conditions.
We also conclude that the frequency response of each configuration varied, and highfrequency signals were often attenuated or distorted due to the op amp's limitations.
The knowledge gained from this experiment can be applied in a wide range of electronic
applications, from signal processing to control systems. By understanding the characteristics of
op amps and their different configurations, engineers, and technicians can design and optimize
electronic circuits to meet specific requirements and achieve desired performance.