1. CTU: EE 415 – Advanced Electronics: Lab 1: Operational Amplifiers 1
Colorado Technical University
EE 415 – Advanced Electronics
Lab 1: Operational Amplifiers
July 2010
Loren K. Schwappach
ABSTRACT: This lab report was completed as a course requirement to obtain full course credit in EE415,
Advanced Electronics at Colorado Technical University. This report introduces some powerful features of operational
amplifiers and a few applications in their use.
If you have any questions or concerns in regards to this laboratory assignment, this laboratory report, the process
used in designing the indicated circuitry, or the final conclusions and recommendations derived, please send an email to
LSchwappach@yahoo.com.
I. INTRODUCTION IV. PROCEDURES / RESULTS
Operational amplifiers (Op-Amps) in feedback This section outlines the procedures required to
circuitry can be utilized for advanced signal conditioning as reproduce this lab and obtain similar results.
well as linear amplification. Their performance is generally
locked upon their frequency linearity and feedback design.
A. PART 1 – INVERTING AMPLIFIER
The inverting amplifier is one of the most widely
II. OBJECTIVES used op-amp circuit designs used. The amplifier operates in a
closed loop feedback configuration producing an inverted
In this report an investigation into operational signal (180 degree phase shift) with signal amplification based
amplifiers used in signal conditioning, mathematical upon the resistive feedback network of the design.
operations, and linear amplification is conducted. The test
and design of operational amplifiers is completed for an
inverter, integrator, and differentiator configuration. Finally i. CALCULATIONS:
the frequency response is evaluated for each design for
consideration on the practical uses of each configuration. (1)
III. DESIGN APPROACHES/TRADE-OFFS (2)
(3)
For all three amplifier designs the basic equations for
an inverter, integrator, and differentiator were used (see
calculations sections), however after designing the ii. EQUIPMENT:
differentiating Op-Amp a modification to the final design
became necessary to improve noise reduction. This
improvement is approached in the differentiator section of To effectively reproduce the circuits built in this lab
this report. you will require the following components/parts/software.
 +/- 5 Volts Direct Current (VDC) Power Source
 Signal Generator
 Breadboard
 Three (3) 1k Ohm Resistors
 One (1) 10k Ohm Resistor
 One (1) 100k Ohm Resistor
 741 Op-Amp

2. CTU: EE 415 – Advanced Electronics: Lab 1: Operational Amplifiers 2
 Multisim Version 11, by National Instruments
 Oscilloscope
iii. CIRCUIT DIAGRAM:
In designing the inverting amplifier three separate
designs were required to account for three separate gain
analysis. The first inverting Op-Amp was designed with a gain
of one, so R2 = 1k ohm (Figure 1). The second inverting Op-
Amp was designed with a gain of 10, so R2 = 10k ohm (Figure
2). The third inverting Op-Amp was designed with a gain of
100, so R=100k ohm (Figure 3). The results of each design
can be found in the results section.
Figure 2: Circuit Schematic of Inverting Op-Amp with a gain
of 10.
Figure 1: Circuit Schematic of Inverting Op-Amp with a gain
of 1.
Figure 3: Circuit Schematic of Inverting Op-Amp with a gain
of 100.
iv. RESULTS:
A Multisim software simulation of each design was
completed by going to Simulate/Analysis/Transient-Analysis
and Simulate/Analysis/AC-Analysis in Multisim. The result of
these analyses is displayed in the figures below.

3. CTU: EE 415 – Advanced Electronics: Lab 1: Operational Amplifiers 3
Figure 4: Multisim Transient Analysis Results of Inverter Figure 6: Multisim Transient Analysis Results of Inverter
with a gain of 1. with a gain of 100.
From Figure 4 above it is observed that the inverting From Figure 6 above it is observed that the inverting
amplifier correctly inverted the input 1k Hertz signal. By amplifier correctly inverted the input 1k Hertz signal. By
ensuring R2 and R1 were equal (1k ohm), a gain of 1 was ensuring R2 and R1 were not equal (R1 = 1k ohm, R2 = 100k
observed. Ohm), a gain of 100 was achieved.
Figure 5: Multisim Transient Analysis Results of Inverter Figure 7: Multisim AC Analysis (Bode Plot) results of
with a gain of 10. Inverter with a gain of 1.
From Figure 5 above it is observed that the inverting As Figure 7 demonstrates our Op-Amp configuration
amplifier correctly inverted the input 1k Hertz signal. By using circuit 1 (Figure 1) ensured a Bandwidth of 471k Hertz
ensuring R2 and R1 were not equal (R1 = 1k ohm, R2 = 10k when designed using a gain of 1. Thus the gain bandwidth
Ohm), a gain of 10 was achieved. product (GBW) using (3) is GBW = 471,000.

4. CTU: EE 415 – Advanced Electronics: Lab 1: Operational Amplifiers 4
Figure 8: Multisim AC Analysis (Bode Plot) results of Figure 10: Multisim AC Analysis (Phase Plot) results of
Inverter with a gain of 10. Inverter with a gain of 1.
As Figure 8 demonstrates our Op-Amp configuration As Figure 10 demonstrates our Op-Amp
using circuit 2 (Figure 2) ensured a Bandwidth of 87k Hertz configuration using circuit 1 (Figure 1) produces an initial
when designed using a gain of 10. Thus, the gain bandwidth phase shift of +180 degrees (Zero #1), followed by a phase
product (GBW) using (3) is GBW = 870,000. It can said that by shift of -45 degrees by the time our corner frequency of 456k
increasing the gain we have decreased the bandwidth of the Hertz enters the circuit (Pole #1). This phase decrease
circuit, however we have increased the gain bandwidth continues to drop thanks to another pole at 27.5M Hertz
product, GBW. (Pole #2). Thus the inverting amplifier with a gain of 1 only
inverts a perfect 180 degrees when the input frequency is
much less than the corner frequency (approx <50k Hertz).
Figure 11: Multisim AC Analysis (Phase Plot) results of
Figure 9: Multisim AC Analysis (Bode Plot) results of Inverter with a gain of 10.
Inverter with a gain of 100.
As Figure 11 demonstrates our Op-Amp
As Figure 9 demonstrates our Op-Amp configuration configuration using circuit 2 (Figure 2) produces an initial
using circuit 3 (Figure 3) ensured a Bandwidth of 9.5k Hertz phase shift of +180 degrees (Zero #1), followed by a phase
when designed using a gain of 100. Thus, the gain bandwidth shift of -45 degrees by the time our corner frequency of 87k
product (GBW) using (3) is GBW = 950,000. It can said again Hertz enters the circuit (Pole #1). This phase decrease
that by increasing the gain we have decreased the bandwidth continues to drop thanks to another pole at 270M Hertz (Pole
of the circuit, however we have increased the gain bandwidth #2). Thus the inverting amplifier with a gain of 10 only inverts
product, GBW. a perfect 180 degrees when the input frequency is much less
than the corner frequency (approx <5k Hertz).

5. CTU: EE 415 – Advanced Electronics: Lab 1: Operational Amplifiers 5
ii. EQUIPMENT:
 +/- 15 VDC Power Source
 Signal Generator
 Breadboard
 One (1) 1k Ohm Resistor
 One (1) 53.2k Ohm Resistor
 One (1) 4.7nF Capacitor
 741 Op-Amp
 Multisim Version 11, by National Instruments
 Oscilloscope
iii. CIRCUIT DIAGRAM:
An integrator Op-Amp configuration consists of
a capacitor in the negative feedback loop path and a
Figure 12: Multisim AC Analysis (Phase Plot) results of resistor in the input path as illustrated by Figure 13
Inverter with a gain of 100. below. The 1k ohm resistor to ground is for ground noise
isolation purposes only. Using the provided capacitor
As Figure 12 demonstrates our Op-Amp value of 4.7n Farads a required R1 value of 53.2k ohms
configuration using circuit 3 (Figure 3) produces an initial was calculated to provide the output 1 k Hertz, 10 Vpp
phase shift of +180 degrees (Zero #1), followed by a phase triangle wave.
shift of -45 degrees by the time our corner frequency of 9.5k
Hertz enters the circuit (Pole #1). This phase decrease
continues to drop thanks to another pole at 2.61G Hertz (Pole
#2). Thus the inverting amplifier with a gain of 10 only inverts
a perfect 180 degrees when the input frequency is much less
than the corner frequency (approx <500 Hertz). Thus our 1k
Hertz signal is not exactly +180 degrees, it is actually closer to
+175 degrees.
B. PART 2 – INTEGRATOR
The next phase of the lab involved designing an
integrator Op-Amp configuration that could perform
integration on a known input signal (10 Volt peak to peak
(Vpp) square wave). From basic signals and systems we
learned that the integral of a square wave is a triangle wave,
just as the integral of a step function is a ramp. Thus the
following calculations were needed to create a 1k Hertz, 10
Vpp triangle wave from a 1k Hertz, 10 Vpp square wave, using
an integrator Op-Amp configuration with a 4.7n Farad
capacitor.
i. CALCULATIONS: Figure 13: Multisim circuit diagram of integrator
configuration.
(4)
iv. RESULTS:
(5)
A Multisim software simulation of each design was
completed by going to Simulate/Analysis/Transient-Analysis
(6)

6. CTU: EE 415 – Advanced Electronics: Lab 1: Operational Amplifiers 6
and Simulate/Analysis/AC-Analysis in Multisim. The result of
these analyses is displayed in the figures below.
Figure 16: Multisim AC Analysis (Phase) Results of
Integrator.
Figure 14: Multisim Transient Analysis results of integrator
configuration. C. PART 3 –DIFFERENTIATOR
As indicated by Figure 14 above the integrator circuit The final phase of the lab involved designing a
correctly produced the 1k Hertz, 10Vpp triangle wave (green) differentiator Op-Amp configuration that could perform
from an input 1kHz, 10Vpp square wave (red). It was also differentiation on a known input signal (10 Volt peak to peak
observed that the triangle wave now contained a DC (Vpp) triangle wave). From basic signals and systems we
component of +5V. Thus an integrated signal will contain a learned that the differentiation of a triangle wave is a square
DC component when integrated using an Op-Amp integrator. wave, just as the differentiation of a ramp function is a step.
This DC component could be isolated using a coupling Thus the following calculations were needed to create a 1k
capacitor at the output. Hertz, 10 Vpp square wave from a 1k Hertz, 10 Vpp triangle
wave, using an differentiator Op-Amp configuration with a
4.7n Farad capacitor.
i. CALCULATIONS:
(7)
(8)
(9)
ii. EQUIPMENT:
 +/- 15 VDC Power Source
Figure 15: Multisim AC Analysis (Bode Plot) Results of  Signal Generator
Integrator.  Breadboard
 One (1) 1k Ohm Resistor
 One (1) 3k Ohm Resistor
 One (1) 53.2k Ohm Resistor
 One (1) 4.7nF Capacitor
 741 Op-Amp

7. CTU: EE 415 – Advanced Electronics: Lab 1: Operational Amplifiers 7
 Multisim Version 11, by National Instruments
 Oscilloscope
iii. CIRCUIT DIAGRAM:
An differentiator Op-Amp configuration consists of a
capacitor in the input path and a resistor in the negative
feedback loop path as illustrated by Figure 17 below. The 1k
ohm resistor to ground is for ground noise isolation purposes
only. Using the provided capacitor value of 4.7n Farads a
required R1 value of 53.2k ohms was again calculated to
provide the output 1 k Hertz, 10 Vpp square wave.
Figure 18: Improved Multisim differentiator Op-Amp
configuration.
By adding a small 3k ohm resistor (Rn) before the
differentiator capacitor (C1) you help eliminate input noise
fluctuations (figure 19), resulting in a cleaner output (figure
20). A good formula is to have Rn be approximately 10% of
R1.
iv. RESULTS:
.
Figure 17: Multisim differentiator Op-Amp configuration.
.
Figure 19: Multisim Transient Analysis results of
differentiator configuration.
As indicated by Figure 19 above the differentiator
circuit correctly produced the 1k Hertz, 10Vpp square wave
(green) from an input 1kHz, 10Vpp triangle wave (red). It was
also observed that the square wave contained noise causing
the fluctuations at the top of the square wave. Thus a small

8. CTU: EE 415 – Advanced Electronics: Lab 1: Operational Amplifiers 8
noise isolating resistor Rn was added to the design to remove
the noise.
Figure 12: Multisim AC Analysis (Bode Plot) Results of
Improved Differentiator.
Figure 10: Improved Multisim Transient Analysis results of
improved differentiator configuration.
The results of Figure 20 illustrate the signal
improvement benefits of adding the 3k ohm resistor Rn.
Figure 13: Multisim AC Analysis (Phase Plot) Results of
Differentiator.
.
Figure 11: Multisim AC Analysis (Bode Plot) Results of
Differentiator.

9. CTU: EE 415 – Advanced Electronics: Lab 1: Operational Amplifiers 9
V. CONCLUSIONS
The inverting amplifier is a critical component to
analog systems. Utilizing the linear amplification and
characteristics of the 741 op-amp, aids in the development of
desired input-output ratios. The feedback resistor R1 divided
by the input resistor determines the voltage gain. Gain
variation is proportional to the frequency response of the
741. This is called the Gain Band Width Product or GBW. The
product is linear and thus stays within a finite range of values.
As the gain increases the cutoff frequency value decreases.
The physical results was very close to the Multisim results
(<10% error). As predicted from the Multisim output, the
design from the actual output created a ripple that was about
10% of the output voltage, which were eliminated.
Figure 14: Multisim AC Analysis (Phase Plot) Results of The integrator operational amplifier is another
Improved Differentiator. important component in analog systems. The voltage gain is
similar to the inverting op-amp where the feedback element
is divided by the input element and a 180 degree phase shift.
The capacitor is dependent on frequency thus the whole
system needs to be redesigned for alternate frequencies or
resistor values.
The differentiator performs the opposite operation
of the integrator by switching the positions of the resistor and
capacitor. The differentiator is very susceptible to incoming
noise variation which can be amplified greatly at the output.
This problem is corrected by introducing a small resistor at
the input of the op amp.
REFERENCES
[1] Neamen, D. A., “Microelectronics Circuit Analysis and
rd
Design 3 Edition” John Wiley & Sons, University of New
Mexico, 2007.