2 ee414 - adv electroncs - lab 1 - loren schwappach

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 [email protected].

I. INTRODUCTION

Operational amplifiers (Op-Amps) in feedback

circuitry can be utilized for advanced signal conditioning as well as linear amplification. Their performance is generally locked upon their frequency linearity and feedback design.

II. OBJECTIVES

In this report an investigation into operational

amplifiers used in signal conditioning, mathematical operations, and linear amplification is conducted. The test and design of operational amplifiers is completed for an inverter, integrator, and differentiator configuration. Finally the frequency response is evaluated for each design for consideration on the practical uses of each configuration.

III. DESIGN APPROACHES/TRADE-OFFS

For all three amplifier designs the basic equations for

an inverter, integrator, and differentiator were used (see calculations sections), however after designing the differentiating Op-Amp a modification to the final design became necessary to improve noise reduction. This improvement is approached in the differentiator section of this report.

IV. PROCEDURES / RESULTS

This section outlines the procedures required to

reproduce this lab and obtain similar results.

A. PART 1 – INVERTING AMPLIFIER

The inverting amplifier is one of the most widely used op-amp circuit designs used. The amplifier operates in a closed loop feedback configuration producing an inverted signal (180 degree phase shift) with signal amplification based upon the resistive feedback network of the design.

i. CALCULATIONS:

(1)

(2)

(3)

ii. EQUIPMENT:

To effectively reproduce the circuits built in this lab

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


741 Op-Amp

mailto:[email protected]?subject=CTU%20-%20EE414%20-%20Adv.%20Electronics%20-%20Lab%201


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 1: Circuit Schematic of Inverting Op-Amp with a gain of 1.



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.


Figure 4: Multisim Transient Analysis Results of Inverter with a gain of 1. From Figure 4 above it is observed that the inverting amplifier correctly inverted the input 1k Hertz signal. By ensuring R2 and R1 were equal (1k ohm), a gain of 1 was observed.

Figure 5: Multisim Transient Analysis Results of Inverter with a gain of 10. From Figure 5 above it is observed that the inverting amplifier correctly inverted the input 1k Hertz signal. By ensuring R2 and R1 were not equal (R1 = 1k ohm, R2 = 10k Ohm), a gain of 10 was achieved.

Figure 6: Multisim Transient Analysis Results of Inverter with a gain of 100.

From Figure 6 above it is observed that the inverting amplifier correctly inverted the input 1k Hertz signal. By ensuring R2 and R1 were not equal (R1 = 1k ohm, R2 = 100k Ohm), a gain of 100 was achieved.

Figure 7: Multisim AC Analysis (Bode Plot) results of Inverter with a gain of 1. As Figure 7 demonstrates our Op-Amp configuration using circuit 1 (Figure 1) ensured a Bandwidth of 471k Hertz when designed using a gain of 1. Thus the gain bandwidth product (GBW) using (3) is GBW = 471,000.


Figure 8: Multisim AC Analysis (Bode Plot) results of Inverter with a gain of 10. As Figure 8 demonstrates our Op-Amp configuration using circuit 2 (Figure 2) ensured a Bandwidth of 87k Hertz when designed using a gain of 10. Thus, the gain bandwidth product (GBW) using (3) is GBW = 870,000. It can said that by increasing the gain we have decreased the bandwidth of the circuit, however we have increased the gain bandwidth product, GBW.

Figure 9: Multisim AC Analysis (Bode Plot) results of Inverter with a gain of 100. As Figure 9 demonstrates our Op-Amp configuration using circuit 3 (Figure 3) ensured a Bandwidth of 9.5k Hertz when designed using a gain of 100. Thus, the gain bandwidth product (GBW) using (3) is GBW = 950,000. It can said again that by increasing the gain we have decreased the bandwidth of the circuit, however we have increased the gain bandwidth product, GBW.

Figure 10: Multisim AC Analysis (Phase Plot) results of Inverter with a gain of 1. As Figure 10 demonstrates our Op-Amp configuration using circuit 1 (Figure 1) produces an initial phase shift of +180 degrees (Zero #1), followed by a phase shift of -45 degrees by the time our corner frequency of 456k Hertz enters the circuit (Pole #1). This phase decrease continues to drop thanks to another pole at 27.5M Hertz (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 Inverter with a gain of 10. As Figure 11 demonstrates our Op-Amp configuration using circuit 2 (Figure 2) produces an initial phase shift of +180 degrees (Zero #1), followed by a phase shift of -45 degrees by the time our corner frequency of 87k Hertz enters the circuit (Pole #1). This phase decrease continues to drop thanks to another pole at 270M 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 <5k Hertz).


Figure 12: Multisim AC Analysis (Phase Plot) results of Inverter with a gain of 100. As Figure 12 demonstrates our Op-Amp configuration using circuit 3 (Figure 3) produces an initial phase shift of +180 degrees (Zero #1), followed by a phase 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:

(4)

(5)

(6)

ii. EQUIPMENT:

+/- 15 VDC Power Source

Signal Generator

Breadboard


One (1) 53.2k Ohm Resistor

One (1) 4.7nF Capacitor

741 Op-Amp


Oscilloscope


An integrator Op-Amp configuration consists of a capacitor in the negative feedback loop path and a resistor in the input path as illustrated by Figure 13 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 calculated to provide the output 1 k Hertz, 10 Vpp triangle wave.

Figure 13: Multisim circuit diagram of integrator configuration.

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.

Figure 14: Multisim Transient Analysis results of integrator configuration. As indicated by Figure 14 above the integrator circuit correctly produced the 1k Hertz, 10Vpp triangle wave (green) from an input 1kHz, 10Vpp square wave (red). It was also observed that the triangle wave now contained a DC component of +5V. Thus an integrated signal will contain a DC component when integrated using an Op-Amp integrator. This DC component could be isolated using a coupling capacitor at the output.

Figure 15: Multisim AC Analysis (Bode Plot) Results of Integrator.

Figure 16: Multisim AC Analysis (Phase) Results of Integrator.

C. PART 3 –DIFFERENTIATOR

The final phase of the lab involved designing a differentiator Op-Amp configuration that could perform differentiation on a known input signal (10 Volt peak to peak (Vpp) triangle wave). From basic signals and systems we learned that the differentiation of a triangle wave is a square wave, just as the differentiation of a ramp function is a step. Thus the following calculations were needed to create a 1k 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

Signal Generator

Breadboard



One (1) 53.2k Ohm Resistor

One (1) 4.7nF Capacitor

741 Op-Amp



Oscilloscope


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 17: Multisim differentiator Op-Amp configuration. .

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 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


noise isolating resistor Rn was added to the design to remove the noise.

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 11: Multisim AC Analysis (Bode Plot) Results of Differentiator.

Figure 12: Multisim AC Analysis (Bode Plot) Results of Improved Differentiator.

Figure 13: Multisim AC Analysis (Phase Plot) Results of Differentiator. .


Figure 14: Multisim AC Analysis (Phase Plot) Results of Improved Differentiator.

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. The integrator operational amplifier is another 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 Design 3

rd Edition” John Wiley & Sons, University of New

Mexico, 2007.

2 ee414 - adv electroncs - lab 1 - loren schwappach

Technology

Transcript of 2 ee414 - adv electroncs - lab 1 - loren schwappach