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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 operationalamplifiers and a few applications in their use. If you have any questions or concerns in regards to this laboratory assignment, this laboratory report, the processused in designing the indicated circuitry, or the final conclusions and recommendations derived, please send an email toLSchwappach@yahoo.com. I. INTRODUCTION IV. PROCEDURES / RESULTS Operational amplifiers (Op-Amps) in feedback This section outlines the procedures required tocircuitry can be utilized for advanced signal conditioning as reproduce this lab and obtain similar results.well as linear amplification. Their performance is generallylocked 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 basedamplifiers used in signal conditioning, mathematical upon the resistive feedback network of the design.operations, and linear amplification is conducted. The testand design of operational amplifiers is completed for aninverter, integrator, and differentiator configuration. Finally i. CALCULATIONS:the frequency response is evaluated for each design forconsideration on the practical uses of each configuration. (1) III. DESIGN APPROACHES/TRADE-OFFS (2) (3) For all three amplifier designs the basic equations foran inverter, integrator, and differentiator were used (seecalculations sections), however after designing the ii. EQUIPMENT:differentiating Op-Amp a modification to the final designbecame necessary to improve noise reduction. Thisimprovement is approached in the differentiator section of To effectively reproduce the circuits built in this labthis 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
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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 separatedesigns were required to account for three separate gainanalysis. The first inverting Op-Amp was designed with a gainof one, so R2 = 1k ohm (Figure 1). The second inverting Op-Amp was designed with a gain of 10, so R2 = 10k ohm (Figure2). The third inverting Op-Amp was designed with a gain of100, so R=100k ohm (Figure 3). The results of each designcan 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 gainof 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.
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CTU: EE 415 – Advanced Electronics: Lab 1: Operational Amplifiers 3Figure 4: Multisim Transient Analysis Results of Inverter Figure 6: Multisim Transient Analysis Results of Inverterwith 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 invertingamplifier correctly inverted the input 1k Hertz signal. By amplifier correctly inverted the input 1k Hertz signal. Byensuring R2 and R1 were equal (1k ohm), a gain of 1 was ensuring R2 and R1 were not equal (R1 = 1k ohm, R2 = 100kobserved. Ohm), a gain of 100 was achieved.Figure 5: Multisim Transient Analysis Results of Inverter Figure 7: Multisim AC Analysis (Bode Plot) results ofwith 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 configurationamplifier correctly inverted the input 1k Hertz signal. By using circuit 1 (Figure 1) ensured a Bandwidth of 471k Hertzensuring R2 and R1 were not equal (R1 = 1k ohm, R2 = 10k when designed using a gain of 1. Thus the gain bandwidthOhm), a gain of 10 was achieved. product (GBW) using (3) is GBW = 471,000.
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CTU: EE 415 – Advanced Electronics: Lab 1: Operational Amplifiers 4Figure 8: Multisim AC Analysis (Bode Plot) results of Figure 10: Multisim AC Analysis (Phase Plot) results ofInverter 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-Ampusing circuit 2 (Figure 2) ensured a Bandwidth of 87k Hertz configuration using circuit 1 (Figure 1) produces an initialwhen designed using a gain of 10. Thus, the gain bandwidth phase shift of +180 degrees (Zero #1), followed by a phaseproduct (GBW) using (3) is GBW = 870,000. It can said that by shift of -45 degrees by the time our corner frequency of 456kincreasing the gain we have decreased the bandwidth of the Hertz enters the circuit (Pole #1). This phase decreasecircuit, however we have increased the gain bandwidth continues to drop thanks to another pole at 27.5M Hertzproduct, 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 ofFigure 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 initialusing circuit 3 (Figure 3) ensured a Bandwidth of 9.5k Hertz phase shift of +180 degrees (Zero #1), followed by a phasewhen designed using a gain of 100. Thus, the gain bandwidth shift of -45 degrees by the time our corner frequency of 87kproduct (GBW) using (3) is GBW = 950,000. It can said again Hertz enters the circuit (Pole #1). This phase decreasethat by increasing the gain we have decreased the bandwidth continues to drop thanks to another pole at 270M Hertz (Poleof the circuit, however we have increased the gain bandwidth #2). Thus the inverting amplifier with a gain of 10 only invertsproduct, GBW. a perfect 180 degrees when the input frequency is much less than the corner frequency (approx <5k Hertz).
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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 aFigure 12: Multisim AC Analysis (Phase Plot) results of resistor in the input path as illustrated by Figure 13Inverter 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 ohmsconfiguration using circuit 3 (Figure 3) produces an initial was calculated to provide the output 1 k Hertz, 10 Vppphase shift of +180 degrees (Zero #1), followed by a phase triangle wave.shift of -45 degrees by the time our corner frequency of 9.5kHertz enters the circuit (Pole #1). This phase decreasecontinues to drop thanks to another pole at 2.61G Hertz (Pole#2). Thus the inverting amplifier with a gain of 10 only invertsa perfect 180 degrees when the input frequency is much lessthan the corner frequency (approx <500 Hertz). Thus our 1kHertz 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 anintegrator Op-Amp configuration that could performintegration on a known input signal (10 Volt peak to peak(Vpp) square wave). From basic signals and systems welearned that the integral of a square wave is a triangle wave,just as the integral of a step function is a ramp. Thus thefollowing calculations were needed to create a 1k Hertz, 10Vpp triangle wave from a 1k Hertz, 10 Vpp square wave, usingan integrator Op-Amp configuration with a 4.7n Faradcapacitor. 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)
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CTU: EE 415 – Advanced Electronics: Lab 1: Operational Amplifiers 6and Simulate/Analysis/AC-Analysis in Multisim. The result ofthese analyses is displayed in the figures below. Figure 16: Multisim AC Analysis (Phase) Results of Integrator.Figure 14: Multisim Transient Analysis results of integratorconfiguration. C. PART 3 –DIFFERENTIATOR As indicated by Figure 14 above the integrator circuit The final phase of the lab involved designing acorrectly produced the 1k Hertz, 10Vpp triangle wave (green) differentiator Op-Amp configuration that could performfrom an input 1kHz, 10Vpp square wave (red). It was also differentiation on a known input signal (10 Volt peak to peakobserved that the triangle wave now contained a DC (Vpp) triangle wave). From basic signals and systems wecomponent of +5V. Thus an integrated signal will contain a learned that the differentiation of a triangle wave is a squareDC 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 1kcapacitor 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 SourceFigure 15: Multisim AC Analysis (Bode Plot) Results of Signal GeneratorIntegrator. 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
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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 acapacitor in the input path and a resistor in the negativefeedback loop path as illustrated by Figure 17 below. The 1kohm resistor to ground is for ground noise isolation purposesonly. Using the provided capacitor value of 4.7n Farads arequired R1 value of 53.2k ohms was again calculated toprovide 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
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CTU: EE 415 – Advanced Electronics: Lab 1: Operational Amplifiers 8noise isolating resistor Rn was added to the design to removethe noise. Figure 12: Multisim AC Analysis (Bode Plot) Results of Improved Differentiator.Figure 10: Improved Multisim Transient Analysis results ofimproved differentiator configuration. The results of Figure 20 illustrate the signalimprovement 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 ofDifferentiator.
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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 anotherImproved 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.
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