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1. OBJECTIVE The purpose of this experiment is to first verify the characteristics of the common linear op-amp circuits, and then use the knowledge acquired to design an amplifier suitable for a given temperature sensor. 2. LABORATORY This experiment is conducted in Electronics Laboratory located at N4-B1c-17. 3. EQUIPMENT 3.1 Instruments Description Quantity Power Supply 1 Oscilloscope, Digital Dual Channel 1 Function Generator 1 Digital Multimeter 1 Breadboard 1 3.2 Components Description Quantity Op-Amp LM741 1 Potentiometer 0-10KΩ 1 Resistor 10 KΩ 1 Resistor 15 KΩ 2 Resistor 27 KΩ 1 Resistor 68 KΩ 2 4. INTRODUCTION In this experiment, a potentiometer and the widely used “industry standard” op-amp, “741”, is used. The pinout of a 741 op-amp Features of LM741 op-amp (abstracted from National Semiconductor’s LM741 datasheet): This op-amp was used to investigate following linear op-amp circuits in this experiment: Inverting Amplifier Non-Inverting Amplifier Unity Gain Amplifier Difference Amplifier Finally, based on the knowledge acquired, a design for temperature transducer was completed. 5. EXPERIMENT 5.1 Inverting Amplifier An amplifier circuit with the potentiometer output Vs connected to its Vin as shown in Figure 1 was assembled on the breadboard. 5.1.1 Vout and Vin were measured for values of Vin from 0V to 5V in 1V intervals. The results are shown in Table 1 Vin Vout 0.025 V -0.045 V 0.989 V -2.732 V 2.015 V -5.595 V 3.030 V -8.402 V 4.012 V -11.099 V 4.998 V -13.021 V Table 1 Table 1’s figures are plotted on Graph 1 with a linear trend line of these figures drawn. 1 2 3 4 5 6 0 Vin in Volts -0.045 -2 -2.732 -4 -5.595 Vout in Volts -6 Trendline -8.402 -8 -10 -11.099 y = -2.6511x -12 -13.021 -14 Graph 1 From Graph 1, the gain (Vout/Vin) is derived to be the slope of the trend line, which is -2.6511. Discussion In this part of experiment, the theoretical value of gain is – (RF / RI) = -2.7 However, the experimented value is -2.6511 as shown above. The cause of this difference may be due to the tolerance of the components used and systematic error of apparatus. Following table shows the differences between some relevant measured values and expected values. RF RI Gain Measured Value 26.808 KΩ 9.866 KΩ -2.6511 Expected Value 27 KΩ 10 KΩ -2.7 Difference 0.7% 1.3% 1.8% RF and RI could be part of the sources of difference. Since all differences are within 2%, the experimented value is quite acceptable. 5.1.2 Part 5.1.1 was repeat with Rf = 68 KΩ. The results are shown in Table 2. Vin 0.032 V 0.997 V 2.008 V 3.021 V 3.978 V 4.974 V Vout -0.225 V -6.872 V -13.037 V -13.042 V -13.042 V -13.041 V Table 2 The results in Table 2 are plotted on Graph 1 as well. 1 2 3 4 5 0 Vin in Volts -0.045 -0.225 -2 -2.732 -4 27 KΩ -5.595 -6 68 KΩ -6.872 Vout in Volts -8.402 Trendline -8 27KΩ Trendline -10 -11.099 68KΩ -12 -13.021 -13.037 -14 -13.042 -13.042 -13.041 Discussion Viewed from Table 2 and the graph, the behavior of inverting amplifier with a 68 KΩ RF is not as expected. A linear trend line can’t be drawn for the data. After the input reaches 2V, the output doesn’t increase any more even input continues increasing. This is because the amplifier reaches its saturation condition. Moreover, the amplifier is saturated at around -13V, but not -15V which is the –Vcc of the amplifier. The explanation is amplifier’s internal circuitry consumes some of the power supply range for itself. Since this condition brings incorrect op-amp behavior, saturation is to be avoided at all times. 5.1.3 Vs was set to 2V. The potentiometer output Vs was disconnected from the amplifier Vin and Vs was measured again. Vs was measured to be 2.535V. Discussion This difference is caused by the loading effect. Since input impedance of an inverting amplifier is equal to RI which is finite, the source output impedance will divide a part of the source voltage according voltage divider rule. In this case, it divides 2.535 - 2 = 0.535V. 5.1.4 Rf was set back to 27 KΩ. The Vin terminal of the amplifier was connected to the output of a function generator. The –Ve terminal of the function generator was connected to GND of the power supply. The function generator was set to supply a 1KHz sine wave of 3Vpk-pk amplitude. Following waveforms were observed on the oscilloscope. 5 Volts/V 3 Vin 1.5V 1 Time/ms 0 1 2 3 -1 -1.5V -3 -5 5 Volts/V 4.1V 3 Vout 1 Time/ms 0 1 2 3 -1 -3 -4.1V -5 Discussion V in is a 1kHz sine wave with 3Vpk-pk amplitude. Vout is a 1KHz sine wave with 8.2Vpk-pk amplitude. The phase difference between Vout and Vin is exactly 180 degree. The gain (Vout/Vin) is -2.73. The difference with theoretical value -2.7 is 1.2%. 5.2 Non-Inverting Amplifier and Unity Gain Amplifier The circuit was connected as shown in Figure 2. 5.2.1 VOUT and VIN were measured for values of VIN from 0V to 5V in 1V intervals. The results are shown in Table 3. Vin 0.067 V 1.028 V 2.072 V 3.052 V 4.058 V 5.046 V Vout 0.104 V 1.704 V 3.431 V 5.052 V 6.714 V 8.338 V Table 3 5.2.2 VOUT against VIN is plotted on Graph 2. 10 8.338 8 6.714 Vout in Volts 6 5.052 y = 1.652x 4 Trendline 3.431 2 1.704 0.104 0 Vin in Volts 1 2 3 4 5 6 Graph 2 A trend line of the points is drawn and hence gain, (Vout/Vin), is derived to be 1.652. Discussion The theoretical value of gain of this non-inverting amplifier is (1+R1 / R2) = 1.67 Similarly to part 5.1, the cause of this difference may be due to the tolerance of the components used and the systematic error of apparatus.. Following table shows the difference between measured value and expected value in this part. R1 R2 Gain Measured Value 9.866 KΩ 14.988 KΩ 1.652 Expected Value 10 KΩ 15 KΩ 1.667 Difference 1.3% 0.1% 0.8% R1 and R2 could be part of the sources of difference. Since all differences are within 2%, and the gain’s difference is only 0.8%, again the experimented value is quite acceptable. 5.2.3 Vs was set to 2V. The potentiometer output Vs was disconnected from the amplifier Vin and Vs was measured again. Vs was measured to be 2.017V. Discussion From the measurement, there is no significant difference of Vs after disconnected from a non-inverting amplifier. This behavior is different from inverting amplifier. For a non-inverting amplifier, the current flow through the source is almost 0. As a result, the input impedance of non-inverting amplifier could be considered as infinite. However, since the real amplifier is not ideal, there are tiny leakage currents drawn at its input terminals. Therefore, the source output impedance could divide a very small portion of source voltage. In this case, it divides 0.017V out of 2.017V. This loading effect is actually quite small and can be neglected at almost times. This is the explanation of such different behavior compared with part 5.1.3 5.2.4 The Vin terminal of the amplifier was connected to the output of a function generator. The –Ve terminal of the function generator was connected to GND of the power supply. The function generator was set to supply a 1KHz sine wave of 3V pk-pk amplitude. Following waveforms were observed on the oscilloscope. 3 Volts/V 2 Vin 1.5V 1 0 Time/ms 0 1 2 3 -1 -1.5V -2 -3 3 Volts/V 2.64V 2 Vout 1 0 Time/ms 0 1 2 3 -1 -2 -2.40V -3 Discussion VIN is a 1kHz sine wave with 3Vpk-pk amplitude. VOUT is a 1KHz sine wave with 5.04Vpk-pk amplitude. There is no phase difference between Vout and Vin. The gain (VOUT/VIN) is 1.68. The difference with theoretical value 1.67 is 0.5%. Note that the amplitude of VOUT’s maximum is not equal to its minimum. The explanation is there is a small leakage current drawn into the amplifier. This input current generate voltage that act like unmodeled input offset. 5.2.5 R1 was replaced with a short-circuit. R2 was removed. The circuit is shown in Figure 3. VOUT and VIN were measured for values of VIN from 0V to 5V in 1V intervals. The results are shown in Table 4 Vin 0.026 V 1.000 V 2.009 V 3.026 V 4.041 V 5.053 V Vout 0.026 V 1.000 V 2.010 V 5.051 V 4.043 V 5.053 V Table 4 and were plotted on Graph 3. 6 5.053 y = 1.003x 4 4.043 Vin in Volts 3.051 Trendline 2 2.01 1 0 0.026 Vout in Volts 1 2 3 4 5 6 Graph 3 Discussion From the trend line drawn, the gain of this amplifier is 1.003, which has a 0.3% difference with expected value 1. Since unity amplifier is just a special case of non-inverting amplifier, the cause of difference is same as discussed in part 5.2.2. Additionally, from this part, we can see that a less number of components used, resulting a smaller error, which is a indirect proof that the resistors used in part 5.2.2 are a part of sources of difference. 5.2.6 The Vin terminal of the amplifier was connected to the output of a function generator. The –Ve terminal of the function generator was connected to GND of the power supply. The function generator was set to supply a 1KHz sine wave of 3V pk-pk amplitude. Following waveforms were observed on the oscilloscope. 2 Volts/V Vin 1.5V 1 0 Time/ms 0 1 2 3 -1 -1.5V -2 2 Volts/V Vout 1.5V 1 0 Time/ms 0 1 2 3 -1 -1.5V -2 Discussion VIN is a 1kHz sine wave with 3Vpk-pk amplitude. VOUT is a 1KHz sine wave with 3Vpk-pk amplitude. There is no phase difference between Vout and Vin. The gain (VOUT/VIN) is 1. In conclusion, VIN and VOUT are the same signal. Comment on Inverting, Non-inverting and Unity Gain Amplifier For inverting amplifier: For non-inverting amplifier: For unity gain amplifier: The gain is always 1. The presence of the negative sign in inverting amplifier’s equation is a convention indicating that the polarity or phase of output is inverted. Therefore the output of an inverting amplifier is always 180° out of phase with the input signal. The advantage of inverting amplifier is that we can design it to acquire an amplifier whose gain’s absolute value is smaller than 1. However, inverting amplifier only has a small impedance which is equal to RI, so the application of inverting amplifier needs to consider the loading effect and etc. For non-inverting amplifier, its gain is always greater than 1. Its output has no phase or polarity inversion with input. Since there’s only a small leakage current drawn at its input terminals, a non-inverting amplifier has very high input impedance. The small leakage current is acting as a noise on the output signal. Unity gain amplifier is a special case of non-inverting amplifier which has a gain that is always 1. Therefore the major application of it is using its high impedance to minimizing the loading effect of a circuit. For all the three amplifiers, the saturation limits of them is about 90% of their Vcc and –Vcc because amplifier’s internal circuitry consumes some of the power supply range for itself. Since output approaching the saturation limit always leads to unexpected behavior of amplifier, in application, saturation limit should be avoided at all times. 5.3 Difference Amplifier 5.3.1 Following circuit was connected. 5.3.2 Terminal V2 was connected to a function generator which supplies a 1KHz sine wave of 2Vpk-pk amplitude. Following are waveforms of V1, V2 and VOUT observed for values of V1 from 0V to 4V in 1V intervals. When V1 = 0.0023V Volts/V 4 V1 2 Y = 0.0023 Time/ms 0 0 1 2 3 2 Volts/V Y = sin(2πt) V2 1 0 Time/ms 0 1 2 3 -1 -2 5 -4.8V Volts/V Y = 4.7 x sin(2πt) + 0.3 3 Vout 1 Time/ms 0 1 2 3 -1 -3 -4.4V -5 Discussion: Difference amplifier has following equation: For the given condition, the theoretical value of Vout is 4.53 x sin(2πt). The experimented gain 4.7 has a 3.75% difference with 4.53. As the result is within 5% difference, it’s acceptable here. This difference may be caused by the tolerance of components. The 0.3V DC offset may have 2 sources. First, V1 is not 0 but 0.0023V and is amplified by a gain 4.7. Second, the small leakage current drawn at inputs as an offset and be amplified. When V1 = 1.002V Volts/V 4 Y = 1.002 V1 2 Time/ms 0 0 1 2 3 2 Volts/V Y = sin(2πt) V2 1 0 Time/ms 0 1 2 3 -1 -2 0 Time/ms Volts/V 0 1 2 -0.2V 3 Y = 4.2 x sin(2πt) - 4.4 -3 Vout -6 -8.6V -9 Discussion: For the given condition, the theoretical value of Vout is 4.53 x sin(2πt) – 4.53. The expression experimented is 4.2 x sin(2πt) - 4.4 For coefficient of AC part, the 7.28% difference may be brought by the tolerance of components, the systematic error of apparatus, and the small leakage(offset) current drawn at the input. The cause of this big difference is further discussed in a followed comparison experiment. For DC part, the result is quite satisfied as the difference is only 2.87%. The cause of this difference is same as AC part. When V1 = 2.017V Volts/V 4 Y = 2.017 V1 2 Time/ms 0 0 1 2 3 2 Volts/V Y = sin(2πt) V2 1 0 Time/ms 0 1 2 3 -1 -2 0 Time/ms Volts/V 0 1 2 3 Y = 4.1 x sin(2πt) - 9.1 -5 Vout -10 -13.2V -15 Discussion: For the given condition, the theoretical value of Vout is 4.53 x sin(2πt) – 9.06. The expression experimented is 4.1 x sin(2πt) – 9.1 For coefficient of AC part, the 9.49% difference may be brought by the tolerance of components, the systematic error of apparatus, the small leakage(offset) current drawn at the input. The cause of this big difference is further discussed in a followed comparison experiment. For DC part, the result is quite satisfied as the difference is only 0.44%. The cause of this difference is same as AC part. When V1 = 3.003 V Volts/V 4 Y = 3.003 V1 2 Time/ms 0 0 1 2 3 2 Volts/V Y = sin(2πt) V2 1 0 Time/ms 0 1 2 3 -1 -2 0 Time/ms Volts/V 0 1 2 3 -5 Vout 460μs -9.4V -10 -13.2V -15 Discussion: For the given condition, the theoretical value of Vout is 4.53 x sin(2πt) – 13.59. The expression experimented is 4.1 x sin(2πt) – 13.5. Although the output meets the saturation limit, this expression is derived from the measured time and voltage of Vout changing from Vmin to Vmax. For coefficient of AC part, the 9.49% difference may be brought by the tolerance of components, the systematic error of apparatus, the small leakage(offset) current drawn at the input. Additionally, as the saturation limit met, there may be distortion in output signal. For DC part, the result is quite satisfied as the difference is only 0.66%. The cause of this difference is same as AC part. When V1 = 4.000V Volts/V 4 Y = 4.000 V1 2 Time/ms 0 0 1 2 3 2 Volts/V Y = sin(2πt) V2 1 0 Time/ms 0 1 2 3 -1 -2 0 Time/ms Volts/V 0 1 2 3 80μs -5 Vout -10 -13V -13.2V -15 Discussion: For the given condition, the theoretical value of Vout is 4.53 x sin(2πt) – 18.12. The expression experimented is 4.1 x sin(2πt) – 17.1. Although the output meets the saturation limit, this expression is derived from the measured time and voltage of V out changing from Vmin to Vmax. For coefficient of AC part, the 9.49% difference may be brought by the tolerance of components, the systematic error of apparatus, the small leakage(offset) current drawn at the input. Additionally, as the saturation limit met, there may be distortion in output signal. For DC part, the difference is 5.63%. The cause of this difference is same as AC part. Comparison Experiment: If connected V1 to non-inverting input and V2 to inverting input. When V1 = 0.0045V Before interchanging 5 Volts/V Y = 4.7 x sin(2πt) + 0.3 3 Vout 1 Time/ms -1 0 1 2 3 -3 -5 -4.4V After interchanging 5 4.6V Volts/V Y = - 4.6 x sin(2πt) 3 Vout 1 Time/ms -1 0 1 2 3 -3 -5 -4.6V When V1 = 1.001V Before interchanging 0 Time/ms Volts/V 0 1 2 -0.2V 3 Y = 4.2 x sin(2πt) - 4.4 -3 Vout -6 -9 -8.6V After interchanging 10 Volts/V 9.2V Vout 5 Y = - 4.6 x sin(2πt) + 4.6 0 Time/ms 0 1 2 3 When V1 = 2.001V Before interchanging 0 Time/ms Volts/V 0 1 2 3 -5 Y = 4.1 x sin(2πt) - 9.1 Vout -10 -13.2V -15 After interchanging 15 Volts/V 13.8V 10 Vout Y = - 4.6 x sin(2πt) +9.2 5 4.6V Time/ms 0 0 1 2 3 When V1 = 3.017V Before interchanging 0 Time/ms Volts/V 0 1 2 3 -5 Vout Y = 4.1 x sin(2πt) - 13.5 -9.4V -10 -13.2V -15 After interchanging 15 14.6V Volts/V 10 9.4V Y = - 4.6 x sin(2πt) +14 540μs Vout 5 Time/ms 0 0 1 2 3 When V1 = 4.000V Volts/V 0 Time/ms 0 1 2 3 -5 Vout -10 Y = 4.1 x sin(2πt) - 17.1 -13V -13.2V -15 15 14.6V Volts/V 14V Y = - 4.6 x sin(2πt) +18.6 10 Vout 5 160μs Time/ms 0 0 1 2 3 Discussion: As can be seen from the graph, after interchanging, the output is 180° out of phase with the original output as well as the AC input V2. In this comparison experiment, the theoretical value of Vout is -4.53 x sin(2πt) + 4.53 x V1 For all 5 sets of waveforms, the coefficient of AC part is -4.6 which has only 1.55% difference with theoretical value -4.53. Such difference is much better than that before interchanging. Therefore I guess that the leakage(offset) currents are mainly drawn into the amplifier at non-inverting input. Under this theory, in previous experiment, AC input is connected to non-inverting input. Both Vmax and Vmin are affected by the leakage(offset), so the leakage(offset) has doubled the error. This is a reasonable way to explain the large difference of AC part before interchanging. Following table summarizes the differences of DC part. V1 0 1 2 3 4 Theoretical 0V 4.53 V 9.06 V 13.59 V 18.12 V Experimented 0V 4.6 V 9.2 V 14 V 18.6 V Difference 0 1.55% 1.55% 3.02% 2.65% For DC part, the differences are quite acceptable. The bigger difference for V1 when it’s 3V and 4V may be brought by the distortion as the output has met the saturation limit. 5.4 Amplifier Design for Temperature Transducer A thermistor Microchip’s MCP9701 has following characteristic. An amplifier circuit that will produce approximately a 0V – 5V output for temperature varying between 0 °C and 100 °C was asked to be designed. Analysis: From the characteristics of MCP9701, we know its Vout is approximately 0.4V at 0 °C and 2.4V at 100 °C. Since we need 0V – 5V output for temperature varying between 0 °C and 100 °C, we can set following simultaneous equations: k x 0.4 + b = 0 (1) k x 2.4 + b = 5 (2) Solve the equations: k = 2.5 b = -1 Therefore the circuit we designed should have following characteristic: Vout = 2.5 x Vin – 1V (3) For such equation, we can choose either difference amplifier or summation amplifier. In this experiment, difference amplifier is a better choice. Following circuit was designed using the components provided. 27 15 Thermistor Potentiometer 10 68 Base on difference amplifier’s equation: The designed circuit has following equation: Vout = 2.44 x V1 – 1.8 x V2 Compare with equation (3), 2.44 over 2.5 is 0.976. However, this is already the best plan that can be achieved based on the given resistors. Besides, 1.8 x V2 needs to be equal to 1. Therefore V2 connected to potentiometer shoul be applied a 1/1.8 = 0.556V dc voltage. Experiment: The circuit designed above was connected. In the process of connection, the resistors were measured to be: R1 = 9.886 KΩ R2 = 15.016 KΩ R3 = 70.76 KΩ R4 = 26.810 KΩ Since R4/ R2 = 1.785 but not 1.8 which previously calculated, V2 applied is amended to be 0.56V. Therefore based on measurement and adjustment, the circuit has following equation: Vout = 2.44 x V1 – 1V Verification: The room temperature was measured to be 21.1°C. The output of thermistor was measured to be 0.8157V. The output of the amplifier was measure to be 0.9958V. 0.9958V / 5V x 100°C = 19.87°C Since it was asked to design an approximate 0V – 5V output for temperature varying between 0 °C and 100 °C, the 1.23°C difference with real value should be acceptable. Viewed from another way, 0.8157 x 2.44 - 1 is equal to 0.9947. The difference between measured output of amplifier 0.9958V and 0.9947V is only 0.16%. Further verification: Limited by the experiment environment, it is impossible to examine the design from 0°C to 100°C. Instead, a function generator was used to provide a DC offset to V 1 to simulate a thermistor works under an environment whose temperature changes from 0°C to 100°C. The table below shows the experimented values. Simulated Temperature DC voltage applied Output of op-amp Calculated temperature 0°C 0.4003V -0.0217V -0.43°C 20°C 0.8018V 0.9567V 19.13°C 40°C 1.2032V 1.9323V 38.65°C 60°C 1.6017V 2.9092V 58.18°C 80°C 2.0017V 3.8850V 77.70°C 100°C 2.4005V 4.8590V 97.18°C Compare the simulated temperature and temperature calculated from output of op-amp, the result is acceptable. And the relationship between input and output voltage is very close to designed euqation: Vout = 2.44 x V1 – 1V Output against simulated temperature is plotted. 5 4.859 4 3.885 3 2.9092 Vout in Volts 2 1.9323 Trendline 1 0.9567 0 -0.0217 Temperature 0 20 40 60 80 100 120 -1 The characteristics generally satisfies the requirement of the lab manual. 6. CONCLUSION In part 5.1, I learned the characteristics of inverting amplifier. Inverting amplifier’s gain is –(RF/RI), which means it can be designed to have a gain whose absolute value is less than 1 and the negative sign mean’s the output is always 180 degree out of phase with its input signal. Knowledge of amplifier’s saturation limit and concept of loading effect are also learned. Saturation limit of Vout should be avoided at all times since it brings unexpected behavior of op-amp. Loading effect is important since it needs to be seriously considered when in application. In part 5.2, both non-inverting amplifier and its special case, unity gain amplifier, are investigated. Non-inverting amplifier has similar circuit connection to inverting amplifier other than input signal is connected to non-inverting terminal. The gain of non-inverting amplifier is always greater than 1 and unity gain amplifier is always 1. One more limitation of real amplifier is learned, the input impedance of non-inverting amplifier is not ideally infinite. There are small leakage currents drawn into the non-inverting amplifier. The different performance of inverting and non-inverting amplifier on loading effect is discussed. The application of unity gain amplifier is discussed. In part 5.3, the characteristics of difference amplifier is studied. Sets of experiments are done on difference amplifier to learn how it is used to find the difference between two voltage inputs. In part 5.4, a real-world question is solved, designing circuits for temperature sensor. I learned hands-on skill of how to design a specified-purpose amplifier and how to verify its performance. 7. REFERENCE 1. Lecture Notes 2. Laboratory Manual 3. National Semiconductor’s LM741 Operational Amplifier datasheet http://www.national.com/ds/LM/LM741.pdf 4. Wikipedia: Operational amplifier http://en.wikipedia.org/wiki/Operational_amplifier 5. Wikipedia: Operational amplifier applications http://en.wikipedia.org/wiki/Operational_amplifier_applications

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