Lab 7 – Getting started with Operational Amplifier Circuits

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Northeastern University *

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2150

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Electrical Engineering

Date

Oct 30, 2023

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Lab 7 – Getting started with Operational Amplifier Circuits Student: Celine Habr Instructor: Dr. Iman Salama Lab Partner: Mateo Wu Chen October 24, 2023

1. Introduction The goal of this experiment was to study operational amplifiers (op amps) and their applications. We built and simulated four different types of op amp circuits on a protoboard, being inverting, non ‐ inverting, differencing, and summing amplifiers. 2. Results 2.1 Part 1 and 2: In Part 1, we built an inverting operational amplifier circuit on a protoboard following the schematics seen in figure 1. A 741 Op-Amp DIP, figure 2, was used for this circuit. Figure 1: Inverting op-amp circuit Source: Dr. Iman Salama. “Lab 7 - Operational Amplifier Circuits.” Northeastern University. 12 October 2023. Figure 2: Diagram of Op-Amp used Source: Dr. Iman Salama. “Lab 7 - Operational Amplifier Circuits.” Northeastern University. 12 October 2023.

In part 2, we built an inverting op-amp with resistors R i and R f . The circuit had to have a gain G of 10, therefore, to find the resistor values needed, the following equation was used. (1) 𝐺 = 𝑉 ??? 𝑉 𝑖? = − 10 = 𝑅 𝑓 𝑅 𝑖 As a result, we chose 10 kΩ for R f and 1 kΩ for R i . The completed circuit on the protoboard is seen in figure 3 . Figure 3: Diagram of Op-Amp used Source: Dr. Iman Salama. “Lab 7 - Operational Amplifier Circuits.” Northeastern University. 12 October 2023.

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Next, the DC power supply's two outputs were connected to Vcc+ and Vcc-. The terminals were switched for Vcc- in order to make sure it got -10V instead of 10V, which would be its voltage without polarity reversal. Then, the waveform generator's output was attached to v n , the input voltage, and the oscilloscope. The v p terminal, which is non-inverting, was grounded. Lastly, the voltage output v out pin was connected to another oscilloscope input. The waveform generator was then turned on and adjusted to give a 1.0V peak-to-peak sine wave V in at a frequency of 1000 Hz. The DC power supply was configured to deliver a steady 10V, resulting in Vcc+ being 10V and Vcc- being -10V. The oscilloscope displayed the voltage-time graph for both V in and V out , as shown in figure 4 . Figure 4: Graphs of voltage inputs on an oscilloscope. We then measured the amplitudes of the input sine wave and the output sine wave, in figure 4 , using the cursor. The amplitude for V in (green wave) was 9.6V peak-to-peak and 1.01V for V out (yellow wave). Using these values and Eq.1, the gain was calculated as 9.6 1.01 = 9. 505. Moving on, we then increased the amplitude of the sine wave input to 2.4V peak-to-peak, resulting in the waves seen in figure 5.

Figure 5: Sinusoids of V in and V out when input is 2.4V peak-to-peak. 2.2 Part 3: In the third part of the lab, the inverting op-amp setup from the second part was adjusted to produce a summing and inverting op-amp circuit, as shown in figure 6 . The objective for this change of the op-amp was to incorporate a negative 1V DC to the output signal, V o . In this context, V 1 and R 1 represent the initial AC input voltage and resistance from the first and second segments, while V 2 and R 2 correspond to a DC source and a suitably chosen resistor, ensuring the DC gain results in an output equals (2) ? ? = − 𝑅 𝑓 𝑅 1 ? 1 − 𝑅 𝑓 𝑅 2 ? 2

Figure 6: Summing inverting amplifier. The gains for the two inputs are –R f / R 1 and −R f / R 2 . Source: Dr. Iman Salama. “Lab 7 - Operational Amplifier Circuits.” Northeastern University. 12 October 2023. 3. Conclusion In the first and second parts, we built an inverting op-amp circuit and used the input and output voltage signals displayed on the oscilloscope to determine the gain of the system. The gain of a system is given by Eq. 1, so using that and the values of V in and V out , being 9.6V and 1.01V respectively, we obtain G as 9.505. Thus, it can be said that this measured value agrees with the predicted value of 10. Nonetheless, a slight deviation of 0.495 can be seen. This may be due to the uncertainty of the oscilloscope as well as that of the waveform generator. We were also able to verify that the gain of the circuit is negative because there is a 180º phase shift between the V in wave and the V out wave. Once the input amplitude was changed to 2.4V, the resulting output wave changed as well by having a flat peak, rather than a rounded one like a normal sine wave. Consequently, this is because the op-amp was no longer in linear mode, since it exceeded the bounds of Vcc+ (10V) and Vcc- (-10V), as the peak-to-peak amplitude is now 17.9V. This hence indicates that the wave is saturated.

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In part 3, we created a summing and inverting op-amp circuit in order to add −1V DC to the output signal, v o . Therefore, given Eq. 2, the aim is for to equal –1, where R f = 𝑅 𝑓 𝑅 2 × ? 2 10kΩ and v 2 = 10V . As a result, R 2 should be 100 kΩ in order to add –1 V DC to the output signal. 4. References Dr. Iman Salama. “Lab 7 - Operational Amplifier Circuits.” Northeastern University. 12 October 2023.