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Jan 9, 2024

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ECEN 214 - Lab Report Lab Number: 7 Lab Title: AC Response of a 1st Order RC Circuit

Introduction/Objective Goals: The goal of this lab is to gain a deeper understanding of how 1st order circuits respond to different types of periodic inputs. When the input voltage of a circuit is a sinusoidal wave, it will output a sinusoidal wave as well that will have a slight change in amplitude and a phase shift to it. However, in this lab we will see what happens when the input voltage are different types of waveforms and how that affects what the output voltage waveform looks like. We will also look at how the use of an op amp in the circuit will affect the output voltage. Procedure: This lab consists of three parts to it, each producing different sinusoidal waves for the output of the circuit. The first task is to transform an input of a triangular wave in the circuit and create an output that is sinusoidal. Start by creating a first order filter seen in Figure 1 which is below and use the resistor and capacitor values found in the table for the circuit. Using the signal generator, create a triangular wave that has an amplitude of two volts and a frequency of 250 Hz. Use the oscilloscope to see the waveform of the input and the output of the circuit. The last step for this task is to vary the input frequency and find a value that makes the output appear more sinusoidal. Make sure to take pictures of all the waveforms that are being generated. Figure 1: Circuit Configuration to change the input triangle wave to a square wave. Where R and C are values chosen using Equation 1.

The next part of this lab is taking a square wave input and transforming it into a sine wave. The same circuit created in task one can be used, but the input voltage should be changed from a triangular wave to a square wave. Take pictures of the input and output waveforms when the input frequency is 250 Hz as well as the input frequency that makes the output appear the most sinusoidal. The next step is to create a back-to-back first order circuit in order to improve the sine wave in the output. Create the back-to-back first order in Figure 2 and use the same resistor and capacitor values from the previous task for the first stage, the second stage should use different resistors and capacitors to see what the changes in frequency do. Be sure to take pictures of all the waveforms that are being produced. Figure 2: Circuit Configuration to change the input square wave to a sine wave. Where values R and C are values chosen from Equation 1. The last part of this lab is creating three different waveforms simultaneously depending on where you measure the output. Start by creating an op-amp based oscillating circuit as seen in Figure 3 using a potentiometer as a voltage divider on the first op amp. Using the R1 and C1 values from Table 3, set the potentiometer to have a voltage division ratio of 0.5. Start to adjust the potentiometer until the voltage measure at the inverting input of the op amp looks triangular. Record all values into the lab notebook. Using the R2 and C2 values from table three, will then change the triangular wave into a sinusoidal wave. Take pictures of all the waveforms generated.

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Figure 3: Circuit Configuration where the oscilloscope probe location is adjusted to display three different waveforms (sine, square, and triangle). Circuit also includes a potentiometer to adjust the voltage division ratio to best show the chosen waveform. Data Tables: Table 1 shows the values where the input frequency creates the sinusoidal wave. Because the input frequency is higher than the original frequency of 250 Hz, it can be inferred that as frequency increases, the output wave looks more sinusoidal. Resistance(Ω) Capacitance(nF) Input Frequency(Hz) 10000 100 500 Table 1 : Input frequency where the output wave looks most sinusoidal at a certain resistance and capacitance.

Table 2 records the changes in resistance, capacitance, cutoff frequency, and input frequency in Task 2, Part B. Resistance(Ω) Capacitance(nF) Input Frequency(Hz) Cutoff Frequency(Hz) 10000 100 900 1000 10000 10 3000 10000 100000 100 1200 100 Table 2 : Recorded Values from Task 2, Part B. These values show the impact changes in resistance and capacitance can have on the output wave in Figures 8, 9, and 10 . Data and Waveforms: Task 1: Triangle wave to sine wave Part A: To have a cutoff frequency near 1kHz, Equation 1 is used. With the use of this equation, it is found that a resistance of 10000Ω and capacitance 100nF comes closest to a cutoff frequency of 1kHz. From Figure 4 and 5 it can be seen that as the frequency increases, the wave output becomes more sinusoidal. Part B: Figure 4: An image that shows the conversion of a triangle wave input(yellow) to a sinusoidal wave output(green) at a frequency of 250 Hz.

Part C: Figure 5: An image that shows that the triangle wave input(yellow) converts best to a sinusoidal wave output(green) at an input frequency of 500 Hz. Task 2: Square wave to sine wave Part A: The same resistance and capacitance values are used from Task 1, Part A. From Figure 6 and 7 it can be seen that as the frequency increases, the wave output becomes more sinusoidal. However, it must be noted that it took a much higher frequency for the square wave input to output a sine wave output.

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Figure 6: An image that shows the conversion of a square wave input(yellow) to a sinusoidal wave output(green) at a frequency of 250 Hz. Figure 7: An image that shows that the square wave input(green) converts best to a sinusoidal wave output(yellow) at an input frequency of 3000 Hz. Part B: We found that the most sinusoidal output wave was when the resistance was increased and the input frequency was at 1200 Hz, which is shown in Figure 11 . From Figure 10 , we can see that the output wave has the most curve(yet still looks like a square wave) when the cutoff frequency is decreased. In Figure 8 and 9 , we can see that the output wave still looks very square compared to Figure 10 .

Cutoff frequency = 1 kHz: R2 = 10kOhm C2 = 100 nF Figure 8: Waveform of equal cutoff frequencies, where the square input wave is green and the output wave is yellow. Cutoff frequency = 10 kHz: R2 = 10kOhm C2 = 10 nF Figure 7: Waveform of increased cutoff frequency, where the square input wave is green and the output wave is yellow.

Cutoff frequency = 100 Hz: R2 = 100kOhm C2 = 100 nF Figure 10: Waveform of decreased cutoff frequency, where the square input wave is green and the output wave is yellow. Figure: An image that displays the most sinusoidal wave output(yellow) from an input square wave(green) at input frequency 1200 Hz and cutoff frequency 100 Hz.

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Task 3: Square, triangle, and sine wave R1 = 360 kOhm C1 = 10 nF R2 = 360 kOhm C2 = 10 nF Potentiometer: R1 = 1.97 kOhm R2 = 7.68 kOhm Figure 9: All waveforms combined

Calculations: Cutoff Frequency Equation: To theoretically calculate the resistor and capacitor values to achieve a cutoff frequency of 2000π rad/sec or 1kHz, the cutoff frequency equation given in the lab manual is used. Equation 1 ω 𝑐 = 1 𝑅𝐶 Where is the cutoff frequency, which in this case equals 1kHz, and R is the resistance ω 𝑐 value in Ohm’s, and C is the capacitance in Farads. Rearranging and plugging in the cutoff frequency in equation 1 will result in , where R is 10kΩ and C is 𝑅𝐶 = 1 1000𝐻𝑧 100 nF. Discussion: This lab allowed us to become more familiar with the use of oscilloscopes to measure the frequency at a given location and amplitude. It also showed the effects of cutoff frequency and input frequency can have on making the waveform look more sinusoidal. The lab also taught us how the location of the probe can affect the waveform you are shown in the oscilloscope. For example, depending on where you put the oscilloscope probe in the circuit, the oscilloscope will either display a triangular, square, or sine wave. Conclusion: The lab goal was accomplished as we saw how the output of the circuits changed depending on the shape of the input wave, the input frequency, and the cutoff frequency from having specific resistance and capacitance values. The first two tasks allowed us to see that a triangular wave is much easier to convert to a sinusoidal shaped wave than a square wave. The tasks also allowed us to see how much effect changing the capacitance or resistance can have on the cutoff frequency, which would also affect the output.

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