Lab 6

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Texas A&M University *

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214

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Electrical Engineering

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Jan 9, 2024

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ECEN 214 - Lab Report Lab Number: 6 Lab Title: Transient Response of a 1st Order RC Circuit

Introduction and Lab Goals: In this lab, we examine the transient behavior of a 1st order circuit. This is accomplished by creating a circuit that causes an LED to flash at a chosen frequency. This lab includes the use of capacitors and op-amps in order to cause the LEDs to flash. The lab also allows us to learn more on how to use an oscilloscope. ● Examine the transient behavior of a 1st order circuit. Procedure: The purpose of this lab is to understand the transient behavior of a 1st order circuit using a flashing LED. In task 1, the circuit in Figure 6.5 is built. To ensure the circuit is working correctly, the two LEDs should alternately flash once every two second intervals. The AD2 is then used to measure, for and , the actual frequency of oscillation, peak-to-peak 𝑉 1 (𝑡) 𝑉 2 (𝑡) voltage, and root-mean-square (RMS) voltage. Where is the voltage at the noninverting 𝑉 1 (𝑡) port of the op-amp and is the inverting port of the op-amp. 𝑉 2 (𝑡) In task 2, resistors and in Figure 6.5 are replaced with a potentiometer. The potentiometer 𝑅 1 𝑅 2 creates a variable voltage divider, which is adjusted to make the circuit oscillate at a frequency of 1Hz. The values of and in the potentiometer are then recorded, as well as the 𝑅 1 𝑅 2 waveforms created. The voltage division ratio is then calculated with the formula, γ = 𝑅 2 𝑅 1 +𝑅 2

The resistance in resistor R, in Figure 6.7 connected to the inverting input, is then halved. The new frequency of oscillation and waveforms is then recorded. With this halved resistance, the potentiometer is adjusted until the circuit oscillates at 1Hz again. The and in the 𝑅 1 𝑅 2 potentiometer, voltage division ratio, and the waveforms are recorded again. Data Tables and Data Plots: Measured Data: Task 1: Figure 1: Waveforms in Task 1 using values from Prelab 6.

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Measured Values of Waveform using Circuit Element Values in Prelab Actual frequency of oscillation (mHz) Peak-to-peak Voltage (V) Root-Mean-Square (RMS) Voltage (V) 𝑉 1 265.60 6.1470 3.0047 𝑉 2 273.70 6.0560 3.0047 Table 1: Measure Values using Circuit Element Values in Prelab In Prelab 6, the magnitudes of and are theoretically the same value. The 𝑉 1, ??𝑎? 𝑉 2, ??𝑎? measured voltages in this lab do support this idea as 6.1470V is relatively equal to 6.0560V. However, in the Prelab the peak to peak voltage is found to be 8V which is higher than the measured value. The lower peak-to-peak voltage could be caused by the op-amp saturating at a lower voltage value than it would theoretically. The calculated frequency of the oscillation, with capacitance 1 , R = 470k Ω , = 2k Ω , and = 8k Ω in Figure 6.3, is 0.48417 Hz. This is found µ𝐹 𝑅 1 𝑅 2 by using this equation where . The actual frequency of oscillation is ? ? =− 1 2τ??( 1−γ 1+γ ) τ = 𝑅𝐶 seen to be much less, this could be due to the resistors used in the lab are often inaccurate and are a lower value than they are supposed to be. This would increase the value of ln function, therefore lowering the frequency. The RMS voltage in the Prelab is larger than the measured value. This could be due to the voltage saturation in the real circuit being much less than the theoretical value which would decrease the value of RMS voltage. The resistor values could also lower the RMS voltage as the real resistor values are typically less than what they are supposed to be.

Task 2: A) Figure 2: Waveforms in Task 2a at frequency of 1Hz with potentiometer. Resistance Values of Potentiometer for the Circuit to Output 1Hz Resistance (k Ω ) 𝑅 1 3.46

𝑅 2 5.7 Table 2: Resistance Values of Potentiometer at 1Hz Output To calculate the voltage division ratio, the following equation is used. = γ = 𝑅 2 𝑅 1 +𝑅 2 0.622. Where and is the split resistances in the potentiometer, which are dependent on 𝑅 1 𝑅 2 the slider position. The resultant voltage division ratio, after plugging in the and , is 0.622. 𝑅 1 𝑅 2 B) Figure 3: Waveforms in Task 2b with resistor R value halved. Frequency of oscillation after resistor R is halved in value. Frequency (Hz)

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𝑉 1 2.0693 𝑉 2 2.0693 Table 3: Frequency of Waveforms with resistor R halved in value. C) Figure 4: Waveforms in Task 2c when potentiometer is adjusted for the circuit to produce 1Hz. Resistance Values of Potentiometer for the Circuit to Output 1Hz with R Value Halved Resistance (k Ω )

𝑅 1 5.28 𝑅 2 3.82 Table 2: Resistance Values of Potentiometer at 1Hz Output with R value halved To calculate the voltage division ratio, the following equation is used. = 0.420 γ = 𝑅 2 𝑅 1 +𝑅 2 Where and is the split resistances in the potentiometer, which are dependent on the 𝑅 1 𝑅 2 slider position. The resultant voltage division ratio, after plugging in the and , is 0.420. 𝑅 1 𝑅 2 Equations: To calculate The voltage division ratio is then calculated with the formula, (1) γ = 𝑅 2 𝑅 1 +𝑅 2 The calculated frequency of the oscillation, with capacitance 1 , R = 470k Ω , = 2k Ω , µ𝐹 𝑅 1 and = 8k Ω in Figure 6.3, is 0.48417 Hz. This is found by using this equation 𝑅 2 where (2) ? ? =− 1 2τ??( 1−γ 1+γ ) τ = 𝑅𝐶 Discussion: In Prelab 6, we found V2 peak-to-peak and V2 RMS to be 8V and 1.392V respectively. In this lab, we found the V2 peak-to-peak and V2 RMS were measured to be 6.056V and 3.0047V. One factor that may have caused the measurement for peak-to-peak voltages to be lower than the ones found in the prelab could be the op-amp saturated. This would result in a lower peak-to-peak voltage. Conclusion:

The lab helped us further understand the transient behavior of a 1st order circuit. It also allowed us to familiarize ourselves with using the oscilloscope to measure the waveforms the circuit produces. We were able to properly create the circuit and flash the LEDs at our chosen frequency. Overall, all the lab goals were met. Signatures of Proof:

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