Lab 9

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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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pdf

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9

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ECEN 214 - Lab Report Lab Number: 9 Lab Title: Sinusoidal Steady State Response of a 2nd Order Circuit
Purpose/Goals: The main purpose of this lab is to help us understand how circuits respond to sinusoidal input voltages. This is done by replicating the circuit from Lab 8, but replacing the input voltage with a sinusoidal (AC) voltage. The resistors and capacitors are then switched to see how the response of the circuit changes. We also worked on how to use complex phasors to a practical sinusoidal signal. Understand the response of circuits due to a sinusoidal input. Procedure: This lab is broken up into two tasks. The first part is to build the Sallen-Key which can be seen in Figure 1. Figure 1: Sallen-Key Order Circuit (the image on the right is the circuit diagram, while the 2 ?? image on the left is the diagram built in the lab) The values of the components should produce a Q-factor of 1.5 and frequency of 400 Hz. Using the wave generator, generate a sine wave for the input voltage and record the input and output voltages of the oscillator. Be sure to measure the amplitude of the input and output voltage as well as the phase difference between the input and output voltage. Measure and record the input and output voltage of the circuit while varying the input frequency for the circuit. The
next step for this task is to adjust the frequency of the input sine wave until the amplitude of the output to the input amplitude has a ratio of 0.707. This is referred to as the cut-off frequency so be sure to record this value as well as the phase difference at this frequency. The next part of this lab is to repeat the last task, but using the modified circuit in Figure 2 to see how the placement of the capacitors and resistors will affect the output and input voltages. Figure 2: Modified Sallen-Key Order Circuit (the image on the right is the circuit diagram, 2 ?? while the image on the left was the circuit built in the lab) Results: For Task 1 and Task 2, we used the values = 1500 Ohms, = 5100 Ohms, = 470 ? 1 ? 2 𝐶 1 nF, and = 39 nF. These values were found by plugging them into Equations 1, 2, and 3. This 𝐶 2 gave us a closest approximation for the Q-factor of 1.5 and radian frequency of 800π. Data Tables: By analyzing the data in Table 1, we see that as the input frequency increases, the amplitude of output voltage decreases. At 1000Hz, the amplitude of output voltage basically becomes zero. It is important to note that at the input frequency of 316Hz, the amplitude of output voltage unreasonably increases. This could be due to improper measurements by either the machine or human error. Based on the data in Table 1, it can be concluded that the circuit in Figure 1 is a low-pass filter. The cutoff frequency for the Figure 1 circuit is found to be 590Hz, which agrees with our data because as input frequency increases the amplitude of output voltage should decrease. This leads to a lower ratio in the amplitude of output voltage to input voltage.
By analyzing the data in Table 2, we see that as the input frequency increases, the amplitude of output voltage increases. This is the opposite trend we saw in Table 1. Therefore, it can be reasonably assumed that the circuit in Figure 2 is a high-pass filter. This idea is supported as the amplitude of output voltage is relatively similar to the input voltage at higher frequencies. At low frequencies, for example at a frequency of 10Hz, the amplitude of output voltage is practically zero. It is found that the cutoff frequency for Figure 2 is 620Hz, which is supported by the data. The cutoff frequency equation is represented by Equation 4. Input freq (Hz) Amplitude input (V) Amplitude output (V) Phase difference (degrees) 10 2.21 2.21 3.13 18 2.17 2.21 2.82 32 2.21 2.21 5.50 56 2.21 2.25 5.4 100 2.17 2.33 11.88 178 2.21 2.53 19.1 316 2.37 3.54 59.19 562 2.17 1.57 138.94 590 2.13 1.53 142.4 1000 2.13 600 mV 175.37 1778 2.13 400 mV -747.0 3162 2.13 320 mV -187.3 5600 2.13 320 mV -409.3 10000 2.05 280 mV 166.62 Table 1: Values measured for the Sallen-Key Order Circuit as the input frequency is 2 ?? increased to 10000Hz.
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