The purpose of this lab was to find the gains and phase differences between the input current and input voltage at three different frequencies and compare them to the theoretical values.
As a pre-lab exercise, we found the cut-off frequency (ωc) based on the circuit elements R and L. Then, we calculated three frequencies that were proportional to this cut-off frequency as shown in Figure 1 (we also converted these frequencies from rad/s to Hz). Using these values, we were able to derive the gains and the phase differences of the circuit at each frequency (Figure 1).
PROCEDURES
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| Figure 2 |
After completing the pre-lab, we set up the circuit as shown in Figure 2. We applied a 1 V sinusoidal voltage to the circuit and measured the output voltage across the resistor (vr(t)) and across the inductor (vl(t)). We also set up a math channel to find the input current by using the formula i(t) = [v(t) - vl(t)]/R. The resulting graphs at each frequency are shown below in Figures 3, 4, and 5.
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| Figure 3: 748 Hz |
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| Figure 4: 74.8 kHz |
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| Figure 5: 7.48 kHz |
From the resulting graphs, we were able to find the gains and phase differences between i(t) and v(t). We found the gain by dividing the amplitude of i(t) by the amplitude of v(t). We found these values to be 0.0143, 0.0021, and 0.0197, respectively. These were very close to the values found in the pre-lab. As a matter of fact, the percent differences between the theoretical and experimental values were only 4.67, 0.51, and 7.08 percent, respectively. Therefore, we concluded that our experimental values were valid. In addition, the phase differences were calculated by using the formula ϕ = Δt/T x 360°. The resulting values were 45.78, 88.86, and 5.39 degrees. These values were also pretty accurate as their percent differences were 2.14, 5.47, and 5.07 percent, respectively.
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