A simple band-pass filter can be realized by an RLC circuit (Figure 6.73), which passes frequencies within a certain range and attenuates frequencies outside that range. Assume that the parameter values are \(R=500 \Omega, L=100 \mathrm{mH}\), and \(C=10 \mu \mathrm{F}\). The circuit is connected to an AC voltage source, which has an amplitude of \(1 \mathrm{~V}\) and a varying frequency.

a. Build a Simscape model of the physical system and find the output voltage \(v_{0}(t)\) when the frequency of the input voltage is 1000, 800, and \(1200 \mathrm{rad} / \mathrm{s}\).

b. Derive the transfer function \(V_{\mathrm{o}}(\mathrm{s}) / V_{\mathrm{a}}(\mathrm{s})\), build a Simulink model of the system based on this transfer function, and verify the results obtained in Part (a).

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FIGURE 6.73 Problem 4. www R elle Va +