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  3. 6 figure 3 shows a highpass filter consisting of a...

Question: 6 figure 3 shows a highpass filter consisting of a...

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6. Figure 3 shows a high-pass filter consisting of a capacitor (with capacitance C) and a resistor (with resistance R). The filter has input voltage u(t) and output voltage y(t). Moreover, the output voltage y(t) is governed by the following first-order ordinary differential equation dy(t) dt du t) dt RC Initially, the system is quiet, i y(0) = 0. Answer the following questions (a) What is the time constant τ of the high-pass filter. (b) At t0, the input voltage u(t) in the form of a ramp is turned on, i.e., a(t)-) Tnt, t > 0 0, t< 0 where m is the slope of the ramp. Determine the output voltage y(t) for t > 0 (c) Alternatively, at t = 0, the input voltage u(t) in the form of a unit step is turned on. 1, t>0 u(t), t<0 Determine the output voltage y(t) for t > 0.

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