Prelab 4

In this lab step responses of RC and RLC circuits will be generated and studied.

1. Construct the circuit shown in figure 1.

• Generate a step input, v_in(t) = u(t), by using a 1V square wave with a period sufficiently long (i.e., at least 10τ) so that the output reaches steady-state before the input transitions.
• Sketch the response and record the specified step response metrics of figure 2 in a table similar to the following. Compare the predicted and measured values.

2. Determine values of R, L, and C for the circuit shown in figure 3 so that the step response is a damped sinusoid with an exponential decay governed by an α of 10⁵ (i.e. the damped sinusoidal response goes to e^-1 of its final value in 10 μseconds) and a frequency of 1MHz. Use the 0.47mH inductor in your parts kit for L.

• Observe the step response and compare the theoretical response with your measurements in a table similar to that shown below. For this underdamped RLC circuit, the response should have the form v_out(t) = v_out,ss (1 - e^-αtcos(ωt + θ))u(t).