Question

# Problem 3 (20 Points Total): A circuit is shown below. An input voltage, e;(t), is applied. The output voltage,e.(t), is measured across the resistor, R3. (a) (8 points) Find the transfer function using the impedance method and fill in the missing entries below insymbolic form. \frac{E_{o}(s)}{E_{i}(s)}=\frac{[] s^{2}+[] s+[]}{[] s^{2}+[] s+[]} (b) (3 points) The input is a step function e;(t) = vo · u(t) where v, has units of volts. Find the initial voltagedrop at the output, lim e. (t), and find the steady state voltage drop at the output, eoss = lim e,(t). Entert→0t→∞them below. (Hint: This answer can be obtained either mathematically by applying the initial valuetheorem (IVT) and final value theorem to the result in part (a), or through physical reasoning.) e.(0) %3Deo,ss (c) (3 points) The circuit has the following parameter values: L = 120 mH, C = 1.5 µF, R1= 1000 N,R2 := 2200 2, R3 = 200 Q. Compute the natural frequency wn and damping ratio 3 of the circuit.Round to three significant digits. Units are already given. Note: First calculate the rounded value of wn. Use this value to find the damping ratio 3 and roundagain. Wnrad/s ) (6 points) The magnitude step input, v,, is 24V. Using the component value already given and zeroinitial conditions, choose the graph that best represents the response of the circuit e,(t). Physicallyjustify your answers not just to proove your math is correct, but to check to see if your math is not right.If your intuition does not agree with the mathematics, and you have time, check the mathematics!  Fig: 1  Fig: 2  Fig: 3  Fig: 4  Fig: 5  Fig: 6  Fig: 7  Fig: 8  Fig: 9  Fig: 10  Fig: 11  Fig: 12  Fig: 13