ECE 624 ASSIGNMENT 1

The Nyquist plot that has semicircles and the straight lines is commonly used to estimateimpedances at various stages of the electrochemical devices. For some devices thesemicircles are not perfect semicircle but are somewhat open as shown below. What is thereason for it?

Two parter- Using this form how would I derive Lasas, Lasbs, Larbr, Lasbr, Larar, when g is constant I know Lasar is W_as and W_ar into the first equation, I am also thinking Lasas is W_x=W_as and W_y =W_as in the first equation. Part B where does the theta come from.

H.W: Consider the sys. shown below, where the dead time Ta is (0.5) sec. R Ke-Tas s(s2 + 2s + 1) Use Routh's criteria to determine the critical value of (k) for stability of the closed loop sys. and the crossing points on the imaginary axis then find the locations of all roots for the sys. char. eq.

Two masses are connected by sprchgs as shown in the accompanycng diagram. Bolh sprchgs constant, and the end ö have the same spochg f is bixed. 16 x, and X, represent the equilibreum position, derive a system of second - order that describes the birst spreing the displace ments brom dibterential motion equations of the system. the

earch 10:13 PM Tue 13 Dec B Problem F.7: DFT Properties Each part of this problem is independent of the others. Suppose the DFT, X[k], of a sequence r[n] below, is real. That is, X* [k] = X[k] for k = 0,..., 6. Can the unknown values of x[n] be determined? If yes, give the missing values. If no, then justify your answer. {1,7, ?, ?, 6, 5, 7} + 89 % 1 :

A resistor, an inductor, and a capacitor are connected in parallel to an ac source with voltage amplitude V and angular frequency v. Let the source voltage be given by v = Vcosvt. (a) Show that each of the instantaneous voltages vR, vL, and vC at any instant is equal to v and that i = iR + iL + iC, where i is the current through the source and iR, iL, and iC are the currents through the resistor, inductor, and capacitor, respectively. (b) What are the phases of iR, iL, and iC with respect to v? Use current phasors to represent i, iR, iL, and iC. In a phasor diagram, show the phases of these four currents with respect to v. (c) Use the phasor diagram of part (b) to show that the current amplitude I for the current i through the source is                              I = √(I2R) + (IC - IL)2 .   (d) Show that the result of part (c) can be written as I = V/Z, with 1/Z = √ (1/R2) + [ωC - (1/ωL)]2.

For the given circuit, graph i,(t) Please and thank you :)

The derivative mode is combined with the proportional and integral modes to reduce ....... settling time steady state error rising time overshoot