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ELEC S201F 2021 Assignment 2 Question 1 This question carries 25% of the marks for this assignment

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ELEC S201F 2021 Assignment 2

Question 1 This question carries 25% of the marks for this assignment.

Use Quine-McCluskey (Tabular) method to find the minimum expression for P. A B C D A B C D

Don’t care: A? B ?C ? D , A? B ?C ? D , A? B ?C ? D (25 marks) Hint: http://www.ee.surrey.ac.uk/Projects/Labview/minimisation/tabular.html (You need to find both prime implicants and essential prime implicants.)

Question 2 This question carries 15% of the marks for this assignment. For the circuit in Figure Q2, determine the output voltage Vout for input voltages Va = 5V, Vb = 0.2V and Vc = 5V. Given R1 = 2 k?, R2 = 4 k?, R3 = 8 k? and Rf = 20 k?. Assume the op amp is ideal. Hint: Use the two Golden Rules of ideal op amp and apply KCL

Question 3 This question carries 30% of the marks for this assignment. Consider the AC circuit in Figure Q3. Given: VS1(t) = 15 cos(4×103 t) V, IS2(t) = 6 cos(4×103 t + 20?) A, C = 50 ?F, L = 3 mH, R = 8 ?.

(a) Reproduce the circuit in Figure Q3 with the corresponding phasors. (5 marks) (b) Use nodal voltage analysis to find the nodal voltages. (18 marks) (c) Find the current passing through the capacitor iC(t). (4 marks) (d) Find the voltage across the inductor vL(t). (3 marks)

Question 4 This question carries 30% of the marks for this assignment. Consider the circuit in Figure Q4, the switch has been closed for a long time prior to t = 0. The switch opens at t = 0. Given: IS = 12 mA, R1 = 2 k?, R2 = 4 k?, R3 = 5 k? and L = 6 mH. (a) For t < 0, find the current flows in the inductor iL(t) in the steady state. (4 marks) (b) For t > 0, find iL(t) in the steady state. (5 marks) (c) Consider the circuit at t = 0 (the switch just opens) (i) Find the Thevenin equivalent circuit between terminals A and B. (i.e. ignore the inductor and then determine VT and RT for the circuit seen between A and B). (8 marks) (ii) Use your circuit in (i) to find an ODE in terms of iL(t). (4 marks) (iii) Solve the ODE to find an expression for iL(t). (9 marks)

Appendix KCL: ? in ? ? out I I KVL: ? ? 0 i Vi in a loop v = iR, dt dv t ti C )( )( ? , dt di t tv L )( )( ? Impedance: j C ZC ? 1 ? and ZL ? j?L , where ? = 2?f Power: P = V I Impedance in series: Z = Z1 + Z2 Impedance in parallel: 1 2 1 1 1 Z Z Z ? ? Transformer: 1 2 1 2 N N e e ? For the 1st order ODE: tx A dt dx t ? )( ? )( ? the general solution is: 1 2 )( exp( ) K t tx ? K ? ? ? , where K1 and K2 are constants