FInal Exam Solutions (No All of Them Are in Details) Problem I A

FInal Exam Solutions (No All of Them Are in Details)
Problem I
A. (10 pt.) For the circuit shown in gure 1, nd Vo, knowing that;
Vs1 = cos(2 × 106 t)V, Vs2 = cos(4 × 106 t)V, R = 1.5 kΩ, C = 0.5nF, L = 0.5mH,
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B. (10 pt.) For the circuit shown in gure 2, nd Ib and Z , if Vg = 25]0o V & Ia = 5]90o A
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Problem II
A. (10 pt.) For the shown band-pass lter in gure 3, the values of the elements as follows : R = 300Ω, C = 25nF,
L = 40µH, nd:
1. H(s),
2. fo , fc1 , fc2 , β, Q
Refrence is section 14.4 you have formulas and the derivation of the Transfer function
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B. (10 pt.) Design an active low pass lter using an Op-Amp with a pass-band gain of 10 dB and cuto frequency of 1
kHz.
1. Explain briey the choice of components values.
2. Draw the circuit showing the components you have chosen.
3. What will be the output of your lter for the given input signals: (ignore the phase shift)
(a) f1 (t) = 0.5cos(1000t)V
(b) f2 (t) = 0.5cos(6300t)V
at f1, the frequency is much less than cuto so we expect 3.16 times the input voltage due to the lter's gain, so output
would be (3.16)(0.5cos(1000t))V
at f2, the frequency is at cuto, so it would be gain * 0.7 hence, output would be (0.7)(3.16)0.5cos(6300t)V
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Problem III
(20 pt.) In a balanced 3-phase system, the source has an abc sequence, its y-connected and Van = 120]20o V . The source
feeds two loads both of which are y-connected. The impedance of load 1 is 8 + j6Ω per phase. The complex power of phase a
of the second load is 600]36o V A. Find the total complex power supplied by the source and the power factor of the source.
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Problem IV
(20 pt.) The elements of the circuit shown in gure 4 had no energy stored before it was connected. If the voltage source
had a value of 325u(t) V. Find:
1. Vo (s) & Io (s)
2. vo (t) & io (t)
3. Does your results make sense? How?
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Problem V
A. (10 pt.) Find the Laplace transform for f (t) =
d
−at
cos(ωt))
dt (e
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B. (10 pt.) Given the Laplace transform of f (t) to be F (s) = 3ss3+12s+9
−16s , nd f (0)
The answer is 3, you can refer to intial and nal value theorm section 12.9 in the book to get the answer.
A longer way is to do partial fraction and nd the time domian then substitute 0 for t and nd the value, it should be
the same 3.
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