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Posted By: k vishaal Member Level: Gold Posted Date: 05 Sep 2008
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2008 Jawaharlal Nehru Technological University R05310205 Set No. 2,III B.Tech I Semester Supplimentary Examinations, February 2008,LINEAR AND DISCRETE SYSTEMS ANALYSIS Question paper
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Code No: R05310205 Set No. 2
III B.Tech I Semester Supplimentary Examinations, February 2008
LINEAR AND DISCRETE SYSTEMS ANALYSIS
(Electrical & Electronic Engineering)
Time: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
? ? ? ? ?
1. (a) Write the state equations for the network given as shown in figure 1a.
Figure 1a
(b) Use the eigen method, find the state transition matrix for the system with the
following parameter matrices.
A = -4 1
-2 -1 B = 1
0
2
-1
0
1
C = -3 1 D = -1 0 1
[8+8]
2. (a) Find the Fourier series of the waveform shown in figure 2a using exponential
form. Plot the amplitude and phase spectrum.
Figure 2a
(b) Determine the effective voltage, effective current and average power supplied
to a passive network of the applied voltage is ?(t) = 100 + 50 cos (10t + 30) +
25 cos (30t + 60) volts and the resulting current is i(t) = 2 cos (10t + 75?) +
3 cos (30t + 78?)amp. [10+6]
3. (a) Determine the F.T. of a trapzoidal function and triangular RF pulse f(t) shown
in figure 3(a)i, figure 3(a)ii. Draw its spectrum.
1 of 3
Code No: R05310205 Set No. 2
i. Figure 3(a)i
Figure 3(a)i
ii. figure 3(a)ii
Figure 3(a)ii
(b) Show that a normalized Gaussian pulse is its own fourier transform. [8+8]
4. (a) Find the LT of
i. f(t) = cos (t - p/4) u (t - p/4)
ii. f(t) =
-(t+ )
e cos (?t + ß)
(b) Find the LT of x(t) = e-5t [u(t) - u(t - 5)] and its ROC. [8+8]
5. (a) What is Hurwitz polynomial? State the properties of Hurwitz polynomial.
(b) Test whether the polynomial P(s) = s4 + s3 + 2s2 + 3s + 4 is Hurwitz or not.
[8+8]
6. Synthesize the following functions in Cauer form.
(a) Z(s) = s3+2s2+s+1
s3+s2+s
(b) Z(s) = s3+2s2+2s+1
s4+s3+3s2+s+1 . [2 × 8]
7. Find the mean square value of the output voltage vo(t) of an RC network shown
in figure 7 if the input voltage has a power density spectrum Si(w) given by
(a) Si (w)= k
(b) Si (w)= G2(w) [gate function with cutoff at w=1]
(c) Si (w)= p [d(w + 1)+d(w - 1)]
In each case, also calculate the power of the input signal. [16]
2 of 3
Code No: R05310205 Set No. 2
Figure 7
8. (a) Deduce the relation between Z-plane and S-plane.
(b) Using the relation in (a) if a pole is located at ‘-a’ in S-plane then where does
this get located in Z-plane? [8+8]
? ? ? ? ?
3 of 3
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