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Code No: R05310205

Set No. 2

III B.Tech I Semester Examinations,November 2010 LINEAR AND DISCRETE SYSTEMS ANALYSIS Electrical And Electronics Engineering Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ????? 1. (a) Discuss the condition which must be satisfied by a non-periodic function f(t), so that its Fourier series may contain only sine wave. (b) A series RLC circuit with R=5Ω, L= H mH, C = 50µF has an applied voltage ν(t) = 150 sin 1000t+100 sin 200t+75 sin 300t. Determine the effective current and average power. [8+8] 2. (a) What are the properties of LC driving point immitance function? (b) Find the range of ‘a’ so that H(s) = 2s44 + s33 + as22 + s + 2 is Hurwitz. [8+8] 6

4

2

+6.75s +2.25 3. Let F (s) = s +5ss5 +3s then realize the network in Foster-I, Foster-II, Cauer-I 3 +2s and Cauer-II forms. [16]

4. (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. 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]

5. The system matrices for  state variable representation of a system are   the    0 −1 1 c= 1 0 b= A= 1 0 −2

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www.QuestionPaperDownload.com Code No: R05310205

R05

Set No. 2

Determine the complete stateresponse and the output response of the system for −1 and a ramp input applied at t = 1. Sketch the time the initial state x(0) = 0 response. [6+6+4] 6. (a) Explain how sampling is done in the case of band pass signals and how the message is reconstructed from its samples. (b) A band pass signal has a center frequency fo and extends from fo -5 KHz to fo +5 KHz. The signal is sampled at a rate fs = 25 KHz. As the center frequency fo varies from fo = 5KHz to fo = 50KHz. Find the ranges of fo for which the sampling rate is adequate. [8+8] 7. Consider a system described by the Differential Equation y(n) = y(n−1)−y(n−2)+ 0.5x(n)+0.5x(n−1) Find the response of this system to the input x(n) = (0.5)n u(n) [16] with initial conditions y (-1) = 0.75 & y(-2) = 0.25. 8. (a) Determine the response of the series RLC circuit shown in figure 8a, with an initial current in the inductor and an initial voltage across the capacitor.

Figure 8a (b) Find the value of v(t) if ν(s) = and t = α.

s+2 . s(s+1)(s+3)

What is the value of v(t) at t = 0+ [8+8]

?????

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Code No: R05310205

Set No. 4

III B.Tech I Semester Examinations,November 2010 LINEAR AND DISCRETE SYSTEMS ANALYSIS Electrical And Electronics Engineering Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ????? 1. (a) What are the properties of LC driving point immitance function? (b) Find the range of ‘a’ so that H(s) = 2s44 + s33 + as22 + s + 2 is Hurwitz. [8+8] 6

4

2

+6.75s +2.25 then realize the network in Foster-I, Foster-II, Cauer-I 2. Let F (s) = s +5ss5 +3s 3 +2s and Cauer-II forms. [16]

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. 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) Discuss the condition which must be satisfied by a non-periodic function f(t), so that its Fourier series may contain only sine wave. (b) A series RLC circuit with R=5Ω, L= H mH, C = 50µF has an applied voltage ν(t) = 150 sin 1000t+100 sin 200t+75 sin 300t. Determine the effective current and average power. [8+8] 5. Consider a system described by the Differential Equation y(n) = y(n−1)−y(n−2)+ 0.5x(n)+0.5x(n−1) Find the response of this system to the input x(n) = (0.5)n u(n) with initial conditions y (-1) = 0.75 & y(-2) = 0.25. [16]

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R05

Set No. 4

6. The system matrices for  state variable representation of a system are   the    0 −1 1 c= 1 0 b= A= 1 0 −2 Determine the complete stateresponse and the output response of the system for −1 and a ramp input applied at t = 1. Sketch the time the initial state x(0) = 0 response. [6+6+4] 7. (a) Explain how sampling is done in the case of band pass signals and how the message is reconstructed from its samples. (b) A band pass signal has a center frequency fo and extends from fo -5 KHz to fo +5 KHz. The signal is sampled at a rate fs = 25 KHz. As the center frequency fo varies from fo = 5KHz to fo = 50KHz. Find the ranges of fo for which the sampling rate is adequate. [8+8] 8. (a) Determine the response of the series RLC circuit shown in figure 8a, with an initial current in the inductor and an initial voltage across the capacitor.

Figure 8a (b) Find the value of v(t) if ν(s) = and t = α.

s+2 . s(s+1)(s+3)

What is the value of v(t) at t = 0+ [8+8]

?????

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www.QuestionPaperDownload.com Code No: R05310205

R05

Set No. 1

III B.Tech I Semester Examinations,November 2010 LINEAR AND DISCRETE SYSTEMS ANALYSIS Electrical And Electronics Engineering Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ????? 1. (a) Determine the response of the series RLC circuit shown in figure 8a, with an initial current in the inductor and an initial voltage across the capacitor.

Figure 8a (b) Find the value of v(t) if ν(s) = and t = α.

s+2 . s(s+1)(s+3)

What is the value of v(t) at t = 0+ [8+8]

2. (a) Explain how sampling is done in the case of band pass signals and how the message is reconstructed from its samples. (b) A band pass signal has a center frequency fo and extends from fo -5 KHz to fo +5 KHz. The signal is sampled at a rate fs = 25 KHz. As the center frequency fo varies from fo = 5KHz to fo = 50KHz. Find the ranges of fo for which the sampling rate is adequate. [8+8] 3. The system matrices for  state variable representation of a system are   the    0 −1 1 c= 1 0 b= A= 1 0 −2 Determine the complete stateresponse and the output response of the system for −1 and a ramp input applied at t = 1. Sketch the time the initial state x(0) = 0 response. [6+6+4] 4. (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. i. Figure 3(a)i

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Code No: R05310205

Set No. 1

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]

5. (a) What are the properties of LC driving point immitance function? (b) Find the range of ‘a’ so that H(s) = 2s44 + s33 + as22 + s + 2 is Hurwitz. [8+8] 6

4

2

+6.75s +2.25 then realize the network in Foster-I, Foster-II, Cauer-I 6. Let F (s) = s +5ss5 +3s 3 +2s and Cauer-II forms. [16]

7. Consider a system described by the Differential Equation y(n) = y(n−1)−y(n−2)+ 0.5x(n)+0.5x(n−1) Find the response of this system to the input x(n) = (0.5)n u(n) with initial conditions y (-1) = 0.75 & y(-2) = 0.25. [16] 8. (a) Discuss the condition which must be satisfied by a non-periodic function f(t), so that its Fourier series may contain only sine wave. (b) A series RLC circuit with R=5Ω, L= H mH, C = 50µF has an applied voltage ν(t) = 150 sin 1000t+100 sin 200t+75 sin 300t. Determine the effective current and average power. [8+8] ?????

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Code No: R05310205

Set No. 3

III B.Tech I Semester Examinations,November 2010 LINEAR AND DISCRETE SYSTEMS ANALYSIS Electrical And Electronics Engineering Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ????? 1. (a) What are the properties of LC driving point immitance function? (b) Find the range of ‘a’ so that H(s) = 2s44 + s33 + as22 + s + 2 is Hurwitz. [8+8] 2. Consider a system described by the Differential Equation y(n) = y(n−1)−y(n−2)+ 0.5x(n)+0.5x(n−1) Find the response of this system to the input x(n) = (0.5)n u(n) with initial conditions y (-1) = 0.75 & y(-2) = 0.25. [16] 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. 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. 6

4

[8+8]

2

+6.75s +2.25 4. Let F (s) = s +5ss5 +3s then realize the network in Foster-I, Foster-II, Cauer-I 3 +2s and Cauer-II forms. [16]

5. (a) Discuss the condition which must be satisfied by a non-periodic function f(t), so that its Fourier series may contain only sine wave. (b) A series RLC circuit with R=5Ω, L= H mH, C = 50µF has an applied voltage ν(t) = 150 sin 1000t+100 sin 200t+75 sin 300t. Determine the effective current and average power. [8+8]

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R05

Set No. 3

6. The system matrices for  state variable representation of a system are   the    0 −1 1 c= 1 0 b= A= 1 0 −2 Determine the complete stateresponse and the output response of the system for −1 and a ramp input applied at t = 1. Sketch the time the initial state x(0) = 0 response. [6+6+4] 7. (a) Explain how sampling is done in the case of band pass signals and how the message is reconstructed from its samples. (b) A band pass signal has a center frequency fo and extends from fo -5 KHz to fo +5 KHz. The signal is sampled at a rate fs = 25 KHz. As the center frequency fo varies from fo = 5KHz to fo = 50KHz. Find the ranges of fo for which the sampling rate is adequate. [8+8] 8. (a) Determine the response of the series RLC circuit shown in figure 8a, with an initial current in the inductor and an initial voltage across the capacitor.

Figure 8a (b) Find the value of v(t) if ν(s) = and t = α.

s+2 . s(s+1)(s+3)

What is the value of v(t) at t = 0+ [8+8]

?????

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