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3.13. Consider the system shown in Figure 3.75. As- sume that the average value of m (t) is zero and that the maximum value of [m (1) is M. Also assume that the square-law device is defined by y(t) = 4x(t) + 2x²(1) (a) Write the equation for y(t). (b) Describe the filter that yields an AM signal for g(t). Give the necessary filter type and the fre quencies of interest. (c) What value of M yields a modulation index of 0.1)

3.13. Consider the system shown in Figure 3.75. As- sume that the average value of m (t) is zero and that the maximum value of [m (1) is M. Also assume that the square-law device is defined by y(t) = 4x(t) + 2x²(1) (a) Write the equation for y(t). (b) Describe the filter that yields an AM signal for g(t). Give the necessary filter type and the fre quencies of interest. (c) What value of M yields a modulation index of 0.1)

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
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Q3.13

188 CHAPTER 3 BASIC MODULATION TECHNIQUES 40 25 10 0 FIGURE 3.73 3.8. Rework Problem 3.7 for the message signal m (1) 9 cos 20x1 +7 cos 60mt A.S. An AM modulator has output xe (t) = 40 cos 2m (200) + 4 cos 2 (180)r +4 cos2x (220) (a) Determine the modulation index and the effi- ciency. (b) Derive the envelope of x, (f) using Hilbert trans- form techniques. 3.10. An AM modulator has output x (1) = A cos 2m (200) + B cos 2x (180) +Bcos 2T (220) The carrier power is 100W and the efficiency is 40 per- cent. Determine A, B, and the modulation index. 3.12 An AM modulator has output xe (t) = 20 cos 2m (150)r +6 cos 2m (160) +6 cos 2m (140) Determine the modulation index and the efficiency. m(1) m(r) (1) cos x(1) FIGURE 3.75 Square-law ( device Filter mn S.12. 3.12. An AM modulator is operating with an index of 0.7. The modulation input is m(1) 2 cos (2f1) +cos (4x f1) +2cos (10mfl) (a) Sketch the spectrum of the modulator outpu showing the weights of all impulse functions. (b) What is the efficiency of the modulation process? 3.13. Consider the system shown in Figure 3.75. As sume that the average value of m (1) is zero and that the maximum value of m (1) is M. Also assume that the square-law device is defined by y(t)= 4x()+2x³) (a) Write the equation for y(r). (b) Describe the filter that yields an AM signal for g(r). Give the necessary filter type and the fre quencies of interest. (c) What value of M yields a modulation index of 0.1 (d) What is an advantage of this method of modula tion? 3.14. Redraw Figure 3.7 to illustrate the generation upper-sideband SSB. Give the equation defining th upper-sideband filter. Complete the analysis by deri ing the expression for the output of an upper-sidebar SSB modulator. 3.15. An upper-sideband SSB modulator has d message signal m (t) = A cost. The unmodulat carrier is given by c(t)= A, sin at. Sketch the mo ulator output x, (). Repeat for a lower-sideband S modulator. 3.16. The VSB filter illustrated in Figure 3.131
Transcribed Image Text:188 CHAPTER 3 BASIC MODULATION TECHNIQUES 40 25 10 0 FIGURE 3.73 3.8. Rework Problem 3.7 for the message signal m (1) 9 cos 20x1 +7 cos 60mt A.S. An AM modulator has output xe (t) = 40 cos 2m (200) + 4 cos 2 (180)r +4 cos2x (220) (a) Determine the modulation index and the effi- ciency. (b) Derive the envelope of x, (f) using Hilbert trans- form techniques. 3.10. An AM modulator has output x (1) = A cos 2m (200) + B cos 2x (180) +Bcos 2T (220) The carrier power is 100W and the efficiency is 40 per- cent. Determine A, B, and the modulation index. 3.12 An AM modulator has output xe (t) = 20 cos 2m (150)r +6 cos 2m (160) +6 cos 2m (140) Determine the modulation index and the efficiency. m(1) m(r) (1) cos x(1) FIGURE 3.75 Square-law ( device Filter mn S.12. 3.12. An AM modulator is operating with an index of 0.7. The modulation input is m(1) 2 cos (2f1) +cos (4x f1) +2cos (10mfl) (a) Sketch the spectrum of the modulator outpu showing the weights of all impulse functions. (b) What is the efficiency of the modulation process? 3.13. Consider the system shown in Figure 3.75. As sume that the average value of m (1) is zero and that the maximum value of m (1) is M. Also assume that the square-law device is defined by y(t)= 4x()+2x³) (a) Write the equation for y(r). (b) Describe the filter that yields an AM signal for g(r). Give the necessary filter type and the fre quencies of interest. (c) What value of M yields a modulation index of 0.1 (d) What is an advantage of this method of modula tion? 3.14. Redraw Figure 3.7 to illustrate the generation upper-sideband SSB. Give the equation defining th upper-sideband filter. Complete the analysis by deri ing the expression for the output of an upper-sidebar SSB modulator. 3.15. An upper-sideband SSB modulator has d message signal m (t) = A cost. The unmodulat carrier is given by c(t)= A, sin at. Sketch the mo ulator output x, (). Repeat for a lower-sideband S modulator. 3.16. The VSB filter illustrated in Figure 3.131
3.13. Consider the system shown in Figure 3.75. As- sume that the average value of m (t) is zero and that the maximum value of (m (t) is M. Also assume that the square-law device is defined by y(t) = 4x(t) + 2x²(1) (a) Write the equation for y(t). (b) Describe the filter that yields an AM signal for g(t). Give the necessary filter type and the fre quencies of interest. (c) What value of M yields a modulation index of 0.1) (d) What is an advantage of this method of modula tion?
Transcribed Image Text:3.13. Consider the system shown in Figure 3.75. As- sume that the average value of m (t) is zero and that the maximum value of (m (t) is M. Also assume that the square-law device is defined by y(t) = 4x(t) + 2x²(1) (a) Write the equation for y(t). (b) Describe the filter that yields an AM signal for g(t). Give the necessary filter type and the fre quencies of interest. (c) What value of M yields a modulation index of 0.1) (d) What is an advantage of this method of modula tion?
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