5.2.4 For the sinusoidally modulated DSB-LC waveform shown in Fig. P-5.2.4: a) Find the modulation index. b) Write an expression for the waveform in the form of Eq. (5.18). c) Sketch a line spectrum of the waveform. d) Show that the sum of the two sideband lines in part (c), divided by the carrier line, yields the modulation index. e) Determine the amplitude and phase of the additional carrier which must be added to the waveform shown to attain a modulation index of 20%. f) Repeat part (e) to attain a modulation index of 80%. 125 25 -25 -125 Figure P-5.2.4. P5.2.4 b) AM (t) d) (12.5 a) Using Eq. (5.19), m = 100/150 = = 66.7%. 75 [1+0.667 cos w t] cos w₁t. 12.5)/37.5 = 25/37.5 = 66.7% = m. e) (t) = (75+ A) cos w₁t + 50 cos watcos w₁t; m = 50/(75 + A) f) 50/(75 + A) 0.80; == solving, A = -12.5 0.20; == c) See graph below. solving, A = 175 V /0°. 12.5V/180°. 62 § (w) 37.5 12.5 0 WC ...... +