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Question 29

An amplitude modulated signal is plotted below. Which one of the following best describes the above signal?

$$V(t) = [A_c + A_m \sin(\omega_m t)] \sin(\omega_c t)$$

$$V_{\text{max}} = 10\text{ V}, \quad V_{\text{min}} = 8\text{ V}, $$ $$T_m = 100\ \mu\text{s}, \quad T_c = 8\ \mu\text{s}$$

$$A_c = \frac{V_{\text{max}} + V_{\text{min}}}{2} = \frac{10 + 8}{2} = 9\text{ V}$$

$$A_m = \frac{V_{\text{max}} - V_{\text{min}}}{2} = \frac{10 - 8}{2} = 1\text{ V}$$

$$\omega_m = \frac{2\pi}{T_m} = \frac{2\pi}{100 \times 10^{-6}} = 2\pi \times 10^4\text{ rad/s}$$

$$\omega_c = \frac{2\pi}{T_c} = \frac{2\pi}{8 \times 10^{-6}} = 2.5\pi \times 10^5\text{ rad/s}$$

$$V(t) = (9 + \sin(2\pi \times 10^4 t)) \sin(2.5\pi \times 10^5 t)\text{ V}$$

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