Question

A rectangular pulse train m(t) shown in Figure P3 has peak-to-peak amplitude A = 2 V, period $T_0$ = 1 ms, pulse width $\tau$ = 0.5 ms. The pulse train is centered at t = 0. The peak amplitude of m(t) is 1V. The signal m(t) frequency modulates a carrier $cos(2\pi300,000t)$. Assume $k_f$ = $2\pi35000$ rad/s/V ($f_d$ = 35000 Hz/V). Also assume that the bandwidth of m(t) is B $\approx$ 5/$T_0$ Hz. (a) Find the maximum frequency deviation $\Delta f$ and the modulation index $\beta$. (b) Find the Carson's rule bandwidth. (c) Plot the instantaneous frequency $\omega_i(t)$ as a function of time for -2ms $\le$ t $\le$ 2ms. (d) Plot the FM wave as a function of time for -2ms $\le$ t $\le$ 2ms.

          A rectangular pulse train m(t) shown in Figure P3 has peak-to-peak amplitude A = 2 V, period $T_0$ = 1 ms, pulse width $\tau$ = 0.5 ms. The pulse train is centered at t = 0. The peak amplitude of m(t) is 1V. The signal m(t) frequency modulates a carrier $cos(2\pi300,000t)$. Assume $k_f$ = $2\pi35000$ rad/s/V ($f_d$ = 35000 Hz/V). Also assume that the bandwidth of m(t) is B $\approx$ 5/$T_0$ Hz.
(a) Find the maximum frequency deviation $\Delta f$ and the modulation index $\beta$.
(b) Find the Carson's rule bandwidth.
(c) Plot the instantaneous frequency $\omega_i(t)$ as a function of time for -2ms $\le$ t $\le$ 2ms.
(d) Plot the FM wave as a function of time for -2ms $\le$ t $\le$ 2ms.

A rectangular pulse train m(t) shown in Figure P3 has peak-to-peak amplitude A = 2 V, period T0 = 1 ms, pulse width τ = 0.5 ms. The pulse train is centered at t = 0. The peak amplitude of m(t) is 1V. The signal m(t) frequency modulates a carrier cos(2π300,000t). Assume kf = 2π35000 rad/s/V (fd = 35000 Hz/V). Also assume that the bandwidth of m(t) is B ≈ 5/T0 Hz.
(a) Find the maximum frequency deviation Δ f and the modulation index β.
(b) Find the Carson's rule bandwidth.
(c) Plot the instantaneous frequency (t) as a function of time for -2ms ≤ t ≤ 2ms.
(d) Plot the FM wave as a function of time for -2ms ≤ t ≤ 2ms.

Added by Mary J.

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