Question #116609

a) The information signal given Vm (t) = 0.20 sin (2 x 10^3 t ) + 0.25 sin (2 x 10^3 t)

is superimposed over the carrier Vc (t) = 10 sin (2π x 100 x 10^6 t) V to give AM modulated wave. Calculate the AM modulation index, bandwidth of AM signal and total power radiated when AM wave is transmitted using half wave dipole antenna.

b) A 2000 Hz modulating signal of the maximum amplitude of 2 V is fed into a FM

generator produces a frequency deviation of 4.25 kHz. What is the modulation index? If

the amplitude of the modulating voltage is kept constant but its frequency is raised to 6

kHz, what is the new frequency deviation (∆f).

is superimposed over the carrier Vc (t) = 10 sin (2π x 100 x 10^6 t) V to give AM modulated wave. Calculate the AM modulation index, bandwidth of AM signal and total power radiated when AM wave is transmitted using half wave dipole antenna.

b) A 2000 Hz modulating signal of the maximum amplitude of 2 V is fed into a FM

generator produces a frequency deviation of 4.25 kHz. What is the modulation index? If

the amplitude of the modulating voltage is kept constant but its frequency is raised to 6

kHz, what is the new frequency deviation (∆f).

Expert's answer

As per the question,

"V_m (t) = 0.20 \\sin (2 \\times 10^3 t ) + 0.25 \\sin (2\\times 10^3 t) =0.45\\sin(2\\times 10^3t)"

"Vc (t) = 10 \\sin (2\u03c0 \\times 100\\times 10^6 t) V"

Hence, amplitude modulation,

"V_{AM}=(V_c+V_m\\cos (2\\pi f_m t))\\cos(2\\pi f_ct)"

"V_{AM}=10+0.45=10.45V"

band width of AM = "2(f_1+f_2)=(\\dfrac{2\\times 10^3+2\\pi\\times 100\\times 10^6}{\\pi})"

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