Question

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).

Answer 1

As per the question,

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

$Vc (t) = 10 \sin (2π \times 100\times 10^6 t) V$

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 = $2(f_1+f_2)=(\dfrac{2\times 10^3+2\pi\times 100\times 10^6}{\pi})$