Consider frequency modulation with a sinusoidal message signal (tone modulation) m(t) = a cos(2πfmt). The modulated...

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Consider frequency modulation with a sinusoidal message signal (tone modulation) m(t) = a cos(2πfmt). The modulated...

Consider frequency modulation with a sinusoidal message signal (tone modulation) m(t) = a cos(2πf_mt). The modulated signal is: v_FM(t) = Ac cos[2πf_ct + βf sin(2πf_mt)]. with βf = k_fa/f_m being the modulation index. What is the bandwidth of the modulated signal.

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Answer 1

Answer #1

S:

Given the modulated signal is

VFM(t) = Ac cos(2πfct + f sin(2πfmt))

Where f= kf.a/fm = f/fm

f - modulation index

fm - maximum frequency

f - frequency deviation ( f= kf.a)

The bandwidth of the modulated signal is calculated by Carson's rule, which states that nearly all of the power of a frequency- modulated signal lies within the bandwidth B i,e

B = 2(f +f_m) kHz (or) Hz

= 2f_m(1+f)

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Answer 2

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