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Chapter 1

Q. 1.1.13

In a double side-band (DSB) full carrier AM transmission system, if the modulation index is doubled, then the ratio of total sideband power to the carrier power increases by a factor of _____.

Step-by-Step

Verified Solution

Ratio of P_{S B} to PC

g_{+}(t)=e^{-a t} e^{+j\left(w_{c} t+\Delta w\right) t}

 

\left(\frac{P_{S B}}{P}\right)_{1}=\frac{\mu^{2} T}{2}

and \left(\frac{P_{S B}}{P_{C}}\right)_{2}=\frac{\mu_{0}^{2}}{2}

where  \mu_{2}=2 \mu

Hence,  \left(\frac{\frac{P_{S B}}{P_{C}}}{\frac{P_{SB}}{P_{C}}}\right)=\frac{1}{4}

Four times.
Therefore,

The Fourier transform of output y(t) of the high pass filter centroid at fc is

Now, the output of second multiplier is y(t).w(t) = z(t)

After passing through the low pass filter centred at f_{ c } the Fourier transform of output S(t) is

Thus, bandwidth = (A B) – 0
= 100 – 40
= 60 Hz