Communication Systems

The modulation index ($\mu$) in amplitude modulation (AM) is defined as the ratio of the amplitude of the message signal ($V_m$) to the amplitude of the carrier signal ($V_C$). This can be expressed as :

$ \mu = \frac{V_m}{V_C} $

Given the modulation index $\mu = \frac{1}{2}$ and the amplitude of the message signal $V_m = 2$, we need to find the amplitude of the carrier signal $V_C$.

Using the formula for the modulation index :

$ \mu = \frac{V_m}{V_C} $

Substitute the given values :

$ \frac{1}{2} = \frac{2}{V_C} $

To find $V_C$, solve for $V_C$ :

$ V_C = 2 \times 2 $

$ V_C = 4 $

Therefore, the amplitude of the carrier signal $V_C$ is 4.

Correct answer :

Option A : 4

When a radiowave of frequency less than maximum usable frequency sent at certain angle towards the given layer of ionosphere, gets multiple reflection from different layers of ionosphere and finally returns to earth.

The ionosphere reflection is similar to the total internal reflection and also similar to the total internal reflection in miraj.

In ionospheric reflection, frequency and phase do not changed of reflected radiowave.

Hence, both assertion and reason are true and reason is correct explanation of assertion.

Amplitude modulation is less noise immunity than frequency modulation, hence amplitude modulation shows more interference than frequency modulation with noise. Interference (noise) depends mostly upon amplitudes signal to noise ratio for frequency modulation is more than amplitude modulation.

In amplitude modulation, the change in amplitude can actually modulate the signal and be pick up in the AM system. As a result, AM system are very sensitive to random noise. In FM system, mostly frequency of carrier wave is changed according to the modulating signal, hence noise does not interfere FM signal directly. Therefore, FM systems are far better at rejecting noise than AM systems.

Hence, both assertion and reason are true and reason is the correct explanation of assertion.

$\begin{aligned} \therefore \tau=R C & =100 \times 10^3 \times 250 \times 10^{-12} \mathrm{~s} \\ & =2.5 \times 10^7 \times 10^{-12} \mathrm{~s}=2.5 \times 10^{-5} \mathrm{~s} \end{aligned}$

The higher frequency which can be detected with tolerable distortion is

$\begin{aligned} f & =\frac{1}{2 \pi m_a R C}=\frac{1}{2 \pi \times 0.6 \times 2.5 \times 10^{-5}} \mathrm{~Hz} \\ & =\frac{100 \times 10^4}{25 \times 1.2 \pi} \mathrm{~Hz}=\frac{4}{1.2 \pi} \times 10^4 \mathrm{~Hz} \\ & =10.61 \mathrm{~kHz} \end{aligned}$

This condition is obtained by applying the condition that rate of decay of capacitor voltage must be equal or less than the rate of decay modulated signal voltage for proper detection of modulated signal.