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The efficient transmission of signals is...

The efficient transmission of signals is achieved by superimposing electrical audio signals on a high frequency carrier wave (the process is known as modulation). When the amplitude of high frequency carrier wave is changed in accordance with the intensity of modulating signal, it is called amplitude modulation. The extent to which the amplitude of carrier wave is changed by the signal is described by modulation factor. It is given as
`m="Amplitude change of carrier wave"/"Amplitude of unmodulated carrier wave"`
Let a carrier wave is represented by
`V_c=V_c cos omega_ct`
Let the modulation factor be m, the maximum change in amplitude of carrier wave is `mV_c`
So, modulating signal can be represented as `v_m=mV_c cosomega_mt`
So, the amplitude of modulated wave is `=V_c+mV_c cosomega_m t`
Using this value, the instantaneous voltage of modulated wave is
`E=V_c cos omega_c t+ (mV_c)/2 cos (omega_c+omega_m)t + (mV_c)/2 cos (omega_c-omega_m ) t`
The above wave contains three frequencies namely, `f_c, f_c+f_m` and `f_c-f_m` . The frequencies `f_c+f_m` and `f_c-f_m` are called side band frequencies , USB and LSB respectively.
If modulation factor is 100% , the amplitude change of carrier wave is

A

Equal to amplitude of modulating signal

B

Equal to amplitude of unmodulated carrier wave

C

Equal to amplitude of modulated wave

D

Equal to zero

Text Solution

Verified by Experts

The correct Answer is:
B
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The efficient transmission of signals is achieved by superimposing electrical audio signals on a high frequency carrier wave (the process is known as modulation). When the amplitude of high frequency carrier wave is changed in accordance with the intensity of modulating signal, it is called amplitude modulation. The extent to which the amplitude of carrier wave is changed by the signal is described by modulation factor. It is given as m="Amplitude change of carrier wave"/"Amplitude of unmodulated carrier wave" Let a carrier wave is represented by V_c=V_c cos omega_ct Let the modulation factor be m, the maximum change in amplitude of carrier wave is mV_c So, modulating signal can be represented as v_m=mV_c cosomega_mt So, the amplitude of modulated wave is =V_c+mV_c cosomega_m t Using this value, the instantaneous voltage of modulated wave is E=V_c cos omega_c t+ (mV_c)/2 cos (omega_c+omega_m)t + (mV_c)/2 cos (omega_c-omega_m ) t The above wave contains three frequencies namely, f_c, f_c+f_m and f_c-f_m . The frequencies f_c+f_m and f_c-f_m are called side band frequencies , USB and LSB respectively. The fraction of total power carried by side band frequencies is

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