question_answer

Define modulation index. Give its physical significance. For an amplitude modulated wave, the maximum amplitude is found to be \[\mathbf{10}\text{ }\mathbf{V}\] while the m minimum amplitude is\[\mathbf{2}\text{ }\mathbf{V}\]. Determine the modulation index \[\mu \].                

Answer:

                Modulating index for an AM wave is defined as the ratio of change in the amplitude of the carrier wave to the amplitude of the original carrier wave. \[\text{ }\!\!\mu\!\!\text{  =}\frac{\text{Change in the amplitde of carrier wave}}{\text{Amplitude of the original carrier wave}}\] \[=\frac{{{A}_{m}}}{{{A}_{c}}}\] When a and b are the maximum and minimum amplitudes of the AM wave, then \[{{A}_{m}}=\frac{a-b}{2}\] and        \[{{A}_{c}}=a-{{A}_{m}}=a-\frac{a-b}{2}=\frac{a+b}{2}\] \[\therefore \]  \[\mu =\frac{{{A}_{m}}}{{{A}_{c}}}=\frac{(a-b)/2}{(a+b)/2}=\frac{a-b}{a+b}\] Modulation index determines the strength and quality of the transmitted signal. Maximum amplitude, \[{{A}_{\max }}=\text{10V}\] Minimum amplitude, \[{{A}_{\min }}=\text{3V}\] Modulation index, \[\mu =\frac{{{A}_{\max }}-{{A}_{\min }}}{{{A}_{\max }}+{{A}_{\min }}}\] \[=\frac{10+3}{10-3}=\frac{13}{7}=\mathbf{1}\mathbf{.85}\]