asked by bhupendar8818, 13 days ago

# If a and b are the max and min amplitude of amplitude modulated wave , write the expression for the modulation index

0

Answer:Modulation index for an AM wave:

The modulation index of an amplitude modulated wave is defined as the ratio of the amplitude of modulating signal (Em) to the amplitude of carrier wave (Ec) i.e.,

Amplitude modulation index, ma =begin mathsize 14px style straight E subscript straight m over straight E subscript straight c end style

For a modulated wave,

ma=begin mathsize 14px style fraction numerator straight E subscript max minus straight E subscript min over denominator straight E subscript max plus straight E subscript min end fraction end style

Em < Ec, to avoid distortion.

Modulation index for an AM wave for which the maximum amplitude is 'a' while the minimum amplitude id 'b':

Modulation index, begin mathsize 14px style straight a subscript straight m equals straight E subscript straight m over straight E subscript straight c end style    ... (1)

Maximum amplitude of modulated wave, a = Ec + Em    ... (2)

Mimimum amplitude of modulated wave, b = Ec - Em    ... (3)

From eqn (2) and (3), we get,

begin mathsize 14px style straight E subscript straight c equals fraction numerator straight a plus straight b over denominator 2 end fraction space comma space space straight E subscript straight m equals fraction numerator straight a minus straight b over denominator 2 end fraction therefore From space left parenthesis 1 right parenthesis comma space we space get comma Modulation space index comma space straight a subscript straight m equals straight E subscript straight m over straight E subscript straight c equals fraction numerator begin display style fraction numerator left parenthesis straight a minus straight b right parenthesis over denominator 2 end fraction end style over denominator begin display style fraction numerator left parenthesis straight a plus straight b right parenthesis over denominator 2 end fraction end style end fraction equals fraction numerator left parenthesis straight a minus straight b right parenthesis over denominator left parenthesis straight a plus straight b right parenthesis end fraction end style

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