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  • An amplitude modulated signal is represented by x(t)=  <img alt="(25+ 5 \sin (200 \pi t )) \cos (2 \pi t \times 10 ^5)V" src="https://learn.careers360.com/latex-image/?%2825&plus

An amplitude modulated signal is represented by x(t)= 

(25+ 5 \sin (200 \pi t )) \cos (2 \pi t \times 10 ^5)V  . The modulation index will be 

Option: 1

25


Option: 2

5


Option: 3

0.2


Option: 4

125


Answers (1)

best_answer

As we have learned

Modulation Index if maximum and minimum amplitude is given -

m_{a}= \frac{E_{max}-E_{min}}{E_{max}+E_{min}}

- wherein

if K = 1

 

 m_a = \frac{E_{max}-E_{min}}{E_{max}+E_{min}}

E_{max }= 25+5 \sin (200 \pi t )|_{maximum}= 25+5= 30

E_{min }= 25+5 \sin (200 \pi t )|_{minimum}= 25-5= 20

m_a = \frac{30-20 }{30+20}

= 10 /50

Alternate solution :

A typical AM wave is e = (E_C+E_m \sin w_m t ) \cos w_c t     

Comparing it with x (t) E_c = 25 , E_m = 5

Modulated index = E_m /E_c = 5 /25= 0.2

 

 

 

 

 

Posted by

Gunjita

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