Browse by Stream
QnA
Home
Search for Exam, Articles, Questions
QnA
get app
Go To Your Study Dashboard
  1. Home
  2. A signal of low frequency is to be transmitted using a carrier wave of frequency . Derive
# School

A signal of low frequency f_{m} is to be transmitted using a carrier wave of frequency f_{c}. Derive the expression for the amplitude modulated wave and deduce expressions for the lower and upper sidebands produced. Hence, obtain the expression for modulation index.

 

 

Answers (1)
S safeer

Let's derive an expression for amplitude modulated wave:-

Let a carrier wave be given by;

C(t)=A_{c}\sin \; \omega _{c}t

where, \omega _{c}= 2\pi fc and

A signal wave be -

m(t)=A_{m}\sin \; \omega_{m}t

where, \omega _{m}=2\pi f_{m}

The modulated signal is given by :

C_{m}(t)= (A_{c}+A_{m}\sin \omega _{m}t)\sin \omega _{c}t

C_{m}(t)=A_{c} (1+A_{m}/A_{c}\sin \omega _{m}t)\sin \omega _{c}t

C_{m}(t)=A_{c} \sin \omega _{c}t+ \frac{\mu}{2} \; \cos (\omega _{c}-\omega _{m})t-\mu \frac{A_{c}}{2} \; \cos (\omega _{c}+\omega _{m})t

Hence, the lower sideband frequency is given as, (\omega _{c}-\omega _{m}) and the upper sideband frequency is given as, (\omega _{c}+\omega _{m}).

The modulation index, \mu =\frac{A_{m}}{A_{c}}

Similar Questions

Related Chapters

Preparation Products

Knockout JEE Main April 2021 (One Month)

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Mentorship from our Experts, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 14000/- ₹ 4999/-
Buy Now
Knockout NEET Aug 2021 (One Month)

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Mentorship from our Experts, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 14000/- ₹ 4999/-
Buy Now
Knockout JEE Main May 2021

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Mentorship from our Experts, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 22999/- ₹ 9999/-
Buy Now
Knockout NEET Aug 2021

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Mentorship from our Experts, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 22999/- ₹ 9999/-
Buy Now
Test Series JEE Main May 2021

Unlimited Chapter Wise Tests, Unlimited Subject Wise Tests, Unlimited Full Mock Tests, Get Personalized Performance Analysis Report,.

₹ 6999/- ₹ 2999/-
Buy Now
Boost your Preparation for JEE Main with our Foundation Course
Start Now
 
Exams
Articles
Questions