written 6.7 years ago by | • modified 2.8 years ago |
Subject : Principle of Communication Engineering
Topic : Amplitude Modulation and Demodulation
Difficulty : High
written 6.7 years ago by | • modified 2.8 years ago |
Subject : Principle of Communication Engineering
Topic : Amplitude Modulation and Demodulation
Difficulty : High
written 6.6 years ago by | • modified 6.6 years ago |
Fig1. Generation of DSBSC signal using balanced modulator
a.)The primary current of the output transformer is i1=id1−id2.
Where,
b) id1=a+b(vc+vm)+c(vc+vm)^2 anThe primary current of the output transformer is i1=id1−id2.
Where,
id1=a+b(vc+vm)+c(vc+vm)^2 and id2=a+b(vc−vm)+c(vc−vm)^2
Thus, we get,
i1=id1−id2=2bvm+4cvmvc
The modulating and carrier voltage are represented as,
vm=Vmsinωmt andvc=Vcsinωct
Substituting for vm and vc and simplifying, we get,
i1=2bVmsinωmt+4cmVc^2cos(ωc−ωm)t−4cmVc^2cos(ωc+ωm)t
The output voltage v0 is proportional to primary current i1 and assume constant of proportionality as α, which can be expressed as,
v0=αi1=2αbVmsinωmt+4αcmVc^2cos(ωc−ωm)t−4αcmVc^2cos(ωc+ωm)t
Let P=2αbVm and Q=2αcmVc^2.
Thus we have,
v0=Psinωmt+2Qcos(ωc−ωm)t−2Qcos(ωc+ωm)t
The above equation shows that carrier has been cancelled out , leaving only two sidebands and the modulating frequencies.
The modulating frequencies from the output is eliminated by the tuning of the output transformer, which results in the below equation of the generated DSBSC wave.
v0=2Qcos(ωc−ωm)t−2Qcos(ωc+ωm)tdid2=a+b(vc−vm)+c(vc−vm)2
Thus, we get,
c) i1=id1−id2=2bvm+4cvmvc
The modulating and carrier voltage are represented as,
d) vm=Vmsinωmt andvc=Vcsinωct
Substituting for vm and vc and simplifying, we get,
e.) i1=2bVmsinωmt+4cmVc^2cos(ωc−ωm)t−4cmVc^2cos(ωc+ωm)t
f. )The output voltage v0 is proportional to primary current i1 and assume constant of proportionality as α, which can be expressed as,
g) v0=αi1=2αbVmsinωmt+4αcmVc^2cos(ωc−ωm)t−4αcmVc^2cos(ωc+ωm)t
Let P=2αbVm and Q=2αcmVc^2.
Thus we have,
h) v0=Psinωmt+2Qcos(ωc−ωm)t−2Qcos(ωc+ωm)t
The above equation shows that carrier has been cancelled out , leaving only two sidebands and the modulating frequencies.
The modulating frequencies from the output is eliminated by the tuning of the output transformer, which results in the below equation of the generated DSBSC wave.
v0=2Qcos(ωc−ωm)t−2Qcos(ωc+ωm)t
written 6.6 years ago by |
As indicated in the Fig1, the input voltage at diode D1 is (vc+vm) and input voltage at diode D2 is (vc−vm).
Fig1. Generation of DSBSC signal using balanced modulator
a.)The primary current of the output transformer is
i1=id1−id2.
Where,
id1=a+b(vc+vm)+c(vc+vm)^2 and
id2=a+b(vc−vm)+c(vc−vm)^2
Thus, we get,
i1=id1−id2=2bvm+4cvmvc
The modulating and carrier voltage are represented as,
vm=Vmsinωmt andvc=Vcsinωct
Substituting for vm and vc and simplifying, we get,
i1=2bVmsinωmt+4cmVc^2cos(ωc−ωm)t−4cmVc^2cos(ωc+ωm)t
The output voltage v0 is proportional to primary current i1 and assume constant of proportionality as α, which can be expressed as,
v0=αi1=2αbVmsinωmt+4αcmVc^2cos(ωc−ωm)t−4αcmVc^2cos(ωc+ωm)t
Let P=2αbVm and Q=2αcmVc^2.
Thus we have,
v0=Psinωmt+2Qcos(ωc−ωm)t−2Qcos(ωc+ωm)t
The above equation shows that carrier has been cancelled out , leaving only two sidebands and the modulating frequencies.
The modulating frequencies from the output is eliminated by the tuning of the output transformer, which results in the below equation of the generated DSBSC wave.
*v0=2Qcos(ωc−ωm)t−2Qcos(ωc+ωm)tdid2
=a+b(vc−vm)+c(vc−vm)2***
Thus, we get,
c) i1= id1−id2 = 2bvm+4cvmvc
The modulating and carrier voltage are represented as,
d) vm=Vm sinωmt and vc=Vc sinωct
Substituting for vm and vc and simplifying, we get,
e.) i1=2bVmsinωmt+4cmVc^2cos(ωc−ωm)t−4cmVc^2cos(ωc+ωm)t
f. )The output voltage v0 is proportional to primary current i1 and assume constant of proportionality as α, which can be expressed as,
g) v0=αi1=2αbVmsinωmt+4αcmVc^2cos(ωc−ωm)t−4αcmVc^2cos(ωc+ωm)t
Let P=2αbVm and Q=2αcmVc^2.
Thus we have,
h) v0=Psinωmt+2Qcos(ωc−ωm)t−2Qcos(ωc+ωm)t
The above equation shows that carrier has been cancelled out , leaving only two sidebands and the modulating frequencies.
The modulating frequencies from the output is eliminated by the tuning of the output transformer, which results in the below equation of the generated DSBSC wave.
v0=2Qcos(ωc−ωm)t−2Qcos(ωc+ωm)t