If a carrier wave c(t) = A sin ωc t is amplitude modulated by a modulator signal m(t) = A sin ωm t then the equation of modulated signal [Cm(t)] and its modulation index are respectively

Question

If a carrier wave c(t) = A sin ωc t is amplitude modulated by a modulator signal m(t) = A sin ωm t then the equation of modulated signal [Cm(t)] and its modulation index are respectively (A) Cm (t) = A (1 + sin ωm t) sin ωc t and 2 (B) Cm (t) = A (1 + sin ωm t) sin ωm t and 1 (C) Cm (t) = A (1 + sin ωm t) sin ωc t and 1 (D) Cm (t) = A (1 + sin ωc t) sin ωm t and 2

Tardigrade Admin · Accepted Answer

Modulation index ma = (Em/Ec) = (A/A) = 1 Equation of modulated signal [Cm(t)] = E(c) + maE(c) sin ωm t = A(1+sin wc t)sin ωm t (As E(c) = A sinωct)

Q. If a carrier wave $c (t) = A s in ω_{c} t$ is amplitude modulated by a modulator signal $m (t) = A s in ω_{m} t$ then the equation of modulated signal $[C_{m} (t)]$ and its modulation index are respectively

$C_{m} (t) = A (1 + s in ω_{m} t) s in ω_{c} t$ and $2$

$C_{m} (t) = A (1 + s in ω_{m} t) s in ω_{m} t$ and $1$

$C_{m} (t) = A (1 + s in ω_{m} t) s in ω_{c} t$ and $1$

$C_{m} (t) = A (1 + s in ω_{c} t) s in ω_{m} t$ and $2$

Modulation index
$m_{a} = \frac{E _{m}}{E _{c}} = \frac{A}{A} = 1$
Equation of modulated signal $[C_{m} (t)]$
$= E_{(c)} + m_{a} E_{(c)} s in ω_{m} t$
$= A (1 + s in w_{c} t) s in ω_{m} t$
$(A s E_{(c)} = A s in ω_{c} t)$

Q. If a carrier wave c(t)=Asinωc​t is amplitude modulated by a modulator signal m(t)=Asinωm​t then the equation of modulated signal [Cm​(t)] and its modulation index are respectively

Cm​(t)=A(1+sinωm​t)sinωc​t and 2

Cm​(t)=A(1+sinωm​t)sinωm​t and 1

Cm​(t)=A(1+sinωm​t)sinωc​t and 1

Cm​(t)=A(1+sinωc​t)sinωm​t and 2