Why do we use the band pass filter for the production of amplitude modulated wave? (ω_m and ω_c are the angular frequency of the modulating signal and the carrier wave respectively)

CONCEPT:

Production of amplitude modulated wave:

• Amplitude modulation can be produced by a variety of methods.
• A conceptually simple method is shown in the block diagram given below,

• Here the modulating signal is added to the carrier signal to produce the signal x(t).
• After that this signal x(t) is passed through a square-law device which is a non-linear device that produces an output,

⇒ y(t) = Bx(t) + Cx2(t)

Where B and C are constants

• After that, the output of the square-law device is passed through a bandpass filter.
• The bandpass filter rejects dc and the sinusoids of frequencies ωm, 2ωm, and 2ωc and retains the frequency ωc, (ωc - ωm) and (ωc + ωm).
•  The output of the bandpass filter is an amplitude modulated wave.
• It is to be mentioned that the modulated signal cannot be transmitted as such.
• The modulator is to be followed by a power amplifier which provides the necessary power and then the modulated signal is fed to an antenna of an appropriate size.

EXPLANATION:

• From the above, it is clear that the bandpass filter rejects dc and the sinusoids of frequencies ωm, 2ωm, and 2ωc and retains the frequency ωc, (ωc - ωm) and (ωc + ωm). Hence, option 3 is correct.