Identify the mathematical expression for amplitude modulated...

Identify the mathematical expression for amplitude modulated wave $\quad$ [NCERT Exemplar] (a) $A_{c} \sin \left[\left\{e_{-}+k_{1} v_{m}(t)\right\} t+\phi\right]$ (b) $A_{c} \sin \left\{a_{c} t+\phi+k_{2} v_{m}(t)\right\}$ (c) $\left\{A_{c}+k_{2} v_{m}(t)\right\} \sin \left(\omega_{e} t+\phi\right)$ (d) $A_{c} v_{m}(t) \sin (\omega, t+\phi)$

Identify the mathematical expression for amplitude modulated wave $\quad$ [NCERT Exemplar]
(a) $A_{c} \sin \left[\left\{e_{-}+k_{1} v_{m}(t)\right\} t+\phi\right]$
(b) $A_{c} \sin \left\{a_{c} t+\phi+k_{2} v_{m}(t)\right\}$
(c) $\left\{A_{c}+k_{2} v_{m}(t)\right\} \sin \left(\omega_{e} t+\phi\right)$
(d) $A_{c} v_{m}(t) \sin (\omega, t+\phi)$

Key Concepts

Amplitude Modulation

Amplitude modulation (AM) is a technique used in electronic communication, most commonly for transmitting information with a radio carrier wave. In AM, the amplitude of the high-frequency carrier signal is varied in direct proportion to that of the information-bearing modulating signal, while the frequency and phase remain constant.

Carrier Signal

The carrier signal in amplitude modulation is a high-frequency sinusoidal waveform that serves as the base for the transmission. Its primary role is to transmit the modulating signal by changing its amplitude, and it is typically represented by a sine or cosine function with a specific frequency and phase.

Modulating Signal

The modulating signal carries the actual information to be transmitted and is usually of a much lower frequency compared to the carrier wave. Its amplitude determines the extent of the modulation, and it directly influences the envelope of the resulting modulated wave.

Mathematical Expression of an AM Wave

The mathematical representation of an amplitude modulated wave typically shows the carrier wave whose amplitude is varied by the modulating signal. A common form of this expression is (A_c + k v_m(t)) sin(?_c t + ?), where A_c is the carrier amplitude, v_m(t) is the modulating signal, k is a constant relating to the modulation index, ?_c represents the angular frequency of the carrier, and ? is the phase.

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