# Amplitude modulation

The process of changing the amplitude of a carrier wave in accordance with the amplitude of the audio frequency (AF) signal is known as amplitude modulation (AM). In AM frequency of the carrier wave remains unchanged. The amplitude of modulated wave is varied in accordance with the amplitude of modulating wave (Fig. 10).

**Fig. 10**

# Modulation index

The ratio of change of amplitude of the carrier wave to the amplitude of original carrier wave is called the modulation factor or degree of modulation or modulation index (

*m*_{a}).where

*k*is a factor which determines the maximum change in the amplitude for a given amplitude*E*_{m}of the modulating signal. If*k*= 1, thenIf a carrier wave is modulated by several sine waves, the total modulated index

*m*_{t}is given by# Voltage equation for AM wave

Suppose voltage equations for carrier wave and modulating wave are

*e*_{c}=*E*_{c}cos*Ï‰*_{c}*t*and*e*_{m}=*E*_{m}sin*Ï‰*_{m}*t*=*mE*_{c}sin*Ï‰*_{m}*t*, where*e*_{c}is the instantaneous voltage of carrier wave,*E*amplitude of carrier wave,_{c}*Ï‰*(=2_{c}*Ï€**f*) angular velocity at carrier frequency_{c}*f*_{c},*e*_{m}instantaneous voltage of modulating,*E*_{m}amplitude of modulating wave, and*Ï‰*_{m}(=2*Ï€**f*_{m}) angular velocity of modulating frequency*f*_{m}.Voltage equation for AM wave is

The above AM wave indicated that the AM wave is equivalent to the summation of three sinusoidal waves, one having amplitude

*E*and the other two having amplitude_{c}*m*/2._{a}E_{c }# Side band frequencies

An AM wave contains three frequencies:

*f*_{c}(called carrier frequency), (*f*_{c}+*f*_{m}), and (*f*_{c}â€“*f*_{m}) (latter two called side band frequencies).(

*f*_{c}+*f*_{m}): Upper side band (USB) frequency(
Side band frequencies are generally close to the carrier frequency.

*f*_{c}â€“*f*_{m}): Lower side band (LSB) frequency# Bandwidth in AM wave

The two side bands lie on either side of the carrier frequency at equal frequency interval

*f*_{m}. So, bandwidth = (*f*_{c}+*f*_{m}) â€“ (*f*_{c}â€“*f*_{m}) = 2*f*_{m}.

**Fig. 11**

# Power in AM waves

Power dissipated in any circuit,

*P*=*V*^{2}_{rms}/*R*. Hence,Carrier power,

Total power of side bands,

Total power of AM wave,

*P*

_{total}=

*P*

_{c}+

*P*

_{sb}

and

Maximum power in AM (without distortion) will occur when

*m*= 1, i.e.,_{a}*P*= 1.5_{t}*P*= 3*P*_{sb}If

*I*= unmodulated current and_{c}*I*= total or modulated current, then â‡’_{t}# Limitations of amplitude modulation

- Noisy reception
- Low efficiency
- Small operating range
- Poor audio quality