Amplitude Modulation (AM) is one of the fundamental techniques used in communication systems for transmitting information over long distances. In AM transmission, the amplitude of the carrier wave is varied in accordance with the message signal, while the frequency and phase of the carrier remain constant. An important aspect of AM transmission is the distribution of power among the carrier and the sidebands.
Table of Contents
AM Wave Representation
An amplitude modulated wave can be expressed as
\[
v(t) = V_c(1 + m \cos \omega_m t)\cos \omega_c t
\]
where
\(V_c\) = amplitude of carrier signal
\(m\) = modulation index
\(\omega_c\) = carrier angular frequency
\(\omega_m\) = modulating signal angular frequency
The modulation index indicates the degree of modulation.
\[
m = \frac{V_m}{V_c}
\]
where \(V_m\) is the amplitude of the modulating signal.
Carrier Power
When no modulation is applied, only the carrier wave is transmitted.
The carrier power is given by
\[
P_c = \frac{V_c^2}{2R}
\]
where
\(V_c\) = peak carrier voltage
\(R\) = load resistance (antenna resistance)
This power exists even when no information is transmitted, which means a large
portion of AM transmitter power is wasted in the carrier.
Sideband Power
When modulation takes place, two sidebands are produced:
• Upper Sideband (USB)
• Lower Sideband (LSB)
Each sideband carries useful information.
Power contained in each sideband is
\[
P_{USB} = P_{LSB} = \frac{m^2}{4} P_c
\]
Thus, the total sideband power becomes
\[
P_{SB} = \frac{m^2}{2} P_c
\]
Total Power in AM Wave
The total transmitted power is the sum of carrier power and sideband powers.
\[
P_t = P_c\left(1 + \frac{m^2}{2}\right)
\]
where
\(P_t\) = total transmitted power
\(P_c\) = carrier power
\(m\) = modulation index
This expression shows that total power increases with modulation index.
Power Distribution in AM
The total transmitted power is distributed as follows:
Carrier power
\[
P_c
\]
Upper sideband power
\[
P_{USB} = \frac{m^2}{4}P_c
\]
Lower sideband power
\[
P_{LSB} = \frac{m^2}{4}P_c
\]
Total sideband power
\[
P_{SB} = \frac{m^2}{2}P_c
\]
Thus,
\[
P_t = P_c + P_{USB} + P_{LSB}
\]
Efficiency of AM Transmission
The transmission efficiency of an AM system is defined as the ratio of sideband power
to total transmitted power.
\[
\eta = \frac{P_{SB}}{P_t}
\]
Substituting the values
\[
\eta = \frac{\frac{m^2}{2}P_c}{P_c\left(1+\frac{m^2}{2}\right)}
\]
\[
\eta = \frac{m^2}{2+m^2}
\]
For 100% modulation (\(m = 1\)):
\[
\eta = \frac{1}{3} = 33.33\%
\]
Thus, even at maximum modulation, only one-third of the transmitted power carries useful information.
Important Observations
• Carrier consumes most of the transmitted power.
• Sidebands contain the actual message information.
• Maximum efficiency of conventional AM is 33.33%.
• Efficiency increases with the modulation index.
• Techniques such as DSB-SC and SSB improve efficiency by suppressing the carrier or one sideband.