6.3.5 Power Contained In An AM Wave

We now need to look at the power contained in an AM wave because it will help us identify the efficiency of the AM process and point to some ways to make better use of available power. Re-writing Equation (6.8) in terms of the modulation factor gives:

υ (t) = V_{c} \sin ω_{c} t + \frac{m V_{c}}{2} [\cos (ω_{c} - ω_{m}) t - \cos (ω_{c} + ω_{m}) t]

(6.15)

The power developed in a resistance R by an AM wave is the sum of the powers developed by each of the carrier frequency, the upper sidefrequency and the lower sidefrequency components. The carrier power is:

{(\frac{V_{c}}{\sqrt{2}})}^{2} \frac{1}{R} o r \frac{V_{c}^{2}}{2 R} (W)

(6.16)

and the power developed by each of the two sidefrequencies is:

{(\frac{m V_{c}}{2 \sqrt{2}})}^{2} \frac{1}{R} o r \frac{m^{2} V_{c}^{2}}{8 R} (W)

(6.17)

so that the total power is:

P_{t} = \frac{V_{c}^{2}}{2 R} + 2 (\frac{m^{2} V_{c}^{2}}{8 R}) = \frac{V_{c}^{2}}{2 R} (1 + \frac{m^{2}}{2}) = P_{c} (1 + \frac{m^{2}}{2}) (W)

(6.18)

From Equation (6.18) it can be seen that, even in the ideal case at 100% modulation (m = 1), two-thirds of the transmitted power resides in the carrier and only one-third in the two sidebands combined. Lower modulation factors develop even less power in the sidefrequencies. Since each sideband contains a complete representation of the baseband signal, the transmission of AM is very inefficient in its use of power. Receiver design is much simpler for full AM, however, and the power inefficiency of the transmitter is less important in commercial broadcasting systems that normally only have one transmitter and many receivers, and the availability of inexpensive receivers is the predominant cost factor.

For other applications, such as radio communications networks, the power inefficiency of AM cannot be tolerated. The following sections discuss more power-efficient schemes that have been developed: double-sideband suppressed-carrier AM (DSB); single-sideband suppressed-carrier AM (SSB); independent-sideband AM (ISB); and vestigial-sideband AM (VSB).