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AM, FM, and Digital Modulated Systems Chap. 5
The highest efficiency that can be attained for a 100% AM signal would be 50% (for the case
when square-wave modulation is used).
Using Eq. (4–18), we obtain the normalized peak envelope power (PEP) of the AM signal:
P PEP = A c 2
{1 + max [m(t)]}2
(5–11)
2
The voltage spectrum of the AM signal is given by Eq. (4–20a) of Example 4–3 and is
S(f) = A c
2 [d(f - f c) + M(f - f c ) + d(f + f c ) + M(f + f c )]
(5–12)
The AM spectrum is just a translated version of the modulation spectrum plus delta functions
that give the carrier line spectral component. The bandwidth is twice that of the modulation.
As shown is Sec. 5–6, the spectrum for an FM signal is much more complicated, since the
modulation mapping function g(m) is nonlinear.
Example 5–3 POWER OF AN AM SIGNAL
The FCC rates AM broadcast band transmitters by their average carrier power; this rating system
is common in other AM audio applications as well. Suppose that a 5,000-W AM transmitter is connected
to a 50-Ω load; then the constant A c is given by 2 A c 2 >50 = 5,000. Thus, the peak voltage
1
across the load will be A c = 707 V during the times when there is no modulation. If the transmitter
is then 100% modulated by a 1,000-Hz test tone, the total (carrier plus sideband) average power
will be, from Eq. (5–9),
1.5c 1 2 a A c 2
bd = (1.5) * (5,000) = 7,500 W
50
because 8m 2 (t)9 = 1 2
for 100% sinusoidal modulation. Note that 7,500 W is the actual power, not
the normalized power. The peak voltage (100% modulation) is (2) (707) = 1414 V across the
50-Ω load. From Eq. (5–11), the PEP is
4c 1 2 a A c 2
bd = (4)(5,000) = 20,000 W
50
The modulation efficiency would be 33%, since 8m 2 (t)9 = 1 2 .
There are many ways of building AM transmitters. One might first consider generating the
AM signal at a low power level (by using a multiplier) and then amplifying it. This, however,
requires the use of linear amplifiers (such as Class A or B amplifiers, discussed in Sec. 4–9) so that
the AM will not be distorted. Because these linear amplifiers are not very efficient in converting
the power-supply power to an RF signal, much of the energy is wasted in heat. † Consequently,
high-power AM broadcast transmitters are built by amplifying the carrier oscillator signal to a high
† Do not confuse this conversion efficiency with modulation efficiency, which was defined by Eq. (5–10).