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AM, FM, and Digital Modulated Systems Chap. 5
Compared with an AM signal, the percentage of modulation on a DSB-SC signal is infinite,
because there is no carrier line component. Furthermore, the modulation efficiency of a DSB-SC
signal is 100%, since no power is wasted in a discrete carrier. However, a product detector (which
is more expensive than an envelope detector) is required for demodulation of the DSB-SC signal.
If transmitting circuitry restricts the modulated signal to a certain peak value, say, A p , it can be
demonstrated (see Prob. 5–11) that the sideband power of a DSB-SC signal is four times that of a
comparable AM signal with the same peak level. In this sense, the DSB-SC signal has a fourfold
power advantage over that of an AM signal.
If m(t) is a polar binary data signal (instead of an audio signal), then Eq. (5–13) is a
BPSK signal, first described in Example 2–22. Details of BPSK signaling will be covered in
Sec. 5–9. As shown in Table 4–1, a QM signal can be generated by adding two DSB signals
where there are two signals, m 1 (t) and m 2 (t), modulating cosine and sine carriers, respectively.
5–4 COSTAS LOOP AND SQUARING LOOP
The coherent reference for product detection of DSB-SC cannot be obtained by the use of
an ordinary phase-locked tracking loop, because there are no spectral line components at
; f c . However, since the DSB-SC signal has a spectrum that is symmetrical with respect to
the (suppressed) carrier frequency, either one of the two types of carrier recovery loops
shown in Fig. 5–3 may be used to demodulate the DSB-SC signal. Figure 5–3a shows the
Costas PLL and Fig. 5–3b shows the squaring loop. The noise performances of these two
loops are equivalent [Ziemer and Peterson, 1985], so the choice of which loop to implement
depends on the relative cost of the loop components and the accuracy that can be realized
when each is built.
As shown in Fig. 5–3a, the Costas PLL is analyzed by assuming that the VCO is locked
to the input suppressed carrier frequency, f c , with a constant phase error of u e . Then the voltages
v 1 (t) and v 2 (t) are obtained at the output of the baseband low-pass filters as shown. Since
u e is small, the amplitude of v 1 (t) is relatively large compared to that of v 2 (t) (i.e., cos u e sin
u e ). Furthermore, v 1 (t) is proportional to m(t), so it is the demodulated (product detector) output.
The product voltage v 3 (t) is
v 3 (t) = 1 2 11 2 A 0A c 2 2 m 2 (t) sin 2u e
The voltage v 3 (t) is filtered with an LPF that has a cutoff frequency near DC, so that this filter
acts as an integrator to produce the DC VCO control voltage
v 4 (t) = K sin 2u e
where K = 1 and m 2 (t) is the DC level of m 2 2 11 2 A 0A c 2 2 8m 2 1t29 8 9
(t). This DC control voltage
is sufficient to keep the VCO locked to f c with a small phase error u e .
The squaring loop, shown in Fig. 5–3b, is analyzed by evaluating the expression for
the signal out of each component block, as illustrated in the figure. Either the Costas PLL
or the squaring loop can be used to demodulate a DSB-SC signal, because, for each case,
the output is Cm(t), where C is a constant. Furthermore, either of these loops can be used to