B. P. Lathi, Zhi Ding - Modern Digital and Analog Communication Systems-Oxford University Press (2009)

154 AMPLITUDE MODULATIONS AND DEMODULATIONS
of an AM signal is
A+ m(t) ::::: 0 for all t (4.9a)
If m(t) ::::: 0 for all t, then A = 0 already satisfies condition (4.9a). In this case there is no need
to add any carrier because the envelope of the DSB-SC signal m(t) cos (i)ct is m(t) and such a
DSB-SC signal can be detected by envelope detection. In the following discussion we assume
that m(t) f. 0 for all t; that is, m(t) can be negative over some range of t.
Message Signals m(t) with Zero Offset: Let ±mp be the maximum and the minimum
values of m(t), respectively (see Fig. 4.8). This means that m(t) ::::: -mp. Hence, the condition
of envelope detection (4.9a) is equivalent to
(4.9b)
Thus, the minimum carrier amplitude required for the viability of envelope detection is mp.
This is quite clear from Fig. 4.8. We define the modulation index µ as
mp
µ = Ā
(4. 10a)
For envelope detection to be distortionless, the condition is A ::::: mp. Hence, it follows that
(4.10b)
is the required condition for the distortionless demodulation of AM by an envelope detector.
When A < mp , Eq. ( 4.1 0a) shows that µ > 1 ( overmodulation). In this case, the option of
envelope detection is no longer viable. We then need to use synchronous demodulation. Note
that synchronous demodulation can be used for any value of µ, since the demodulator will
recover signal A + m(t). Only an additional de block is needed to remove the DC voltage A.
The envelope detector, which is considerably simpler and less expensive than the synchronous
detector, can be used only for µ :S 1.
Message Signals m(t) with Nonzero Offset: On rare occasions, the message signal
m(t) will have a nonzero offset such that its maximum mmax and its minimum m min are not
symmetric, that is,
In this case, it can be recognized that any offset to the envelope does not change the shape of
the envelope detector output. In fact, one should note that constant offset does not carry any
fresh information.
In this case, envelope detection would still remain distortionless if
(4. 1 l a)
with a modified modulation index definition of
mmax - lnmin
µ=-------
2A + lnmax + lnmin
(4. llb)
Example 4.4
Sketch (/JAM (t) for modulation indices of µ = 0.5 and µ = I , when m(t) = b cos (JJ 111
t. This
case is referred to as tone modulation because the modulating signal is a pure sinusoid ( or
tone).