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Sec. 4–16 Transmitters and Receivers 291
or, equivalently,
v(t) = R(t) cos[v c t + u(t)]
(4–114)
and
v(t) = x(t) cos v c t - y(t) sin v c t
(4–115)
where the complex envelope
g(t) = R(t)e ju(t) = x(t) + jy(t)
(4–116)
is a function of the modulating signal m(t). The particular relationship that is chosen for g(t) in terms
of m(t) defines the type of modulation that is used, such as AM, SSB, or FM. (See Table 4–1.) A
generalized approach may be taken to obtain universal transmitter models that may be reduced to
those used for a particular type of modulation. We will also see that there are equivalent models that
correspond to different circuit configurations, yet they may be used to produce the same type of
modulated signal at their outputs. It is up to the designer to select an implementation method that
will maximize performance, yet minimize cost, based on the state of the art in circuit development.
There are two canonical forms for the generalized transmitter, as indicated by Eqs.
(4–114) and (4–115). Equation (4–114) describes an AM–PM type of circuit, as shown in
Fig. 4–27. The baseband signal-processing circuit generates R(t) and u (t) from m(t). The R
and u are functions of the modulating signal m(t), as given in Table 4–1 for the particular
type of modulation desired. The signal processing may be implemented by using either nonlinear
analog circuits or a digital computer that incorporates the R and u algorithms under
software program control. In the implementation using a digital computer, one ADC will be
needed at the input and two DACs will be needed at the output. The remainder of the
AM–PM canonical form requires RF circuits, as indicated in the figure.
Figure 4–28 illustrates the second canonical form for the generalized transmitter. This
uses in-phase and quadrature-phase (IQ) processing. Similarly, the formulas relating x(t) and
y(t) to m(t) are shown in Table 4–1, and the baseband signal processing may be implemented
by using either analog hardware or digital hardware with software. The remainder of the
canonical form uses RF circuits as indicated.
Basebands circuits
R(t)
RF circuits
v(t)=R(t) cos[v c t+¨(t)]
Modulated signal out
m(t)
Modulation
in
Baseband signalprocessing
(Type I)
circuit may
be nonlinear
¨ (t)
Carrier
oscillator f c
Phase
modulator
cos[v c t+¨(t)]
Figure 4–27
Generalized transmitter using the AM–PM generation technique.