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Bandpass Signaling Principles and Circuits Chap. 4
A(t) represents the envelope that is fading, and m(t) is the modulation (e.g., audio) signal. It
follows that the limiter output is proportional to
v 1 (t) = V L cos[v c t + u(t)]
(4–84)
and the output of the differentiator becomes
v 2 (t) =-V L cv c + du(t)
dt
d sin[v c t + u(t)]
(4–85)
The output of the envelope detector is the magnitude of the complex envelope for v 2 (t):
Because du>dt in practice, this becomes
w c
Using Eq. (4–83), we obtain
v out (t) = ` - V L cv c + du(t) d `
dt
v out (t) = V L cv c + du(t) d
dt
v out (t) = V L v c + V L K f m(t)
(4–86)
which indicates that the output consists of a DC voltage V L v c , plus the ac voltage
V L K f m(t), which is proportional to the modulation on the FM signal. Of course, a capacitor
could be placed in series with the output so that only the ac voltage would be passed to
the load.
The differentiation operation can be obtained by any circuit that acts like a frequencyto-amplitude
converter. For example, a single-tuned resonant circuit can be used as illustrated
in Fig. 4–16, where the magnitude transfer function is |H(f)| = K 1 f + K 2 over the linear
(useful) portion of the characteristic. A balanced FM detector, which is also called a balanced
discriminator, is shown in Fig. 4–17. Two tuned circuits are used to balance out the DC when
the input has a carrier frequency of f c and to provide an extended linear frequency-to-voltage
conversion characteristic.
Balanced discriminators can also be built that function because of the phase-shift
properties of a double-tuned RF transformer circuit with primary and secondary windings
[Stark, Tuteur, and Anderson, 1988]. In practice, discriminator circuits have been replaced by
integrated circuits that operate on the quadrature principle.
The quadrature detector is described as follows: A quadrature signal is first obtained
from the FM signal; then, through the use of a product detector, the quadrature signal is
multiplied with the FM signal to produce the demodulated signal v out (t). The quadrature signal
can be produced by passing the FM signal through a capacitor (large) reactance that is
connected in series with a parallel resonant circuit tuned to f c . The quadrature signal voltage
appears across the parallel resonant circuit. The series capacitance provides a 90° phase
shift, and the resonant circuit provides an additional phase shift that is proportional to the