563489578934

Sec. 4–13 Detector Circuits 279
Frequency-toamplitude
converter
Envelope detector
R
C
v in (t)
L
(a) Circuit Diagram of a Slope Detector
0
(b) Magnitude of Filter Transfer Function
f c
C 0 R 0
v out (t)
Frequency band for linear
frequency-to-amplitude conversion
|H(f)|
f
Figure 4–16
Slope detection using a single-tuned circuit for frequency-to-amplitude conversion.
instantaneous frequency deviation (from f c ) of the FM signal. From Eqs. (4–84) and (4–83),
the FM signal is
v in (t) = V L cos[v c t + u(t)]
(4–87)
and the quadrature signal is
v quad (t) = K 1 V L sincv c t + u(t) + K du(t)
2 d
dt
(4–88)
where K 1 and K 2 are constants that depend on component values used for the series capacitor
and in the parallel resonant circuit. These two signals, Eqs. (4–87) and (4–88), are multiplied
together by a product detector (e.g., see Fig. 4–14) to produce the output signal
v out (t) = 1 2 K 1V 2 L sincK du(t)
2 d
dt
(4–89)