SA604A_15 Datasheet, PDF (16/31 Pages) NXP Semiconductors – High-performance low-power FM IF system

NXP Semiconductors
SA604A
High-performance low-power FM IF system
13.5 Frequency discriminator design equations
9RXW
Fig 13. Frequency discriminator
DDD
V_O
=
-------^C----^S--------
C_P + C_S

-------------------¹---------------------
1
+
--^-----¹--
Q₁S
+


_{--S---1}
2

V_I
N
(1)
where:
₁
=
---------------¹-----------------
LC_P + C_S
and
Q₁
=
RC_P + C_S₁
From Equation 1, the phase shift between nodes 1 and 2, or the phase across C_S will be:
---^----¹---

= <V_O – <V_IN
= t_g^–1 
-------^Q----¹---^---------
1
–


-^-_---¹-_
2
(2)
Figure
5 is the plot of

as a function of


-^-_---¹-_
. It is notable that at

=
₁ , the phase shift
is
_--
2
and the response is close to a straight line with a slope of
^-----^--
=
-²---^Q----¹-
₁
.
The signal V_O
would
have a phase shift of
_--
2
–
2_----Q_----1-
₁

with
respect to the
V_IN.
If V_IN = A sin(t) =>
V_O
=
A sin
t
+
_--
2
–
2_----Q_----1-
₁


(3)
Multiplying the two signals in the mixer, and low pass filtering yields:
V_IN  V_O
=
A² sin t  sin
t
+
_--
2
–
2_----Q_----1-
₁


(4)
After low pass filtering =>
V_O
=
1_--A2 _cos
2
_--
2
–
2_----Q_----1-
₁


=
1_--A2 _sin
2
2_----Q_----1-
₁


(5)
SA604A
Product data sheet
All information provided in this document is subject to legal disclaimers.
Rev. 4.1 — 30 March 2015
© NXP Semiconductors N.V. 2015. All rights reserved.
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