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SA604A
(Rev.:2015)

High-performance low-power FM IF system

NXP Semiconductors. 

NXP Semiconductors

SA604A

High-performance low-power FM IF system

13.5 Frequency discriminator design equations

9RXW

Fig 13. Frequency discriminator

DDD

VO

=

-------C----S--------

CP + CS



-------------------1---------------------

1

+

-------1--

Q1S

+





--S---1

2



VI

N

(1)

where:

1

=

---------------1-----------------

LCP + CS

and

Q1

=

RCP + CS1

From Equation 1, the phase shift between nodes 1 and 2, or the phase across CS will be:

-------1---



= <VO – <VIN

= tg–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 VO

would

have a phase shift of

--

2

–

2----Q----1-

1



with

respect to the

VIN.

If VIN = A sin(t) =>

VO

=

A sin

t

+

--

2

–

2----Q----1-

1





(3)

Multiplying the two signals in the mixer, and low pass filtering yields:

VIN  VO

=

A2 sin t  sin

t

+

--

2

–

2----Q----1-

1





(4)

After low pass filtering =>

VO

=

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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