AN535

6

MOTOROLA SEMICONDUCTOR APPLICATION INFORMATION

Figure 7. Phase-Locked Loop Circuit Parameters

Phase Detector

Programmable

Filter

VCM

( 42 )

N min +

fo min

fi

+

fo min

fstep

+ 2MHz

100KHz

+ 20

( 43 )

N max +

fo max

fstep

+ 3MHz

100KHz

+ 30

( 44 )

Kn +

1

20

to 1

30

A type 2 system is required to produce a phase coherent

output relative to the input (See Table 1). The root locus

contour is shown in Figure 5 and the system step response is

illustrated by Figure 6.

The operating range of the MC4024/4324 VCM must cover

2MHz to 3MHz. Selecting the VCM control capacitor

according to the rules contained on the data sheet yields

C = 100pF. The desired operating range is then centered

within the total range of the device. The input voltage versus

output frequency is shown in Figure 8.

Figure 8. MC4324 Input Voltage versus Output

Frequency (100pF Feedback Capacitor)

5.5

6.0

5.0

4.0

3.0

2.0

1.0

0

5.0

4.0

3.0

2.0

1.0

0

+125°C

-55°C

+25°C

-55°C

+25°C

+125°C

The transfer function of the VCM is given by:

( 45 )

Ko +

Kv

s

of the slope.

Kv +

4MHz

* 1.5MHz

5V

* 3.6V

2

p rad s V

( 46 )

Thus

Ko +

11.2 x106

s

rad s V

( 47 )

The s in the denominator converts the frequency

characteristics of the VCM to phase, i.e., phase is the integral

of frequency.

The gain constant for the MC4044/4344 phase detector is

Kp +

DFHigh

* UFLow

2(2

p)

+ 2.3V * 0.9V

4

p

+ 0.111V rad

( 48 )

Since a type 2 system is required (phase coherent output)

the loop transfer function must take the form of Equation 19.

function and relating it to Equation 19

G(s)H(s)

+

Kp Kv Kn Kf

s

+

K(s

) a)

s2

( 49 )

Kf +

s

) a

s

( 50 )

in order to provide all of the necessary poles and zeroes for the

required G(s) H(s). The circuit shown in Figure 9 yields the

desired results.

Figure 9. Active Filter Design

C

A

Freescale Semiconductor, Inc.

For More Information On This Product,

Go to: www.freescale.com