FUNCTIONAL DESCRIPTION (continued)

VIII.2 - How to choose the value of the time

constant ?

The time response of the PLL is given by its char-

acteristic equation which is :

Where :

(LD[5:0] = value of the LINE DURATION register,

A = value of the 1st time constant, AF or AS and

B = value of the 2

As you can see, the solution depend only on the

LINE DURATION and the TIME CONSTANTS

given by the I

If

ble

and its response is like this presented on

Figure 11.

t

PLL

Frequency

t

Input

Frequency

Figure 11 : Time Response of the PLL/Charac-

teristic Equation Solutions

(with Real Solutions)

If

this presented on Figure 12.

In this case the PLL is stable if

τ > 0.7 (damping

coefficient).

t

PLL

Frequency

t

Input

Frequency

Figure 12 : Time Response of the PLL/Charac-

teristic Equation Solutions (with

Complex Solutions)

The Table 2 gives some good values for A and B

constants for different values of the LINE DURA-

TION.

Summary

For a good working of the PLL :

- A and B time constants must be chosen among

values for which the PLL is stable,

- B must be equal or greater than A and the differ-

ence between them must be less than 3,

- The greater (A, B) are, the faster the capture is.

An optimal choice for the most of applications might

be :

- For locking condition : AS = 0 and BS = 1,

- For capture process : AS = 2 and BS = 4.

But for each application the time constants can be

calculated by solving the characteristic equation

and choosing the best response.

Table 2 : Valid Time Constants Examples

B \ A

0

1

234

5

6

0

YYYY

YYYY

YYYY

YYYN

YNNN

NNNN

NNNN

1

YYYY

YYYY

YYYY

YYYN

YNNN

NNNN

NNNN

2

NYYY

YYYY

YYYY

YYYN

YNNN

NNNN

NNNN

3

NNNY

YYYY

YYYY

YYYN

YNNN

NNNN

NNNN

4

NNNN

NYYY

(1)

YYYY

YYYN

YNNN

NNNN

NNNN

5

NNNN

NNNY

YYYY

YYYN

YNNN

NNNN

NNNN

6

NNNN

NNNN

NYYY

YYYN

YNNN

NNNN

NNNN

7

NNNN

NNNN

NNNY

YYYN

YNNN

NNNN

NNNN

Note : 1. Case of A[2:0] = 1 (001) and B[2:0] = 4 (100) :

LD

16

32

48

63

Valid Time Constants

NY

Y

Y

Value of LINE DURATION Register (@ 3FF0) :

LD = 16 : LD[5:0] = 010000

LD = 32 : LD[5:0] = 100000

LD = 48 : LD[5:0] = 110000

LD = 63 : LD[5:0] = 111111

Table meaning :

N = No possible capture

Y = PLL can lock

STV9420 - STV9421

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