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10 of 14

Fig. 14 Bode Plot for PLL Transfer Function

The 3dB bandwidth of the transfer function is approximately

9.2 Transfer Function Peaking

There are two causes of peaking in the PLL transfer function

given by Equation 1.

The first is the quadratic

which has

and

This response is critically damped for Q = 0.5.

Thus, to avoid peaking:

or

Therefore,

reduce the high frequency content on the loop filter.

The second is the zero-pole combination:

This causes lift in the transfer function given by

To keep peaking to less than 0.05dB,

9.3 Selection of Loop Filter Components

Based on the above analysis, select the loop filter

1. Calculate

where

N is the divider modulus.

2

2

0

FREQUENCY

w

3dB

w

BW

12

w

BW

w

P2

------------

–

w

⁄

()

2

12

w

BW

w

P2

------------

–

----------------------------------

+

----------------------------------------------------------------------

w

BW

0.78

------------

≈

=

s

2

C

L

R

LF

---------

1

++

w

O

1

C

--------------------

=

QR

LF

C

LF2

L

-------------

=

R

LF

C

LF2

L

-------------

1

2

---

<

1

R

-----------------------

L

R

LF

---------

4

>

sC

1

+

sC

L

R

LF

-----------

–



 1

+

-----------------------------------------------------------

s

w

Z

-------

1

+

s

w

P1

----------

1

+

--------------------

=

20 LOG

w

P1

w

Z

----------

20 LOG

1

1

w

Z

w

BW

------------

–

---------------------

=

2N

Ι

ƒ

L =