LMX1501AM datasheet(15/22 Pages) NSC

15 / 22 page

Application Information

LOOP FILTER DESIGN

A block diagram of the basic phase locked loop is shown

TLW12340 – 30

FIGURE 1 Basic Charge Pump Phase Locked Loop

An example of a passive loop filter configuration including

the transfer function of the loop filter is shown in

Figure 2

TLW12340 – 31

Z(s) e

s (C2

R2) a 1

s2 (C1

C2 R2) a sC1 a sC2

FIGURE 2 2nd Order Passive Filter

Define the time constants which determine the pole and

zero frequencies of the filter transfer function by letting

T2 e R2

(1a)

and

T1 e R2

C1 a C2

(1b)

The PLL linear model control circuit is shown along with the

open loop transfer function in

Figure 3 Using the phase

detector and VCO gain constants Kw and KVCO and the

loop filter transfer function Z(s)

the open loop Bode plot

can be calculated The loop bandwidth is shown on the

Bode plot (0p) as the point of unity gain The phase margin

is shown to be the difference between the phase at the unity

gain point and b180

TLW12340 – 33

Open Loop Gain e ii ie e H(s) G(s)

Kw Z(s) KVCO Ns

Closed Loop Gain e io ii e G(s) 1 a H(s) G(s)

TLW12340 – 32

FIGURE 3 Open Loop Transfer Function

Thus we can calculate the 3rd order PLL Open Loop Gain in

terms of frequency

G(s)

H(s)

ls e j 0 e

KVCO (1 a j0 T2)

02C1

N(1 a j0 T1)

(2)

From equation 2 we can see that the phase term will be

dependent on the single pole and zero such that

(0) e tanb1 (0

T2) b tanb1 (0 T1) a 180

(3)

By setting

1 a (0

T2)2

1 a (0

T1)2

(4)

we find the frequency point corresponding to the phase in-

flection point in terms of the filter time constants T1 and T2

This relationship is given in equation 5

0p e 1

0T2 T1

(5)

For the loop to be stable the unity gain point must occur

before the phase reaches b180 degrees We therefore

want the phase margin to be at a maximum when the magni-

tude of the open loop gain equals 1 Equation 2 then gives

C1 e

KVCO T1

0p2 N T2

(1 a j0p T2)

(1 a j0p T1)

(6)

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