LMX3161VBH datasheet(13/14 Pages) NSC

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Loop Filter Design Consideration

Loop Gain Equations

A linear control system model of the phase feedback for a

PLL in the locked state is shown in

Figure 2. The open loop

gain is the product of the phase comparator gain (K φ ), the

VCO gain (K

vco/s), and the loop filter gain Z(s) divided by the

gain of the feedback counter modulus (N). The passive loop

filter configuration used is displayed in

Figure 3, while the

complex impedance of the filter is given in

Equation (2).

PASSIVE LOOP FILTER

Open loop gain = H(s) G(s) =

θi/θe = Kφ Z(s)K

VCO/Ns

(1)

(2)

The time constants which determine the pole and zero fre-

quencies of the filter transfer function can be defined as

(3)

and

T2 = R2

• C2

(4)

The 3rd order PLL Open Loop Gain can be calculated in

terms of frequency,

ω, the filter time constants T1 and T2,

and the design constants Kφ,Kvco, and N.

(5)

From

Equations (3), (4) we can see that the phase term will

be dependent on the single pole and zero such that the

phase margin is determined in

Equation (6).

φ (ω) = tan −1 (ω • T 2) − tan−1 (ω • T 1) + 180˚ (6)

DS012815-8

FIGURE 1. Conventional PLL Architecture

DS012815-9

FIGURE 2. PLL Linear Model

DS012815-10

FIGURE 3. Passive Loop Filter

LMX3161VBH Datasheet(PDF) 13 Page - National Semiconductor (TI)

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