LMX2301TM datasheet(12/14 Pages) NSC

12 / 14 page

Application Information (Continued)

Therefore if we specify the loop bandwidth 0p and the

phase margin wp Equations 1 through 6 allow us to calcu-

late the two time constants T1 and T2 as shown in equa-

tions 7 and 8 A common rule of thumb is to begin your

design with a 45 phase margin

T1 e

secwp b tanwp

(7)

T2 e

0p2 # T1

(8)

From the time constants T1 and T2 and the loop band-

width 0p the values for C1 R2 and C2 are obtained in

equations 9 to 11

C1 e

# KVCO

0p2 # N

01a(

0p # T2)2

1 a (0p # T1)2

(9)

C2 e C1

#T2T1b1J

(10)

R2 e

(11)

KVCO (MHzV)

Voltage Controlled Oscillator (VCO)

Tuning Voltage constant

The fre-

quency vs voltage tuning ratio

Kw (mA)

Phase detectorcharge pump gain

constant The ratio of the current out-

put to the input phase differential

Main divider ratio Equal to RFopt fref

RFopt (MHz)

Radio Frequency output of the VCO at

which the loop filter is optimized

fref (kHz)

Frequency of the phase detector in-

puts Usually equivalent to the RF

channel spacing

In choosing the loop filter components a trade off must be

made between lock time noise stability and reference

spurs The greater the loop bandwidth the faster the lock

time will be but a large loop bandwidth could result in higher

reference spurs Wider loop bandwidths generally improve

close in phase noise but may increase integrated phase

noise depending on the reference input VCO and division

ratios used The reference spurs can be reduced by reduc-

ing the loop bandwidth or by adding more low pass filter

stages but the lock time will increase and stability will de-

crease as a result

THIRD ORDER FILTER

A low pass filter section may be needed for some applica-

tions that require additional rejection of the reference side-

bands or spurs This configuration is given in

Figure 4 In

order to compensate for the added low pass section the

component values are recalculated using the new open

loop unity gain frequency The degradation of phase margin

caused by the added low pass is then mitigated by slightly

increasing C1 and C2 while slightly decreasing R2

The added attenuation from the low pass filter is

ATTEN e 20 log (2qfref # R3 # C3)2 a 1

(12)

Defining the additional time constant as

T3 e R3

# C3

(13)

Then in terms of the attenuation of the reference spurs add-

ed by the low pass pole we have

T3 e

010ATTEN20b1

(2q

# fref)2

(14)

We then use the calculated value for loop bandwidth 0c in

equation 11 to determine the loop filter component values

in equations 15 – 17 0c is slightly less than 0p therefore

the frequency jump lock time will increase

T2 e

0c2 # (T1 a T3)

(15)

0c e

tanw

# (T1 a T3)

(T1 a T3)2 a T1

# T3

01a(T1aT3)

2 a T1 # T3

tanw

# (T1 a T3) 2

(

(16)

C1 e

# KVCO

0c2 # N

(1 a 0c2 # T22)

(1 a 0c2 # T12)(1 a 0c2 # T32)

(

(17)

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