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LMX2305 Datasheet(PDF) 12 Page - National Semiconductor (TI)

[Old version datasheet] Texas Instruments acquired National semiconductor.
Part No. LMX2305
Description  PLLatinumTM 550 MHz Frequency Synthesizer for RF Personal Communications
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Maker  NSC [National Semiconductor (TI)]
Homepage  http://www.national.com
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LMX2305 Datasheet(HTML) 12 Page - National Semiconductor (TI)

 
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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
0p
(7)
T2 e
1
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
T1
T2
#
Kw
# KVCO
0p2 # N
01a(
0p # T2)2
1 a (0p # T1)2
(9)
C2 e C1
#
#T2T1b1J
(10)
R2 e
T2
C2
(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
N
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
1
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
b
1
(
(16)
C1 e
T1
T2
#
Kw
# KVCO
0c2 # N
#
(1 a 0c2 # T22)
(1 a 0c2 # T12)(1 a 0c2 # T32)
(
(17)
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