LMX1501 National Semiconductor, LMX1501 Datasheet - Page 16

• Manufacturer Part Number: LMX1501
• Description: PLLatinumTM 1.1 GHz Frequency Synthesizer for RF Personal Communications
• Manufacturer: National Semiconductor

Application Information
Therefore if we specify the loop bandwidth
phase margin
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
From the time constants T1 and T2 and the loop band-
width
equations 9 to 11
K
K (mA)
N
RF
f
ref
VCO
opt
(kHz)
(MHz V)
(MHz)
T2
C1
p
c
C1
e
e
the values for C1 R2 and C2 are obtained in
e
e
T1
T2
(T1
c 2
T1
T2
p
tan
C2
a
Equations 1 through 6 allow us to calcu-
K
T1
(T1
K
1
Voltage Controlled Oscillator (VCO)
Tuning Voltage constant The fre-
quency vs voltage tuning ratio
Phase detector charge pump gain
constant The ratio of the current out-
put to the input phase differential
Main divider ratio Equal to RF
Radio Frequency output of the VCO at
which the loop filter is optimized
Frequency of the phase detector in-
puts Usually equivalent to the RF
channel spacing
T3)
c 2
e
e
T2
a
K
(T1
p
2
C1
sec
R2
VCO
e
2
N
a
K
T3)
VCO
a
e
N
T1 T3
p
p
T3)
2
T2
C2
T2
T1
b
1
p
(1
T1
1
1
tan
b
a
a
a
1
(
(
p
c 2
(Continued)
(1
p
p
1
a
T1
T2)
T1)
a
2
2
2
(T1
) (1
c 2
p
tan
and the
opt
a
a
T2
T3)
(10)
(11)
2
f
)
(7)
(8)
(9)
ref
c 2
(T1
2
a
T3
a
16
T1 T3
2
T3)
)
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
Defining the additional time constant as
Then in terms of the attenuation of the reference spurs add-
ed by the low pass pole we have
We then use the calculated value for loop bandwidth
equation 11 to determine the loop filter component values
in equations 15 – 17
the frequency jump lock time will increase
2
b
1
ATTEN
e
T3
20 log (2 f
e
T3
c
is slightly less than
10
e
ATTEN 20
(2
R3 C3
ref
f
ref
R3 C3)
)
b
2
1
2
a
p
1
therefore
(12)
(13)
(14)
(15)
(16)
(17)
c
in