Datasheet

LTC6945
18
6945f
APPLICATIONS INFORMATION
INTRODUCTION
A PLL is a complex feedback system that may conceptually
be considered a frequency multiplier. The system multiplies
the frequency input at REF
±
and outputs a higher frequency
at RF
±
. The PFD, charge pump, N divider, and external VCO
and loop filter form a feedback loop to accurately control
the output frequency (see Figure 15). The R and O dividers
are used to set the output frequency resolution.
Using the above equations, the output frequency resolution
f
STEP
produced by a unit change in N is given by Equation 5:
f
STEP
=
f
REF
R•O
(5)
LOOP FILTER DESIGN
A stable PLL system requires care in selecting the external
loop filter values. The Linear Technology PLLWizard ap-
plication, available from www.linear.com, aids in design
and simulation of the complete system.
The loop design should use the following algorithm:
1. Determine the output frequency, f
RF
, and frequency
step size, f
STEP
, based on application constraints. Using
Equations 2, 3, 4 and 5, change f
REF
, N, R and O until
the application frequency constraints are met. Use the
minimum R value that still satisfies the constraints.
2. Select the loop bandwidth BW constrained by f
PFD
. A
stable loop requires that BW is less than f
PFD
by at least
a factor of 10.
3. Select loop filter component R
Z
and charge pump cur-
rent I
CP
based on BW and the VCO gain factor K
VCO
.
BW (in Hz) is approximated by the following equation:
BW ≅
I
CP
•R
Z
•K
VCO
2•π •N
or :
R
Z
=
2•π •BW•N
I
CP
•K
VCO
(6)
where K
VCO
is in Hz/V, I
CP
is in Amps, and R
Z
is in Ohms.
K
VCO
is the VCO’s frequency tuning sensitivity, and
may be determined from the VCO specifications. Use
I
CP
= 11.2mA to lower in-band noise unless component
values force a lower setting.
Figure 15. PLL Loop Diagram
R_DIV
N_DIV
÷R
÷N
÷O
f
PFD
LTC6945
REF
±
(f
REF
)
(f
VCO
)
K
PFD
K
VCO
RF
±
(f
RF
)
CP
R
Z
C
I
C
P
LOOP FILTER
LF(s)
6945 F15
VCO
±
I
CP
O_DIV
OUTPUT FREQUENCY
When the loop is locked, the frequency f
VCO
(in Hz)
produced at the output of the VCO is determined by the
reference frequency f
REF
, and the R and N divider values,
given by Equation 2:
f
VCO
=
f
REF
•N
R
(2)
Here, the PFD frequency f
PFD
produced is given by the
following equation:
f
PFD
=
f
REF
R
(3)
and f
VCO
may be alternatively expressed as:
f
VCO
= f
PFD
• N
The output frequency f
RF
produced at the output of the O
divider is given by Equation 4:
f
RF
=
f
VCO
O
(4)