RF2513
nected to the charge pump output through an internal
4kΩ resistor. The loop filter is then connected in paral-
lel to this point at pin 23 (LOOP FLT). This limits the
loop filter topology to a second order filter usually con-
sisting of a shunt capacitor and a shunt series RC. A
passive filter is most common, as it is a low cost and
low noise design. An additional pole could be used for
reducing the reference spurs, however there is not a
way to add the series resistor. This should not be a
reason for concern however.
RESNTR+
L
RESNTR-
L
LOOP
FLT
4 k
Ω
The schematic of the loop filter is as follows.
Charge Pump
VCO
Loop Filter
C1
VCC
To tune the VCO the designer only needs to calculate
the value of the inductors connected to pins 18 and 20
(RESNTR- and RESNTR+). The inductor value is
determined by the following equation.
R2
C2
ö2
ø
1
1 1
--- --
æ
è
----------------
L =
2 π f
C 2
In this equation, f is the desired operating frequency
and L is the value of the inductor required. The value C
is the amount of capacitance presented by the varac-
tor, capacitor and parasitics. The factor of one half is
due to the inductors being in each leg.
The transfer function is
s τ2 + 1
------------------------------------------
s τ2 (s τ1 + 1)
F(s) = R2
The setup of the VCO can be summarized as follows.
First, open the loop. Next, get the VCO to run on the
desired frequency by selecting the proper inductor and
capacitor values. The capacitor value will need to
include the varactor and circuit parasitics. After the
VCO is running at the desired frequency, then set the
VCO sensitivity.
where the time constants are defined as
C1 C2
------------------
C1 + C2
τ2 = R2 C2 and τ1 = R2
11
The frequency at which unity gain occurs is given by
The sensitivity is determined by connecting the control
voltage input point to ground and noting the frequency.
Then connect the same point to the supply and again
note the frequency. The difference between these two
frequencies divided by the supply voltage is the VCO
sensitivity expressed in Hz/V. Increasing the inductor
value while decreasing the capacitor value will
increase the sensitivity. Decreasing the inductor value
while increasing the capacitor value will lower the sen-
sitivity.
1
------------------
ωLBW
=
τ1 τ2
This is also the loop bandwidth.
If the phase margin (PM) and the loop bandwidth
(ωLBW) are known, it is possible to calculate the time
constants. These are found using the following equa-
tions.
When increasing or decreasing component values,
make sure that the center frequency remains constant.
Finally, close the loop.
sec(PM) – tan(PM)
1
-------------------------------------------------- --------------------------
and τ2 =
τ1
=
ω2
τ1
ωLBW
LBW
With these known, it is then possible to determine the
values of the filter components.
External to the part, the designer needs to implement a
loop filter to complete the PLL. The loop filter converts
the output of the charge pump into a voltage that is
used to control the VCO. Internally, the VCO is con-
Rev B8 010509
11-29
RFMD [ RF MICRO DEVICES ]
