SP8861 Mitel Networks, SP8861 Datasheet - Page 10

• Manufacturer Part Number: SP8861
• Description: 13GHz Low Power Single-Chip Frequency Synthesiser
• Manufacturer: Mitel Networks

10
SP8861
LOOP CALCULATIONS
loop with a loop filter of the form shown in Fig. 9.
in Fig. 9) is often added to reduce noise from the amplifier. In
addition, any feedthrough capacitor or local decoupling at the
VCO will be added to the value of C
components in fact form a third order loop and, if the values
are chosen correctly, the additional filtering provided can
considerably reduce the level of reference frequency sidebands
and noise without adversely affecting the loop settling time.
below.
Second Order Loop
time constants
where
K
K
N is the division ratio from VCO to reference frequency
v
z
a conventional voltage source and has a gain factor specified
in A/radian. Since the equations deal with a filter where R
is feeding the virtual earth point of an operational amplifier
from a voltage source, R
similar to the circuit shown in Fig. 10 – where a current source
phase detector is connected directly to the virtual earth point
of the operational amplifier.
calculated by assuming a value for R
in V/radian which would produce the set current.
over a range of 2
gain is given by:
For R
of 50 A, the phase detector gain is therefore:
This value can now be inserted in equation 1 to obtain a value
for C
u
0
n
FROM PHASE
Many frequency synthesiser designs use a second order
In practice, an additional RC time constant (shown dashed
The calculations of values for both types of loop are shown
For this filter, two equations are required to determine the
The SP8861 phase detector is a current source rather than
The equivalent voltage gain of the phase detector can be
The digital phase detector used in the SP8861 is linear
DETECTOR
is the phase detector gain factor in V/radian
is the VCO gain factor = 2
is the natural loop frequency = 500Hz
is the damping factor = 0·7071
1
1
and equation 2 used to determine a value for R
Fig. 9 Standard form of second order loop filter
= 1k and assuming a value of phase detector current
K
u
=
Phase detector current setting
t
1
p
(= C
radians and therefore the phase detector
R1
1
K
R
u
1
t
t
= 0·00796V/radian
1
) and
=
1
2
sets the input current to the filter –
=
=
50 A
C1
K
v
2
2
2
v
p
p
u
p
n
t
2
K
z
n
N
2
310MHz/V
R2
0
(= C
310
1
1
3
R
and calculating a gain
2
2
); the equations are:
R3
. These additional
A/radian
C2
TO VCO
2
…(1)
…(2)
.
1
Example
parameters:
Frequency to be synthesised
Reference frequency
Division ration N
From equation (1),
From equation (2),
Now, since
and, since
Third Order Loop
shows the circuit redrawn to use an RC time constant after the
amplifier, allowing any feedthrough capacitance on the VCO
line to be included in the loop calculations. Where the modified
form in Fig. 12 is used, it is advantageous to connect a small
capacitor C
reduce sidebands caused by the amplifier being forced into
non-linear operation by the phase comparator pulses
constants
for Fig. 11
and for Fig. 12
The equations are:
Calculate values for a second order loop with the following
The third order loop is normally as shown in Fig. 11. Fig. 12
Three equations are required to determine the time
Fig. 10 Modified form of second order loop filter
t
t
X
1
DETECTOR
t
2
,
of typically 100pF (shown dashed) across R
1
PHASE
t
= C
= C
2
, and
1
1
R
R
t
t
t
t
t
t
t
t
t
2
1
2
3
1
2
3
1
2
3
1
t
= C
= R
= C
=
=
=
= C
= C
= C
3
, where
2tan F
v
K
v
C
R
1
2
2
t
t
t
1
1
2
u
n
C
R
t
n
1
2
2
R
R
1
2
R
R
R
K
( C
t
1
2
2
1
N
1
2
1
2
0
3
1
2
3
2
=100kHz
=
= 8000
= 6·334 s
= 450 s
=
=
=
=
C1
= 6·33nF
1
= 71k
(2p3500)
1 C
230·7071
800MHz
6·334310
100kHz
6·33310
11
11
0·079632p310
2p3500
v
0
4·5310
1
n
R2
2
v
v
cos F
)
10
= 800MHz
n
n
2
2
1
t
t
3
2
3
2
2
24
29
2
0
26
38310
1
2
6
3
…(3)
…(4)
…(5)
2
to