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SP8853AHC Datasheet(PDF) 10 Page - Mitel Networks Corporation

Part # SP8853AHC
Description  1쨌3GHz Professional Synthesiser
Download  14 Pages
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Manufacturer  MITEL [Mitel Networks Corporation]
Direct Link  http://www.mitel.com
Logo MITEL - Mitel Networks Corporation

SP8853AHC Datasheet(HTML) 10 Page - Mitel Networks Corporation

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10
SP8853A/B
Fig. 9 Standard form of second order loop filter
Fig. 10 Modified form of second order loop filter
LOOP CALCULATIONS
Many frequency synthesiser designs use a second order
loop with a loop filter of the form shown in Fig. 9.
In practice, an additional RC time constant (shown dashed
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
C2. These additional
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.
The calculations of values for both types of loop are shown
below.
Second Order Loop
For this filter, two equations are required to determine the
time constants
t
1 (= C1R1) and t2 (= C1R2); the equations are:
…(1)
…(2)
KuK0
vn2N
t1 =
2
z
vn
t2 =
where
Ku is the phase detector gain factor in V/radian
K0 is the VCO gain factor = 2p310MHz/V
N is the division ratio from VCO to reference frequency
vn is the natural loop frequency = 500Hz
z
is the damping factor = 0·7071
The SP8853 phase detector is a current source rather than
a conventional voltage source and has a gain factor specified
in
µA/radian. Since the equations deal with a filter where R
1
is feeding the virtual earth point of an operational amplifier
from a voltage source,
R1 sets the input current to the filter –
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.
The equivalent voltage gain of the phase detector can be
calculated by assuming a value for
R1 and calculating a gain
in V/radian which would produce the set current.
The digital phase detector used in the SP8853 is linear
over a range of 2
p radians and therefore the phase detector
gain is given by:
Phase detector current setting
2
p
For
R1 = 1kΩ and assuming a value of phase detector current
of 50
µA, the phase detector gain is therefore:
µA/radian
+
R1
C1
R2
R3
C2
FROM PHASE
DETECTOR
TO VCO
+
C1
R2
PHASE
DETECTOR
Ku =
50
µA
2
p
Ku =
3
103
This value can now be inserted in equation 1 to obtain a value
for
C1 and equation 2 used to determine a value for R2.
= 0·00796V/radian
Example
Calculate values for a second order loop with the following
parameters:
Frequency to be synthesised
= 800MHz
Reference frequency
=100kHz
= 8000
Division ration
N
=
From equation (1),
t
1 =
800MHz
100kHz
From equation (2),
t
2 =
Now, since
t
1 = C1R1 ,
C1 =
230·7071
2p3500
0·079632p3106
(2p3500)2383103
t
1 = 6·334µs
t
2 = 450µs
∴C
1 = 6·33nF
6·33431026
103
and, since
t
2 = C1R2 ,
R2 =
∴R
2 = 71k
4·531024
6·3331029
Third Order Loop
The third order loop is normally as shown in Fig. 11. Fig. 12
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
CX of typically 100pF (shown dashed) across R2 to
reduce sidebands caused by the amplifier being forced into
non-linear operation by the phase comparator pulses
Three equations are required to determine the time
constants t1, t2, and t3, where
for Fig. 11
and for Fig. 12
The equations are:
t
1 = C1R1
t
2 = R2 (C11C2)
t
3 = C2R2
t
1 = C1R1
t
2 = C1R2
t
3 = C2R3
t
2 =
1
vn2t3
2
…(4)
2
tan F0 1
t
3 =
…(5)
vn
…(3)
t
1 =
KuK0
vn2N
11
vn
2 t
2
2
11
vn
2 t
3
2
1
2
1
cos F0


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