AN31 SILABS [Silicon Laboratories], AN31 Datasheet - Page 4

• Manufacturer Part Number: AN31
• Description: INDUCTOR DESIGN FOR THE Si41XX SYNTHESIZER FAMILY
• Manufacturer: SILABS [Silicon Laboratories]

AN31
4. Calculate the measured external inductance, L
5. Refining the Implementation of
If the measured center frequency (f
2% away from the desired center frequency (f
suggested that the external inductor be adjusted to
provide maximum manufacturing margin.
If the inductor is implemented with a discrete chip
inductor, change the nominal value of this inductor
using Equation 9.
where L
If the inductor is implemented with a printed trace,
change the D dimension of the trace using Equation 10.
where D
After the inductor has been adjusted, check the new
value of L
4
using Equation 8.
where L
D
L
L
MEAS
NEW
L
L
D
L
L
X
ext
OLD
MEAS
CALC
MEAS
OLD
NEW
NEW
L
f
f
EXT
f
C
L
NEW
MIN
MAX
MEAS
=
MEAS
PKG
=
NOM
D
---------------------------------------------- - L
(
= measure minimum frequency of operation
as described in the previous section.
= measured maximum frequency of operation
= nominal external inductance for next
= nominal external inductance from
= measured external inductance from
= dimension shown in Figure 2 for next
= dimension shown in Figure 2 from
= calculated value of external inductance
= measured external inductance from
= constant of proportionality for MLP
2πf
OLD
=
= package inductance from synthesizer
= measured center frequency
= nominal tank capacitance from
implementation
current implementation
current implementation
= measured external conductance
implementation in mm
current implementation in mm
from current implementation in nH
current implementation in nH
(X
data sheet
2L
MEAS
synthesizer data sheet
+
MLP
OLD
L
----------------------------------------
1
CALC
) or TSSOP (X
) C
2
–
L
NOM
MEAS
–
X
L
MEAS
–
PKG
(Equation 9)
MEAS
TSSOP
(Equation 10)
(Equation 8)
) is more than
) in nH/mm
CEN
MEAS
), it is
Rev. 1.3
,
6. Example 1
Assume that the application requires the center
frequency of the RF1 synthesizer on the Si4133-BM to
be 1.6 GHz. The thickness of the dielectric is 210 µm.
The first step is to calculate the required external
inductance value, L
Since the value is less than 3 nH, a printed trace
implementation
proportionality is calculated from Equation 4:
Finally, from Equation 6:
This is the calculated value in Table 1 for Figure 2,
showing the appropriate printed trace inductor for this
application.
7. Example 2
Assume that the application requires the center
frequency of the IF synthesizer on the Si4133-BM to be
550 MHz. The thickness of the dielectric is 210 µm. The
first step is to calculate the required external inductance
value, L
Since the value is greater than 3 nH, a discrete “chip”
inductor is recommended for the implementation. An
inductor with a nominal value of 10.0 nH must be placed
according to Figure 1 with the J dimension calculated by
rearranging terms in Equation 3:
Note that the inductor must have a Q greater than 40 at
550 MHz, and the tolerance must be ±10% or better.
L
EXT
EXT
=
X
=
MLP
---------------------------------------------------------------------- -
(
EXT
--------------------------------------------------------------------- -
(
2π550 10
=
2π1.6 10
J
11.28 10.0
------------------------------- - mm 0.3 mm
, from Equation 2:
=
=
0.620 1 0.823e
0.519
⋅
L
------------------------------------------------------------ - 0.3 mm
⋅
EXT
–
D
will
6
9
X
⎛
⎜
⎝
1
)
EXT
)
(
1
=
2
MLP
2
nH
(
(
–
6.5 10
-------------- -
0.519
4.3 10
0.80
, from Equation 2:
) L
be
(
nH/mm
–
⋅
⋅
–
NOM
=
used.
–
–
12
12
–
------------ -
130
1.54 mm
210
)
(
)
)
nH
–
–
⎞
⎟
⎠
(
(
1.6 10
1.5 10
=
)
–
The
=
0.519 nH/mm
⋅
⋅
2.17 mm
–
–
9
9
constant
)
)
=
=
11.28 n
0.80 nH
of