AN31 Datasheet, PDF (2/8 Pages) Silicon Laboratories – INDUCTOR DESIGN FOR THE Si41XX SYNTHESIZER FAMILY

AN31
3.2. Using a Printed Trace Inductor
If the required value of L_EXT is less than 3 nH, it is
recommended that a PCB trace be used as shown in
Figure 2.
device pad
inductor trace
The constant of proportionality, X_MLP or X_TSSOP, is given
by Equations 4 and 5 for an MLP and a TSSOP,
respectively:
X_MLP
=
⎛
0.620⎜1
⎝
–
0.823 e ^{1--–--3-H--0--}⎟⎞
⎠
--ⁿ---^H----
mm
(Equation 4)
E
C
F
E
G
B
A
D
Figure 2. Printed Trace Inductor
Table 1 lists the dimensions to be used with a micro
leadframe package (MLP), and Table 2 lists the
dimensions to be used with a thin shrink small outline
package (TSSOP).
X_TSSOP
=
⎛
0.700⎜1
⎝
–
0.857 e ^{1--–--4-H--0--}⎟⎞
⎠
--ⁿ---^H----
mm
(Equation 5)
where
X_MLP = constant of proportionality for MLP
X_TSSOP= constant of proportionality for TSSOP
H = thickness of dielectric between inductor
trace and ground plane in µm
In each of these equations, H is the thickness of the
dielectric between the “top” layer metal and the layer
containing the ground plane measured in µm. Figure 3
illustrates the dimension H.
traces
E T1
Table 1. Dimensions to be used with MLP
dielectric
H
Dimension
A
B
C
D
E
F
G
Value (mm)
0.80
0.30
0.20
(calculated)
0.30
0.20
0.80
Table 2. Dimensions to be used with TSSOP
Dimension Value (mm)
A
1.50
B
0.30
C
0.35
D
(calculated)
E
0.30
F
0.35
G
0.95
The inductance of the shape shown in Figure 2 is
directly proportional to the D dimension.
ground
T2
Figure 3. Side View of Printed Circuit Board
It is recommended that the H dimension be greater than
100 µm to reduce the sensitivity of the printed trace
inductance to thickness variation in the PCB dielectric.
To accomplish this, it may be necessary to remove
copper from layer 2 and locate the ground plane on
layer 3. In any case, H is the distance from the bottom
of the inductor trace to the top of the ground plane. The
thickness of the ground plane, T2, and the trace on
layer 1, T1, do not have a material effect on the
calculations and should be ignored.
Once the constant of proportionality (X) has been
calculated using Equation 4 (MLP) or Equation 5
(TSSOP), it is necessary to calculate the length of the
inductor trace. This is accomplished using Equation 6.
D
=
L_{----E----X---T-}
X
(Equation 6)
where D = trace length shown in Figure 2 in mm
L_EXT = calculated value of external inductance
required
X = constant of proportionality for MLP (X_MLP)
or TSSOP (X_TSSOP)
With this calculation complete, the trace can be
implemented as shown in Figure 2.
2
Rev. 1.3