AN31: Inductor Design For the Si41XX Synthesizer Family

AN31
I NDUCTOR D E S I G N
F O R THE
Si41 X X S YNTHESIZER F AM ILY
1. Introduction
3.1. Using a Discrete “Chip” Inductor
Silicon Laboratories’ family of frequency synthesizers
integrates VCOs, loop filters, reference and VCO
dividers, and phase detectors in standard CMOS
technology. Depending on the synthesizer being used,
the frequency of operation may require an external
inductance to establish the desired center frequency of
operation. This may be implemented with either a
printed circuit board (PCB) trace or a discrete “chip”
inductor. This application note provides guidelines for
designing these external inductors to ensure maximum
manufacturing margin for frequency tuning.
If the required value for LEXT is greater than 3 nH, it is
recommended that a discrete “chip” inductor be used.
This inductor should be placed as close as possible to
the device pins as shown in Figure 1.
printed trace
discrete
inductor
2. Determining LEXT
J
inductor device pad
The center frequency for many of Silicon Laboratories’
frequency synthesizers is established using an external
inductor. The value for this inductor is determined by
Equations 1 and 2:
1
f CEN = --------------------------------------------------------------2 C
NOM  L PKG + L EXT 
(Equation 1)
from which
1
- – L PKG
L EXT = -----------------------------------------2
 2f CEN  CNOM
(Equation 2)
where fCEN = desired center frequency of synthesizer
CNOM = nominal tank capacitance from
synthesizer data sheet
LPKG = package inductance from synthesizer
data sheet
LEXT = external inductance required
3. Implementing LEXT
Figure 1. Placement of Discrete
“Chip” Inductor
While close placement will minimize the inductance of
the traces connecting the discrete inductor to the
synthesizer, these traces, nonetheless, contribute to the
total overall inductance.
The total external inductance includes contributions
from both the discrete inductor and the connecting
traces as indicated in Equation 3:
L EXT = L NOM + X  J + 0.3 
where
(Equation 3)
LEXT = external inductance
LNOM = nominal value of discrete “chip”
inductor
X = constant of proportionality for MLP
(XMLP) or TSSOP (XTSSOP) (nH/mm)
J = dimension shown in Figure 1 (mm)
Once the required value of external inductance is
determined given the desired center frequency, a choice
must be made regarding the implementation of the
inductor. The two possible implementations are a
discrete “chip” inductor or a printed circuit board trace.
Rev. 1.3 1/15
synthesizer device pad
Note that the term “J + 0.3” is the effective D dimension
used in the next section. Also, the determination of X is
described in the next section.
The discrete inductor should be selected such that the
Q of the inductor is greater than 40, and the tolerance of
the inductance is ±10% or better.
Copyright © 2015 by Silicon Laboratories
AN31
AN31
3.2. Using a Printed Trace Inductor
If the required value of LEXT is less than 3 nH, it is
recommended that a PCB trace be used as shown in
Figure 2.
device pad
The constant of proportionality, XMLP or XTSSOP, is given
by Equations 4 and 5 for an MLP and a TSSOP,
respectively:
–H
----------

130 nH
X MLP = 0.620  1 – 0.823e  ---------
 mm
inductor trace
–H
E
F
C
E
----------

140 nH
X TSSOP = 0.700  1 – 0.857e  ---------
 mm
G
where
(Equation 5)
XMLP = constant of proportionality for MLP
XTSSOP= constant of proportionality for TSSOP
B
A
H = thickness of dielectric between inductor
trace and ground plane in µm
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).
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.
E
Dimension
Value (mm)
A
0.80
B
0.30
C
0.20
D
(calculated)
E
0.30
F
0.20
G
0.80
T1
traces
H
dielectric
Table 1. Dimensions to be used with MLP
ground
T2
Figure 3. Side View of Printed Circuit Board
Table 2. Dimensions to be used with TSSOP
It is recommended that the H dimension be greater than
100 m 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.
Dimension
Value (mm)
A
1.50
B
0.30
C
0.35
D
(calculated)
E
0.30
F
0.35
LEXT = calculated value of external inductance
required
G
0.95
X
L EXT
D = ------------X
where D
The inductance of the shape shown in Figure 2 is
directly proportional to the D dimension.
2
(Equation 4)
(Equation 6)
= trace length shown in Figure 2 in mm
= constant of proportionality for MLP (XMLP)
or TSSOP (XTSSOP)
With this calculation complete, the trace can be
implemented as shown in Figure 2.
Rev. 1.3
AN31
4. Checking the Value of LEXT
Once the desired inductor has been implemented, and
the PCB has been fabricated, the value of LEXT should
be verified. This can be done by following the steps
listed below:
1. Measure the minimum operating frequency of the
VCO in open-loop mode. This is accomplished by
performing a sequence of register writes as
described below.

For the IF synthesizer:
A. 0x000062 (hexadecimal)—power IF
synthesizer
and reference amplifier.
B. 0x00024F—test register.
C. 0x000F2D—test register.
D. 0x010010—set the test bit in the main
configuration register.
E. 0x07FF1D—set the VCO to its minimum
frequency.

For the RF1 synthesizer:
A. 0x000052 (hexadecimal)—power RF
synthesizer
and reference amplifier.
B. 0x010003—dummy write to select RF1
synthesizer.
C. 0x00024F—test register.
D. 0x000F2D—test register.
E. 0x010010—set the test bit in the main
configuration register.
F. 0x07FF0D—set the VCO to its minimum 
frequency.

For the RF2 synthesizer:
A. 0x000052 (hexadecimal)—power IF
synthesizer
and reference amplifier.
B. 0x010004—dummy write to select RF2
synthesizer.
C. 0x00024F—test register.
D. 0x000F2D—test register.
E. 0x010010—set the test bit in the main
configuration register.
F. 0x07FF0D—set the VCO to its minimum
frequency.

After programming the VCO to its minimum openloop frequency, measure the value of fMIN. Note that
this sequence of register writes leaves the device in
a test mode. All the registers described in the data
sheet should be re-written with normal values for
proper closed-loop operation.
2. Measure the maximum operating frequency of the
VCO in open-loop mode. This is accomplished by
performing a sequence of register writes as
described below.

For the IF synthesizer:
A. 0x000062 (hexadecimal)—power IF
synthesizer
and reference amplifier.
B. 0x00024F—test register.
C. 0x000F2D—test register.
D. 0x010010—set the test bit in the main
configuration register.
E. 0x00001D—set the VCO to its maximum
frequency.

For the RF1 synthesizer:
A. 0x000052 (hexadecimal)—power RF
synthesizer
and reference amplifier.
B. 0x010003—dummy write to select RF1
synthesizer.
C. 0x00024F—test register.
D. 0x000F2D—test register.
E. 0x010010—set the test bit in the main
configuration register.
F. 0x00000D—set the VCO to its maximum
frequency.

For the RF2 synthesizer:
A. 0x000052 (hexadecimal)—power IF
synthesizer
and reference amplifier.
B. 0x010004—dummy write to select RF2
synthesizer.
C. 0x00024F—test register.
D. 0x000F2D—test register.
E. 0x010010—set the test bit in the main
configuration register.
F. 0x00000D—set the VCO to its maximum
frequency.
After programming the VCO to its maximum openloop frequency, measure the value of fMAX. Note that
this sequence of register writes leaves the device in
a test mode. All the registers described in the data
sheet should be re-written with normal values for
proper closed-loop operation.
3. Calculate the measured center frequency for the
synthesizer using Equation 7.
f MIN + f MAX
f MEAS = -----------------------------2
(Equation 7)

where fMEAS = measured center frequency
Rev. 1.3
3
AN31
fMIN = measure minimum frequency of operation
fMAX = measured maximum frequency of operation
4. Calculate the measured external inductance, LMEAS,
using Equation 8.
1
- – L PKG
L MEAS = ---------------------------------------------2
 2f MEAS  CNOM
(Equation 8)
where LMEAS = measured external conductance
fMEAS = measured center frequency
CNOM = nominal tank capacitance from
synthesizer data sheet
LPKG = package inductance from synthesizer 
data sheet
Since the value is less than 3 nH, a printed trace
implementation will be used. The constant of
proportionality is calculated from Equation 4:
– 210
X MLP
5. Refining the Implementation of
Lext
If the inductor is implemented with a discrete chip
inductor, change the nominal value of this inductor
using Equation 9.
(Equation 9)
0.80
D = --------------- = 1.54 mm
0.519
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 m. The
first step is to calculate the required external inductance
value, LEXT, from Equation 2:
where LNEW = nominal external inductance for next
implementation
LOLD = nominal external inductance from
current implementation
LMEAS = measured external inductance from
current implementation
EXT
If the inductor is implemented with a printed trace,
change the D dimension of the trace using Equation 10.
(Equation 10)
where DNEW = dimension shown in Figure 2 for next
implementation in mm
DOLD = dimension shown in Figure 2 from 
current implementation in mm
LCALC = calculated value of external inductance
from current implementation in nH
LMEAS = measured external inductance from
current implementation in nH
X
= constant of proportionality for MLP
(XMLP) or TSSOP (XTSSOP) in nH/mm
1
–9
- –  1.6  10  = 11.28 n
= ---------------------------------------------------------------------6 2
– 12
 2550  10   6.5  10 
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:
L EXT  nH  – L NOM  nH 
J = ------------------------------------------------------------- – 0.3 mm
X MLP  nH/mm 
11.28 – 10.0
= -------------------------------- mm – 0.3 mm = 2.17 mm
0.519
Note that the inductor must have a Q greater than 40 at
550 MHz, and the tolerance must be ±10% or better.
After the inductor has been adjusted, check the new
value of LEXT as described in the previous section.
4
-------------

130
= 0.620  1 – 0.823e
 = 0.519 nH/mm


Finally, from Equation 6:
If the measured center frequency (fMEAS) is more than
2% away from the desired center frequency (fCEN), it is
suggested that the external inductor be adjusted to
provide maximum manufacturing margin.
L CALC – L MEAS
D NEW = D OLD + ---------------------------------------X
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 m.
The first step is to calculate the required external
inductance value, LEXT, from Equation 2:
1
–9
- –  1.5  10  = 0.80 nH
L EXT = --------------------------------------------------------------------9 2
– 12
 21.6  10   4.3  10 

L NEW = 2L OLD – L MEAS
6. Example 1
Rev. 1.3
AN31
8. Verifying Margin in Design
code. This value should be less than 0x780
(hexadecimal) if the unit has adequate tuning
margin.
Important: Please note that this procedure is only intended
for initial verification of the design of the board and
external VCO tuning inductor.
RF2 synthesizer:
It is possible to determine the frequency tuning margin
on a design implementation. This is accomplished by
reading back from the synthesizer register values which
indicate the tuning range of the VCOs using the
following procedure:
2. Write 0x0000DE (hexadecimal) to enable a read of
the RF tuning code.
IF synthesizer:
1. Program the IF synthesizer to its highest frequency
in the application.
2. Write 0x0001DE (hexadecimal) to enable a read of
the IF tuning code.
3. Read 18 bits from the serial interface. (See “Serial
Read Timing.")
4. The 18-bit value read from the interface is the tuning
code. This value should be greater than 0x40
(hexadecimal) if the unit has adequate tuning
margin.
5. Program the IF synthesizer to its lowest frequency in
the application.
6. Write 0x0001DE (hexadecimal) to enable a read of
the IF tuning code.
7. Read 18 bits from the serial interface. (See “Serial
Read Timing.")
8. The 18-bit value read from the interface is the tuning
code. This value should be less than 0x780
(hexadecimal) if the unit has adequate tuning
margin.
RF1 synthesizer:
1. Program the RF1 synthesizer to be active and at its
highest frequency in the application.
2. Write 0x0000DE (hexadecimal) to enable a read of
the RF tuning code.
1. Program the RF2 synthesizer to be active and at its
highest frequency in the application.
3. Read 18 bits from the serial interface. (See “Serial
Read Timing.")
4. The 18-bit value read from the interface is the tuning
code. This value should be greater than 0x40
(hexadecimal) if the unit has adequate tuning
margin.
5. Program the RF2 synthesizer to be active and at its
lowest frequency in the application.
6. Write 0x0000DE (hexadecimal) to enable a read of
the RF tuning code.
7. Read 18 bits from the serial interface. (See “Serial
Read Timing.")
8. The 18-bit value read from the interface is the tuning
code. This value should be less than 0x780
(hexadecimal) if the unit has adequate tuning
margin.
8.1. Serial Read Timing
In addition to the functions described in the data sheet,
the AUXOUT pin can be used to read the contents of
some synthesizer registers. By writing the values of
0x0001DE and 0x0000DE as described above, the
serial interface is configured to read the tuning codes.
During the readback, the function of the AUXOUT pin is
to provide the serial data output from the device. Writing
to any of the registers described in the data sheet will
cause the function of AUXOUT to revert to its previously
programmed function. This is illustrated in Figure 4
below. Refer to Table 3 for timing values.
3. Read 18 bits from the serial interface. (See “Serial
Read Timing.")
4. The 18-bit value read from the interface is the tuning
code. This value should be greater than 0x40
(hexadecimal) if the unit has adequate tuning
margin.
5. Program the RF1 synthesizer to be active and at its
lowest frequency in the application.
6. Write 0x0000DE (hexadecimal) to enable a read of
the RF tuning code.
7. Read 18 bits from the serial interface. (See “Serial
Read Timing.")
8. The 18-bit value read from the interface is the tuning
Rev. 1.3
5
AN31
80%
50%
20%
t RE H
SCLK
t RE H
tRE S U
SENB
SDA TA
D17
D16
A1
A UXOUT
programmed f unc tion
A0
tEA
tCA
OD17
OD16
programmed
f unc tion
OD0
Figure 4. Read Timing Diagram
Table 3. Serial Read Timing Values
Parameter
Symbol
Minimum
Maximum
Units
Read Operation SCLK to SEN Hold Time
tREH
16
—
ns
Read Operation SEN to SCLK Setup Time
tRESU
16
—
ns
SCLK to AUXOUT
tCA
—
16
ns
SEN to AUXOUT
tEA
—
16
ns
9. Summary
Silicon Laboratories’ frequency synthesizers have been designed to provide robust operation over extreme
conditions. This application note provides the designer with information to maximize the operating margins of both
the synthesizer and the system in which it is to be used.
6
Rev. 1.3
AN31
NOTES:
Rev. 1.3
7
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