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AN31
I N D U C T O R DESIGN
1. Introduction
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.
FOR THE
Si41 X X S Y N T H E S I Z E R F A M I L Y
3.1. Using a Discrete "Chip" Inductor
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 J
2. Determining LEXT
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 )
inductor device pad
synthesizer device pad
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 )
(Equation 1)
from which
1 L EXT = ------------------------------------------ - L PKG 2 ( 2f 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
(Equation 3)
where
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)
3. Implementing LEXT
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.
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.
Rev. 1.3 4/06
Copyright (c) 2006 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 inductor trace E C B A D F E G
The constant of proportionality, XMLP or XTSSOP, is given by Equations 4 and 5 for an MLP and a TSSOP, respectively:
--------- 130 nH X MLP = 0.620 1 - 0.823e -------- mm --------- 140 nH X TSSOP = 0.700 1 - 0.857e -------- mm -H -H
(Equation 4)
(Equation 5)
where
XMLP = constant of proportionality for MLP XTSSOP= constant of proportionality for TSSOP H = thickness of dielectric between inductor trace and ground plane in m
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 m. Figure 3 illustrates the dimension H. E T1 H T2
traces dielectric ground
Table 1. Dimensions to be used with MLP Dimension
A B C D E F G
Value (mm)
0.80 0.30 0.20 (calculated) 0.30 0.20 0.80
Figure 3. Side View of Printed Circuit Board
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.
L EXT D = -----------X
Table 2. Dimensions to be used with TSSOP Dimension
A B C D E F G
Value (mm)
1.50 0.30 0.35 (calculated) 0.30 0.35 0.95
(Equation 6)
where D
= trace length shown in Figure 2 in mm
LEXT = calculated value of external inductance required X = constant of proportionality for MLP (XMLP) or TSSOP (XTSSOP)
The inductance of the shape shown in Figure 2 is directly proportional to the D dimension.
2
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 3
Rev. 1.3
AN31
fMIN = measure minimum frequency of operation fMAX = measured maximum frequency of operation
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 m. The first step is to calculate the required external inductance value, LEXT, from Equation 2:
1 -9 L EXT = --------------------------------------------------------------------- - ( 1.5 10 ) = 0.80 nH 92 - 12 ( 21.6 10 ) ( 4.3 10 )
4. Calculate the measured external inductance, LMEAS, using Equation 8.
1 L MEAS = ---------------------------------------------- - L PKG 2 ( 2f 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:
------------ 130 = 0.620 1 - 0.823e = 0.519 nH/mm - 210
5. Refining the Implementation of Lext
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. If the inductor is implemented with a discrete chip inductor, change the nominal value of this inductor using Equation 9.
L NEW = 2L OLD - L MEAS
X MLP
Finally, from Equation 6:
0.80D = -------------- = 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:
EXT
(Equation 9)
where LNEW = nominal external inductance for next implementation LOLD = nominal external inductance from current implementation LMEAS = measured external inductance from current implementation If the inductor is implemented with a printed trace, change the D dimension of the trace using Equation 10.
L CALC - L MEAS D NEW = D OLD + ---------------------------------------X
1 -9 = ---------------------------------------------------------------------- - ( 1.6 10 ) = 11.28 n 62 - 12 ( 2550 10 ) ( 6.5 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 After the inductor has been adjusted, check the new value of LEXT as described in the previous section.
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.
4
Rev. 1.3
AN31
8. Verifying Margin in Design
Important: Please note that this procedure is only intended for initial verification of the design of the board and external VCO tuning inductor.
code. This value should be less than 0x780 (hexadecimal) if the unit has adequate tuning margin. RF2 synthesizer: 1. Program the RF2 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. 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.
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: 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. 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
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.
Rev. 1.3
5
AN31
80% 50% 20% SCLK t RE H SENB t RE H tRE S U
SDA TA tCA A UXOUT programmed f unc tion OD17 OD16 OD0
D17
D16
A1
A0 tEA programmed f unc tion
Figure 4. Read Timing Diagram Table 3. Serial Read Timing Values
Parameter Read Operation SCLK to SEN Hold Time Read Operation SEN to SCLK Setup Time SCLK to AUXOUT SEN to AUXOUT Symbol tREH tRESU tCA tEA Minimum 16 16 -- -- Maximum -- -- 16 16 Units ns ns ns 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
AN31
CONTACT INFORMATION
Silicon Laboratories Inc. 4635 Boston Lane Austin, TX 78735 Tel: 1+(512) 416-8500 Fax: 1+(512) 416-9669 Toll Free: 1+(877) 444-3032 Email: RFinfo@silabs.com Internet: www.silabs.com
The information in this document is believed to be accurate in all respects at the time of publication but is subject to change without notice. Silicon Laboratories assumes no responsibility for errors and omissions, and disclaims responsibility for any consequences resulting from the use of information included herein. Additionally, Silicon Laboratories assumes no responsibility for the functioning of undescribed features or parameters. Silicon Laboratories reserves the right to make changes without further notice. Silicon Laboratories makes no warranty, representation or guarantee regarding the suitability of its products for any particular purpose, nor does Silicon Laboratories assume any liability arising out of the application or use of any product or circuit, and specifically disclaims any and all liability, including without limitation consequential or incidental damages. Silicon Laboratories products are not designed, intended, or authorized for use in applications intended to support or sustain life, or for any other application in which the failure of the Silicon Laboratories product could create a situation where personal injury or death may occur. Should Buyer purchase or use Silicon Laboratories products for any such unintended or unauthorized application, Buyer shall indemnify and hold Silicon Laboratories harmless against all claims and damages. Silicon Laboratories and Silicon Labs are trademarks of Silicon Laboratories Inc. Other products or brandnames mentioned herein are trademarks or registered trademarks of their respective holders.
8
Rev. 1.3

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