designfeature By A Fox, D Maxwell, and C O’Keeffe, Analog Devices
ADVANCES IN FRACTIONAL-N SYNTHESIS AND DIGITALTEMPERATURE-SENSOR ACCURACY IMPROVE FREQUENCY
STABILITY FOR REFERENCE-FREQUENCY IMPLEMENTATIONS
AT A REDUCED COST AND CURRENT CONSUMPTION.
Fractional-N synthesis
improves reference-frequency
implementations
LLs serve as programmable-frequency generators in a long list of RF applications, including cellular-phone base stations and handsets,
cable-TV tuners, wireless-LANs, and low-power radios. The reference frequency is a critical element in
these systems. It is multiplied up to the PLL RF output and is critical to the frequency accuracy, stability, and overall phase-noise performance of the loop.
Traditional frequency-reference implementations
include large, power-hungry OCXOs (oven-controlled crystal oscillators), which base stations favor
P
because of their excellent stability. Space- and power-conscious handset manufacturers use the heavily tested crystal/compensation-circuit combination
of TCXOs (temperature-compensated crystal oscillators).
The availability of new ranges of fractional-N synthesizers with system spurious levels approaching
those of integer-N PLLs offers an alternative for crystal and oscillator options (Table 1). Many fractional-N PLLs support resolution on the order of hundreds of hertz. (Integer-N technology supports the
3.50-PPM ERROR AT BOTH RECEIVER AND TRANSMITTER:
FILTER CUTOFF: 80⫹2⳯100 kHz
1-GHz SYSTEM, 20-kBPS DATA RATE, 400-kHz CHANNEL SEPARATION
1. BANDWIDTH OCCUPIED BY 20-kBPS DATA
WITH MODULATION INDEX OF 1
2. CHANNEL-SELECTION FILTER MUST TAKE ACCOUNT
OF THE Ⳳ5-PPM ERROR IN BOTH TRANSMITTER AND RECEIVER
SIDES; TOTAL BANDWIDTH⳱100 kHz
3. Ⳳ50-PPM ERROR IN BOTH TRANSMITTER AND RECEIVER
SIDES INCREASES REQUIRED CHANNEL-SELECTION-FILTER BANDWIDTH
TO 280 kHz, RESULTING IN A MAXIMUM 4-dB LOSS IN SNR
2.5-PPM ERROR AT BOTH RECEIVER AND TRANSMITTER:
FILTER CUTOFF: 80⫹2⳯10 kHz
1. NO FREQUENCY ERROR 80 kHz
915.2 MHz
⫹X-PPM
TRANSMITTER
ERROR
24-dB/
OCTAVE
ROLL-OFF
INTERFERENCE REJECTION ON 400 kHz (LOWER LIMIT OF ADJACENT
CHANNEL) BASED ON FOURTH-ORDER BANDPASS FILTER
1. NO ERROR (f3 dB⳱200 kHz Ⳳ40 kHz)⳱⫺46 dB
2. COMPENSATED (f3 dB⳱200 kHzⳲ50 kHz)⳱⫺38 dB
3. UNCOMPENSATED (f3 dB⳱200 kHzⳲ140 kHz)⳱⫺4 dB
200 kHz
10.7 MHz
200 kHz
DEMODULATOR
915.2 MHz
⫺10.7 MHz
⫹Y-PPM ERROR
(RECEIVER CRYSTAL)
⫹
_
ERROR BETWEEN RECEIVER/TRANSMITTER LOCAL OSCILLATOR VERSUS
NUMBER OF PREAMBLE BITS REQUIRED TO FIND THRESHOLD VOLTAGE
OF DETECTOR TO 10%
10.7 MHz
⫺200 MHz
⫹Y-PPM ERROR
(RECEIVER CRYSTAL)
0.1
50-PPM ERROR=50 PREAMBLE BITS
Figure 1
DETECTOR
OUTPUT
0.08
0.06
0.04
25-PPM ERROR=32 PREAMBLE BITS
0.02
5-PPM ERROR=17 PREAMBLE BITS
0
0 10 20 30 40 50 60 70 80
NUMBER OF RECEIVED PREAMBLE BITS
As the crystal reference generates larger frequency errors, receiver performance significantly degrades.
www.ednmag.com
June 13, 2002 | edn 81
designfeature Fractional-N synthesis
typical minimum of 25 kHz.) This programmable accuracy coupled with improving temperature-sensor technology
and the availability of low-cost, predictable crystals allows designers of costsensitive RF-links to consider indirectly
compensating for temperature effects.
SOURCES OF FREQUENCY ERROR
Temperature plays a major role in the
frequency stability of a crystal (see sidebar “Quartz crystals and crystal oscilla-
tors”). However, temperature is not the
only factor to consider when seeking a
stable crystal. Other significant sources
of frequency error include initial-crystalfrequency error, mismatching of load capacitance, and crystal aging.
Every quartz crystal has a significant
initial frequency error associated with it.
However, once the driving circuit makes
the crystal oscillate with parallel capacitors, the initial frequency error often appears much larger. This situation is due
to a mismatch between the crystal’s capacitance and the loading capacitors,
which causes a shift in the resonance frequency. Because these two errors are constant over temperature, they can be combined and compensated for using an
offset calibration at 25⬚C.
Over time, a crystal’s frequency tends
to change. This frequency error, or aging,
generally occurs due to crystal contamination, excessive drive level, or both. The
aging curve is logarithmic in nature, so
QUARTZ CRYSTALS AND CRYSTAL OSCILLATORS
perature beyond the intrinsic crystal stability.
TCXOs (temperaturecontrolled crystal oscillaPOSITIVE AT CUT
tors) typically consist of
a varactor diode in series with a crystal. A
thermistor network genTEMPERATURE
erates a correction voltage proportional to the
90⬚C
25⬚C
frequency error. This
correction voltage is
usually applied to a varactor diode, altering its
flawless synthetic cryscapacitance and resulttals to specific shapes
BT CUT
ing in a frequency shift
and sizes. Oscillator circuits using a quartz crys- Different frequencies and temperature characteristics exist for the AT, BT, and SC crystal approximately equal to and
opposite from the frequental vibrate at the crystal’s cuts.
cy error due to temperature
resonant frequency. The
(FFigure B). TCXO stability can apperature than the AT cut. A heat
resonant frequency depends on
more often used in low-frequenproach 0.1 ppm (at a cost). TCXsource is usually required to opthe thickness of the crystal slab;
cy crystals, whereas AT cuts are
Os are preferable to oven oscillaerate an SC-cut crystal at its opticommon in higher frequency
thinner slabs have a higher resomum elevated temperature, mak- tors in low-power applications
crystals. Because the AT curve is
nant frequency.
and when a warm-up period is
ing it a good candidate for
cubic, it offers good temperature
Exposing a quartz crystal to
not applicable.
OCXOs (oven-controlled crystal
stability over the industrial temheat expands it, changing the
An OCXO consists of an insuperature range (⫺40 to ⫹85⬚C); oscillators).
shape and the resonant frequenlated oven block that houses the
A stand-alone quartz crystal is
cy of the crystal (FFigure A). Differ- however, the AT-cut temperature
not an oscillator. External circuitry quartz crystal, oscillator circuitry,
characteristics depend strongly
ent frequencies and temperature
a temperature sensor, and heatmust drive the quartz crystal to
on the angle deviation from the
characteristics exist, depending
ing elements at a precise and
make it oscillate. Noncompensatideal AT cut. Another frequently
on the way that the crystal is
constant elevated temperature.
ed crystal oscillators employ no
used cut is the SC (stress-com“cut” from the natural crystal.
OCXOs allow the use of SC-cut
pensated) cut, which is more pre- correction or control to reduce
AT and BT are the most comthe frequency variation over tem- crystals, which offer superior
cise but deviates less over temmon crystal cuts. BT cuts are
characteristics but are impractical
EQUAL-AND-OPPOSITE
for ordinary TCXOs
CRYSTAL
COMPENSATING
Figure B
due to their steep freCHARACTERISTICS
CIRCUITRY
quency
drop
at cooler temperaIMPROVED FREQUENCY STABILITY
tures. OCXOs provide significantFREQUENCY
FREQUENCY
ly better temperature stability
than TCXOs, but the power consumption is much higher—typically, 1 to 2W at 25⬚C. They also
TEMPERATURE
TEMPERATURE
require a few minutes to warm
Performing frequency compensation in TCXOs improves frequency stability.
up.
CRYSTALQuartz crystals integrate
FREQUENCY
mechanical and electriERROR
cal characteristics described by the piezoelectric effect. This integration is the basis for
using quartz in crystal
manufacturing. Although natural crystals
are abundant, they are
SC CUT
likely to contain impurities. AlternativeFigure A
ly, you can grow
82 edn | June 13, 2002
NEGATIVE AT CUT
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designfeature Fractional-N synthesis
60
most of the frequency change occurs in
the initial time stages. Crystals are
C=ⳮ4
Figure 2
usually preaged at high temperatures
40
C=ⳮ2
to help alleviate this initial steep freC=0
quency change. Aging is generally speci20
fied as X ppm in the first year and Y
C=2
ppm/year after that.
CRYSTALC=4
The frequency alignment of the transFREQUENCY
0
ERROR ⳮ50
ⳮ25
0
25
50
75
100
C=6
mitter and receiver local oscillators is crit(PPM)
ical in designing a robust wireless-comC=8
ⳮ20
munication system. Large frequency
C=10
errors impact the receiver SNR, adjacentⳮ40
channel rejection, and required preamble
C=12
length. Often, to compensate for the subC=14
sequent reduced sensitivity, a designer
ⳮ60
must select higher output power on the
TEMPERATURE (⬚C)
transmitting side and increased receiver
sensitivity. Doing so, however, comes at a An uncompensated quartz crystal with various randomly chosen angles of cut cannot operate withcost of higher current consumption to in the desired limits of ⫾5 ppm.
maintain the required link budget.
The data bandwidth, the deviation more attenuation of unwanted large sigMany systems require high oscillator
from the receiver local oscillator of the nals in the next band.
accuracy but cannot afford to include an
frequency tone, and the error in the
The FSK (frequency-shift-keying) de- expensive TCXO. Digital compensation
transmitting/receiving crystal set the re- modulator has time to acquire its re- can minimize the frequency error of a
quired bandwidth of the IF or the base- quired threshold voltage during the pre- standard quartz crystal to provide a costband filters (depending on the receiver amble sequence. The frequency error effective option for these systems. To
architecture). For a low-data-rate system directly affects the length of time it takes compensate for the frequency error of a
with a low modulation index, the error in to acquire this threshold. Minimizing the crystal, you must first predict the error.
the crystal becomes significant. For each transmitting/receiving error reduces the Because AT cut crystals are the most
doubling of the filter bandwidth, you lose number of preamble bits that the system common, this discussion will concenas much as 3 dB of SNR. Reducing the requires, allowing for lower duty cycles trate on them, but the same ideas apply
modulation index can improve the SNR. on both the transmitting and the receiv- for any crystal. You can characterize the
Controlling the frequency accuracy of ing sides (Figure 1).
crystal-frequency error of an AT cut crysboth the transmitter and the receiver loReceiver performance degrades signif- tal over temperature (relative to the error
cal oscillators allows more efficient use of icantly as the crystal reference generates at 25⬚C) by the following third-order
available spectrum allocation. By re- larger frequency errors, and including a equation:
stricting the error, you can place hopping highly accurate oscillator to improve sta- Error (ppm)⫽
channels in closer proximity and, there- bility can be costly. Any system trade-off 106⫻[⫺8.585⫻10⫺8C(T⫺25)⫹
fore, use more channels. This higher must balance the desired frequency sta- (3.9⫻10⫺10⫺7.833⫻10⫺11C)(T⫺25)2⫹
channel density is particularly important bility and the associated cost. For low- (1.095⫻10⫺10⫺3.3⫻10⫺14C)(T⫺25)3],
in the congested, unlicensed ISM (in- power radio applications, a frequency er- where C is the angle of cut in minutes
dustrial, scientific, and medical) bands. ror of ⫾5 ppm allows the bandwidth of and T is the temperature in degrees
As well as reducing unwanted transmis- the channel-select filter to be narrow Celsius.
An uncompensated quartz crystal with
sion to the adjacent channel, frequency enough to achieve good receiver sensicompensation allows designers to reduce tivity and sufficient rejection of the busy various randomly chosen angles of cut
cannot operate within the desired limits
the IF-filter bandwidth, and thus achieve adjacent channels in the ISM bands.
of ⫾5 ppm (Figure 2). Knowing the angle of cut of the crystal allows you to preOSCILLATOR
CIRCUITRY
dict and compensate for the freFigure 3
quency error of the crystal. The
easy way to learn the angle of cut of the
CRYSTAL
crystal is to buy a crystal with a particuTEMPERATURE
lar angle of cut directly from the crystal
ADC
MICROCONTROLLER
DAC
SENSOR
manufacturer. Crystal manufacturers can
supply crystals guaranteed to stay within ⫾2 ppm of a known temperature
VARACTOR
characteristic.You can typically buy these
DIODE
crystals for less than $1. Alternatively, you
In a typical system, a sensor and ADC measure the temperature, and a DAC and varactor diode pull
can measure the crystal-frequency error
the oscillator back to its nominal frequency.
(relative to 25⬚C) at two further temper-
84 edn | June 13, 2002
www.ednmag.com
designfeature Fractional-N synthesis
RF TRANSMITTER
atures and predict the angle of cut of
PFD=6.4 MHzⳮ1-PPM ERROR
crystal based on these values. However,
PFD/
doing so adds to your test cost.
CHARGE
VCO
PUMP
Designs have used direct digital comOUTPUT=915.2 MHz
pensation to calculate the estimated freⳮ1-PPM CRYSTAL ERROR
CRYSTAL
⫹1-PPM COMPENSATION
quency error and then attempt to “pull”
the crystal frequency back to the nomiTEMPERATURE
nal frequency. A lower cost and simpler
N⫹(F/215)
SENSOR
alternative is now possible using indirect
frequency compensation. Indirect comSPI
pensation uses fractional-N technology
LOOK-UP
to correct for the estimated freTABLE
Figure 4
T
F
quency error in the PLL.
ⳮ40 10010...
In direct-digital compensation, a var84 01010...
MICROCONTROLLER
85 11011...
actor diode in the feedback network pulls
the crystal frequency back to its nominal frequency in a similar way to TCXOs. In indirect-digital-frequency compensation, a digital temperature sensor close to the crystal measThe key difference is that in direct-digi- ures the temperature.
tal-frequency compensation, the compensation resides in the digital domain. only in steps of tens of kilohertz, beIn indirect-digital-frequency compenIn a typical system, a temperature sensor cause you can move the output of an in- sation, a digital temperature sensor close
close to the crystal measures the crystal teger-N PLL only in multiples of the to the crystal measures the temperature
temperature (Figure 3). The analog out- comparison PFD (phase-frequency-de- (Figure 4). Based on the temperature, a
put from the sensor is conditioned and tector) frequency. Reducing the PFD to microcontroller predicts the frequency
scaled to match the input range of the 1 kHz to gain sufficient resolution to error and writes a corresponding value
ADC, converting it to the digital domain. compensate requires generating a large from its look-up table to the fractionalOnce the microcontroller reads the tem- N-divider value. Because noise is mul- N register to compensate for the freperature from the ADC, it uses a look-up tiplied up to the output by 20logN, us- quency error. The accuracy of indirecttable to find out what DAC output is nec- ing an integer-N PLL results in poor digital-frequency compensation is limessary to pull the oscillator back to its phase noise and long delays in moving ited by how closely the crystal follows the
nominal frequency. The accuracy of di- frequency due to the narrow loop band- estimated temperature-characteristic
rect-digital-frequency compensation is width required for the loop to lock.
curve and the accuracy of the temperaThe recent improvements in fraction- ture sensor. A crystal with a frequency
limited by how closely the crystal follows
the estimated temperature-characteristic al-N spurious performance offer an al- stability following a known temperaturecurve, the accuracy of the ADC and DAC, ternative to direct compensation. Tradi- characteristic curve within ⫾2 ppm in a
and the predictability of the capacitance tionally, fractional-N spurious levels have system with a ⫾1⬚C accurate temperaof the varactor diode. With a 12-bit-ac- restricted its use to a limited number of ture sensor, guarantees a compensated
curate ADC and DAC, this system typi- applications with limited flexibility in the frequency stability of ⫾3 ppm. You can
cally keeps the frequency error of a well- fractional divider. The small fractions keep the frequency error using indirect
behaved crystal at ⫾5 to ⫾10 ppm over now available on fractional-N synthesiz- compensation at less than ⫾5 ppm over
the industrial temperature range (⫺40 to ers allow moving the output of the VCO the industrial temperature range, which
in steps of as little as 0.1 ppm. It is there- is better than what you can achieve with
⫹85⬚C).
fore possible to use indirect-digital-fre- the direct method.
DIGITAL-CRYSTAL-FREQUENCY COMPENSATION quency compensation to accurately comOne of the key advantages of this apTraditionally, with integer-N technol- pensate for the frequency error of the proach is that once you assume a particogy, you can change the output of the crystal over temperature within registers ular error, the error correction is guaranVCO (voltage-controlled oscillator) of the PLL itself.
teed to be the same on all systems, because
TABLE 1—SUMMARY OF CRYSTAL AND OSCILLATOR OPTIONS
Stability (ppm over
Typical price (1000)
⫺10 to ⫹70°C)
⫺10 to ⫹70°C)
Type
(⫺
⫾5 to ⫾100
⫾50 ppm), 70 cents (⫾
⫾5 ppm)
Quartz crystal
20 cents (⫾
⫾10 to ⫾100
⫾50 ppm), $7 (⫾
⫾10 ppm)
Crystal oscillator
$2 (⫾
⫾10 to ⫾100
⫾20 ppm)
VCXO
$4 (⫾
⫾0.1 to ⫾5
⫾2.5 ppm), $40 (⫾
⫾0.5 ppm)
TCXO
$8 (⫾
⫾0.0001 to ⫾5
⫾0.3 ppm), $125 (⫾
⫾0.02 ppm)
OCXO
$80 (⫾
⫾5
⫾5 ppm)
Direct-digital-frequency
$3* (⫾
compensation
⫾3
⫾3 ppm)
Indirect-digital-frequency
$1 to $2* (⫾
compensation
*Additional cost of implementing compensation in system
86 edn | June 13, 2002
Comment
Small and inexpensive but unstable
Inexpensive and relatively small but unstable
Relatively small and suited to compensation but expensive
Very good stability but expensive
Excellent stability but large, power-hungry, and expensive
Lower cost option than TCXOs but requires
significant design
Good stability, inexpensive, and easy to implement
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designfeature Fractional-N synthesis
all compensation is performed in the dig40
ital domain. Compensating in the digital
domain avoids problems due to ana30
Figure 5
log layout and grounding, greatly simplifying the design and significantly re20
ducing oscillator current consumption.
VCO-OUTPUT
Using the indirect method saves costs beFREQUENCY
10
ERROR
cause it requires neither an ADC nor a
(PPM)
DAC. Many systems already have a tem0
ⳮ50
ⳮ30
ⳮ10
10
30
50
90
110
70
perature sensor, so including one incurs
no additional cost. The receiver synchroⳮ10
nizing to the accurate base-station clock
during data transmission delivers imⳮ20
proved accuracy in cellular communicaTEMPERATURE (⬚C)
UNCOMPENSATED SYSTEM
tions. The fractional-N resolution allows
COMPENSATED SYSTEM
dynamic correction for Doppler, aging,
and temperature effects previously per- In indirect digital-frequency compensation, the compensation happens indirectly within the fracformed directly with a DAC and a VCXO. tional-N PLL of the RF transmitter.
This indirect method alleviates the stress
that regular compensation can place on and a 19.2-MHz quartz crystal with an limit. Because the crystal had a cut of
the crystal of the VCXO, which can result angle of cut of C앒3. The output fre- C앒3, the uncompensated system perin excessive aging and worsening of in- quency of the VCO was measured from formed within the ⫾5-ppm limit from
band phase noise.
⫺40 to ⫹85⬚C in compensated and un- ⫺25 to ⫹80⬚C. Crystals with different
Figure 4 depicts an indirect-crystal- compensated systems (Figure 5). The cuts have larger frequency errors over this
frequency-compensation implementa- compensated system worked well with a temperature range. However, the temtion using an 8051 microcontroller, a maximum frequency error of ⫺1.52 perature-compensation algorithm comtemperature sensor, an RF transmitter, ppm, which is well within the ⫾5-ppm pensates for the larger frequency errors
88 edn | June 13, 2002
www.ednmag.com
designfeature Fractional-N synthesis
of these crystals. Larger errors start to occur in the compensated system at 85 to
105⬚C. You may be unable to achieve a
frequency stability of ⫾5 ppm in this
range, because the error in crystal frequency changes greatly with temperature
(1 to 2.5 ppm/⬚C), the crystal may not
follow the temperature-characteristic
curve to within ⫾2 ppm, and the temperature-sensor accuracy decreases at the
increased temperatures. Using a more accurate temperature sensor, such as the
ADT7301, can reduce the contribution of
the temperature-sensor errors.
Sigma-delta fractional-N synthesizers
offer advances in spurious performance,
giving you an alternative for generating
accurate local-oscillator frequencies in
low-cost systems. They improve phase
noise and offer a faster lock time than
current integer-N parts. They also allow
PLLs to output the resolution necessary
(0.1 ppm) to compensate for temperature effects in crystals.
Digitally performed indirect compensation offers the benefits of cost reduction, ease of implementation, and im-
90 edn | June 13, 2002
proved accuracy. Although the example
setup achieved frequency stability within ⫾5 ppm, improving temperature-sensor and crystal technology will eventually offer less costly and more accurate
options.왏
References
1. Analog Devices, “ADF7010 ISM
Band Transmitter Datasheet.”
2. Socki, Jim, “Quartz Crystal Oscillator Training Seminar,” Crystal Engineering, November 2000.
3. Bujanos, Norman, “Choosing the
Right Crystal for Your Oscillator,” Circuit
Cellar Ink, February 1998.
4. Analog Devices, “ADuC814 MicroConverter Datasheet.”
5. Analog Devices, “AD7301 Digital
Temperature Sensor Datasheet.”
6. Fry, Steven, Oscillator Handbook.
Acknowled gments
Special thanks to Philip Quinlan and the
rest of the RF team at Analog Devices for
their inputs. Also, thanks to the engineers
at Vectron International, MF Electronics,
and Fox Crystals for their contributions.
Authors’ bio graphies
Adrian Fox works at Analog Devices (Limerick, Ireland) as an applications engineer
supporting ISM-band and PLL-synthesizer products. He has a bachelor’s degree in
electronic engineering from the University
of Limerick. He enjoys opera music, walking his dog, and surfing.
Darragh Maxwell works at Analog Devices
(Limerick, Ireland) as an applications engineer supporting the firm’s MicroConverter products. He has a bachelor’s degree
in electronic engineering from the National University of Ireland (Dublin). He enjoys sports.
Claire O’Keeffe works as a marketing engineer for Analog Devices’ ADCs and
Thermal and System Monitoring Groups
(Limerick, Ireland). She has a bachelor of
science degree in applied physics and electronics from the National University of Ireland (Galway). She enjoys skiing, surfing
and skydiving.
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