reference frequency stability

www.ednmag.com June 13, 2002 | edn 81

ADVANCES IN FRACTIONAL-N SYNTHESIS AND DIGITAL-

TEMPERATURE-SENSOR ACCURACY IMPROVE FREQUENCY

STABILITY FOR REFERENCE-FREQUENCY IMPLEMENTATIONS

AT A REDUCED COST AND CURRENT CONSUMPTION.

PLLs serve as programmable-frequency gener-ators in a long list of RF applications, includ-ing cellular-phone base stations and handsets,cable-TV tuners, wireless-LANs, and low-power ra-dios. The reference frequency is a critical element inthese systems. It is multiplied up to the PLL RF out-put and is critical to the frequency accuracy, stabil-ity, and overall phase-noise performance of the loop.

Traditional frequency-reference implementationsinclude large, power-hungry OCXOs (oven-con-trolled crystal oscillators), which base stations favor

because of their excellent stability. Space- and pow-er-conscious handset manufacturers use the heavi-ly tested crystal/compensation-circuit combinationof TCXOs (temperature-compensated crystal oscil-lators).

The availability of new ranges of fractional-N syn-thesizers with system spurious levels approachingthose of integer-N PLLs offers an alternative for crys-tal and oscillator options (Table 1). Many fraction-al-N PLLs support resolution on the order of hun-dreds of hertz. (Integer-N technology supports the

Fractional-N synthesis improves reference-frequencyimplementations

_

915.2 MHz10.7 MHz

Y-PPM ERROR(RECEIVER CRYSTAL)

915.2 MHzX-PPM

TRANSMITTERERROR

10.7 MHz200 MHz

Y-PPM ERROR(RECEIVER CRYSTAL)

10.7 MHz 200 kHz

200 kHz

1. NO FREQUENCY ERROR 80 kHz

2.5-PPM ERROR AT BOTH RECEIVER AND TRANSMITTER:FILTER CUTOFF: 80210 kHz

3.50-PPM ERROR AT BOTH RECEIVER AND TRANSMITTER:FILTER CUTOFF: 802100 kHz

DEMODULATOR

ERROR BETWEEN RECEIVER/TRANSMITTER LOCAL OSCILLATOR VERSUSNUMBER OF PREAMBLE BITS REQUIRED TO FIND THRESHOLD VOLTAGEOF DETECTOR TO 10%

50-PPM ERROR=50 PREAMBLE BITS



NUMBER OF RECEIVED PREAMBLE BITS

DETECTOROUTPUT

0 10 20 30 40 50 60 70 80

0.1

0.08

0.06

0.04

0

0.02

24-dB/OCTAVE

ROLL-OFF

1-GHz SYSTEM, 20-kBPS DATA RATE, 400-kHz CHANNEL SEPARATION1. BANDWIDTH OCCUPIED BY 20-kBPS DATA WITH MODULATION INDEX OF 12. CHANNEL-SELECTION FILTER MUST TAKE ACCOUNT OF THE 5-PPM ERROR IN BOTH TRANSMITTER AND RECEIVER SIDES; TOTAL BANDWIDTH100 kHz3. 50-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

INTERFERENCE REJECTION ON 400 kHz (LOWER LIMIT OF ADJACENT CHANNEL) BASED ON FOURTH-ORDER BANDPASS FILTER1. NO ERROR (f3 dB200 kHz 40 kHz)46 dB2. COMPENSATED (f3 dB200 kHz50 kHz)38 dB3. UNCOMPENSATED (f3 dB200 kHz140 kHz)4 dB

As the crystal reference generates larger frequency errors, receiver performance significantly degrades.

F igure 1

designfeature By A Fox, D Maxwell, and C OKeeffe, Analog Devices

designfeature Fractional-N synthesis

82 edn | June 13, 2002 www.ednmag.com

typical minimum of 25 kHz.) This pro-grammable accuracy coupled with im-proving temperature-sensor technologyand the availability of low-cost, pre-dictable crystals allows designers of cost-sensitive RF-links to consider indirectlycompensating for temperature effects.

SOURCES OF FREQUENCY ERROR

Temperature plays a major role in thefrequency stability of a crystal (see side-bar Quartz crystals and crystal oscilla-

tors). However, temperature is not theonly factor to consider when seeking astable crystal. Other significant sourcesof frequency error include initial-crystal-frequency error, mismatching of load ca-pacitance, and crystal aging.

Every quartz crystal has a significantinitial frequency error associated with it.However, once the driving circuit makesthe crystal oscillate with parallel capaci-tors, the initial frequency error often ap-pears much larger. This situation is due

to a mismatch between the crystals ca-pacitance and the loading capacitors,which causes a shift in the resonance fre-quency. Because these two errors are con-stant over temperature, they can be com-bined and compensated for using anoffset calibration at 25C.

Over time, a crystals frequency tendsto change. This frequency error, or aging,generally occurs due to crystal contami-nation, excessive drive level, or both. Theaging curve is logarithmic in nature, so

Quartz crystals integratemechanical and electri-cal characteristics de-scribed by the piezo-electric effect. This inte-gration is the basis forusing quartz in crystalmanufacturing. Al-though natural crystalsare abundant, they arelikely to contain impuri-ties. Alternative-ly, you can growflawless synthetic crys-tals to specific shapesand sizes. Oscillator cir-cuits using a quartz crys-tal vibrate at the crystalsresonant frequency. Theresonant frequency depends onthe thickness of the crystal slab;thinner slabs have a higher reso-nant frequency.

Exposing a quartz crystal toheat expands it, changing theshape and the resonant frequen-cy of the crystal (FFiigguurree AA). Differ-ent frequencies and temperaturecharacteristics exist, dependingon the way that the crystal iscut from the natural crystal.

AT and BT are the most com-mon crystal cuts. BT cuts are

more often used in low-frequen-cy crystals, whereas AT cuts arecommon in higher frequencycrystals. Because the AT curve iscubic, it offers good temperaturestability over the industrial tem-perature range (40 to 85C);however, the AT-cut temperaturecharacteristics depend stronglyon the angle deviation from theideal AT cut. Another frequentlyused cut is the SC (stress-com-pensated) cut, which is more pre-cise but deviates less over tem-

perature than the AT cut. A heatsource is usually required to op-erate an SC-cut crystal at its opti-mum elevated temperature, mak-ing it a good candidate forOCXOs (oven-controlled crystaloscillators).

A stand-alone quartz crystal isnot an oscillator. External circuitrymust drive the quartz crystal tomake it oscillate. Noncompensat-ed crystal oscillators employ nocorrection or control to reducethe frequency variation over tem-

perature beyond the in-trinsic crystal stability.

TCXOs (temperature-controlled crystal oscilla-tors) typically consist ofa varactor diode in se-ries with a crystal. Athermistor network gen-erates a correction volt-age proportional to thefrequency error. Thiscorrection voltage isusually applied to a var-actor diode, altering itscapacitance and result-ing in a frequency shift

approximately equal to andopposite from the frequen-cy error due to temperature

(FFiigguurree BB). TCXO stability can ap-proach 0.1 ppm (at a cost). TCX-Os are preferable to oven oscilla-tors in low-power applicationsand when a warm-up period isnot applicable.

An OCXO consists of an insu-lated oven block that houses thequartz crystal, oscillator circuitry,a temperature sensor, and heat-ing elements at a precise andconstant elevated temperature.OCXOs allow the use of SC-cutcrystals, which offer superiorcharacteristics but are impractical

for ordinary TCXOsdue to their steep fre-

quency drop at cooler tempera-tures. OCXOs provide significant-ly better temperature stabilitythan TCXOs, but the power con-sumption is much highertypi-cally, 1 to 2W at 25C. They alsorequire a few minutes to warmup.

CRYSTAL-FREQUENCYERROR

TEMPERATURE

SC CUT

BT CUT

25C 90C

NEGATIVE AT CUT

POSITIVE AT CUT

Different frequencies and temperature characteristics exist for the AT, BT, and SC crystalcuts.

QUARTZ CRYSTALS AND CRYSTAL OSCILLATORS

FREQUENCY

TEMPERATURE

FREQUENCY

TEMPERATURE

CRYSTALCHARACTERISTICS

EQUAL-AND-OPPOSITECOMPENSATING

CIRCUITRY

IMPROVED FREQUENCY STABILITY

Performing frequency compensation in TCXOs improves frequency stability.

F igure A

F igure B



most of the frequency change occurs inthe initial time stages. Crystals areusually preaged at high temperaturesto help alleviate this initial steep fre-quency change. Aging is generally speci-fied as X ppm in the first year and Yppm/year after that.

The frequency alignment of the trans-mitter and receiver local oscillators is crit-ical in designing a robust wireless-com-munication system. Large frequencyerrors impact the receiver SNR, adjacent-channel rejection, and required preamblelength. Often, to compensate for the sub-sequent reduced sensitivity, a designermust select higher output power on thetransmitting side and increased receiversensitivity. Doing so, however, comes at acost of higher current consumption tomaintain the required link budget.

The data bandwidth, the deviationfrom the receiver local oscillator of thefrequency tone, and the error in thetransmitting/receiving crystal set the re-quired bandwidth of the IF or the base-band filters (depending on the receiverarchitecture). For a low-data-rate systemwith a low modulation index, the error inthe crystal becomes significant. For eachdoubling of the filter bandwidth, you loseas much as 3 dB of SNR. Reducing themodulation index can improve the SNR.

Controlling the frequency accuracy ofboth the transmitter and the receiver lo-cal oscillators allows more efficient use ofavailable spectrum allocation. By re-stricting the error, you can place hoppingchannels in closer proximity and, there-fore, use more channels. This higherchannel density is particularly importantin the congested, unlicensed ISM (in-dustrial, scientific, and medical) bands.As well as reducing unwanted transmis-sion to the adjacent channel, frequencycompensation allows designers to reducethe IF-filter bandwidth, and thus achieve

more attenuation of unwanted large sig-nals in the next band.

The FSK (frequency-shift-keying) de-modulator has time to acquire its re-quired threshold voltage during the pre-amble sequence. The frequency errordirectly affects the length of time it takesto acquire this threshold. Minimizing thetransmitting/receiving error reduces thenumber of preamble bits that the systemrequires, allowing for lower duty cycleson both the transmitting and the receiv-ing sides (Figure 1).

Receiver performance degrades signif-icantly as the crystal reference generateslarger frequency errors, and including ahighly accurate oscillator to improve sta-bility can be costly. Any system trade-offmust balance the desired frequency sta-bility and the associated cost. For low-power radio applications, a frequency er-ror of 5 ppm allows the bandwidth ofthe channel-select filter to be narrowenough to achieve good receiver sensi-tivity and sufficient rejection of the busyadjacent channels in the ISM bands.

Many systems require high oscillatoraccuracy but cannot afford to include anexpensive TCXO. Digital compensationcan minimize the frequency error of astandard quartz crystal to provide a cost-effective option for these systems. Tocompensate for the frequency error of acrystal, you must first predict the error.Because AT cut crystals are the mostcommon, this discussion will concen-trate on them, but the same ideas applyfor any crystal. You can characterize thecrystal-frequency error of an AT cut crys-tal over temperature (relative to the errorat 25C) by the following third-orderequation:Error (ppm)106[8.585108C(T25)(3.910107.8331011C)(T25)2(1.09510103.31014C)(T25)3],where C is the angle of cut in minutesand T is the temperature in degrees Celsius.

An uncompensated quartz crystal withvarious randomly chosen angles of cutcannot operate within the desired limitsof 5 ppm (Figure 2). Knowing the an-gle of cut of the crystal allows you to pre-

dict and compensate for the fre-quency error of the crystal. The

easy way to learn the angle of cut of thecrystal is to buy a crystal with a particu-lar angle of cut directly from the crystalmanufacturer. Crystal manufacturers cansupply crystals guaranteed to stay with-in 2 ppm of a known temperaturecharacteristic.You can typically buy thesecrystals for less than $1.Alternatively, youcan measure the crystal-frequency error(relative to 25C) at two further temper-

In a typical system, a sensor and ADC measure the temperature, and a DAC and varactor diode pullthe oscillator back to its nominal frequency.

OSCILLATORCIRCUITRY

CRYSTAL

ADC DACMICROCONTROLLERTEMPERATURE

SENSOR

VARACTORDIODE

F igure 3

An uncompensated quartz crystal with various randomly chosen angles of cut cannot operate with-in the desired limits of 5 ppm.

C=4

C=2

C=0

C=2

C=4

C=6

C=8

C=10

C=12

C=14

60

40

20

0

20

40

60

50 25 0 25 50 75 100

TEMPERATURE (C)

CRYSTAL-FREQUENCY

ERROR(PPM)

F igure 2



atures and predict the angle of cut ofcrystal based on these values. However,doing so adds to your test cost.

Designs have used direct digital com-pensation to calculate the estimated fre-quency error and then attempt to pullthe crystal frequency back to the nomi-nal frequency. A lower cost and simpleralternative is now possible using indirectfrequency compensation. Indirect com-pensation uses fractional-N technologyto correct for the estimated fre-quency error in the PLL.

In direct-digital compensation, a var-actor diode in the feedback network pullsthe crystal frequency back to its nomi-nal frequency in a similar way to TCXOs.The key difference is that in direct-digi-tal-frequency compensation, the com-pensation resides in the digital domain.In a typical system, a temperature sensorclose to the crystal measures the crystaltemperature (Figure 3). The analog out-put from the sensor is conditioned andscaled to match the input range of theADC, converting it to the digital domain.Once the microcontroller reads the tem-perature from the ADC, it uses a look-uptable to find out what DAC output is nec-essary to pull the oscillator back to itsnominal frequency. The accuracy of di-rect-digital-frequency compensation islimited by how closely the crystal followsthe estimated temperature-characteristiccurve, the accuracy of the ADC and DAC,and the predictability of the capacitanceof the varactor diode. With a 12-bit-ac-curate ADC and DAC, this system typi-cally keeps the frequency error of a well-behaved crystal at 5 to 10 ppm overthe industrial temperature range (40 to85C).

DIGITAL-CRYSTAL-FREQUENCY COMPENSATION

Traditionally, with integer-N technol-ogy, you can change the output of theVCO (voltage-controlled oscillator)

only in steps of tens of kilohertz, be-cause you can move the output of an in-teger-N PLL only in multiples of thecomparison PFD (phase-frequency-de-tector) frequency. Reducing the PFD to1 kHz to gain sufficient resolution tocompensate requires generating a largeN-divider value. Because noise is mul-tiplied up to the output by 20logN, us-ing an integer-N PLL results in poorphase noise and long delays in movingfrequency due to the narrow loop band-width required for the loop to lock.

The recent improvements in fraction-al-N spurious performance offer an al-ternative to direct compensation. Tradi-tionally, fractional-N spurious levels haverestricted its use to a limited number ofapplications with limited flexibility in thefractional divider. The small fractionsnow available on fractional-N synthesiz-ers allow moving the output of the VCOin steps of as little as 0.1 ppm. It is there-fore possible to use indirect-digital-fre-quency compensation to accurately com-pensate for the frequency error of thecrystal over temperature within registersof the PLL itself.

In indirect-digital-frequency compen-sation, a digital temperature sensor closeto the crystal measures the temperature(Figure 4). Based on the temperature, amicrocontroller predicts the frequencyerror and writes a corresponding valuefrom its look-up table to the fractional-N register to compensate for the fre-quency error. The accuracy of indirect-digital-frequency compensation is lim-ited by how closely the crystal follows theestimated temperature-characteristiccurve and the accuracy of the tempera-ture sensor. A crystal with a frequencystability following a known temperature-characteristic curve within 2 ppm in asystem with a 1C accurate tempera-ture sensor, guarantees a compensatedfrequency stability of 3 ppm. You cankeep the frequency error using indirectcompensation at less than 5 ppm overthe industrial temperature range, whichis better than what you can achieve withthe direct method.

One of the key advantages of this ap-proach is that once you assume a partic-ular error, the error correction is guaran-teed to be the same on all systems, because

In indirect-digital-frequency compensation, a digital temperature sensor close to the crystal meas-ures the temperature.

MICROCONTROLLER

LOOK-UPTABLET F

40 10010...84 01010...85 11011...

N(F/215)

VCO

CRYSTAL

TEMPERATURESENSOR

RF TRANSMITTERPFD=6.4 MHz1-PPM ERROR

OUTPUT=915.2 MHz1-PPM CRYSTAL ERROR1-PPM COMPENSATION

SPI

PFD/CHARGEPUMP

F igure 4

TABLE 1SUMMARY OF CRYSTAL AND OSCILLATOR OPTIONSStability (ppm over Typical price (1000)

Type 10 to 70C) (10 to 70C) CommentQuartz crystal 5 to 100 20 cents (50 ppm), 70 cents (5 ppm) Small and inexpensive but unstableCrystal oscillator 10 to 100 $2 (50 ppm), $7 (10 ppm) Inexpensive and relatively small but unstableVCXO 10 to 100 $4 (20 ppm) Relatively small and suited to compensation but expensiveTCXO 0.1 to 5 $8 (2.5 ppm), $40 (0.5 ppm) Very good stability but expensiveOCXO 0.0001 to 5 $80 (0.3 ppm), $125 (0.02 ppm) Excellent stability but large, power-hungry, and expensiveDirect-digital-frequency 5 $3* (5 ppm) Lower cost option than TCXOs but requires compensation significant designIndirect-digital-frequency 3 $1 to $2* (3 ppm) Good stability, inexpensive, and easy to implementcompensation*Additional cost of implementing compensation in system



all compensation is performed in the dig-ital domain. Compensating in the digitaldomain avoids problems due to ana-log layout and grounding, greatly sim-plifying the design and significantly re-ducing oscillator current consumption.Using the indirect method saves costs be-cause it requires neither an ADC nor aDAC. Many systems already have a tem-perature sensor, so including one incursno additional cost. The receiver synchro-nizing to the accurate base-station clockduring data transmission delivers im-proved accuracy in cellular communica-tions. The fractional-N resolution allowsdynamic correction for Doppler, aging,and temperature effects previously per-formed directly with a DAC and a VCXO.This indirect method alleviates the stressthat regular compensation can place onthe crystal of the VCXO, which can resultin excessive aging and worsening of in-band phase noise.

Figure 4 depicts an indirect-crystal-frequency-compensation implementa-tion using an 8051 microcontroller, atemperature sensor, an RF transmitter,

and a 19.2-MHz quartz crystal with anangle of cut of C3. The output fre-quency of the VCO was measured from40 to 85C in compensated and un-compensated systems (Figure 5). Thecompensated system worked well with amaximum frequency error of 1.52ppm, which is well within the 5-ppm

limit. Because the crystal had a cut ofC3, the uncompensated system per-formed within the 5-ppm limit from25 to 80C. Crystals with differentcuts have larger frequency errors over thistemperature range. However, the tem-perature-compensation algorithm com-pensates for the larger frequency errors

In indirect digital-frequency compensation, the compensation happens indirectly within the frac-tional-N PLL of the RF transmitter.

20

10

0

10

20

30

40

50 30 10 10 30 50 90 11070

TEMPERATURE (C)

VCO-OUTPUT FREQUENCY

ERROR(PPM)

UNCOMPENSATED SYSTEMCOMPENSATED SYSTEM

F igure 5



of these crystals. Larger errors start to oc-cur in the compensated system at 85 to105C. You may be unable to achieve afrequency stability of 5 ppm in thisrange, because the error in crystal fre-quency changes greatly with temperature(1 to 2.5 ppm/C), the crystal may notfollow the temperature-characteristiccurve to within 2 ppm, and the tem-perature-sensor accuracy decreases at theincreased temperatures. Using a more ac-curate temperature sensor, such as theADT7301, can reduce the contribution ofthe temperature-sensor errors.

Sigma-delta fractional-N synthesizersoffer advances in spurious performance,giving you an alternative for generatingaccurate local-oscillator frequencies inlow-cost systems. They improve phasenoise and offer a faster lock time thancurrent integer-N parts. They also allowPLLs to output the resolution necessary(0.1 ppm) to compensate for tempera-ture effects in crystals.

Digitally performed indirect compen-sation offers the benefits of cost reduc-tion, ease of implementation, and im-

proved accuracy. Although the examplesetup achieved frequency stability with-in 5 ppm, improving temperature-sen-sor and crystal technology will eventu-ally offer less costly and more accurateoptions.

References1. Analog Devices, ADF7010 ISM

Band Transmitter Datasheet.2. Socki, Jim, Quartz Crystal Oscilla-

tor Training Seminar, Crystal Engineer-ing, November 2000.

3. Bujanos, Norman, Choosing theRight Crystal for Your Oscillator,CircuitCellar Ink, February 1998.

4. Analog Devices, ADuC814 Micro-Converter Datasheet.

5. Analog Devices, AD7301 DigitalTemperature Sensor Datasheet.

6. Fry, Steven, Oscillator Handbook.

AcknowledgmentsSpecial thanks to Philip Quinlan and therest of the RF team at Analog Devices fortheir inputs. Also, thanks to the engineersat Vectron International, MF Electronics,

and Fox Crystals for their contributions.

Authors biographiesAdrian Fox works at Analog Devices (Lim-erick, Ireland) as an applications engineersupporting ISM-band and PLL-synthesiz-er products. He has a bachelors degree inelectronic engineering from the Universityof Limerick. He enjoys opera music, walk-ing his dog, and surfing.

Darragh Maxwell works at Analog Devices(Limerick, Ireland) as an applications en-gineer supporting the firms MicroCon-verter products. He has a bachelors degreein electronic engineering from the Nation-al University of Ireland (Dublin). He en-joys sports.

Claire OKeeffe works as a marketing en-gineer for Analog Devices ADCs andThermal and System Monitoring Groups(Limerick, Ireland). She has a bachelor ofscience degree in applied physics and elec-tronics from the National University of Ire-land (Galway). She enjoys skiing, surfingand skydiving.

reference frequency stability

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