Sampling and Jitter Considerations for GNSS Software Receivers

Transcription

1 International Global Navigation atellite ystems oiety IGN ymposium 006 Holiday Inn urers aradise, Australia 17 1 July 006 ampling and Jitter Considerations or GN otware Reeivers Bilal Amin hool o urveying & patial Inormation ystems, University o New outh Wales, ydney, Australia. Tel: +61 () Fax: +61 () bilal.amin@student.unsw.edu.au A. G. Dempster hool o urveying & patial Inormation ystems, University o New outh Wales, ydney, Australia. Tel: +61 () Fax: +61 () a.dempster@unsw.edu.au resenter Name(s) Bilal Amin ABTRACT This paper examines the sampling and jitter speiiations and onsiderations or (Global Navigation atellite ystems) GN sotware reeivers. otware radio (WR) tehnologies are being used in the implementation o ommuniation reeivers in general and GN reeivers in partiular. With the advent o new G signals, and a range o new Galileo signals soon beoming available, GN is an appliation where WR and sotware-deined radio (DR) are likely to have an impat. The sampling proess is ritial or WR reeivers, where it ours as lose to the antenna as possible. This requires a high-perormane Analog-to-Digital Converter (ADC). Important to the speiiation o both the ADC and hase- Loked Loop (LL) is jitter. Contributing to the system jitter are the aperture jitter o the sample-and-hold swith at the input o ADC and the samplinglok jitter. Aperture jitter eets have usually been modelled as additive noise, based on a sinusoidal input signal, and limits the ahievable ignal-to- Noise Ratio (NR). Jitter in the sampled signal has several soures: phase noise in the Voltage-Controlled Osillator (VCO) within the sampling LL, jitter introdued by variations in the period o the requeny divider used in the sampling LL and ross-talk rom the lok line running parallel to other 1

2 signal lines. Jitter in the sampling proess diretly ats to degrade the noise loor and seletivity o reeiver. Choosing an appropriate VCO or a WR system is not as simple as inding one with right osillator requeny. imilarly, it is important to speiy the right jitter perormane or the ADC. In this paper we will investigate the soures o jitter and a basi jitter budget is alulated that ould assist in the design o WR GN reeivers. We examine dierent ADCs and LLs available in the market and ompare known perormane with the alulated budget. The results obtained are thereore diretly appliable to WR GN reeiver design. KEYWORD: Global Navigation atellite ystems (GN), otware Radio, Analog-to-Digital Converter, Jitter, hase-loked Loop. 1. INTRODUCTION The development o the superheterodyne type reeivers revolutionized reeiver design, relegating previous reeiver arhitetures to oasional, speial-purpose use. The advantages o a digital reeiver solution are signiiant, and inlude redued system ost, inreased temperature stability, iner tuning resolution, aster tuning speed, exellent quadrature hannel phase balane, inreased ilter seletivity, robustness in terms o both hardware and sotware signal proessing algorithms, reonigurability, advaned signal proessing tehniques and the ability to store signals or subsequent o-line proessing. These beneits have resulted in the digitization proess moving loser to the RF ront-end, with the ultimate goal o diretly digitizing the antenna output. The otware Deined Radio (DR) has been realized, allowing reoniguration o signal proessing untions through sotware, and resulting in reonigurable radios apable o operating over multiple air interaes. Researh and development ontinues to extend the apabilities and to inrease the robustness o Global Navigation atellite ystems (GNs) reeivers. otware reeivers are quite valuable in evaluating potential improvements beause o their lexibility as ompared to onventional hardware GN reeivers, and are more suitable or researh and development. The advent o DR as well as the other high speed appliations imposes exeedingly hallenging demands on the state-o-art Analog-to-Digital Converters (ADCs). The ADC is a key omponent in any radio that uses either diret digitization o the RF input signal or ater an initial down onversion to an IF. The important question is that at what rate the signals should be sampled in order to preserve inormation. ampling the reeived signal using lowpass sampling (L), the more usual interpretation o Nyquist sampling theorem, requires a sampling rate o twie the maximum requeny o interest. For GN, this is o order o 3. Gs/s. Analog-to-digital onverters (ADCs) that operate at suh high requenies are not readily available - they are expensive and onsume a great deal o power (Dempster, 004). o in order to avoid these onstraints, a heaper, more eiient method o onversion in a WR is Band-ass ampling (B). In B we an sample the signal at twie the inormation bandwidth and remain onsistent with the Nyquist sampling theorem. Another advantage o using B is that it is easily extendable to multiple distint requeny bands. Akos etal. (1999) proposed a novel multi-band digitization method that utilizes B to signiiantly redue the required ADC sampling requeny. In ase o multi-band sampling, the minimum sampling requeny is twie the sum o all the individual bandwidths o interest. The ilters as shown in igure 1 are narrow bandpass ilters entred about multiple RF arriers o interest. The appropriate sampling requeny, o the ADC is then determined suh that all wanted bandpass signals are aliased into the sampled bandwidth without ausing aliasing. However,

3 in the multiple signal aliasing it is ritial to ind a sampling requeny in whih the resulted aliased bands will not only ross the inormation bandwidth boundaries at 0 and s/, but also not have overlapping requeny bands (Akos etal., 00). Jitter and phase noise desribe the same physial eet. While timing jitter desribes the lutuations o zero-rossings o an osillator output signal, phase noise is the orresponding requeny-domain equivalent. The level o phase noise or jitter that an be tolerated is a ritial ator in designing the sampling iruit. The evolution o high resolution ADCs apable o diret IF-sampling requires system designers to make perormane/ost trade-o deisions on low jitter and phase noise iruits. The ontributions to the system jitter are the aperture jitter o the sample-and-hold swith at the input o ADC and the sampling-lok jitter. Aperture jitter otherwise reerred to as aperture unertainty, is one o the limiting ators in sampling system. Today system designers may not adequately speiy the jitter requirements or the data onverter lok and, as a result, system perormane is degraded. In many ases the sampling lok jitter is several times larger than the ADC aperture jitter and is thereore the dominant ontributor to NR degradation (Kester, 005). It is diiult, though not impossible; to hange the ADC aperture jitter but a number o things an be done to redue the sampling-lok jitter. Walden (1999) and Le et al. (005) produed perhaps the best overviews o the ADC perormane trends. However, our survey is based mainly on the aperture jitter, input sampling requeny and sampling rate o the ADC as we are dealing with very high requeny signals i.e. the L1 signal is GHz. ampling-lok jitter has several soures: phase noise in the VCO within sampling the LL, jitter introdued by variations in the period o requeny divider used in sampling LL and ross-talk rom the lok line running parallel to signal line. ampling lok jitter based on LL design parameters has been subjet o numerous studies whih provide many models to predit the overall jitter at the output o LL (Mansuri (00), Lee (00), Kundert (1997)). Figure 1: GN otware radio reeiver ront-end Dempster (004) evaluated the jitter requirement suh that the noise due to jitter at the arrier requenies o GN signals was 10dB less than the thermal noise. These jitter requirements do not vary very muh with the loosest (6.35ps) being only 3.1 times the tightest (.05ps) or dierent lasses o GN reeiver. The tightest o these jitter requirements is or the G L1 3

4 band. Keeping in mind this requirement o.05ps o jitter at the output o ADC, a budget is designed and various approahes to satisy this requirement based on ADC and LL design parameters is disussed. In setion 4 we desribe the basi phenomenon relating phase noise and jitter and onversion between phase noise and jitter is also disussed. In setion 3 we have disussed the perormane limitations o ADCs, haraterized the dierent ADCs available in the market and ompared the known perormane with that o alulated budget. The dierent noise soures in a LL are disussed and then the jitter budget based solely on VCO phase noise is alulated in setion 4, sine the VCO noise has muh stronger impat on LL jitter than any o the other noise soures (Mansuri, 00). In setion 5, the total jitter budget is alulated.. GN OFTWARE RADIO RECEIVER ystem arhiteture trade-os signiiantly inluene the reeiver design, and reeiver ontend perormane pervasively aets overall system perormane. The GN sotware radio reeiver ront-end is shown in igure 1. A LL is used to lok the sampling lok at the required sampling requeny. ampling and jitter onsiderations or a number o GN example reeivers are examined, restriting interest to G and Galileo signals that are available to the ommerial users. L5(E5a) E5(E5b) MHz L E L MHz E L1 E1 G ignals Galileo Open ervies Galileo Commerial signal Figure : petral Loations o ignals Commerial satellite navigation reeivers have until reently largely been restrited to using the G signal at L1 (arrier MHz) (ICD-G-00D, 004). A Boeing Delta II roket was launhed on 6 th eptember with, a new Lokheed Martin G R-M1 (IIR-14) G satellite. This satellite is apable o broadasting not only on L1 requeny, but also a L 4

5 Civilian (LC) requeny. oon G will provide a new signal on L5 (arrier MHz, hipping rate 10.3Mps) (van Dierendonk, 000). On 8 th Deember 005, the suessul launh o the Galileo demonstrator satellite GIOVE-A by a oyuz roket, tool plae at Baikonour osmodrome in Kazakhstan (GJU, 005). This marks a major step o the Galileo program in spae. Galileo, Europe s global satellite positioning, navigation, and timing system, designed or ivil use, will oer state-o-the-art servies with outstanding auray, integrity and availability. The Galileo Joint Undertaking (GJU) was setup in 00 by European Union (EU) and the European pae Ageny (EA) to manage the development phase o the Galileo rogram. Galileo will provide 10 navigation signals in Right Hand Cirular olarization (RHC) in the requeny ranges MHz (E5a and E5b), MHz (E6) and MHz (E-L1-E1), whih are part o the Radio Navigation atellite ervie (RN) alloation (Hein et al., 00 and ICAO N/WGW: W/36, 004). Open servies (O) are available on E5 and E-L1-E1, known or onveniene as L1. Commerial servies (C) are available on E6 and L1 (Dempster, 004). Combinations o these signals were seleted that are likely to be ommon within a GN reeiver. Alpha is the most expensive reeiver proessing G L1, L, L5 and Galileo O and C, using L1, E5 and E6. Beta uses only the ree to air G L1 and L and Galileo O, on L1 and E5. Charlie uses L1 and E5 (ignoring L) and Delta uses L1 and L (i.e. the G bands that are urrently available, and inorporating the Galileo L1). Gamma is the heapest arrangement, simply using L1 only and inorporating the new Galileo signal. Frequeny E5 (L5) L E6 L1 max (MHz) min (MHz) Alpha Beta Charlie Delta Gamma Table 1: Frequeny Bands or Example GN Reeivers The requeny required or the ive example reeivers are shown in table 1. It an be seen that beause the requeny bands are ontiguous, in all ases, only two bands are required. Alpha, or instane, must reeive in range MHz and MHz. 3. AMLING CONIDERATION The sotware radio has been desribed as a revolutionary advane in reeiver design but the undamental design philosophy is simple. The ADC should be plaed as near as possible to the antenna in the hain o ront-end omponents and the resulting samples should be proessed using a programmable miroproessor. Dempster (004) has desribed two dierent reeiver design types namely IF reeiver and DR using diret digitization, or bandpass sampling. In sotware radio, the goal is to minimize the number o analog omponents, and ideally sample the signal at RF. There are two ways to onsider the required sampling rate o the ADC involved. One is based on entre requeny and the other is based on inormation bandwidth. ampling the reeived signal using low-pass sampling (L), the 5

6 more usual interpretation o Nyquist s sampling theorem, requires a sampling rate o twie the maximum requeny o interest. For GN, this is o order o 3. Gs/s (Dempster, 005). ampling at suh a high requeny will onsume a great deal o power. A heaper, more eiient method o onversion in a WR reeiver is Band-ass ampling (B). Using B we an sample the signal at twie the inormation bandwidth rather than the highest requeny in the signal. At this point we an learly restate the Nyquist Criteria: A signal must be sampled at a rate equal or greater than twie its bandwidth in order to preserve all the signal inormation. As depited in igure 1, the signal enters through the antenna and is ampliied by a Low Noise Ampliier (LNA) along with all requenies within the bandwidth o LNA. The signal then attenuated, when it is passed through a narrow bandpass ilter (BF) entred about the arrier requeny. When several bands are required or downonversion, the minimum sampling rate is twie the sum o bandwidths. o, a sampling requeny s is hosen, whih deines the resulting sampled bandwidth. This an be ensured i ertain onstraints are met as desribed by Akos (1999). I these onstraints are not met a portion o the inormation bandwidth o the signal an old on top o itsel reating intererene. The sampling proess is ritial or sotware radio based GN reeivers with bandpass sampling tehniques as it requires seletion o an appropriate ADC based on ertain design parameters. Another requirement is narrow bandpass ilter entered about the arrier requeny to attenuate all the noise outside the inormation bandwidth. In ase o high requeny narrow band signals, the BF may require a very high Q. GN Reeiver BW 1 (MHz) BW (MHz) Total BW (MHz) Fsmin (Msps) Alpha Beta Charlie Delta Gamma Table : ampling Consideration or GN Reeivers There are a number o parameters that are involved in designing a jitter budget o ADCs or GN sotware reeivers, but we have designed our budget based on three types o perormane parameters or ADCs: sampling rate, jitter and input signal bandwidth. ine the G L1 signal is GHz, we require ADCs whih an operate on suh high requenies. siaki etal. (005), Akos etal. (1996) and Brown (1994) have used diret RF sampling or the design o G reeiver ront ends. siaki etal. (005) has used Dallas emiondutor MAX104 ADC (Anon, 00), with an input bandwidth o. GHz, a maximum sampling rate o 1GHz and an aperture jitter o less than 0.5 pse. The omparisons o dierent ADCs available in the market based on above design parameters are addressed in setion 4 o the paper. 4. JITTER CONIDERATION The arrier requeny or GN reeivers is high enough so that the timing inonsistenies, suh as lok jitter (phase noise) and ADC aperture jitter, an inrease noise when the signal is sampled by the ADC. The noise soures inlude the quantization noise o the onverter (or the a dierential-nonlinearity error), the internal onverter thermal noise, and the system jitter. The ADC quantization noise and thermal noise have a diret eet on the onverter s ignal-to-noise Ratio (NR). The ontributors to the system jitter are the aperture jitter and 6

7 sampling-lok jitter. ine both o these terms are unorrelated they an be ombined in a root-sum-square basis to give the total system jitter (Kester, 005): T = a + (1) where T is the total system jitter. a and is aperture jitter and sampling-lok jitter respetively Aperture Jitter Aperture jitter, also known as aperture unertainty, is the unertainty in the aperture time. Aperture jitter stands or the random sampling time variations in ADCs whih are aused by the thermal noise in sample and hold iruit. Walden (1999) identiied the aperture jitter as the dominating error eet that limits the ahievable ignal-to-noise Ratio (NR). The produt data sheet indiates the aperture jitter speiiation or most o ADCs. Aperture jitter is oten speiied as an rms value, whih represents the standard deviation in the aperture time. Aperture time, also known as aperture delay, is the time during whih the signal is being disonneted rom the hold apaitor ater a hold ommand has been given. Unlike aperture jitter, the aperture time is not limiting ator on maximum requeny or sinusoidal signals beause or sinusoidal signal, the voltage error aused by the aperture time maniests itsel as a phase hange, not an amplitude or requeny hange. Aperture jitter sets an upper limit on the maximum requeny sinusoidal signal that an be aurately sampled by an ADC. Aperture jitter auses unertainty in the timing o sampler signal, degrade the ADC noise loor, and inrease the possibility o Inter-ymbol Intererene (II) (Le, 005). These eets are diretly proportional to the instantaneous rate at whih the input signal is hanging levels, i.e. the signal s slew rate. As a result higher requeny signal suer more extensive signal quality redution rom aperture jitter than lower requeny signals. Eetive Aperture Delay Time Analog Input V Analog Delay Aperture time Logi input with ample Fully Close Digital Delay Hold Fully Open Time Figure 3: ample and Hold Ciruit Figure 4: Aperture Time Le (005) determined the maximal allowable aperture jitter with respet to the input signal s requeny and the ADC s resolution by 1 a = () N. π. where a is the aperture jitter, max is the maximum requeny o the input signal, and N is the stated number o bits. Based on the above equation the analysis or various ADCs max 7

8 available in the market, is shown in table 3. vendor. a is the aperture jitter as speiied by the a (ps) N (bits) a (ps) ADC Input (Hz) ampling Frequeny ower (W) Maxim-.G 1Gsps 5 < MAX104 Maxim-.G 1Gsps 5 < MAX108 Maxim-.G 600Msps 4.6 < MAX106 ATMEL- 3.3G Gsps 4.6 < T8310G ATMEL- 3.0G 1.5Gsps 6.5 < AT84A003 ATMEL- 3.3G.Gsps 4. < AT84A003 Linear- 700M 130Msps 4 < LTC08 Table 3: Jitter speiiations or ommerially available ADCs Maxim ADC s math our speiiations as they have muh lower ost than other low jitter ADC s available in the market. G L1 signal has the highest requeny o all the other signals i.e. 1.5 GHz. o the tightest o the aperture jitter requirements is or the G L1 signal. While using the maxim MAX104 ADC the alulated aperture jitter using equation or the G L1 signal is 0.8ps. 4.. ampling-clok Jitter Clok jitter is a property o the lok generator that eeds the ADC with the lok signal. It is aused by the phase noise o the osillator and generates additional sampling time errors in the ADC (Lohning and Fettweis, 005). Most o the high speed ommuniation systems whih inlude radio transmitters and reeivers use phase-loked loops or requeny synthesis suh as in igure 1. Ideal Waverom Transition too early Figure 5: Clok Jitter uh systems suer rom sampling-lok jitter, deined in the time domain as the random variations in the sampling phase o the signal, or in the requeny domain as phase noise. As shown in igure 5, there are bound to be variations in the length o the period, whih auses unertainty about when the next edge o the signal will our. This unertainty is phase noise or lok jitter. In GN sotware radio reeivers as depited in igure 1, lok jitter an originate in the osillator/synthesizer system that provides the ADC sample lok. ampling requenies have been generated using requeny synthesizers that employ requeny dividers and LLs to develop lok signals based on reerene osillator signals. Jitter Transition too late 8

9 4..1. Relationship between phase noise and jitter Jitter and phase noise haraterize the same phenomenon. However, osillators are most oten speiied in terms o phase noise. Thereore, the approximation o rms jitter based upon phase noise is required. hase noise is deined as the ratio o the noise in a 1Hz bandwidth at a speiied requeny oset, m, to the osillator signal amplitude e at requeny o. hase noise is usually speiied in db/hz at the given oset, where db is the level in db relative to the arrier. In igure 6, phase noise is represented by the ratio o the area o the retangle with hase noise (db/hz) 1 Hz bandwidth at oset m to the total area under the power spetrum urve, approximately the dierene in the height o the spetrum at the entre and at m. The National Institute o tandards and Tehnology (NIT) 1Hz BW has deined ingle-ideband hase Noise Reerened to Carrier, (), as the normalized power in a singlesideband o RF spetrum within a 1Hz bandwidth. m o Mathematially it is expressed as: Figure 6: Osillator power spetrum sideband [db/hz] = 10log10 = 10log10 ( B[1/ Hz]) (3) arrier The quantity is usually displayed by ommerial phase noise meters, due to the limitations o most jitter measuring equipments. For example, most jitter measuring osillosopes are only apable o measuring jitter down to 1ps. Most modern real time osillosopes only have bandwidths up to 7GHz. hase noise equipment on the other hand, an measure noise levels o the best low-noise osillators available (muh less than 1ps in time domain), and oer bandwidth up to 40GHz. In order to relate phase noise to ADC perormane, the phase noise must be onverted into jitter. Let us onsider a sinusoid ontaining phase noise: v( = sin( π t ( ) (4) + φ where and φ ( are arrier requeny and phase noise respetively. Alternatively φ( v( = sin[ π ( t + )] π where φ( π = The spetrum o v( is is the lok jitter. As phase noise is muh smaller thanπ, thereore v( = sinw ( + φ( osw ( The osillator phase noise at a given requeny m is deined as the ratio between noise in a 1Hz bandwidth m oset rom and the arrier. From equation 3 the phase noise is given as ( ) = [ δ( ) + δ( + )] + [ φ ( ) + φ ( )] 4 4 (5) (6) (7) 9

10 ( ) = n m ( ) 10log m (8) ine n( = φ(. Deining the bilateral power density o phase noise as n ( ) is deined or both the positive and negative values o requeny. φ( is a real untion. It ollows that n ( ) = n ( ). The spetral density o phase noise is deined as unilateral power density o phase deviation: (10) ( ) = ( ) + ( ) ( ) Thereore, Beause φ( is a stationary proess, (9) n ( ) = φ ( ) 4 (11) 4 φ ( ) = ( ) n (1) 0 < φ ( >= ( ) d (13) where φ ( ) is the spetral density o φ (. Now, substituting 1 into 13 4 < φ ( >= ( ) d n (14) Using the relationship as expressed in equation 3, we an write o, RM jitter is πt n( ) = n( e dt = φ( e φ 0 0 φ ( ) 10 < φ ( >= 10 d (15) ( ) 10 = φ( = 10 d (16) π π Assuming that phase noise is lose to the arrier and symmetrial, equation 16 an written as 1 1 ( ) 10 = φ( = 10 d (17) π π Kester (005) mentioned a similar expression or onversion o phase noise into jitter, by approximating the phase noise urve into a number o individual line segments, and the end point o eah line segment are deined by data point. The rms jitter in seonds is given by 1 1 A 10 = 10 (18) π The area o the urve A is obtained by integrating the phase noise power over the requeny range o interest. The upper requeny o integration should be twie the sampling requeny πt dt n n = n 10

11 and the lower requeny o integration should be as low as possible. hase Noise-dB/Hz FLICKER HAE NOIE WHITE HAE NOIE Frequeny Oset-LOG ale Figure 7: hase Noise vs. Oset Frequeny Computer programs are available online to alulate the rms jitter. The alulations in this paper are based on the program by Raltron Eletroni Corporation (006) whih onverts phase noise into jitter, using the same tehnique as mentioned above. For the Rakon TCXO used in Zarlink G reeiver, with 10MHz osillation requeny, the phase noise at 10 KHz oset is -140 db/hz. Using Raltron omputer program the alulated lok jitter is 5.63ps whih is the same as alulated by the equations 17 and 18. There are other TCXO s available in the market with omparatively less lok jitter speiiations as shown in table 4. TCXO Frequeny Range CMAC- CFT ~ MHz RFX-L MHz ~.4 GHz CMAC- 9.6 ~ CFT9050 MHz Vetron OC 10 ~ 50 eries MHz Merury-K 10 ~ 3 eries MHz 1KHz (db/hz) 10KHz (db/hz) 100KHz (db/hz) (ps) Table 4: Jitter and hase noise speiiations or ommerially available TCXO s 4... hase noise in the LL In a LL, eah blok ontributes to a ertain extent to the total phase noise but VCO noise is typially the dominant soure (Mansuri, 00). Other soures o noise in a LL system onsist o phase detetor, reerene signal and requeny divider. Thereore other noise soures are negleted or simpliity as VCO noise has muh stronger impat on the LL jitter. When VCOs are embedded inside a LL, the loop dynamis will modiy the noise harateristis. hase noise spetral omponents below the orner requeny, the negative eed bak means that the LL output will losely ollow the LL input, and the phase noise o 11

12 the osillator is attenuated. Above the orner requeny the eed bak alls. This means that the phase noise o the LL output will be inreasingly determined by the phase noise o the osillator and less by input phase noise o reerene signal. It is desirable to have orner requeny (loop bandwidth) as large as possible to attenuate noise, but or stability reasons, the loop bandwidth should not exeed one tenth o the VCO requeny (Hajimiri et al., 1999). The spetrum in igure 7 is shown on a log sale, with phase noise side bands whih all o as 0dB/deade. In pratie, as desribed in (Kester, 005) and (Adler, 1999), there are regions in side bands where phase noise an all as 1,depending on the noise proess involved. Where x=0, orresponds to white phase noise region (slope 0dB/deade), and x=1 orresponding to the liker phase noise region. Also it should be noted that the sidebands in igure 7 grows toward ininity as the oset requeny approahes zero. Leeson (1966) developed an equation to desribe the dierent noise omponents in a VCO. FkT 1 ( ) = 10log (19) A 8QL where: () is single sideband phase noise density. (db/hz) F is the devie noise ator at the opening power level A 3 k is the Boltzmann s onstant, J / K T is Temperature (K) A is osillator output power (W) QL is loaded Q is arrier requeny o osillator is the requeny oset rom arrier Leeson s equation only applies in the region between the liker noise requeny to a requeny beyond whih ampliied white noise dominates (see igure 7). Another assumption is that the oset requeny is greater than the liker orner requeny (1/). Lee (00) gave an expression or the alulation o jitter in a VCO, based on phase noise measurement = 3 where 10log() alls at the rate o 0dB/Hz per deade. LL jitter due to VCO noise an be alulated rom the measured or simulated phase noise o the VCO, whih is typially known beore the LL design. Herzel et al. (004) gave an expression to alulate absolute rms jitter o a LL rom phase noise o the VCO in 0 db/deade region. oset B = (1) 4πB L B is the single sideband phase noise o the VCO, taken at an oset requeny in the region o spetrum with a -0dB/deade slope. B an be measured rom (db/hz) using equation 3. BL is the loop bandwidth o irst order LL. Loop bandwidth is the most ritial system design parameter or a LL, and as stated earlier that the phase noise inside the loop ( ) x (0) 1

13 bandwidth is dominated by VCO. Loop bandwidth has only a small impat on phase noise inside the loop bandwidth but narrower loop bandwidths an redue phase noise outside the loop bandwidth. LL as a irst order system does not give a inite jitter (Herzel etal., 004), so liker noise in the VCO within a seond-order LL model is inluded. o, the equation 1 takes the orm = oset 4π B e BL () where the eetive loop bandwidth is deined by B e L = πw n ςwn + 4π ς ( ς ) (3) In the absene o liker noise we have e ςwn B L = (4) π Herzel et al. (004) suggests that the liker noise an be suppressed by inreasing n to ten times the orner requeny or, that is Based on above equation the lok jitter exhibited by various VCOs is shown in the table 5. ampling lok requeny used in alulations is 10MHz. ine the jitter is dependent only on the phase noise o VCO, thereore all the other quantities are onstant exept VCO phase noise. VCO/LL Frequeny Range 1KHz (db/hz) 10KHz (db/hz) 100KHz (db/hz) (s) Vetron-C550 1 ~ p MHz ADF ~ 50 MHz p Wenzel- /N 10MHz p 501 Wenzel- 10MHz ps WA5100 (LL) RF L MHz ~.4 GHz ps Table 5: Jitter speiiations or ommerially available LLs/VCOs 5. TOTAL YTEM JITTER = oset B n 10 8πς or n The total system jitter is alulated by onsidering the aperture jitter and sampling lok jitter. The total jitter at the output o ADC is given by equation 1. Dempster (004) evaluated the jitter requirement suh that the noise due to jitter at the arrier requenies o GN signals was 10dB less than the thermal noise. These jitter requirements do not vary very muh with (5) 13

14 the loosest (6.35ps) being only 3.1 times the tightest (.05ps). The tightest o these jitter requirements is or the G L1 band. In order to meet these requirements, ADC and LL with the minimum jitter speiiation are onsidered. As shown in table 3, Maxim MAX104 ADC has the best speiiation to meet our requirements with ADC aperture jitter only 0.5 ps and ost is muh less than the other ADC s. imilarly, Wenzel WA 5100 has the best jitter speiiations or 10MHz sampling lok input i.e. 0. ps as shown in table 5. Thereore the total jitter at the output o ADC is T = = 0. 5ps whih is meeting our design requirements. 6. CONCLUION We have investigated the soures o jitter and a basi jitter budget is alulated that ould assist in the design o WR GN reeivers. Aperture jitter and sampling lok jitter is deined and the individual ontribution o eah o them to the total system jitter is alulated. The relationship between phase noise and jitter is mathematially expressed as osillators are most oten speiied in terms o phase noise. Dierent ADCs and LLs available in the market, whih math our speiiations, are examined and known perormane with the alulated budget is ompared. The results obtained are thereore diretly appliable to a WR GN reeiver design. Although it is impossible to address all the possible variations, there are some general reommendations or designing a GN reeiver ront end: Analysis o jitter in ADCs revealed that the appliation iruit annot be hanged to improve the ADC s aperture jitter. However, several tehniques an improve the lok jitter. When designing the reeiver ront end, sampling lok jitter and phase noise should be taken into aount. The lok soure need not be expensive but it must have low noise. Input bandwidth that manuatures mention in datasheets is not an indiation that a devie will hold the perormane up to those input requenies, but it is usually the latness o ADC response vs. input requeny. In order to get more aurate measure o phase noise in a phase loked loop, all the other soures o phase noise should be onsidered as eah noise aets the total output dierentially. REFERENCE Adler JV (1999) Clok-oure Jitter: A Clear Understanding Aids Osillator eletion, EDN, pp Akos DM and Tsui JBY (1996) Design and implementation o a diret digitization G reeiver ront end, IEEE Trans.Mirowave Theory Teh.,vol. 44. Akos DM et al.(1999) Diret Bandpass ampling o Multiple Distint RF ignals, IEEE Trans. on Communiations, vol. 47, no. 7, pp Anon (00) World's Highest-erormane 8-Bit ADC Has 46.dB INAD@1Gsps, Maxim/Dallas emiondutors, visited on 1 Marh 006, < Brown A and Wolt B (1994) Digital L-band reeiver arhiteture with diret digitization G reeiver ront end, IEEE LAN, Las Vegas, NV, pp Dempster AG (004) Aperture Jitter Eets in otware Radio GN Reeivers, Journal o Global ositioning ystems, Vol. 3, No. 1-, pp Dempster AG (004) New GN ignals: Reeiver Design Challenges, ro GN004, ydney. 14

15 GJU (005), visited on nd May 006, < Hein et al.(00) tatus o Galileo Frequeny and ignal Design, ro. IoN G, 00 Hajimiri A, Limotyrakis and Lee TH (1999) Jitter and phase noise in ring osillators, IEEE J. olid tate Ciruits, vol. 34, pp Herzel F, Winkler W and Borngraber J (004) Jitter and hase Noise in Osillators and hase-loked Loops, roeedings o IE, vol. 5473, pp ICD-G-00D (004) Interae Control Doument: Navstar G pae egment/navigation User Interaes, U DoD, IRN-00D-005R1. ICAO N/WGW: W/36, 004, visited on nd May 006, < 0ystem% 0anel%0N%0Galileo%0ignals%0RF%0Charateristis.pd> Kester W (005) The Data Conversion Handbook (seond edition), Analog Devies, In. Kundert K (1997) Modeling and imulation o Jitter in hase-loked Loops, Analog Ciruit Design: RF Analog-to-Digital Converters; ensor and Atuator Interaes; Low-Noise Osillator, LLs and ynthesizers, Kluwer Aademi ublishers. Le B, Rondeau TW, Reed JH and Bostian CW (005) Analog-to-Digital Converters, IEEE ignal roessing Magazine, pp Lee DC (00) Analysis o jitter in phase-loked loops, IEEE Trans. on Ciruits and ystemsii:analog and Digital ignal roessing, vol. 49, pp Leeson DB (1966) A simple model o eedbak osillator noise spetrum, ro. IEEE, vol. 54, pp Löhning M and Fettweis G (003) The eets o aperture jitter and lok jitter in wideband ADCs, ro. International Workshop on ADC Modelling and Testing, pp Mansuri M and Yang C-KK (00) Jitter Optimization Based on hase-loked Loop arameters, IEEE J. olid tate Ciruits, vol 37, pp MNeill JA (1997) Jitter in ring osillators, IEEE J. olid tate Ciruits, vol 3, pp New G atellite Launhed G R-M1, viewed 0 th May 006, < siaki ML, Akos DM and Thor J (005) A Comparison o Diret Radio Frequeny ampling and Conventional GN Reeiver Arhitetures, J. o IoN, vol. 5, no.. pp Thor J and Akos DM (00) A Diret RF ampling Multirequeny G Reeiver, IEEE osition Loation and Navigation ymposium, pp Van Dierendonk AJ (000) The New L5 Civil G ignal, G World, ep 000, pp64-71 Walden RH (1999) Analog-to-digital Converter urvey and Analysis, IEEE J. elet. Areas Commun., vol. 17, no. 4, pp