A PAPER CLOCK MODEL FOR THE CESIUM CLOCK ENSEMBLE OF TL

Transcription

1 A PAPER CLOCK MODEL FOR THE CESIUM CLOCK ESEMBLE OF TL Shnn Yan Ln and Hsn Mn Peng atonal Standard Tme and Frequency Lab., TL, Chunghwa Telecom Co., Ltd. o. Lane 55, Mn-Tsu Rd. Sec. 5, YangMe, TaoYuan, Tawan 36, Republc of Chna Tel: ; Fax: E-mal: syln@cht.com.tw Abstract A paper clock model based on lmted numbers of atomc clocks and a typcal tme nterval counter was developed. The am of ths work s to use a small ensemble of cesum clocks and a tradtonal measurement system to generate a tme scale keepng both short-term and long-term accuracy. We removed each clock s drft, then weghted the resdual fluctuatons. The weght functon s set to be proportonal to the nverse exponental of the ndex of each clock s frequency devaton. We fnd the resultant paper clock to be much more stable and accurate than any contrbutng clock. The paper clock can keep a ± 50 ns phase dfference (compared wth UTC) wthout any calbraton, and the Allan devaton of ths paper clock s about (τ = 0 mnutes, compared wth hydrogen maser). Here, a typcal Allan devaton of the contrbutng cesum clock s.0~ n our measurement system. Fnally, we use ths paper clock to synchronze a hydrogen maser va a phase-lock mechansm. A vrtual test showed the phase dfference between an adjusted hydrogen maser and the paper clock could be kept wthn nanosecond wthout any predcton algorthm. ITRODUCTIO To develop a stable and accurate tme scale s always an endless target for all tme and frequency laboratores. TL owns nne cesum clocks (Aglent 507a) and two hydrogen masers (Kvarz CH-75); we tred to use ths ensemble of clocks to generate a tme scale keepng both short-term and long-term accuracy. Ths tme scale would be a reference to synchronze a hydrogen maser va a mcrophasestepper and then generate the new standard tme scale of TL. We expect that the short-term stablty of the fnal output would follow the hydrogen maser and long-term accuracy would follow the reference paper clock. Based on the analyss of clock data, we assumed that the phase dfference between any cesum clock and an deal clock s almost unchanged at several nanoseconds over tens of days f any drft s removed, so that we can average the resdual fluctuatons of dfferent clocks, and the resultant paper clock would be more stable and accurate than any contrbutng clock. The other beneft of the drft-removal procedure s that the drft rate of paper clock wll not change suddenly when we add a clock to or wthdraw one from 97

2 the ensemble. The weght of each clock s set to be proportonal to the nverse exponental of the ndex of each clock s frequency devaton. We don t need to set any upper lmt for the weght functon because the nverse exponental has an upper lmt tself. We also developed a mechansm for usng ths paper clock to synchronze a hydrogen maser va a mcrophasestepper. We compared the PPS phase dfference between the paper clock and a hydrogen maser, and adjusted the frequency offset by a fxed amount f the phase of hydrogen maser was advanced or retarded wth respect to the paper clock. A smulated result showed that the phase dfference between adjusted clock and paper clock can be kept to about ns. Usng ths mechansm, we can synchronze ths paper clock and a stable real clock wthout any predcton algorthm. Ths s helpful when we set up more than one backup tme scale system; the prmary and backup systems wll be kept n phase automatcally. CLOCK DATA AALYSIS Before we started to develop our algorthm, we had to check the ntal character of our cesum clocks. From the BIPM s monthly reports, we found that the drft rate of all our cesum clocks was not a constant (Fgure ). The varaton of each clock s drft rate s about 3~0 ns/day over ther lfetme. Fgure shows the phase dfference between UTC and each cesum clock; we notce that they are not lnear n the long-term, but are stable durng a short perod. Fgure 4 llustrates that we can have the best stablty when the average tme s 30 days (CS60, CS300, CS0, and CS498) or 60 days (CS500, CS7). Based on the above analyss, we assume the 30~60 day drft rate wll not change too much between the frst and the second 30~60 day perod; that s, we can use the drft rate 30~60 days ago to be the drft rate of the next 30~60 days. Another assumpton s that f the drfts of the clocks are removed, the resdual fluctuatons wll be reduced when we sum and average each phase dfference of the clocks. The assumpton s based on the ndependence of each cesum clock. The ndependence of each clock can be kept f we have a stable operatng envronment. ALGORITHM AD WEIGHTIG PROCEDURE We frst test the equal-weghted average phase dfference, UTC-Clocks. The ensemble tme scale wll be Ens = TL( t) + x... () = Here, we denote x (t) = UTC (TL) - clock, the phase dfference between UTC (TL) and each clock; Ens (t) s the UTC ensemble clock at tme t; and TL (t) = UTC (t) UTC (TL) (t) s the phase dfference between UTC and UTC (TL) at tme t. Lne of Fgure 3 shows the average of phase dfference of each clock; the best paper clock can keep ±30 ns accuracy over 500 days, but we have to know the drft rate of ths ensemble n advance. When we add one clock to ensemble, the drft of the ensemble wll change suddenly (Lne of Fgure 3). If we remove each clock s drft rate every certan perod and then average them, the modfed equaton becomes: 98

3 Ens = TL + [ x ( t t) d ( t t)]..... () = Here, the d (t-δ t) denotes the drft rate of clock at the perod t -Δ t to t, (compared wth Ens (t-δ t) ). Fgure 4 s the result of equaton (); t s much better than the result of equaton (). The result retans good accuracy wthout any calbraton (Lne 3 of Fgure 3). All tme scale algorthms have a weghtng procedure. Gvng each clock a weght can flter out unreasonable or erroneous data and be helpful for short-term stablty. We expect that the weght wll approach zero when the clock s very unstable and approach an upper lmt f t s very stable. So we consder an nverse exponental functon. We set the weght of each clock to be proportonal to the nverse exponental of the ndex of each clock s Allan devaton. We ddn t set any upper lmt of weght because the nverse exponental has an upper lmt tself. where Ens = TL + w [ x ( t t) d ( t t)] (3) w = e = bσ ( t t) e bσ ( t t) = and σ (t-δ t) s the Allan devaton between hydrogen maser and clock durng the perod (t-δ t) to t. Coeffcent b can control the behavor of the weght functon: large b makes the weght functon lke an nverse square weght, and small b makes the weght functon lke an equal weght. Here, we set b = We use clock data from MJD 5499 to MJD 5850 and test the nterval (Δ t) from 5 to 60 days. All results could be kept wthn ± 50 ns when compared wth UTC (Fgure 5). The nterval of 60 days may have the best long-term stablty, but has no sgnfcant dfference compared wth the other ntervals. It would be better f we could analyze more than 3 years of data so that we can verfy a more long-term result. We also tested addng a clock to the ensemble: CS474 was added to ths ensemble at MJD Fgure 6 shows the nfluence of addng a clock to ths ensemble: the long-term drft rate dd not change too much (about 0.~0. ns/day over 00 days); even the drft rate of CS474 was about. ns/day (Fgure 6). Another test s the comparson of dfferent knds of weghtng procedures; we calculated dfferent weghtng procedures and compared ther stablty wth that of a hydrogen maser. We tested: equal weghtng, w = nverse exponental weghtng, w = e = bσ e bσ 99

4 and nverse square weghtng, w = / σ = / σ. As we expected, all results had a much better stablty than that of the contrbutng clocks (Fgure 7). The Allan devaton of the paper clock s about 0-3 (σ = 300 seconds), and that of the contrbutng cesum clocks s about ~ The weghtng procedure dd beneft short-term stablty, but to a very small extent, and we cannot fnd any sgnfcant dfference between nverse exponental weghtng and nverse square weghtng (Fgure 8). PHASE-LOCK MECHAISM Snce an atomc clock (cesum or hydrogen maser) wll not change ts drft rate very rapdly n a short perod, one dea s that we can lock the phase between an atomc clock and ths paper clock just lke a phase-lock loop. A phase-lock mechansm was developed to lock ths paper clock and an atomc clock va a smulated mcro-phasestepper. We compared the phase dfference between the paper clock and an atomc clock every certan nterval, addng or reducng the frequency offset of a vrtual mcrophasestepper wth a fxed amount f the phase of the synchronzed atomc clock s advanced or retarded wth respect to the paper clock; the rule can be stated below: f (phase dfference > a ns) {$drft = $drft + b ns/day} f (phase dfference < -a ns) {$drft = $drft - b ns/day}... (5) We tested two cesum clocks and one hydrogen maser (CS7, CS498, and HM7605). We notced that the coeffcent b and checkng nterval must be correlated to acheve the best synchronous performance; a small coeffcent b s related to frequent checkng and better short-term accuracy. The coeffcent a s a constrant, dependng on how accurate one wants to synchronze. There exsts a lmtaton on coeffcent a: the short-term stablty of clocks; f the -hour Allan devaton of a clock s 0-3, t s about 0.36 ns varaton tself, so that we cannot expect to have an accuracy better than 0.36 ns. Here, we check the phase dfference every hour. The coeffcents a =.0 ns and b = 0.05 ns/day for cesum clocks; a = 0. ns and b = 0.0 ns/day for a hydrogen maser. Fgure 9 s the result of phase-lock mechansm. As we expect, there are only a few sgnfcant phase dfferences between the paper clock and the synchronzed clock ( ± ns for a cesum clock and ± ns for a hydrogen maser), and the hydrogen maser would have the better accuracy because of ts greater stablty. DISCUSSIO AD COCLUSIO There are some advantages of ths paper clock model. The frst one s: ths paper clock just uses a tradtonal measurement system (whch records phase dfference by a swtch system and a tme nterval counter) and smple data processng to generate an accurate and stable tme scale. The second s: we don t need to care that the drft rate wll change rapdly f one clock s wthdrawn from or added to the ensemble. The thrd advantage s: we can use the phase-lock mechansm to synchronze any stable atomc clock wthout any predcton algorthm. Another one s: the dfferent clocks can be synchronzed at the nanosecond level by a sngle tme scale, whch means that we can generate more than one backup 300

5 tme scale system and don t need to take care of the phase dfference between the prmary and backup systems. ACKOWLEDGMETS I greatly apprecate the help of Mr. Imae, Dr. Hanodo, and Dr. Hosokawa; they gave me much support when I was a guest researcher at CRL, Japan, so that I could analyze the clock data of CRL and get the long-term characterstcs of cesum clocks. REFERECES [] D. W. Allan, 978, Tme and Frequency (tme doman) characterzaton, estmaton, and predcton of precson clocks and oscllators, IEEE Transactons on Ultrasoncs, Ferroelectrcs, and Frequency Control, UFFC-34, [] ITU, 997, Handbook on Selecton and Use of a Precse Frequency and Tme System, Chapter 6. [3] J. Azoubb, M. Granveaud, and B. Gunot, 977, Estmaton of the scale unt duraton of tme scales, Metrologa, 3, [4] P. Tavella and C. Thomas, 99, Comparatve study of tme scale algorthms, Metrologa, 8,

6 Fgure. Cesum clocks drft rates (from BIPM monthly reports). Fgure. The phase dfference between UTC and cesum clocks; all drft of each clock s removed. otce that no clock s lnear. 30

7 Fgure 3. The phase dfference between UTC and some test paper clocks. Fgure 4. Allan Devaton of cesum clocks vs. UTC. 303

8 Fgure 5. The test of dfferent drft removal ntervals, from 5 days to 60 days. Fgure 6. The test of addng one clock to the ensemble (CS474, MJD 5650). Drft removal ntervals for 5, 30, 45, and 60 days are tested. 304

9 Fgure 7. Stablty of cesum clocks and the paper clock vs. a hydrogen maser. Fgure 8. The comparson of three knds of weghtng procedures: equal weghtng, nverse exponental 305

10 weghtng, and nverse square weghtng. The equal weghtng procedure s slghtly less stable than the other two, but not sgnfcantly. Fgure 9. Results of a phase-lock mechansm: two cesum clocks (CS498 and CS7) and a hydrogen maser (HM7605) are chosen to be the reference clock. 306

11 QUESTIOS AD ASWERS DAVE HOWE (atonal Insttute of Standards and Technology): I just have a few comments. One s that ordnarly, when you talk about drft n a cesum standard, I just want to be clear that what you are really lookng at s pece-wse drft estmates. The second thng s that your drft estmator s a three-pont estmator, and so I just want to cauton you that the results n the composte wll be optmstc, because the three-pont estmator happens to also be the pont estmator for the Allan varance. When you remove t, the Allan varance wll have a zero result at that averagng tme. When you look at the compostes, be very careful about thnkng that t s as good as the clam of 0. nanoseconds per day n terms of stablty on the long term because of the way you are removng drft pece-wse. The last comment s that ordnarly you can weght clocks of equal types of nose. I thnk t would be useful to look at the addton and deleton of clocks whch may have dfferng mx of nose. That would be a good test. SHI-YA LI: Yes, I agree wth you. But at the begnnng, we were lookng for a very smple clock model. At that stage, we dd not thnk about so many thngs. One of our ponts s that we actually used seven cesums. The estmaton of Clock One has some error. Clock Two has some error. But the error mght be averaged, over several hundred days. We can calbrate the ensemble wth UTC. That s our pont. 307