â, Đ (Very Long Baseline Interferometry, VLBI)
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1 ½ 55 ½ 5 Í Vol.55 No ACTA ASTRONOMICA SINICA Sep., 2014» Á Çý è 1,2 1,2 å 1,2 Ü ô 1,2 ï 1,2 ï 1,2 à 1,3 Æ Ö 3 ý (1 Á Í ) (2 Á Í û À ) ( ) ÇÅè 1.5 GHz Á è, î Í, û ÓÆ Å ò ½Ò ¼ï. è Ò Í ½Å ñ, ò Í ½Åý. ÂÄ, Ù ý ô, é î ³, î Í Þ 112, îñđù 7 s î, ù ÛÂ, ĐÙ 60 s ù 1 Í ; Í 40, îñđù 2.5 s ù ÛÂ, ĐÙ 40 s ù 1 Í. Ù ĐîÑ ù, î Í 1.5, èí ë ¼ï ç. ³ :, àß:, Ç, îñ : P 111; ÞÁ : A 1 â, Đ (Very Long Baseline Interferometry, VLBI), è²», À Ô ù å Ǒ Ç (ù Ǒ Á² ), å Í ß âº ³. Á² ĐÐ î Ù ç² Þ ù Ã. Á ²» Ã.» Á ÁË Þ Ǒ (Roundtrip calibration), Æ Á Í è Ùìõ, À ÙÜ ² Ñ àß, þ ½Ò ð.» ò [1] [2] ù½ò Ý [3 4]. Ùàß Ǒ : Ù½ Ù, ø ½ Đ, ð, ð ù Ô. Ù àßãùæ þ Ú, þ ÍÚ Á á ( ) jqwang@@shao.ac.cn
2 428 Í 55 ë ½½ ² Þ, à ÕÙ à àß, ð, è ù, ÐĐ, ð ½ ß ³ Å. Á Í, ðé î î è. ÁË VLBI é è, ð Ù À Ù X (9 GHz), á ÂÔ K (22 GHz) Q (43 GHz), Á ùâ Ô. ³ Q,  ëä Ù 1 %, ÃÁ ÁÍ ù ÇǑ 1 10 s 1 10 s 1 10 s, Ð Ä, Á ù½ò  Å. ÙÔ, è ð Á, ǑÁË VLBI Í 65 m ö Ù Â Å ½ à. Ù ê ÒÍ Å Ù ð Þ, è îèõ, Ò ¾½ [2] àß; â Í Å ALMA (Atacama Large Millimeter/sub-millimeter Array) ßÁ è à îù àß [4]. Ð, ð,, Ù Á ù Í ; Ù î Æ, Ù Í ùíæ îù ê. ÇÅè î Í è; ûó Å ò ½ Ò ¼ï; î è ûí, óù Á. ÙÌ Ç, Ç ½Å î Íý. 2 Ò ÇÅè è, óùí Å ², Á. 1 Ǒ Çñ, Ǒ 1.5 GHz, è ÙÜ þ «½ è ü Ñ [5 7]. ù Ñ þ, Õ Í. Ñ õ ¾, Ì è Å Í (Þ Í è Ñ, ÙÜ þãèù», ô, í Þ è ÃǑ). 1 f 0 ðå µ Á ², f 2 Ǒ þ «OSC (Oscillator) ², ² Ǒ ² ; f 1 Ǒ ð ó µ «, f 1 = f 0 f 2, ß² 1, Ä Ä 1, L ðùü þ Đ; L 1 ǑÙÜ Ñ Đ.
3 5 è :» Á Çý f 0 =f 1 +f f 1 3 middleware f 1 4 f 0 =f 1 +f 2 6 f 0 =f 1 +f 2 1 transmitter f 1 f 2 L 1 receiver f 2 L OSC f 2 11 Fig.1 1 Òñ The roundtrip calibration block diagram Ä 1 ² Table 1 The signal at each node Node Signal Note 1 S 1 = sin[2π(f 1 + f 2 )t + φ 0 ] 2 S 2 = sin[2πf 2 (t L v ) + φ OSC] filter S 10 and using S 5 3 S 3 = 1 2 cos[2πf L 1t + 2πf 2 v + φ 0 φ OSC ] low-pass filter 4 S 4 = 1 2 cos[2πf 1(t L v ) + 2πf 2 L v + φ 0 φ OSC ] 5 S 5 = sin[2πf 2 t + φ OSC ] 6 S 6 = 1 4 sin[2π(f 1 + f 2 )t + φ 0 2π(f 1 f 2 ) L ] v high-pass filter 7 S 7 = 1 2 cos[2πf 1(t L1 v ) + 2πf 2 L v + φ 0 φ OSC ] 8 S 8 = sin[2πf 2 (t L L 1 ) + φ v OSC ] 9 S 9 = sin[2πf 0 t + 2π(f 2 f 1 ) L 1 v + φ 0 ] high-pass filter 10 S 10 = 1 4 sin[2π(f 1 f 2 )t 2π(f 1 f 2 ) L v + φ 0 2φ OSC ] low-pass filter 11 S 11 = S 2 S 3 = 1 4 sin[2π(f L 1 f 2 )t + 4πf 2 v + φ 0 2φ OSC ] 12 S 12 = 1 4 sin[2π(f 1 f 2 )t 4π(f 1 f 2 ) L v + φ 0 2φ OSC ] filter S 5 and using S 10 ÐÄ 1 Û, þ S 6 Ñ S 9 OSC ³, ų «, Ý î Í. (1) S 1 S 6 «Ǒ 2π(f 1 f 2 ) L v, v Ǒ² þ. (2) S 1 S 9 «Ǒ 2π(f 1 f 2 ) L1 v, L ù L 1 Đ Þ L î, Þ Ǒ 2π(f 1 f 2 ) L v, f 1 = f 0 + f 2 Ä, à ÞǑ 2π(f 1 +f 2 ) L v, è S 6 S 9 Í Å Þ, Í Ǒ f1 f2 f 1+f 2. (3) S 10 S 11 «Ǒ 2π(f 1 + f 2 ) L v, Ä Åê S 10, Ù ³. (4) ð ÝÄ, ó þö S 10 ð, ÄĐ L, ÙÜ, î ² Ǒ S 12, à S 12 = 1 4 sin[2π(f 1 f 2 )t 4π(f 1 f 2 ) L v +φ L 0 2φ OSC ], ù S 12 S 11 «Ǒ 4πf 1 v, Ì þ,
4 430 Í 55 L Ǒ Ë Â Å, L Þ L î, ÞǑ φ = 4πf 1 v. f 0 = f 1 +f 2 = 1.5 GHz, f 2 = 745 MHz î, φ = 2π L v 1510, S 10 S 11 «ÞǑ: φ = 2π(f 1 + f 2 ) L v = 2π L v φ φ «Ǒ 1/150, f 1 f 2, «. Ë φ Ð φ ; ø φ 12 11, φ 10 11, Ǒ. Ǒ φ 12 11» ÙÜðÙ, φ à û ý ( þ S 10 Ë Í ÙÍ ), ð Ý Í., f 1 f 2 Ð, ð Ë ð Ç Â Ý Ù 5 MHz Ñ, ð Ùó Æ ð. Ô á, Õ ç è Þ [7], Ë Ç 10 MHz Ñ. ø «ìõ, ù ýàß Allan ૽ñ [8], Ç : σ(t) = 1 2ωτ < [φ(t + 2τ) 2φ(t + τ) + φ(t)] 2 > 1 2, (1) σ Ǒ Allan à«; ω Ǒ² «; τ Ǒ îñ (Õ îññ ); φ Ǒ ; < > Ä. 3 î ý Ç ó f 0 = f 1 + f 2 = 1.5 GHz, þ OSC f 2 = 745 MHz,, è Ò Í m Đ èùô, ëë ë Ð 6 C Þæ 38 C. Ô ³ ýàß, îñ 1 s, îýå S 10 S 11 «(ê 1.5 GHz), S 1 S 6 «( 1.5 GHz), ø  Ǒè, ³ 2 3 ù, s îñë, è Đî Þ 1.4, î á «0.03 (60 fs), é î Þ 157, Í 112, s Ë, Í Û, æ ÅÒ îä Ì 21 C Ñî, Þ s Ñ 0.2 (0.3 ps) ð è ù Å ý ô Å ç ( ûé è æ). é Allan à«ù 4, î Å T4 å imaser3000 ù Á, è ûéæý. 7 8 s îñë, é ù³ è Å, ð Òµ, Ǒ è þ ² îæ, î ù³ «Å,, è Þ , å Ǒ , è, þ Á , è Þê (8%). 30 s ö, è ù ÞǑ , T4 ùǒ , î è ² ù Þ (0.7%); 60 s ö, ç ù Þ å ù ; û á îñ ºĐ, Þ ç þ Á
5 5 è :» Á Çý 431 ù, s î, ³å ù Þ 1. ð Ù è, á îñ ºĐ, Á ù Þ, ³å ù Phase/( o ) Unstabilized 1.5 GHz Stabilized 1.5 GHz Cable Temperature Temperature/ o C Time/(10 4 s) Fig.2 2 Þî ý The measured phase and cable temperature varied with time Phase/( o ) Unstabilized 1.5 GHz Stabilized 1.5 GHz Cable Temperature Temperature/ o C Time/(10 4 s) GHz Þ Fig.3 The phase varied with time for the stabilized 1.5 GHz case Ù ý ĐǑ 60 m, Þ 6 C 38 C (22±16) C; Ë ô Đ 240 m øæ Þ 18 C 26 C (22±4) C, Þìõ ð., f 2 Þ ð ë ¹îÃ, ð Ù þ 1.5 GHz ²» ð ² ó û á µ, f 1 µ, ð f 1 f 2 ó ¾ á. Ù f 0 ðå µ ², ù èù Ý, f 2 ð Ù þ OSC «µ ², ë, ÃǑ f 1 + f 2 ù. Ǒ, ÇÅè Ù «, Ò 5, Ä 2 Å f 2 = 745 MHz, Á å.
6 432 Í 55 4 î /, è Allan à«þ å ù³ Fig.4 The contributions of Allan variances before/after the real-time phase compensation, in comparison with the stability of a hydrogen maser Ä 2 f 2 = 745 MHz ý Table 2 The measured phase noise of an oscillation source at f 2 =745 MHz Frequency/Hz K 10K 100K 1M Phase noise/dbc MHz MHz 100 MHz Band pass Divider Low pass OSC multiplier Band pass 600 MHz 745 MHz Band pass 4 Íý 5 «Ç Ò Fig.5 Schematics of the oscillation source design è ÇÄ Đ Å Í, ǑÅ Ý», Ä Ý «φ φ èç. ½Ô ýî, îø «φ φ 10 11, 6, φ φ «7, èç. áîñ Þð Ù è ç, û Ç Í 40, «Allan à«8, «Allan à«ä Å è ù
7 5 è :» Á Çý 433 Í, Û, 2.5 s Ñ, è ù ³à ò Í, 40 s ù 1 Â. î ³, 7 á Ù î ( 3), 1 s 10 s 100 s ù ³ î î Í, ð s î, î Í Ù, ð Ù «Þ çå Allan à«èù Þ ( Ǒ î Í î î 112, èù ð Ù è ç),, ³é èî 1.5 Í Phase/( o ) Φ Φ Cable Temperature Temperature/ o C Time/s 6 îù þ 10 MHz ² ÙÜ 10 MHz Þ Fig.6 The phase variations of a 10 MHz signal on both receiver and transmitter sides Phase residual/( o ) Time/s 7 «Fig.7 The phase residuals after compensation
8 434 Í 55 8 / è Allan à«þ Fig.8 The contributions of Allan variance before/after the post phase compensation 5 ½Ò Ç 1 Ù èù Í, Ú½Ò, 9, ÄÖ ½ è Ǒ ½ (EO) ½ (OE), Ý Ë ð Ä Ñ³ ¼ï. Ä ð, ½Ò Ò ½ Ò Ý, ò ð Ç, Ò í á Í, ð EO OE ç Þß í, Рͳ½Ò ç Þ Ǒ. f 1 3 EO fiber OE f 1 4 f 0 =f 1 +f 2 6 f 0 =f 1 +f transmitter f 2 OE cable fiber EO receiver 5 OSC f ½Ò Fig.9 The optical fiber transmission system under test
9 5 è :» Á Çý Åè 1.5 GHz Á è Çý, ÇÄ Å½ Ò í, Äѳ Ý ½Ò ¼ï. Ú Æ ù á,, ÃǑ, ýð è Ù. è î, û½, Ǒ Ë Â Åà. (2 3 s) Í, ù Ô; ð î Ë, ëä. é î ³, è î Í 112, ù îñđù 7 s î ÛÂ, ĐÙ 60 s î 1 Í ; Í Þ 40, ù ĐÙ 2.5 s î ÛÍ, 40 s 1 Í, û á îñ Đ, î ùí 1.5. Ä 3 Å ìõ, î è ùìõ. Ä 3 î è ù Þ Table 3 The stability contributions of the real-time and post compensation Testing object Index Note Real-time phase compensation stability Post phase compensation stability Phase measurement error s s s s s s s s 74 fs (RMS) 60 m cable in temperature control oven, temperature varies from 6 C to 38 C, see Fig. 2 Testing condition similar to real-time phase compensation, temperature curve see Fig GHz phase detecting error is better than 0.04 ç úö ã Ô Á à û. å Ù à. Đ Þ [1] Sigman E H. TDAPR, 1987, 42-92: 89 [2] Napier P J, Thompson A R, Ekers R D. Proceedings of the IEEE, 1983, 71: 1295 [3] Primas L E, Lutes G F, Sydnor R L. TDAPR, 1989, 42-97: 10 [4] Shillue B. ALMA Memo #443, 2002 [5] Little A G. ITAP, 1969, 17: 547 [6] Oh H J, Kondo T, Lee J, et al. IVS 2010 General Meeting Proceedings, 2010: 449 [7] Thompson R, Moran J M, Swenson G W. Interferometery and Synthesis in Radio Astronomy. 2nd ed. Weinheim: WILEY-VCH Verlag, 2001: [8] Rogers A E E, Moran J M. ITIM, 1981, 4: 283
10 436 Í 55 Design and Testing of a Ground-based System for Phase Stabilized Standard Frequency Transmission WANG Jin-qing 1,2 JIANG Yong-chen 1,2 GOU Wei 1,2 YU Lin-feng 1,2 LIU Qing-hui 1,2 FAN Qing-yuan 1,2 LOU Fang-xun 1,3 LAO Bao-qiang 3 (1 Shanghai Astronomical Observatory, Chinese Academy of Sciences, Shanghai ) (2 Key Laboratory of Radio Astronomy, Chinese Academy of Sciences, Nanjing ) (3 Guilin University of Electronic Technology, Guilin ) ABSTRACT In this paper, a 1.5 GHz phase stabilized frequency transmission system is described. Compatible with the coaxial cable and optical fiber transmission media, the system has both the capabilities of real-time and post phase compensation. The phase stabilizing principle of the equipment is analyzed, and its performance is evaluated. Under the test environment, the results of the prototype system based on a coaxial cable show that the real-time compensation mode can improve the phase stabilities by more than 112 times in comparison with the uncompensated cables. The frequency stabilities are also improved significantly with a 7-second integration time, and one order-of-magnitude improvement is achieved after 60 seconds. The post compensation mode can improve phase fluctuations by 40 times. The frequency stabilities can be improved significantly after 2.5-second integration, while a 10-fold enhancement is achieved after 40 seconds. With longer integration time, both real-time and post compensation modes can improve the frequency stabilities by more than 1.5 orders of magnitude. The proposed equipment can effectively reduce slowly stretching effects due to the factors such as the temperature coefficient variations of the transmission medium and mechanical disturbances. Key words instrumentation: interferometers, methods: data analysis, statistical, time
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