58 30 [5] [6] SAWDDL (Chirp) SAWDDL [7] 1 (<1 ps) 1 ( ) ( )

Size: px

Start display at page:

Download "58 30 [5] [6] SAWDDL (Chirp) SAWDDL [7] 1 (<1 ps) 1 ( ) ( )"

吹锯马
5 years ago
Views:

1 30 4 Vol. 30, No PROGRESS IN ASTRONOMY Nov., (01) ,,3 1, 1, 3 ( ) (<1 ps) 3 SAWDDL P145 A 1 (1 ps= 10 1 s) [1 4] 0 30 ps 100 ps rms (SAWDDL, Surface Acoustic Wave Dispersive Delay Lie) ( )

2 58 30 [5] [6] SAWDDL (Chirp) SAWDDL [7] 1 (<1 ps) 1 ( ) ( )

3 4 59 [8] [9,10] [11 14] 3 (SAWDDL) SAWDDL SAWDDL SAWDDL τ f f s(t) = { A cos(πf1 t + µt /), t 1 t t 0, t. (1) µ = π f/τ f = f f 1 τ = t t 1 A D = τ f D 1 4 [15] { A τ/ f, f fo f/ S(f) = 0, f f o > f/. ()

4 f o 4 D D 1 [16 0] 1 [1,] 1 SAWDDL SAWDDL 30 MHz 1.5 GHz 1% 65% µs 0 55 db 1 50 db (SAWDDL) s 1 (t) = s(t), (3) s (t) = s(t θ), (4) θ s 1 (t) s (t) r(ϑ) = s 1 (t)s (t ϑ)dt. (5)

5 4 531 R(f) = S 1 (f)s (f) = S(f)S (f)e jπfθ = S(f) e jπfθ, (6) S 1 (f) S (f) S(f) s 1 (f) s (f) s(t) (6) R(f) ϕ(f) = πfθ, (7) ϕ(f) f (7) θ = 1 ϕ π f. (8) s 1 (t) s (t) x 1 (T s ) = s 1 (T s ) + w 1 (T s ), (9) x (T s ) = s (T s ) + w (T s ), (10) T s w 1 (T s ) w (T s ) x 1 (T s ) x (T s ) R(k) = X 1 (k)x (k) = S 1 (k)s (k) + S 1 (k)w (k) + S (k)w 1 (k) + W 1 (k)w (k), (11) X 1 (k) X (k) W 1 (k) W (k) x 1 (T s ) x (T s ) w 1 (T s ) w (T s ) w 1 (T s ) w (T s ) x 1 (T s ) x (T s ) N (11) R(k) S 1 (k)s (k) = S(k) W kθ N ( = S(k) exp j π ) N kθ, (1) S 1 (k) S (k) S(k) s 1 (T s ) s (T s ) s(t s ) (1) R(k) ϕ(k) π kθ. (13) N ϕ(k) k θ ˆθ 5 x 1 (T s ) x (T s ) ˆx 1 (t) ˆx (t) ˆx 1 (t) ˆx (t) ˆθ ˆx 1 (t) ˆx (t) ˆr(ϑ) = ˆx 1 (t)ˆx (t ϑ)dt. (14)

6 53 30 ˆθ = arg max ˆr(ϑ). (15) ˆθ θ = ˆθ θ, (16) (15) ϑ = ˆθ ˆr(ϑ) ˆr(ϑ) 0 ˆr(ϑ) = 0. (17) (17) θ ˆr(θ) + (ˆθ θ) ˆr(θ) = 0. (18) = ˆr(θ) ˆr(θ). (19) ˆx 1 (t) ˆx (t) S(f) + T s ˆX 1 (f) = S(f)e jπfθ + T s ˆX (f) = w 1 (T s )e jπfts, f < f s 0, f f s w (T s )e jπfts, f < f s 0, f f s, (0). (1) S(f) s(t) ˆr(θ) ˆr(θ) = jπ f ˆX 1 (f) ˆX (f)e jπfθ df. () w 1 (T s ) w (T s ) () [ ( ] ˆr(θ) jπt s w (T s ) fs(f)e df) jπf(ts θ) + w 1 (T s ) fs(f)e jπfts df. (3) (3) ˆr(θ) T s [w (T s )ṡ (T s ) + w 1 (T s )ṡ 1 (T s )]. (4)

7 4 533 ṡ 1 (t) ṡ (t) s 1 (t) s (t) ˆr(θ) 4π f S(f) df = Eṡ = Eṡ1 = Eṡ, (5) Eṡ1 Eṡ ṡ 1 (t) ṡ (t) (4) (5) (19) [1] w 1 (T s )ṡ 1 (T s ) w (T s )ṡ (T s ) T s. (6) Eṡ1 + Eṡ (6) (jitter) 5.1 (9) (10) w 1 (T s ) w (T s ) 0 σ w (6) [14] V ar[ ] = σwt s [ṡ 1(T s ) + ṡ (T s )] T s ṡ (T s ) = E ṡ V ar[ ] = σ w f s Eṡ SAWDDL s(t), (7) ṡ (t)dt = Eṡ, (8). (9) Eṡ 4π f o E s, (30) E s s(t) f o s(t) (30) (9) V ar[ ] = σ w π f s f o E s. (31) s(t) P s SNR = P s (31) σw = E s /τ τ s(t) V ar[ ] = 1 π f o f s τ SNR = 1 π f o N SNR, (3)

8 N = f s τ = τ/t s s(t) τ () (3) V ar[ ] = E s = A τ, (33) SNR = P s σ w = A σ w 1 π fo N SNR = 1 π fo N A /σw. (34) (35) (1) f s () s(t) τ SAWDDL (3) s(t) f o SAWDDL (4) SNR = P s σ w = A σw. (35) 1) SAWDDL ) 3) SAWDDL 5. (jitter) (jitter) w j (T s ) σ j T s jitter w 1 (T s ) = w j (T s )ṡ 1 (T s ), (36) w (T s ) = w j (T s )ṡ (T s ). (37) (36) (37) (6) σj Ts [ṡ 4 1(T s ) + ṡ 4 (T s )] V ar[ ] = Eṡ, (38) T s ṡ 4 (T s ) = V ar[ ] = σ j Eṡ f s E ṡ Eṡ s(t) s(t) ṡ 4 (t)dt = Eṡ, (39), (40) Eṡ 16π 4 f 4 o E s, (41)

9 4 535 E s (30) (41) (40) V ar[ ] = σ j E s f s E s. (4) (1) () (43) (33) (4) E s = A4 τ. (43) N = f s τ = τ/t s s(t) τ V ar[ ] = σ j f s τ = σ j N, (44) (44) (41) (jitter) (1) f s () s(t) τ SAWDDL 5.3 (33) s(t) A = Es τ. (45) A/D B (9) (30) q = A = 4Es, (46) B τ B σq = q 1 = Es 3τ B. (47) V ar[ ] = 1 6π τ B f s f o = 1 6π B Nf o. (48) A/D (48) (48) (1) f s () s(t) τ SAWDDL (3) s(t) f o SAWDDL

10 (35) (44) (48) (jitter) Mote-Carlo (35) (44) (48) 4 (f o = 100 MHz 00 MHz 300 MHz 400 MHz) 5 (jitter) τ 4 (N = ) 6 (f o = 100 MHz 00 MHz) (N = ) jitter /ps (jitter)

11 4 537 (35) (44) (48) SAWDDL f o = 150 MHz f = 40 MHz τ = 5 µs SNR = 35 db f s = 1 GHz 8 bits jitter = 5 ps 0.38 ps 3 7 ANALOG DEVICES AD9910 AD bit DAC (DDS) 1 GSPS 400 MHz 8 FPGA AD9910 L1 L cm 150 MHz s 1 cm ps L1 L 9. cm 455 ps AD9910 (35) (44) (48) 00 MHz 100 MHz 150 MHz

538 30 9 3 f o f τ f s 10 3 H HH H HH H HH f o = 100 MHz f o = 100 MHz f o = 150 MHz f = 40 MHz f = 40 MHz f = 40 MHz f s = 1 GHz f s = GHz f s = 1 GHz τ = µs τ = 5 µs τ = µs τ = 5 µs τ = µs τ = 5 µs

12 f o f τ f s 10 3 H HH H HH H HH f o = 100 MHz f o = 100 MHz f o = 150 MHz f = 40 MHz f = 40 MHz f = 40 MHz f s = 1 GHz f s = GHz f s = 1 GHz τ = µs τ = 5 µs τ = µs τ = 5 µs τ = µs τ = 5 µs /ps /ps /ps ( , ( , ( , ( , ( , (451.56, ) ) ) 45.11) 45.88) ) 3 ( , ) 99% 0.1 ps ADC

13 (35) (44) (48) (35) (44) (48) (1) f s () s(t) f o SAWDDL (3) s(t) τ SAWDDL (4) SNR = P s σ w = A σw 1) SAWDDL ) 3) SAWDDL 3 (< 1 ps) [1] Rahkoe T E, Kostamovaara J T. Solid-State Circuits, 1993, 8: 887. [] Raisae-Ruotsalaie E, Rahkoe T E, Kostamovaara J T. Solid-State Circuits, 1995, 30: 984. [3] Mota M, Christiase J. Solid-State Circuits, 1999, 34: [4] Szplet R, Kalisz J, Szymaowski R. Istrumetatio ad Measuremet, 000, 49: 879. [5] Porat D I. Nuclear Sciece, 1973, 0: 36. [6] Kalisz J. Metrologia, 004, 4: 17. [7] Fujiobu Takahashi, Tetsuro Kodo, Yukio Takahashi, Yasuhiro Koyama. Wave Summit Course: Very Log Baselie Iterferometer G Burke Cetre Parkway Burke: IOS Press, 000: 45. [8].. :, 1983: 3. [9].. :, 1984: 9. [10] Hirao H. 1st Meetig o Ferroelectric Materials ad their Applicatios. kyoto: Gordo ad Breach Sciece Press, 1977: 81. [11] Páek P. Istrumetatio ad Measuremet, 008, 57(11): 58 [1] Páek P. sigal processig, 007, 55(7): 1. [13] Páek P, Proch zka I. Rev. Sci. Istrum, 007, 78(9): 1. [14] Páek P. Istrumetatio ad Measuremet, 008, 57(6): 1. [15] Mesa D L. High Resolutio Radar Imagig. Lodo: Artech House, 1981: 11.

14 [16] Namias V. J Ist Math Appl, 1980, 5: 41. [17] McBride A C, Kerr F H. IMA J Appl Math, 1987, 39: 159. [18] Medlovic D, Ozaktas H M. J Opt Sco AM A, 1993, 10(10): [19] Ozaktas H M, Medlovic D. J Opt Sco AM A, 1993, 10(1): 5. [0] Ozaktas H M, Kutay M A, Zalevsky Z. The Fractioal Fourier Trasform with Applicatios i Optics ad Sigal Processig. New York: Joh Wiley & Sos, 000: 56. [1] Owes J M. Microwave System News, 1996, 16(7): 349. []., 1985, 7(1): 108. Research o High Precisio Time Iterval Measuremet Based o Surface Acoustic Wave Dispersive Delay Lie Excitatio BU Zhao-hui 1,,3, HUANG Pei-cheg 1,, ZHU Re-jie 1,, LI Dog-dog 3 (1.Shaghai Astroomical Observatory, Chiese Academy of Scieces, Shaghai 00030, Chia;. Graduate Uiversity of the Chiese Academy of Scieces,Beijig , Chia; 3. Uiversity of Shaghai for Sciece ad Techology, Shaghai 00093, Chia) Abstract: High-precisio time iterval measuremet techiques play a sigificat role i the ecoomy ad the military. The paper deals with a ovel high-precisio time iterval measuremet method up to subpicosecod (< 1 ps) precisio. The method utilizes a surface acoustic wave dispersive delay lie as a time iterpolator. The time iterpolator ca have the form of a time stretcher, so as to get may observatios. Thaks to possible averagig, the overall error ca be greatly reduced. The method is based o the fact that a surface acoustic wave dispersive delay lie excited by a short pulse ca geerate a liear frequecy-modulated sigal. By meas of cross correlatio betwee the resposes to two excitatios ad the firstorder fittig of the phase-frequecy characteristic of the result of cross correlatio, the time iterval betwee the two excitatios ca be precisely estimated evetually. The paper details the derivatios of the measuremet error propagatio model ad focus o aalysis of the measuremet error from three types of mai oises, ad the provides the specific measures to reduce the measuremet error. Key words: time iterval measuremet; time iterpolator; SAWDDL ;cross correlatio; fittig; Chirp

MHz 10 MHz Mbps 1 C 2(a) 4 GHz MHz 56 Msps 70 MHz 70 MHz 23 MHz 14 MHz 23 MHz 2(b)

MHz 10 MHz Mbps 1 C 2(a) 4 GHz MHz 56 Msps 70 MHz 70 MHz 23 MHz 14 MHz 23 MHz 2(b) 2011 32 ANNALS OF SHANGHAI OBSERVATORY ACADEMIA SINICA No. 32, 2011 1,2,3 1 2,3 2,3 2,3 2 1 1 ( 1. 200030 2. 100094 3. 100094 ) V474 1 (CEI) ( VLBI ), CEI 100 nrad ( 50 km) CEI 10 100 km 2 2 2 CEI [1]