透過您的圖書館登入
IP:18.209.66.87
  • 學位論文

18GHz取樣超寬頻即時頻譜式數位相關器

An 18 GSps Ultra-wideband Real Time FX-type Correlator (Implemented with FPGAs)

指導教授 : 闕志鴻教授

摘要


本論文中說明了NTU-Array的數位相關器的研發設計與實測. NTU-Array為ㄧ無線電干涉儀天文望遠鏡陣列, 具六組雙偏振接收機, 操作於W-band並有35GHz之頻寬. 其科學目標是觀測宇宙背景輻射(CMBR)在小角度的非等向性. 相關器的前端是高速的ㄧ位元類比數位轉換器(ADC), 由Maxim 3950晶片實作, 藉由交錯式的取樣達到了18GHz的取樣頻率, 超越了此晶片的最高時鐘頻率近兩倍, 並使用一位元取樣以在有限的資源下實現了對於小訊號最佳的訊噪比(SNR). Maxim 3950同時作為解多工器將8.7GHz串列訊號平行化至544MHz數據率, 進入後端系統時鐘域. 相關器後端為完全同步數位系統, 由11片搭載Xilinx Virtex-4 LX60 FPGA之板組成ㄧ個單元, 而總共有八個單元. FPGA的電路設計同時兼顧系統的簡潔與靈活性. 觀測目標為寬頻連續譜的訊號, 但是相關訊號的震幅與相位仍會隨頻率不同有相當的差異, 需要中等的頻率解析度方能取得最佳化的訊噪比. 因此相關器設計為頻譜式(FX-type), 數據處理管線分為兩個階段, 第一階段是傅立葉轉換(FT)板, 訊號經由有限長度的率波器分為32個頻道的複數分量. 第二階段中來自不同接收機屬於同一頻道的複數分量由相關板計算互相之乘積, 並隨時間累積以增益訊噪比與簡化數據. 在固定的頻率解析度需求下, 頻譜式相關器有效簡化了系統. 針對現階段6接收機之NTU-Array的需求, 相關器系統配置為6片FT板與4片相關板和主時鐘板組成一單元, 負責處理一個8.7GHz頻寬的中頻(IF)訊號. FT板與相關板之間的交叉高速通訊由Category 6 UTP纜線連結, 時鐘同步涵蓋整個單元, 而訊號的完整性由板至板自動校準系統保持. 完成相關器時也建構了數位與類比系統的附屬測試系統. 經由假隨機二元序列(PRBS)模擬白色寬頻訊號, 測試結果後端數位訊號處理系統在5Hz數據轉儲速率下達到40dB的訊噪比增益, 而通訊的位元錯誤率(BER)低於10^-8, 對於數位相關器而言相當足夠. 經由測試亦確定了取樣系統的頻率響應特性. 考慮到NTU-Array系統整合, 仔細探討IF訊號的不平坦頻譜對於相關器效率的影響, 結果顯示此效應對於相關器系統並沒有很大的負面效應.

並列摘要


In this dissertation we report the design, development and verification of a recently completed digital correlator. The system is dedicated for the astronomical microwave interferometer - NTU Array that incorporates 6 W-band dual polarization receivers with 35 GHz instantaneous bandwidth for observations of small-angular-scale fluctuation in the Cosmic Microwave Background Radiation(CMBR). The correlator front-end system contains a fast sampling 1-bit analog-to-digital convertor(ADC), which is implemented with the Maxim 3950 chip. By utilizing the interleave sampling scheme, an 18GHz sampling rate, almost twice the specified clock frequency of the demultiplexer, is achieved. Given the finite resources available to the project, an one-bit sampling precision is adopted currently for the best cost-to-SNR efficiency in small signal applications. Maxim 3950 also serves as a demultiplexer to transform the signals of 8.7GHz bandwidth into the 544MHz clock domain suitable for the back-end logic system. In the back-end system, fully synchronized logic designs are implemented on a stack of 11 Xilinx Virtex-4 LX60 FPGA boards, and the entire system consists of 8 stacks. The methodology for the FPGA design is to keep the system simple and flexible. A continuum spectrum is expected for the input signal but the amplitude and phase variations across the full band of the input can be considerable, and hence a moderate frequency resolution is needed for adjustments to achieve the optimal SNR. An FX-type correlation scheme which consists of two consecutive FPGA boards in the data path is employed for the correlator system. The first stage Fourier transformation (FT) pipelines decompose the data streams into complex components in 32 frequency channels by scalar products with finite length filters. In the second stage, the complex components of the same frequency channel from different receivers are multiplied together in real time by the complex correlators, and these products are accumulated over a finite time interval for SNR gain and for data reduction. This FX scheme with frequency decomposition before correlation reduces the system complexity for the required moderate spectral resolution. In application to NTU Array, the system is configured to receive signals from 6 receivers and 6 FT, 4 correlation and one master clock FPGA boards are utilized for each 8.7GHz IF band of the interferometer. High speed crossbar communications between FT and correlation boards are connected by Category 6 UTP cables. Full clock synchronized design is implemented across these 11 boards, and the signal integrity is assured via an auto-alignment mechanism implemented with tap delay lines in FPGAs. Verification fixtures are also constructed to test both digital and analog components of the system. The correlator system shows a 40dB SNR gain in each frequency channel with a white input spectrum at 5Hz data dumping rate. We conduct the digital verification based on Pseudo-Random Bits Sequence (PRBS) generators to provide the desired white spectrum. The bit error rates of the communications path between boards for the worst channels are below 10^-8, which is much more than enough for the correlator system. We also verify the sampling system by characterizing its spectral response. For integrations of the IF system of NTU Array with the correlator system, we also investigate the impact of non-white spectrum of the IF signals to the correlator system, and find that this effect does not seriously impact the system performance.

參考文獻


[13] C. Holler. In L.-W. Chen, C.-P. Ma, K.-W. Ng, & U.-L. Pen, editor, AMiBA 2001: High-Z Clusters, Missing Baryons, and CMB Polarization, volume 257 of Astronomical Society of the Pacific Conference Series, pages 321{+, 2002.
[1] Bennett, W.R., 1948, Bell System Technical Journal, 27, 446
[2] M. Birkinshaw. Phys. Rep., 310:97{195, March 1999.
[4] Cole, T., 1968, Aust. J. Phys., 21, 273
[6] Cooper, B.F.C., 1970, Aust. J. Phys., 23, 521

延伸閱讀