在FPGA上实现的具有基于延迟线的斜坡比较ADC的低成本快速傅里叶变换光谱仪的观测演示
Observational demonstration of a low-cost fast Fourier transform spectrometer with a delay-line-based ramp-compare ADC implemented on FPGA
摘要：
在这项研究中，一种新型的傅里叶变换无线电频谱仪（称为全数字无线电频谱仪; ADRS）已被开发，其中所有的功能，包括一个无线电频谱仪，包括采样器和傅里叶计算单元被实现为一个现场可编程门阵列（FPGA）上的软核。采用了一种基于延迟线的斜坡比较模数转换器（ADC），并在FPGA上实现了ADC的两个主要部分：模拟-时间转换器（ATC）和时间-数字转换器（TDC）。ADRS $f$的采样率和量化比特率$n$由关系式$τ= \frac{1}{2^{n}f}$限制，其中$τ$是延迟线的延迟元件的等待时间。假定在FPGA上实现的延迟元件的典型延迟为$\sim10$ ps，则采用满足射电天文学要求的低量化比特率有利于实现高达$\sim$ 100 GSa/s的高采样率。此外，由于所提出的\ADRS不需要分立ADC，并且可以在批量生产的评估板上实现，因此其制造成本远低于传统光谱仪。ADRS原型使用PYNQ-Z1评估板制造，其值为$f$ = 600 MSa/s和$n$ = 6.6，$τ$为16.7 ps。测量了样机的性能，包括其线性和稳定性，并使用大坂府立大学1.85米毫米-亚毫米望远镜进行了测试观测;这证实了样机在真实无线电观测中的潜在应用。该样机的性价比（$\sim$ 800 USD GHz $^{-1}$）是传统无线电频谱仪的10倍，有助于在现代接收机系统中经济高效地覆盖$\sim100$ GHz中频（IF）带宽。
英文摘要：
In this study, a novel type of Fourier transform radio spectrometer (termed as all-digital radio spectrometer; ADRS) has been developed in which all functionalities comprising a radio spectrometer including a sampler and Fourier computing unit were implemented as a soft-core on a field-programmable gate array (FPGA). A delay-line-based ramp-compare analog-to-digital converter (ADC), one of completely digital ADC, was used, and two primary elements of the ADC, an analog-to-time converter (ATC) and a time-to-digital converter (TDC), were implemented on the FPGA. The sampling rate of the ADRS $f$ and the quantization bit rate $n$ are limited by the relation, $τ= \frac{1}{2^{n}f}$, where $τ$ is the latency of the delay element of the delay-line. Given that the typical latency of the delay element implemented on FPGAs is $\sim10$ ps, adoption of a low quantization bit rate, which satisfies the requirements for radio astronomy, facilitates the realization of a high sampling rate up to $\sim$100 GSa/s. In addition, as the proposed \ADRS does not require a discrete ADC and can be implemented on mass-produced evaluation boards, its fabrication cost is much lower than that of conventional spectrometers. The ADRS prototype was fabricated with values of $f$ = 600 MSa/s and $n$ = 6.6 using a PYNQ-Z1 evaluation board, with a $τ$ of 16.7 ps. The performance of the prototype, including its linearity and stability, was measured, and a test observation was conducted using the Osaka Prefecture University 1.85-m mm-submm telescope; this confirmed the potential application of the prototype in authentic radio observations. With 10 times better cost performance ($\sim$800 USD GHz$^{-1}$) than conventional radio spectrometers, the prototype facilitates cost-effective coverage of intermediate frequency (IF) bandwidths of $\sim100$ GHz in modern receiver systems.
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