一個高效能的雙層式查表法數位頻率合成器及其應用

Abstract

本論文提出一個新的直接數位頻率合成器(DDFS)的架構，其具備高速、 低複雜度及高頻譜純淨度。本架構主要是以正弦及餘弦泰勒展開式(Taylor’s expansion)為基礎，再結合雙層式查表演算法所構成。這個新的高效率直接數位頻率合成器，只需一個小的查表記憶體；N 位元解析度只需2N/4 組記憶體，少於其他的查表法架構，例如 Madisetti, et al. 於1999年所提出者(需2N/3 組記憶體)。依照運算方式分類，是屬於非遞迴式，因此不會產生錯誤累積的問題。本論文完成MATLAB 模擬，硬體描述語言模擬與電路合成，及FPGA 的實現；並以實際的量測結果驗證本架構在SFDR、切換速度、相位連續性及彈性Fcw範圍等項目具備良好性能。最後，以FSK 調變器來展示直接數位頻率合成器在通訊系統的應用。

This thesis proposes a new direct digital frequency synthesizer (DDFS). It has the merits of high speed, low complexity and high spectrum purity. It is based on the Taylor’s expansion method for sinusoidal and cosine functions, combined with a two-level table-lookup algorithm. The new DDFS is efficient, with a small table size and low computational complexity. In all, this new DDFS needs three lookup tables, each of size 2N/4, which is smaller than the other table-lookup methods, such as Madisetti, et al., (of size 2N/3). The DDFS is non-recursive, which is free of error-propagation problem inherently in the recursive DDFS’s. We perform Matlab simulation, HDL simulation/synthesis and FPGA implementation to verify this algorithm. Expected SFDR, switching speed, phase continuity and flexibility Fcw were confirmed by measurements. Finally, a FSK modulator is realized to demonstrate the application of DDFS technique.