本論文之研究內容係依「高靈敏度快速大麻定量檢測微系統之開發」研究計畫中所需之兩個子系統而進行，包含兩個主題：依曲率非均分拋物線內插法實現之無唯讀記憶體直接頻率合成器(Direct digital frequency synthesizer, DDFS)，以及一頻移讀取電路研製。
因此，本論文首先提出一快速大麻定量檢測微系統架構，係結合彎曲平板波(flexural plate wave sensor, FPW sensor) 生醫感測晶片，並研製一讀取電路，包含控制區塊、直接頻率合成器、數位類比轉換器、振幅電壓轉換器、峰值偵測器等電路，以實現感測訊號讀取。本系統係利用彎曲平板波感測器因待測液蛋白質濃度不同而造成共振頻率偏移的現象，藉由產生一掃頻訊號，通過滴檢體定前與滴定檢體後，儲存各自共振頻率，計算頻率飄移，以推算待測液蛋白質濃度。本系統致力於快速檢測、體積小、低成本、方便攜帶、操作簡易，使其符合現今醫療器材趨勢。
本論文第二個主題係針對前述無唯讀記憶體直接頻率合成器之拋物線內插法的分段方式進行改良與實現，目標在於提高無雜訊動態範圍，且利用TSMC 0.18 um CMOS 製程實現此晶片。本論文提出根據曲率之非均分拋物線內插法，係基於弦波的對稱性，僅需以π/ 2 弧度弦波係數即可以模擬出一完整弦波。且由於弦波在各區段之曲率皆不同，在曲率較高的區段若使用平均分段的方法，誤差將會提高，所以提出一根據弦波曲率變化之非均分法，判斷在何處分段可產生較佳功能。此法能在不改變硬體成本前提下，減少模擬之弦波與理想弦波的誤差，改善無雜訊動態範圍。

This thesis was motivated by an MOST-sponsored project, ”Highly Sensitive Microsystem for Marijuana Rapid Quantitative Test”, where a frequency-shift readout circuit is required to carry out the expected functionality and a ROM-less DDFS (direct digital frequency synthesizer) based on curvature non-equal division parabolic polynomial interpolation method is also proposed to serve as a frequency generator therein to enhance the performance.
The first topic investigates the marijuana rapid quantitative test system. The flexural plate wave (FPW) sensor and a control circuit are integrated, where digital to analog converter (DAC), DDFS, amplitude voltage converter (AVC) and peak detector are all included in the control circuit. By taking the advantage of FPW sensor characteristic, which is the resonant frequency will be shifted before and after titrating the target protein on FPW, a sinusoid signal with different frequency scanning over a pre-defined range is needed to seize the resonant frequencies, before and after titrating the protein. By computing the resonant frequency shift of the same FPW device, we can estimate the concentration by a look-up table searching.
Since the sine wave generator is the key component of the readout circuit, a novel DDFS is proposed to improve the spurious free dynamic range (SFDR). The proposed non-equal division parabolic polynomial interpolation method depending on curvature variation analysis will generate a complete sine wave based on the synthesis of a quarter of a sine wave digital signals due to the symmetry characteristic. The proposed design not only reduces the absolute error between ideal sine wave and generated sine wave, but
also improves the SFDR.

論文審定書. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i
論文摘要. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv
目錄. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v
圖目錄. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii
表目錄. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi
1 研究背景與動機. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 前言. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 研究動機. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3 相關文獻與研究探討. . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.3.1 高靈敏度快速大麻定量檢測微系統. . . . . . . . . . . . . . . 6
1.3.2 適用於FPW 感測晶片之頻移偵測電路. . . . . . . . . . . . . 9
1.3.3 使用內插法之無唯讀記憶體直接數位頻率合成器. . . . . . . 9
1.4 論文大綱. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2 高靈敏度快速大麻定量檢測微系統. . . . . . . . . . . . . . . . . . . . . . . 16
2.1 簡介. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.2 頻移讀取電路系統. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.3 頻移讀取電路架構. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.3.1 控制電路. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.3.2 數位類比轉換器. . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.3.3 振幅電壓轉換器. . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.3.4 峰值偵測器. . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.4 功率偵測器運作說明. . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.5 頻移讀取系統量測. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.6 結果與討論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3 依曲率非均分式拋物線內插法之無唯獨記憶體直接數位頻率合成器. . . . 28
3.1 簡介. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.2 非均分式DDFS 原理與硬體架構. . . . . . . . . . . . . . . . . . . . . 29
3.2.1 輸出頻率與頻率解析度. . . . . . . . . . . . . . . . . . . . . . 32
3.2.2 DDFS 硬體架構. . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.2.3 相位位元長度. . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.2.4 相位振幅轉換方法. . . . . . . . . . . . . . . . . . . . . . . . 36
3.3 電路實現與規格. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.4 電路模擬、驗證與分析. . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.4.1 電路模擬結果. . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.4.2 晶片實作量測與FPGA 驗證結果. . . . . . . . . . . . . . . . 42
3.4.3 晶片實作. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.4.4 FPGA 驗證. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.4.5 晶片量測結果. . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.4.6 結果與討論. . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4 結論與未來研究方向. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
4.1 高靈敏度快速大麻定量檢測微系統. . . . . . . . . . . . . . . . . . . 49
4.2 依曲率非均分式拋物線內插法之無唯獨記憶體直接數位頻率合成器. 50
參考文獻. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

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