- 學位論文
任意傳輸線系統之快速預測眼圖演算法及FIR補償設計
Fast Eye Diagram Algorithm and FIR Compensation Design for General Transmission Line Systems
摘要
高速數位電路系統的設計中，眼圖是評估不同互連線結構之間數位信號品質的一個快速直觀的有利指標。模擬準隨機二元序列（PRBS）響應的傳統取得眼圖方法不僅耗費大量時間與記憶體，也不能得出最差情況的眼圖。本論文首先提出一個快速演算法對於任意步階響應所描述的傳輸線系統預測其最差情況眼圖。基於通道輸出波形可由時間位移的步階響應（step response）乘上對應轉態方向的特性，位於特定視窗時間的眼圖波形是以步階響應上間隔UI的取樣電壓組成。適當操作時間位移、翻轉與疊加，這些取樣電壓的峰值與谷值能夠攜帶所有的ISI效應到同一時間，產生最差情況的眼圖電壓。藉由使用的取樣電壓其位置與轉態方向翻譯得到的輸入位元組合可用於取代PRBS作為模擬最差情況眼圖之用。此外，本演算法也可擴大處理上升時間與下降時間不對稱的信號，只須採用分別描述上升轉態與下降轉態的兩步階響應即可。再者，本文也發展n位元特定組合出現在m位元PRBS的機率模型用以闡述為何PRBS不太可能帶有能產生最差情況眼圖的最差輸入位元組合。 本論文的第二部分主要著眼於一個利用傳送端側外加預加重（pre-emphasis）電路，來對傳輸線損耗以及負載不匹配所導致多重反射的補償設計。由於穩定、線性相位、佔較少面積與低功耗等優點，採用有限脈衝響應濾波器（FIR filter）作為預加重電路。在快速眼圖演算法的幫助下，透過進行以最大化一定視窗時間範圍內眼圖電壓雜訊削減量為目的的時域最佳化，最佳的tap係數組合可被選出。對匹配、下驅（underdriven）與過驅（overdriven）阻抗搭配的傳輸線系統實際應用此預加重補償技術的模擬與實驗結果皆顯示，儘管補償後的頻率響應並未變平坦，眼圖是被重新打開的。
並列摘要
In the modern design of high-speed digital system, eye diagram is a beneficial metric of intuitively and quickly assessing the quality of digital signals through various interconnection structures. The tranditional way of eye-diagram acquisition by simulating the response of a long pseudo-random bit sequence (PRBS) consumes large amounts of time and memory and cannot obtain the worst-case eye diagram. In this thesis, a fast algorithm is first purposed to predict the worst-case eye diagram for the transmission line system with an arbitrary step response. Based on the property that the output waveform of a channel can be generated by time-shifted step responses multiplying corresponding transition polarities, eye-diagram waveform at a certain window time is formed by UI-separated voltage samples on the step response. With a proper manipulation of time-shifting, flipping and superposition, peak and valley values of these voltage samples can carry all ISI effects to the same time, producing a worst-case eye voltage. From the positions and transition polarities of voltage samples that are used, a substitution of PRBS, the input bit pattern is translated for simulating the worst-case eye diagram. Besides, this algorithm can be extended to handle signals with asymmetric rise/fall time if introducing two step responses that describe positive and negative transitions respectively. Furthermore, a probability model of that an n-bit specific pattern appears in an m-bit PRBS is developed to explain why it is not likely for a PRBS to carry the worst-case bit pattern that generates the worst-case eye diagram. The second part of the thesis focuses on the compensation design for the imperfect effects of transmission line loss and multiple reflections due to mismatch loads by adding a pre-emphasis circuit at the transmitter side. Owing to the benefits of stability, linear phase, less area and low power comsumption, the finite impulse response (FIR) filter is adopted as the pre-emphasis circuit. With the aid of fast eye diagram algorithm, the optimal set of the tap coefficients can be extracted by applying the time domain optimization that is to maximize the reduction of voltage noise of the eye diagram within a range of window time. The simulation and experimental results of transmission line systems with matched, underdriven and overdriven impedance schemes that actually employ the pre-emphasis compensation technique are shown that the eye diagrams are reopened even if the compensated frequency responses do not become flat.