在非線性電路中快速預測位元錯誤率

Abstract

隨著電路的傳輸速度越來越快，訊號完整度與電磁相容開始慢慢的被大家重視，而在電路設計中，眼圖是一個判斷數位訊號品質的一個重要依據，而傳統我們利用隨機二元序列(PRBS)來得到眼圖，而此過程可能會浪費相當多的模擬時間，少則是幾個小時，多時則達一天。而使用預測眼圖演算法是一個常見的方法來說縮短模擬時間，而眼圖預測分為兩大類：第一類為PDA(Peak Distortion Analysis)利用輸入簡單的脈衝響應或是步階響應來預測眼圖的最壞內邊界，而此方法只能預測出眼圖的內邊界形狀並無法得知其他眼圖的相關資訊，如：位元錯誤率(Bit error Rate)、眼圖的機率密度函數(Probability density function)也無法得知，也無法將隨機電壓抖動加入預測眼圖模擬當中。 為了解決上述PDA無法完成的部分，第二類為眼圖的統計分析，有一個前提假設在這個分析當中，也就是系統中傳輸0與傳輸１有著相同的機率也就是50%。 還在以前的研究當中，無法做很精準預測因為系統中有著非線性的效應在其中，所以本篇將提供一個全新的預測眼圖演算法，利用不同數目的步階響應，進而預測出位元錯誤率、眼圖的機率密度函數，此演算法分為不同階次，如果利用一個上升步階響應與一個下降步階響應來計算我們稱為第一級，但是為了增加精準度，我們會用兩個上升步階響應與兩個下降步階響應來計算我們稱為第二級，以此類推，當然越多級所耗費的模擬時間將會更長，這裡必須以精準度與模擬時間做一個取捨。此研究在非線性電路中也有其準確性，無論是模擬或是實驗上都有相當好的結果，結果將在本論文的第四章與第五章呈現，另外此研究也大幅縮減了模擬的時間，此演算法僅需不到一分鐘的時間就能預測出與PRBS差不多的結果。

Signal integrity issue has become more and more important in recent years. Eye diagram is a method of testifying the signal quality. PRBS is the conventional method of obtaining eye diagram, but it takes lots of time in simulation .It maybe will take a couple of hours. Eye prediction is a common solution for saving simulation time. There are two kinds of eye prediction: The first one is PDA(Peak Distortion Analysis), the pulse response and step response is used to predict the inner boundary of eye diagram, but it cannot be reveal the information of PDF(Probability Density Function) and BER(Bit Error Rate). Furthermore, we cannot consider the random jitter effect in PDA. In order to remedy the PDA, the statistical analysis is to solve the difficulty. There is an assumption in this kind of prediction. The transmission ‘1’ and transmission ‘0’ have the same probability, both 50%. In the previous studies, the prediction might be inaccurate in the non-linear system. In this paper we propose a new algorithm for solving the non-linear effects by using rising and falling responses. The new proposed method is used in both simulation and experiment, and they both show accurate results. The proposed method takes less than 1 minute in simulation. From these results, we could get a deep understanding of these algorithms.