| 摘要: | 在現今印刷電路板(PCB)的高速信號完整度測試中，準確的校正方法至關重要，因為隨著頻率的提升，獲取待測物的響應會變得更有挑戰性。其中，2x-thru去嵌入法憑藉著方便、快速且精準的優勢，被廣泛應用於PCB電路元件、連接器與電纜的校正中，然而其演算法目前仍存在若干問題。其中一個常被忽略的問題為：經過校正後的待測物之S參數響應，在接近數據的最高頻率(fmax)處會出現異常大的起伏。在我們的實務經驗中，各校正結果的起伏程度不一，有時並不明顯，有時則會出現明顯的異常響應。在某些情況下，其校正結果的回波損耗值(Return Loss)甚至會超過0 dB，違反S參數的被動性原則。因此，2x-thru校正法在接近數據之最高頻率處的精確度常受到質疑。
針對此問題，本論文首先探討了造成此異常響應的原因，發現問題源自於2x-thru校正中由THRU電路獲得接在待測物兩端的夾具(fixture)過程中的時間門控(time gating)步驟。由於有限的量測頻寬，會造成在做time gating後在fmax附近的結果出現誤差，導致得到的fixture以及透過其fixture校正後的結果也會在fmax附近的響應出現異常起伏。基於此分析結果，一個最直接的解決方法為將THRU電路的最高量測頻率提高，並在進行time gating之後再將其截斷至原先的最高頻率，就可以避免此問題。然而，這需要能夠測量更高頻率的網絡分析儀，因此此方法在硬體上具有一定的限制。
本論文提出了另一個解決方案–數據外插。透過數學運算方法，預先對THRU電路進行符合原始資料響應趨勢的數據外插，也可以達到同樣的效果。本論文探討了兩種外插方法：Autoregressive (AR)外插法與Least Squares Convolution (LSC)外插法。在AR外插法的部分，我們成功了擬合原始數據的響應，並外插出符合原始資料趨勢的數據。並且透過了演算法的改進，我們得以實現自動AR外插方法，能夠對SNP檔自動進行數據外插，省去了挑選變數的繁雜步驟。相比之下，儘管LSC外插法能確保其生成的數據之因果性，但在我們的測試中，其經常無法準確擬合原始數據響應，也無法生成符合原始響應趨勢的外插結果。最後，我們將這兩種解決方案實際應用於2x-thru校正法中，並將結果與未經外插以及使用其他外插方法的結果進行比較。結果顯示預先進行外插的確可以有效解決異常響應的問題，突顯了其在2x-thru校正過程中的重要性。此外，透過了不同外插方法的比較，證實了我們提出的自動AR外插方法的有效性與可行性，展現了其在2x-thru校正法中應用的巨大潛力。
;Currently, in the field of high-speed signal integrity testing of printed circuit boards (PCBs) components, accurate calibration methods are crucial, as obtaining the response of the device under test (DUT) becomes increasingly challenging with higher frequencies. Among these methods, 2x-thru de-embedding, with its advantages of convenience, speed, and precision, is widely used for the calibration of PCB circuit components, connectors, and cables. However, its algorithm still has several issues. One commonly overlooked problem is the appearance of spurious fluctuations in the S-parameter responses of the DUT near the highest frequency (fmax) of the data after calibration. In our practical experience, the degree of these fluctuations varies; sometimes they are not significant, while other times, noticeable abnormal responses occur. In some cases, the return loss of the calibration result even exceeds 0 dB, violating the passivity principle of S parameter. This indicates that the accuracy of the 2x-thru calibration near the highest frequency of the data is questionable.
In this thesis, we initially explore the causes of the abnormal responses and find that the problem originates from the time gating step used to obtain the fixtures attached to both ends of the DUT in the THRU circuit. Due to the limited measurement bandwidth, time gating causes errors near fmax, leading to abnormal fluctuations in the fixtures and the calibrated results near fmax. The most direct solution is to increase fmax of the measurement of the THRU circuit by several GHz; However, this requires a vector network analyzer capable of measuring higher frequencies, thus posing certain hardware limitations.
This thesis proposes another solution—data extrapolation. By using mathematical operations to pre-extrapolate the THRU circuit data to match the trend of the original data response, the same effect can be achieved. After calibration, the extrapolated band is truncated back to the original fmax. In this thesis, two extrapolation methods are studied: Autoregressive (AR) extrapolation and Least Squares Convolution (LSC) extrapolation. In AR extrapolation method, we successfully fit the original data response accurately and extrapolate data that follows the trend of the original response. Through algorithm improvements, we also achieve automatic AR extrapolation method that can automatically extrapolate an SNP file data without variable selection. In contrast, although LSC extrapolation method can ensure the causality of the fitted and extrapolated data, our tests show that it often fails to accurately fit the original data response and to produce extrapolated data that aligns with the original response trend. Finally, we apply these two methods to 2x-thru calibration and compare the results with those obtained without extrapolation, as well as with the results using other extrapolation methods. The results show that pre-extrapolation can effectively resolve the issue of abnormal responses, highlighting the importance of performing data extrapolation in the 2x-thru calibration process. Additionally, by comparing different methods, we demonstrate the effectiveness and feasibility of our proposed automatic AR extrapolation method, showing the great potential for application in 2x-thru calibration. |
