| 摘要(英) |
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. |
| 參考文獻 |
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