| 摘要: | 在高速印刷電路板 (PCB) 與高速互連量測中，為了獲得準確的裝置響應，去除治具影響的校正方法極為重要。傳統的TRL校正雖然準確，但需要多種結構，造成設計與量測上的負擔。相較之下，2x-thru校正僅需兩種結構即可完成，兼具簡便與高效率，因此在實務中被廣泛使用。然而，由於實際量測頻寬有限，當接近頻帶上限(f_max)時，經常出現非理想響應，使得校正結果的可靠度降低。
造成此問題的主因在於時間門控(time gating)技術。當對THRU的脈衝響應進行截斷時，對應到頻域即為與 sinc函數卷積。由於頻寬不足，邊帶頻譜無法完整呈現，導致頻帶上限(f_max)附近產生異常響應，進而使得夾具(fixture)模型與待測物(DUT)響應偏離真實結果。理論上，若要抑制此效應，需要將量測頻率延伸至更高範圍，但在硬體上受到限制，因此難以實現。此現象已成為限制2x-thru方法的一大瓶頸。
為解決上述問題，本研究提出頻域外插技術，利用自迴歸(Autoregressive, AR) 模型 並採用伯格(Burg)法進行參數估計，以延伸量測數據至頻寬以外區域，降低截斷效應所帶來的誤差。模擬與量測結果顯示，所提出的 Burg-AR外插法相較傳統方法具有更佳的數值穩定性與物理一致性，能顯著提升 2x-thru 校正在高頻段的準確度與可靠度。
此外，本研究亦對 IEEE 370 標準中的FER3條件進行實際評估。FER3的設計目的是為了確保夾具的被動性 (passivity)，要求THRU結構必須滿足插入損耗(insertion loss)大於回波損耗(return loss)的條件。然而，此規範並未考慮到 頻譜截斷所造成的影響。實驗結果顯示，即使在違反FER3的情況下，若搭配所提出的外插方法，仍能獲得可靠的去嵌結果。此發現指出FER3 在實務應用上具備一定的彈性，並提供了對標準規範更深入的理解。;In high-speed printed circuit board (PCB) and interconnect measurements, calibration methods that eliminate fixture effects are essential for obtaining accurate device responses. Although traditional TRL calibration provides high accuracy, it requires multiple standards, which increases design and measurement complexity. In contrast, the 2x-thru calibration requires only two standards to complete, offering simplicity and efficiency, and is therefore widely adopted in practice. However, due to the limited measurement bandwidth, non-ideal responses often occur near the upper frequency limit (f_max), reducing the reliability of the calibration results.
The primary cause of this phenomenon lies in the time gating technique. When the impulse response of the THRU is truncated, its frequency-domain response corresponds to a convolution with a sinc function. Because of insufficient bandwidth, the sideband spectrum cannot be fully represented, leading to abnormal responses near f_max and causing the fixture model and the device under test (DUT) responses to deviate from the true behavior. In theory, suppressing this effect requires extending the measurement bandwidth to higher frequencies, but this is practically infeasible due to hardware limitations. This has become a major constraint for the 2x-thru method at high frequencies.
To address this issue, this study proposes a frequency-domain extrapolation technique based on the autoregressive (AR) model, with parameters estimated using the Burg method. This approach extends the measured data beyond the available bandwidth, reducing errors introduced by truncation. Simulation and measurement results demonstrate that the proposed Burg-AR extrapolation method provides numerical stability and physical consistency compared to conventional approaches, significantly improving the accuracy and reliability of 2x-thru calibration in the high-frequency range.
Furthermore, this study conducts a practical evaluation of the FER3 condition defined in IEEE 370. FER3 is designed to ensure passivity, requiring that the insertion loss (IL) of the THRU structure be greater than the return loss (RL). However, this requirement does not account for the effects of spectral truncation. Experimental results show that even when FER3 is violated, reliable de-embedding can still be achieved when combined with the proposed extrapolation method. This finding indicates that FER3 possesses a degree of flexibility in practical applications and provides a deeper understanding of the applicability of the IEEE 370 standard. |
