背景介紹

背景主要包括了 多層PCB的優勢，以及引出其中stub和帶狀線的問題；接下來解釋了via stub所帶來的問題，resonance effect；然後介紹了部分文獻所提供的一些模型和考慮的方面；最後介紹了本文的側重點，即通過時域模擬和測量來描述via stub的諧振效應，並給出了綜合考慮訊號過孔和地過孔的原因，即這種方法能夠形成較好的wave guided properties，並且能夠產生low radiation losses。

A multilayer printed circuit board is a type of low-cost interconnect structure which commonly includes through via holes and striplines.

Resonance effects due to a stub in a transition from a through via hole to a stripline in multilayer PCBs can significantly worsen electric performance of the transition at higher frequencies.

In particular, it was indicated on this effect in 1 where differential via holes were considered and effectively modeled as a cascade of capacitances and inductances.

In this letter, we present a study of the resonance stub effect in via structures including ground vias embedded in a multilayer PCB by a three-dimensional electromagnetic field simlator based on the time-domain analysis and measurements at frequencies up to 20 GHz.

Via stub的結構

這裡研究兩種stub結構，如下圖所示，左圖為stub輸出在第10層金屬上，有圖為stub輸出在第3層金屬上。整體結構為12層金屬，圖中引數包括

However, being different in their lengths calls for the establishment of the resonance in the transitions at different frequencies (for the longer stub, the resonance will be shifted to the lower frequencies.)

圖1. 兩種不同的via stub結構

如圖2所示，採用地過孔產生迴流路徑，保證電流連續，地過孔與訊號的距離為l$l$。（”this via configuration corresponds to a cell of a high-density via structure under a large-scale integration chip.”）訊號過孔焊盤直徑dpad=0.5mm$d_{pad}=0.5mm$，焊盤厚度tpad=0.055mm$t_{pad}=0.055mm$，反焊盤大小dcle=0.8mm$d_{cle}=0.8mm$，孔徑(rod diameter)drod=0.8mm$d_{rod}=0.8mm$。地過孔與訊號過孔結構一樣，只是連線了所有的地平面層。
帶狀線的尺寸為w=0.127mm,h1=0.23mm,h2=0.13mm,t=0.035mm$w=0.127mm,h_1=0.23mm,h_2=0.13mm,t=0.035mm$。

圖2. 過孔和帶狀線結構示意

模擬結果

不同長度via stub的模擬結果如圖3所示，其中l=1.0mm$l=1.0mm$，較短via stub的長度H1=0.455mm$H_1=0.455mm$，較長via stub的長度H1=1.91mm$H_1=1.91mm$。上述兩種結構的模擬資料如下圖所示，對於較長stub的情況，其諧振頻點在13.7 GHz，而較短stub的諧振頻點超過了討論的範圍。同時，圖3也討論了有無地過孔對於S引數的影響。

Moreover, comparisons of presented data show that ground vias can improve the performance of through hole via to stripline transitions, but outside the stub resonance range.

圖3. 不同長度、有無地過孔的via stub模擬結果

一方面，stub諧振效應在較長stub情況下會嚴重降低轉接的效能，另一方面，地過孔形式的stub會形成一個高Q值的帶阻結構。

Ground vias can shape a stub resonance structure of a high-Q-factor which can be applied to develop compact bandstop filters.

實驗結果

為了實現前述模擬的情況，我們採用了另外一種更加實際的測試結構。測試PCB包含了銅導體層和FR4層，FR4的ϵ=3.8,tanδ=0.016$ϵ=3.8,tan\delta =0.016$。測試結構包含了兩個相同的訊號過孔，距離為l2$l_2$，而其他引數包括訊號過孔焊盤直徑dpad=1.1mm$d_{pad}=1.1mm$，反焊盤大小dcle=1.6mm$d_{cle}=1.6mm$，孔徑(rod diameter)drod=0.7mm$d_{rod}=0.7mm$，其餘引數可以參考前文。每個訊號過孔被地過孔圍住，地過孔引數為dpad=1.35mm$d_{pad}=1.35mm$，drod=1.0mm$d_{rod}=1.0mm$，l1=5.08mm$l_1=5.08mm$。
單個過孔轉接的插入損耗和回波損耗可以使用引數提取方法進行，這裡假設SMA-帶狀線轉接具有一致性。測試了l2=200mm$l_2=200mm$和l2=400mm$l_2=400mm$兩種情況，這裡需要保證所有測試均從過孔開始。

圖4. 測試結構示意

不同線長的測試結果如圖5所示，模擬和實測結果較為符合，驗證了stub effect的影響。
另外，這裡的諧振頻率為9.0GHz，比圖3的諧振點低，這是由於焊盤和過孔的結構尺寸發生了變化，從而導致等效的L和C發生了變化。這可以用來調節stub的諧振頻率，或者如果想要得到較好的傳輸特性，那麼等效的LC需要足夠小。

One can notice that these properities of via structures can be used to control the resonance frequency of the stub. Also, a transition from a through via hole to a stripline or a set of these transitions having effective capacitance and inductance of the stub as small as possible is a way to minimize the stub resonance effect in interconnect circuits at the considered frequency band.

圖5. 去嵌的S引數結果

個人總結

1. 作為via stub早期的研究，該論文系統展示了via stub的結構，以及via stub在不同長度下的影響。目前，已有部分論文有著更深入的研究，keysight的一個視訊也有所涉及；
2. 該論文的缺陷在於前面模擬的結構和後面的測試結構不一致，這並不能很好地說明諧振點不一致的原因；
3. 對於去嵌這部分，可以參考L-2L去嵌技術，貌似是一樣的操作。

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