印刷電路板嵌入式電容特性分析

Abstract

本文以時域--有限差分法(FDTD)探討嵌入式電容的形狀、尺寸、和(substrate/superstrate)介質常數對電容之高頻性能有何影響。基於考慮電腦資源上的限制，我們僅研究對稱性結構。在本文的分析方法下，我們可以求出從輸入線看進去的有效電容和等效集總電路模型、電容和輸入線間step discontinuity 的等效電路、和fringing effect 的等效電容。 相對於一正方形電容，當電容板面積不變下，改變電容板的寬度對電容的特性會有影響。我們觀察到其等效電容在低頻相差不大，但改變電容形狀將會造成高頻特性的不同。首先，減少電容板的寬度和增加長度，會造成self-resonant frequency(SRF)和第一個最大radiation loss的頻率的降低。當電容板適當地變寬時，其self-resonant frequency(SRF)和第一個最大radiation loss的頻率會被提高，造成電容可使用的頻寬增加。但當寬度過大時，則SRF和第一個最大radiation loss的頻率又降低，因此寬度也不能無限制的增加。所以我們得到一個結論，電容板的寬度適當的大於長度將會比正方形電容和長度大於寬度電容有較好的高頻特性。 當我們將基板的厚度變小後，其等效電容值並沒有成反比的增加，此乃因為基板厚度減小使得fringing 效應減小，因此電容增加的較少，且SRF也變低，乃是因為電容增加，使得L、C共振頻率降低。但第一個最大radiation loss的頻率提高了，則是因fringing 效應變小使得電容板的等效長度增加較少，所以此一頻率變高了。當我們將基板的介電常數變大時，SRF和第一個最大radiation loss的頻率都會變低，但等效面積增加的比例較小。

In this thesis, we use FD-TD method to analyze broadband characteristics of various embedded capacitors with different capacitor shape, size, and substrate/superstrate dielectric constants. Because of the limited computer resource, we consider only the symmetric structures. With the method developed in this thesis, we can find the effective capacitance from the input line, equivalent lumped element model including the equivalent circuit for the step discontinuity between the capacitor and input line and equivalent capacitance representing fringing effect on the open-end of the 1-port capacitor. When the area of capacitance is kept the same and with reference to a square capacitor, change the width of capacitor plate will influence the characteristic of the capacitance. It's observed that which the effective capacitance remains fairly constant at low frequency, changing the shape (i.e., form factor) results in different high-frequency behaviors. Firstly, reducing the width and increasing the length of the capacitor plate results in the lowering of both self-resonant frequency and the frequency of the first radiation loss peak. When the width of capacitor increases appropriately, the self-resonant frequency and the frequency of the first radiation loss peak increase, which result in a broader operation bandwidth. However, when capacitor width becomes too wide, the self-resonant frequency and the frequency of the first radiation loss peak decrease. So the width of capacitor cannot be increased indefinitely. It's therefore concluded that capacitor with width appropriately large than length will exhibit better high-frequency performance than a square capacitor and capacitor with length large than width. When we decrease the thickness of the substrate, the effective capacitance value doesn't increase as an inverse ratio. Since decrease in the thickness of the substrate will also decrease the fringing effect, the capacitance doesn't increase much. Because of the increase of capacitance, the self-resonant frequency decreases, too. Because the fringing effect decrease, the equivalent area doesn't increase as much, and the frequency of the first radiation loss peak increases. When we increase the dielectric constant of the first substrate, self-resonant frequency and the frequency of the first radiation loss peak decrease, and the equivalent area increase only slightly.