本論文提供以多重元件匹配之高階梯度誤差消除的能力，來建構佈局模式的方法。此方法可以消除任意數量元件的任意階梯度誤差，而且透過此方法，佈局工程師將有更大的自由度，依據其創新和電路準確度，來選擇佈局模式。本論文提出了五種可消除線性梯度的多元件同重心佈局， 在此基礎上可透過對稱鏡射和反對稱鏡射構建可消除更高階梯度的佈局。此外，所有的佈局模式已藉由數學推導和MATLAB模擬，證實可以消除梯度誤差。本電路四電流源匹配是以台積電 0.35μm的製程實現。量測後的結果顯示出，提出的佈局模式能達到更佳的元件匹配，且驗證了提出的方法是有效的

This Thesis provides general methodology to construct layout patterns for multiple-device matching with high order gradient cancellation capability. The methodologies help to construct any number of devices for any order gradient cancellation. Furthermore, layout engineers will have more degree of freedom to choose layout pattern according to their innovation or circuit precision. Five terms of common centroid pattern for multiple-device are also presented here. They have the capability of linear gradient cancellation. To construct higher order gradient cancellation, we should apply either symmetrical or anti-symmetrical mirroring based on our proposed rules. Moreover, all layout patterns have been verified in mathematical analysis and MATLAB simulations to ensure the capability of gradient cancellation. A test chip for 4-current source matching is implemented in a 0.35 μm TSMC technology. The measurement results show that the proposed layout patterns achieve better matching performance than conventional ones, and the usefulness of these proposed methodologies are also verifie

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