本論文是研究如何將電路特性以圖的資料形式紀錄，利用圖神經網路的模型來預
測電路的輸出阻抗、負載消耗功率等等電路的特性，並比較不同算法基礎的圖神經網
路找出一個相對最好的模型。
在傳統的電路拓譜分析上，是將電路圖轉換成圖的資料形式，以電路的節點做為
圖中的節點，以被動元件電阻做為圖中的邊，以克希荷夫電路定律作為計算基礎，需
要搜尋出獨立迴圈來針對電流與電壓進行計算，獨立迴圈以圖搜尋法來搜尋出在最少
個獨立迴圈的條件下包含整個電路上的全部路徑的迴圈組合，當我們將所有獨立迴路
定義迴路電流時，使用疊加原理解聯立方程式即可得到各獨立迴路的迴路電流，再以
迴路電流求出真實通過元件的電流，計算出元件分壓、消耗功率等等。而使用這種方
式適合處理低頻理想電路，以方程式的方式計算，但在現實情況下，電路會有許多非
線性的干擾，如因為帶電載子的隨機熱擾動而產生的熱雜訊，因為傳輸線的材質、線
徑、長度等等所產生的傳輸線損耗，在高頻的情況下更會產生非線性頻率響應、寄生
電感效應、電磁相容干擾問題、接腳效應以及集膚效應等等，使得一個電阻並非純電
阻而包含電容及電感效應在內，電容電感與要考慮其電阻效應，這些非線性干擾也會
隨著訊號源的頻率高低而產生不同大小的影響，實際上真實情況難以將所有非線性因
素都以數學式表示，使用實驗量測又需要將實體製作出來，且需要高階 LCR 量測儀
器、時域反射儀等等儀器輔助，所以希望以其他方式得到真實數值。
圖神經網路相比其他深度學習網路，善於處理非歐式空間的資料，更能擷取節點
與節點之間的特徵作為訓練特徵，對於模型學習提供更多訊息，使訓練結果更加貼近
實際值，本論文比較數個圖神經網路模型後最後使用門控式圖卷積網路(Gated – Graph
Convolution Network)來對於低頻電阻電路負載阻抗的功率以及高頻 RLC 電路的輸出
最大功率進行預測，在低頻電阻電路資料集使用門控式圖卷積網路預測輸出功率得到
訓練集 MAE 達到 0.339，驗證集 MAE 達到 0.392，在高頻 RLC 電路資料集使用門
控式圖卷積網路預測輸出功率得到訓練集 MAE 達到 8.25，驗證集 MAE 達到 11.209，
發現將電路問題轉成圖的資料形式，並使用圖神經網路的方式進行預測可以逼近真實
值，爾後可用於輔助我們對於較複雜的電路計算，作為電路設計的參考數值依據。

This thesis is to study how to record circuit characteristics in the form of graph data, use graph neural network models to predict the output load power of the circuit, and compare different graph neural networks to find out a relatively best model.
In circuit topology analysis, the circuit diagram is converted into the data form of the graph. The nodes of the circuit are used as the vertex in the graph, the passive component is used as the edge in the graph. Search for independent loops through the graph search method and use Kirchhoff's law to list the circuit equations to get the voltage and current on the component. Using this method is suitable for processing low-frequency ideal circuits calculated by Kirchhoff equations. But the circuit will have many non-linear interferences, those will cause nonlinear frequency response at high frequencies. If you want to get the true value, you need to consider a lot of interference, and this matter is very difficult, so it is hoped that the real values can be obtained in other ways.
Compared with other deep learning networks, graph neural networks are good at
processing data in non-Euclidean space and extracting the features between nodes as training features. I compare several graph neural network models and propose a gated graph convolution network model to predict the maximum output power of the highfrequency RLC circuit. It is found that the circuit problem is converted into the data form of the graph, and the prediction using the graph neural network can be approximated to the true value, which can be used to assist us in the calculation of more complex circuits, as a reference value for circuit design.

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