基于网孔电流节点电压的特勒根定理证明

Proving Tellegen’s Theorem via Mesh Current or Note Voltage

特勒根定理(包含功率和似功率守恒),是电路分析课程中进一步理解其他诸多定理的重要工具,其证明是教学难点。基于此,从学生熟悉的网孔电流和节点电压出发,给出两种简单的证明方法,并用于互易定理的证明,说明互易定理实际是特勒根定理的特例。这一证明方法有助于降低定理的理解难度,消除特勒根定理的教学障碍。

Tellegen’s theorem,consisting of power conservation and similar power conversation,is a useful tool in the electric circuit.It can help us further understanding others theorems in the course.However,how to prove this theorem always being a teaching difficult point.In this paper,we provide two simple methods to solve this problem,which mainly use mesh current or note voltage.Besides,our method can be used to prove the reciprocity theorem,and shows that reciprocity theorem is a special case of Tellegen’s theorem.This proof method is helpful to reduce the difficulty of understanding the theorem and eliminate the obstacles of teaching and learning Tellegen’s theorem.