求解电阻电路的传递辛矩阵方法

METHOD OF SOLVING THE TRANSFER SYMPLECTIC MATRIX IN RESISTANCE CIRCUIT

本文以电阻一端的电压和电流值作为状态参量,将电阻电路的计算纳入辛体系,以简单电阻电路、电阻多级串联电路以及多支路复杂电阻电路为例给出了电阻电路的传递辛矩阵解法,只需求出传递矩阵,再结合边界条件便可对问题进行求解.这种算法只涉及简单的矩阵计算,易于理解,便于编程,为电阻电路的计算提供了一种新的计算方法.算例验证了本文方法的正确性.将辛方法引入大学物理相关内容的教学之中,有助于学生深入理解与认识物理学内在性质.

In this paper, by using the voltage and current values at the end of a resistor as the state parameters, calculations of resistance circuits are introduced into symplectic system. Taking the simple resistance circuits, the multilevel resistance circuits in series and the complicated resistance circuits as examples, we present the solution method of transfer symplectic matrix. And the problem can be solved by combining the transfer matrix with the boundary conditions. Involving only simple matrix calculations, this method is easy to understand and program. It supplies a new and convenient calculation method for resistance circuits. The validity of this method is demonstrated by numerical examples. Introducing the symplectic method into the college physics teaching helps the students to understand and know the intrinsic properties of physics deeply.