多点同时谐振电路的分析与仿真

Analysis and Simulation of Multi-point Resonance Circuit

电路的谐振现象是对某一频率信号的特殊状态。电路理论中分析多个电感、电容元件串并联时的谐振问题,往往只考虑了在某一频率下电路中发生一点谐振的情况。但如果忽略电感、电容的损耗,同一支路中在某一频率下多点发生了并联谐振,阻抗均为无穷大,它们的电压如何分配?并联支路同时发生串联谐振,阻抗都为零,它们的电流如何分配?本文给出了分压和分流公式,并且通过仿真验证了公式的正确性,同时观察了时域暂态过程。

Resonance phenomenon is the sympathetic vibration of a circuit to a signal. The circuit theory of resonance only considered one- point resonance in some frequency. Then if there are multi - point parallel resonance in a branch, the equivalent impedance of each resonance point are all infinitely-great, how do they distribute the whole voltage？ If there are multiseries resonance in some parallel branches, the equivalent impedance of each resonance point are all zero, how do they distribute the whole current？ By mathematical reasoning we educe the formula of voltage distribution and current distribution, validate the formula by emulator.