基波平衡原理在多端口网络的应用

Fundamental Wave Balance Principle is Applied to Multi-Port Network

对于网络仅含一个压控非线性元件,用基波平衡原理由输入导纳G=0,B=0求振荡频率ω和基波振幅U_m.如果有合理的(ω,U_m)∈R^2,则网络存在有周期振荡或混沌振荡.对于网络含有两个压控的非线性元件,可以用埃米特式计算进入双口网络的实功P和虚功Q,由输入功率P=0,Q=0求振荡频率ω和基波振幅U_m.如果存在有一组合理的(ω,U_m)∈R^2,则网络存在有周期振荡.如果存在有多于两组合理的(ω,U_m)∈R^2,则网络存在有混沌振荡.

Regarding network containing only a voltage-controlled nonlinear element, the oscillation frequency w and first-harmonic amplitude Um can be found from the equation （G, B） = （0, 0） by using the fundamental wave balance principle, where （G, B） represents the input admittance of control port. If there are reasonable （w,Um）∈R^2, network possess cycle or chaotic oscillation. Regarding the nework including two voltage-controlled nonlinear elements, the active power P and reactive power Q received by two-port netword can be calculated by hermitian forms. The oscillation frequency w and first-harmonic amplitude Um can be found from the equation （P, Q） = （0,0）, where （P, Q） represents complex power entering the two-port network. If there is single reasonable（w,Um）∈R^2, network possess cycle oscillation. If there are ore than two reasonable（w,Um）∈R^2, network possess chaotic oscillation.