T he main harmonic components in nonlinear differential equations can be solved by using the harmonic balance principle .The nonlinear coupling relation among various harmonics can be found by balance theorem of frequency domain .The superhet receiver circuit which is de‐scribed by nonlinear differential equation comprising even degree terms includes three main har‐monic components ,the difference frequency and two signal frequencies .Based on the nonlinear coupling relation ,taking superhet circuit as an example ,this paper demonstrates that the every one of three main harmonics in netw orks must individually observe conservation of complex pow‐er .The power of difference frequency is from variable‐frequency device .And total dissipative power of each harmonic is equal to zero .This conclusion is consistent with the traditional harmon‐ic analysis .The oscillation solutions which consist of the mixture of three main harmonics pos‐sess very long oscillation period ,the spectral distribution is very tight .It can be illustrated that the chaos is sufficient or infinite extension of the oscillation period .In fact ,the oscillation solu‐tions plotted by numerical simulation all are certainly a periodic function of discrete spectrum . When phase portrait plotted has not finished one cycle ,it is show n as aperiodic chaos .%根据谐波平衡原理求出的微分方程中一部份主要谐波成分，以及频域平衡定理求出的各谐波成分相互之间的非线性耦合关系，以偶次项与超外差电路为例，证明网络中3个主谐波的每一成分，复功率各自守恒。差频的功率来自变频元件，全网络每一谐波成份的功率总消耗等于零，与用传统谐波分析法的求解结果是一致的。3个主谐波混频造成的振荡解，其公共基频很低，稳态的总体输出有很长的振荡周期，频谱的分布非常密集。事实上，数值仿真画出的一切振荡解，必然都是离散频谱的周期解。当相点画出的相图还没有完成一个周期时，就显示为非周期性的混沌。
展开▼
