Synthesis of electrical oscillators based on principles of symmetry and reflection

The paper discusses the possibility to apply principles of symmetry and reflection for analyzing and synthesizing oscillators of electrical signals. It is established that the principle of symmetry is better to be used for synthesizing oscillating systems based on two-port elements, while the principle of reflection – for synthesizing systems based on one-port elements. The synthesis of oscillating systems using the principle of symmetry is shown to be realized by inverting certain operators of elements of the oscillation system: complex transfer or amplitude characteristics of two-port elements. The synthesis of oscillating systems using the principle of reflection is performed by mirroring amplitude admittance characteristic of a linear one-port element into amplitude admittance characteristic of a nonlinear one-port element. The proposed approach is demonstrated for synthesizing oscillating systems of electrical oscillators; however, it can be applied to analyze any cyclic process.