Preprint Nonlinear Circuit Algebra: When your Impedances Resist Linear Analysis

Nonlinear system behaviour becomes increasingly more important in electrical circuit theory: As system frequencies get higher, physical linearization strategies cease to be effective. Nonlinearity is often a limiting factor of system performance, while at the same time it is often left out of thorough analysis due to the topic's perceived complexity. This work aims at giving an intuitive understanding of nonlinear electrical systems, drawing heavily from well-known principles in electrical engineering. Emphasis is put on the fact that Volterra operators are capable of replacing complex, frequency-dependent impedances, gain functions, or two-ports, be it in circuit analysis or in feedback system design, while keeping the classical notation mostly unchanged. Nonlinear circuits can become mathematical objects, making them accessible to powerful mathematical operations, similar to those that are used on complex numbers. Although designed to be simple, our notation nonetheless relies on a few computationally expensive operators. Since we want to make Volterra series useful, we aim at an easy, yet complete overview; therefore, we also include a section describing the operators in more detail. A practical example of circuit analysis is included at the end, where a class-A amplifier is analyzed, and the similarities to linear circuit theory are demonstrated.