The mathematical and laboratory generation of prescribed periodic waveforms

A mathematical, normal form system, with the minimum dynamical order of two, capable of generating a wide class of periodic waveforms is presented. The techniques of the method may be used to enunciate an autonomous oscillator with the desired waveform appearing as one of the state variables, or the same basic approach will allow the construction of a simple waveshaping network that when driven with externally generated sine and cosine functions, will produce the same prescribed waveform. A canonic circuit is also given that, when used in such a waveshaping network, can obviate the realization of nonmonotonic curves. The oscillator produced by this method can sometimes lead to tunnel points, a concept introduced by Chua and Green. These points are thoroughly discussed in connection with the results, and a simple method is presented that can often eliminate these points, as well as lead to nonlinearities that are easier to realize in practice.