A novel model of general purpose operational amplifiers is made to approximate, at best, the equivalent circuit for real model at high-frequency. With this new model, it appears that certain oscillators, usually studied under ideal considerations or using many existing real models of operational amplifiers, have hidden subtle and attractive chaotic dynamics that have previously been unknown. These can now be revealed. With the new considerations, a ''two-component'' circuit, consisting simply of a capacitor in parallel with a nonmodified (and usually presented as a linear, negative) resistance, tends to exhibit chaotic signals. P-Spice and laboratory experimental results are in good agreement with the theoretical predictions.

In the framework of a project on simple circuits with unexpected high degrees of freedom, we report an autonomous microwave oscillator made of a CLC linear resonator of Colpitts type and a single general purpose operational amplifier (Op-Amp). The resonator is in a parallel coupling with the Op-Amp to build the necessary feedback loop of the oscillator. Unlike the general topology of Op-Amp-based oscillators found in the literature including almost always the presence of a negative resistance to justify the nonlinear oscillatory behavior of such circuits, our zero resistor circuit exhibits chaotic and hyperchaotic signals in GHz frequency domain, as well as many other features of complex dynamic systems, including bistability. This simplest form of Colpitts oscillator is adequate to be used as didactic model for the study of complex systems at undergraduate level. Analog and experimental results are proposed.