Application of bifurcation control to practical circuit design

Bifurcations delimit the operation bands of many nonlinear circuits. Thus, the capability to preset these bifurcations at the desired parameter values will be of invaluable interest for practical design. In this paper, simple conditions for bifurcation control are presented. They are based on the use of auxiliary generators and can be implemented in both in-house and commercial harmonic-balance simulators. The control is performed through the introduction into the circuit of feedback networks, whose values are calculated in order to fulfill the desired bifurcation conditions. Through the control techniques, it is possible to preset the operation bands of complex circuits, such as synchronized and voltage-controlled oscillators and frequency dividers. They also enable the elimination of hysteresis phenomena. They have been tested by means of their application to practical microwave circuits, with very good results in comparison with measurements.