RLC-oscillator with smooth transition from sinusoidal to relaxation oscillations

The paper considers transition from sinusoidal to relaxation oscillations in the RLC-oscillator the frequency of which is tuned by the resonator capacitance. The active element of this oscillator is a transconductance amplifier with limited output current. When the tuning capacitor is large the oscillations are nearly sinusoidal. Diminishing the tuning capacitor value one moves smoothly from sinusoidal to relaxation oscillations, and when this capacitor is reduced to zero value the oscillator becomes an RL-(magnetic) multivibrator. The transition is illustrated using two root loci; the first is called the placement root-locus, and it describes the location of characteristic equation roots when the tuning capacitor changes but the oscillations have not started yet. The second root locus is called the dynamical root locus, and it represents the periodic movement of the root locations within one oscillation period, and the oscillator is in steady-state oscillations. The oscillator was realized using a bipolar transconductance amplifier and then tested, and smooth transition from sinusoidal to relaxation oscillation was confirmed.