Oscillator insights based on circuit Q

The concept of negative circuit Q is introduced as a basic oscillator characteristic necessary for signal growth. A limit cycle at steady state causes the circuit Q to increase asymptotically towards infinity and finally transition to positive Q . The introduction of noise forces the loop gain to be less than unity and the steady-state Q to be finite and positive. Circuit Q is then principally determined by a limiting relationship on loop gain. Examination of a Norton equivalent circuit for a feedback oscillator indicates that positive and negative Q branches are present, and that the closed-loop dissipation factor is nearly zero. By considering the oscillator to be a tuned noise amplifier, the steady-state circuit Q is found to be a determining factor in several areas of oscillator characteristics, including phase noise and frequency modulation. Fundamental limitations on modulation frequency for voltage-controlled oscillators are examined, with experimental data indicating the potential for nonsymmetrical sidebands for modulation frequencies greater than f₀/2Q_L