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The Growth of Oscillations in Two-Resonator Negative-Conductance Oscillators

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The simultaneous nonlinear differential equations for an oscillator having two resonators of different frequencies are solved by means of a simple graphical procedure leading to curves of the square of instantaneous amplitude of voltage across one resonator versus the square of instantaneous amplitude of voltage across the other resonator. Families of these curves for various combinations of resonator parameters show clearly that if the shunt conductances of the two resonators are equal and the capacitances are also equal, the steady-state mode of oscillation is determined by random noise. If the capacitances are equal, but the conductances unequal, the probability is high that steady-state oscillation will be in the mode controlled by the resonator having the lower shunt conductance. If the conductances are equal, but the capacitances unequal, the probability is high that the steady-state mode will be that controlled by the low-capacitance resonator. If one resonator has much larger conductance but much smaller capacitance than the other, the oscillation may first build up rapidly in the mode controlled by the low-capacitance resonator, but reach the steady state in the mode controlled by the low-conductance resonator.

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Circuit Theory, IEEE Transactions on  (Volume:15 ,  Issue: 3 )