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When a negative resistance device is used with a LC tank circuit, whose impedance is frequency dependant, there will be one frequency for which the negative resistance of the device will be exactly equal to the positive resistance of the LC tank circuit. Thus the 2 will completely cancel out and that frequency will have no resistance so will increase in amplitude until it is limited by the negative resistance device and thus will become a stable oscillation.
It is well known that oscillation occurs when magnetic energy transfer to electric energy back and fort between both the Inductor and the Capacitor of the tank circuit. This is what ideally happens when there are no losses. (high quality factor)
Q=ωL/R or 1/(ωRC)
but for practical inductors, or capacitors, we have a resistor modelling the loss in both the inductor and Capacitor, this causes oscillation to decay, or in another words to be a damped oscillation.
-ve resistance devices are used to compensate for that loss, cancelling it's effect at the oscillating frequency, which helps in the stability of oscillation at that frequency, while other frequencies damp or decay.
so we get better Quality factor for the oscillator.
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