If an LC circuit is connected across the input of a positive feedback amplifier like that above, the negative differential input resistance R if can cancel the positive loss resistance r loss inherent in the tuned circuit. If R if = − − r loss this will create in effect a tuned circuit with zero AC resistance (poles on the jω axis). Spontaneous oscillation will be excited in the tuned circuit at its resonant frequency, sustained by the power from the amplifier. This is how feedback oscillators such as Hartley or Colpitts oscillators work. This negative resistance model is an alternate way of analyzing feedback oscillator operation. All linear oscillator circuits have negative resistance although in most feedback oscillators the tuned circuit is an integral part of the feedback network, so the circuit does not have negative resistance at all frequencies but only near the oscillation frequency.