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Why does the tunnel diode current in this circuit oscillate over time? I had trouble understanding the given explanation.

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Specifically, why doesn't the voltage across the tunnel diode rise to a steady state and then dictate the current through the diode based on the V-I curve?

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In Simple Terms, Why does the Tunnel Diode Oscillate in This Circuit?

In simple terms because a tunnel diode's voltage-current characteristic has a region of negative resistance. And, you can make a "theoretical oscillator using a -10 kΩ resistor and a tuned circuit like this: -

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Simulation proof: -

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Here I'm using back-to-back diodes to limit the amplitude of the sinewave. It's all down to negative resistance: -

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Image from OP's link. Between A and B there is negative resistance; as voltage increases, current falls.

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