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Consider a series LCR circuit. Once power source is removed, the electrical energy oscillates for some time before damping out completely. I want a LCR circuit such that 1) it has high resonance frequency , say 1 GHz and 2) it oscillates for some time say 1 min.

Consider following numbers. To achieve 1 GHz, L and C must be very low. Let C=1 pF and L=25nH. This gives us resonance frequency around 1 GHz. At such high frequency the inductor wire will pose some resistance, let us assume R=0.001 Ohm, even though it is likely to be more. The attenuation factor $\alpha=R/2L$ is going to be high, which means the oscillations even if under-damped, will not sustain even for a second. Clearly there is a trade-off between high frequency and longer oscillation.

Is there a way to achieve both? It is ok even it is achieved without removing the power source, however, note that the voltage source is 10-100KV DC. Just keeping the LCR connected to the power source will not result in oscillations, in my understabnding.

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  • $\begingroup$ Inductors have reactance not resistance. $\endgroup$ – Sam Farjamirad Sep 15 '18 at 14:17
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    $\begingroup$ @SamFarjamirad inductors have resistance, they are made of conducting wires. also, as frequency of power supply increases so does the resistance of a wire (of inductor). $\endgroup$ – qazxsw Sep 15 '18 at 14:22
  • $\begingroup$ that's not the resistance of inductor, that's the resistance of the whole wiring circuit, if i take your value say 0.001 the ratio between this and R would results is a very small resistance that we neglect its effect in circuit THE GOOD CIRCUIT IS INDEPENDENT OF ACTUAL VALUES OF ITS COMPONENTS , the skin effect comes in to play when where are talking about large scale circuits like transmission lines. Talking about resistance of inductors is nonsense. $\endgroup$ – Sam Farjamirad Sep 15 '18 at 14:30
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    $\begingroup$ @SamFarjamirad you are missing the point. agreed that wiring will have resistance. but by making smaller in length and thicker in cross section you can reduce its resistance. my point is even if you make resistance of the wirings negligible, you cannot do away with resistance associated with the inductor, which even at very low values prevent me from achieveing the stated objectives. $\endgroup$ – qazxsw Sep 15 '18 at 14:42
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    $\begingroup$ @SamFarjamirad get any real-world inductor, as used in any electronic circuit you like, and put an ohmmeter across it. You are confusing the idealized components used in "AC electrical circuits 101" with the real world. And real world inductors also have self-capacitance - they can resonate all on their own, without an LCR circuit. See wiki.analog.com/university/courses/electronics/comms-lab-isr if you don't believe me. $\endgroup$ – alephzero Sep 15 '18 at 14:44

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