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I have a coil with approximate indutance of 15uH used to detect metal through changes in inductance. I want to use an op amp or 555 to oscillate with frequency based on the inductance. However this frequency needs to be ~< 10kHz to be read by a sound card.

Are there any circuits that can oscillate at these low frequencies with small inductances or is there a limitation?

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It will be a problem getting 15 uH to resonate below 10 kHz but you can always run it at several hundred kHz and divide the frequency down with digital dividers. I'd recommend using a colpitts oscillator and there are plenty of examples on the web: -

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Feed the output to a comparator (maybe a TLV3501) and then onto logic chips that can reduce the frequency to below 10 kHz (maybe a 4040 clock divider).

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