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I created the following square wave oscillator in LTspice, which works fine. But I'm not sure how to choose the values of the components. I manually adjusted the values of C1, C2 and L1 until I got a frequency of approx. 1MHz.

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Is it possible to calculate the resonance frequency similar to this? $$f_0=\frac{1}{2\cdot \pi \cdot \sqrt{L\cdot C}}$$

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Is it possible to calculate the resonance frequency similar to this?

Yes it is.

The type of design is called a colpitts oscillator and the resonant frequency formula used modifies C to be the effective series value of the two 10 nF capacitors i.e. 5 nF.

If you use 5 nF and 5 uH in the formula you get a resonant frequency of 1.00658 MHz.

The theory is a little long winded but here is an example for the common-collector colpitts oscillator used in many RF applications. Note that you can apply the same math to your circuit by regarding the "emitter resistor" as the inverter's output driver resistance. Also L and C2 swap places but the resonant frequency turns out to be exactly the same formula: -

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For a colpitts oscillator that uses an inverter, it needs to be a type that isn't a schmitt trigger device or you will get harder-to-predict results. Maybe try making Vh = 0 and see what happens.

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