Kevin Aylward
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First, what you posted is the generalised Colpitts oscillator. That is, ANY single device configuration that has a capacitor, effectively across its drain source and a capacitor across its gate source. A Pierce is defined as having a resister from the drain in series with the drain capacitor, to form a pi network. This resister is important. It reduces both sensitivity to DC supply, and lowers 1/f up converted phase noise. Always use it, period, unless you simply don’t have enough gain at frequency.
Ignore all the equations. There are useless. All xtals in the known 3 universes from manufactures are specified to run on only a handful of standard load capacitances. These will be, 30p/2, 20p/2 or 13.5pf/2. i.e. make the caps the same. To check enough loop gain stick a voltage source in the gate lead and run Cadence stb analysis. Run transients with a “DeQed” xtal of say, 100 times. i.e. multiply the c1, series capacitor by 100. C1 is typically 1ff to 20ff. Use 10ff X 100 as a starter. The bigger the cap, the more frequency stable but harder to get the gain at high frequencies.
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