[G0HZU_JMR]

What originally caused this debate was the observation of different results when comparing 1 port S11 measurements against 2 port S21 measurements when trying to measure a crystal with a VNA.

The issue here is that the capacitance to free space of one of the crystal legs will effectively be added to predicted parallel capacitance of the crystal when doing an S11 measurement. In the case of a 2 port S21 measurement this capacitance doesn't affect the through 'null' frequency.

There's also capacitance to the holder and then to free space and this is also not accounted for in the classic model. So I would expect to see a difference here of typically >0.2pF for the predicted parallel capacitance when comparing S11 and S22. It's a tiny difference but even a perfect VNA will show a different result for parallel resonance when comparing S11 vs S21. None of this matters in the real world. The existing model for a crystal (although incomplete) is extremely good and well accepted.