The Agilent document goes through a couple of variations on those 3 themes, basically varying the input impedance of the ports on the VNA (1Meg as well as 50 ohm options). Interesting to see how it compares.
I don't understand the purpose of the common mode transformer in the Copper Mountain setup... looks like a way to prevent ground loops? Why would that be necessary, since everything is connected to the same device?
Attached Agilent document for reference.
Yes, they are trying to show you why you may want to use one method over another. It will depend what you are trying to measure. This is what the Copper Mountain document is also trying to convey.
I am not sure what Copper Mountain setup you are referring to that is using a common mode transformer.
Assuming you are actually asking why I am using the two impedance matching transformers with my setup compared with the resistive pads I started out with, then the answer is simple. The pads have too much loss to get reliable results with the Nano, depending on the crystal being measured. The reason that the resistive pads work fine with my older HP systems is that they have a much lower noise floor than the Nano. If you look at the graphs I've provided, the first fixture has a loss of 30dBish compared with 6 with the new fixture. When you are playing with a $50 instrument, you need to give it a little help. IMO, this isn't a big deal. It's $50. The fact I am able to pull out sub PPM data with it is impressive.
When I made the videos for the Nano, I had played with a couple of crystals. One was measured using S11 (shunt) where I provided a simple example of making a model for SPICE. The other, I had one in series showing the resonance. The first thing I did was try to use the crystal directly connected and the standard deviation was very poor. The papers I attached early on are what led me to use the pad to try and improve the match.
I think if you go back and read these papers, you will find I am not doing anything unusual or novel. What I have shown is we have a $50 VNA that can directly making ALL of the required measurements using a single fixture.
Still no work about the reference crystal.