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What I said was more of a general theory rather than exactly what to expect. There are too many variables to say with any certainty.  Look how a parasitic element can change the feed point impedance of an antenna.  Structures near the coax will do the same.  I merely brought it up as a partial explanation for a lack or presence of common-mode current.


If you are going to use a choke, why bother with any of this??


Although I have not tried yet, if I absolutely had to manipulate the common-mode impedance by altering the coax length, I would probably use the vertical as a counterpoise and connect the VNA to the common-mode path (but it would take a custom connector to disconnect the center conductor from the antenna so it wasn't being driven from above).  That should allow me to make adjustments to the coax watching for a high impedance point.


Regarding your lengths, if the polyphasor is grounding the coax shield, then we are talking about odd multiples of quarter wavelenths as a ground a half wavelenth away will appear as the same low impedance at the beginning of the common-mode path.  I also think that using the velocity factor for the inside of the coax will be an issue.  The velocity factor on the outside is much closer to that of the VF in air.  Dielectric constants and the associated formulas for VF, the other conductor needs to be in close proximity confining the signal in that material for it's dielectric constant to matter.  Trim a dipole made of 14ga wire with PVC or THHN coating.  Its VF above 95%,.  Just put a choke on it ad call it a day.