I checked the cable resistance of BF LVDTs.
Results are as follows and BF V2 primary coil seems broken somewhere inside the chamber.

-Port 1-2(Primary coils): these should be around 24 ohms according to the documents

1-6 (V1): 25 ohms
2-7 (V2): overflow (more than several Mega ohms)
3-7 (V3): 24 ohms

-Port 1-4 (Secondary coils): these should be also around 24 ohms according to the documents

1-6 (V1): 24 ohms
2-7 (V2): 24 ohms
3-8 (V3): 24 ohms