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GND pins are connected inside FPGA with mutual impedance of no more then several Ohms and with some parasitic inductance.
When one or more GND pins are disconnected, it will slightly increase FPGA's GND plane resistance (which is of a little importance in most cases) and plane inductance (which can increase ground bounce for fast output drivers in some situations).
It's interesting question! the GND pin was there for a reason. The fist thing I know is the chip will have degrade performance. In CMOS we need path to VCC for the pull up and GND for pull down. If one of the ground pin was disconnect, the pull down resistance will be higher and it wook make a lower transition on falling edge. In general, the propagiation delay will be longer.. It may not affect if your design is working in a very low frequency than the chip's spec, but in general, it will give you a failure
Once I saw a schematic for one of Xilinx FPGAs, GND pins were connected to each other with a ring inside FPGA.
Any how In Virtex-II data sheet there is a limitation for maximum simultenous output switching. This value is defined due to number of VCC , GND pins, e.g. for each VCC and GND pin you can have only 12 simultaneous output switching pins (of course for a special signaling standard and drive strength) . may be, this shows that the correct connection of each GND pin to real ground is some thing important.
Re: What will it be if one GND pin of my FPGA is disconnecte
Your chip will work anyway...
not 100% but....some I/O will not work properly... or if it will work then it will be noisy......
there will be many GND and VCC pins .. these gnd and VCC will be the core voltage of the chip. and some are for I/O voltage....
So it that GND will be related to I/O bank then those I/O wont work... otherwise chip will work nicely..