I'm looking for a low cost method to perform Eye Pattern Testing on 100MBit and 1 Gigabit Ethernet transceivers. I do not own a BERT and I have a 4 channel 500MHz DSO available.
Both 100 Mbps and gigabit ethernet over twisted pair require about the same amount of bandwith, so a 500 MHz scope should be good enough to get an eye diagram for both standards. However, if you are doing gigabit over fiber or SGMII, then this is not the case and you will need a faster scope.
Both 100 Mbps ethernet and gigabit ethernet run at a symbol rate of 125 MHz, so most of the signal is primarily from DC to 62.5 MHz. A 500 MHz scope provides 8x that bandwidth, so you should get a very good picture.
One thing you may want to invest in, however, is a good quality active differential probe so you can make accurate measurements. It is possible to subtract two channels with standard scope probes, but if they aren't exactly matched, you will get common mode to differential gain that can distort your eye measurement.
If you don't need to do automated tests, you can even use a plain old analog oscilloscope, and your 500 MHz DSO should be more than enough. Just hook it up to your ethernet connection using two channels (100 Mbps) or four channels (1 Gbit) and flood-ping the connection for a quasi-continuous signal (e.g. # ping -f 192.168.1.something).
Here's an example picture I took while diving into 10base2 (coax), but 100base-TX or 1000base-T should work in a similar fashion. The scope is a vintage Tek 454A (150 MHz). It's actually good enough for guessing the quality of the eye pattern. I guess even connecting your probes' grounded clips to one of each pair's wires should work because the ethernet transformers offer floating lines.
You won't get a Bit Error Rate value out of a scope unless that is a feature. You won't get a Y/N test value out of a scope unless that is a feature.
And you won't get an Eye Pattern out of a scope unless it has an Eye Pattern trigger setting, or a Window trigger setting. A Window trigger setting is fairly common now: does your scope have that feature?