The Sega Mark III console has RGB output, but it's very weak. This amplifier will cure the problem.
It may also work with later revisions of the SG-1000 II which use an RGB-capable VDP, but this has not been tested.
You can also substitute the above amp with one based around the THS7314 chip. The amp design is based on the one found here, which was originally designed for the N64. The RGB inputs for the THS7314 are tapped directly from the VDP (these outputs are also marked on the motherboard), while 5V and ground can be pulled from the 7805 regulator. The resulting image will be very bright, so you may want to replace the 75 ohm resistors with ones of a higher value. Also make sure to cut the traces for the RGB outputs on the AV jack before wiring up the amplified outputs! For sync, the pre-existing composite sync signal will work fine, although the composite video signal will suffice as well.
As with the amplifier design above, this circuit may also work with the later version of the SG-1000 II.
Many thanks to Backup Technique (バックアップ括用テクニック) magazine (Volumes 8 + 9), from where the diagram for the first circuit came.
Thanks also to Kevin Horton, for helping fix the diagram, which was incorrect.