The apple IIgs, like many computers from the 80's and early 90's, has a analog RGB output at a 15KHz horizontal frequency (same as NTSC/PAL). The majority of modern monitors and TVs will not sync to anything below 31.5KHz on their VGA input. If you have a TV with a SCART connector it is possible to wire the RGB directly to the TV. Most TVs in USA, however, use the YPbPr component instead of SCART making a direct connection not possible. GS2HD converts the IIgs RGB output to a YPbPr signal compatible with HDTVs with a component input.
The schematics is identical to the GS2HD-D00. layout changes were necessary to support RCA connectors with the more common GBR order instead of RGB which are becoming very difficult to find. U1A, U2A and U3A buffer and amplify the RGB signals (standard non inverting configuration with a gain of 2). U1B, U2B and U3B perform the matrix transformation from RGB to YPbPr according to the standard coefficients for SDTV.
Y = 0.299 * R + 0.587 * G + 0.114 * B
Pb = -0.169 * R - 0.331 * G + 0.500 * B
Pr = 0.500 * R - 0.419 * G - 0.081 * B
U5, L1, L2 and the associated capacitors provide a cleaned up power rails for the sensitive video circuits.
The basic circuit will work with pretty much any operational amplifier. However to achieve good video quality a high speed opamp optimized for video applications is required. Suitable devices are Analog Devices AD8056ANZ and Texas Instruments LM6172IN.