FYI, there are no "simple" VGA to component adapters. If you search Amazon and the like you'll find what appear to be VGA to component cables. But they won't work for you. Those are used by older projectors which had for VGA and YPbBr on a single VGA style plug. Check the review for them and they are filled with disappointed people wanting to connect them to a PC and get component output just like you.

It looks like your 7970 has DVI and DP ports. I'd suggest getting a DP -> HDMI adapter, then a HDMI -> component convertor. Bob from RetroRGB has been doing some recent testing, check to see if this might be the right solution for you.
https://www.youtube.com/watch?v=BUgTIOqetYU

If you want to have a fully analog path you could do a more complex setup.
DIV -> VGA
VGA (RGBHV) -> SCART (RGBs)
SCART (RGBs) -> Component (YPrBr)

Update, someone is actually making custom boxes and they are in stock right now, grab one now while you can. Here's a thread discussing it, at the top there's a dead eBay link and a second working one.
https://www.reddit.com/r/crtgaming/comments/l … d_rgbhv_or_vga/

There's a DVI component adapter which should work fine with the DVI-I port on 7970. Some late AMD cards were even shipped with those.

It depends on the operating system.
When connecting a CRT TV to a PC via VGA, two problems arise:
- interlaced frame scanning
- lack of DDC, which means the PC doesn't know what resolutions and frequencies the "monitor" supports
This problem used to be solved with custom-moded drivers, but they no longer work.
The most reasonable solution is a good HDMI-Scart scaler.
https://cpc.farnell.com/pro-signal/psg3369/hd … t=scart%20plugs
HDMI-DVI is a standard passive cable that doesn't cause any problems.
Well, unless it's of absolutely terrible quality.

The Serpent Rider wrote on Yesterday, 00:14:

There's a DVI component adapter which should work fine with the DVI-I port on 7970. Some late AMD cards were even shipped with those.

this? ATI DVI (M) to Component (RGB) HDTV Adapter for Video Cards - 6140016400G

Yeah, this one.

djsabreblade wrote on Yesterday, 09:43:

The Serpent Rider wrote on Yesterday, 00:14:

There's a DVI component adapter which should work fine with the DVI-I port on 7970. Some late AMD cards were even shipped with those.

this? ATI DVI (M) to Component (RGB) HDTV Adapter for Video Cards - 6140016400G

As far as I know, this adapter didn't work with any video card starting with the HD5xxx series.
These video cards effectively stopped supporting analog TV output.
I wonder if it will work with the HD7xxx?