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Since I don't know if your TV can handle AC coupled composite video, I designed this with the luma channel being DC coupled. If you don't like this op amp (it's a dual), you need to pick one with at least 30 MHz gain-bandwidth product, and capable of driving at least +/- 20ma. With the op amp shown, vcc and vee can be +/-5 volts to +/-15 volts. You should have a 10uF tantalum cap from each supply voltage to GND, and a 0.1uF ceramic cap from each power supply pin to GND, with the leads and the power traces as short as possible.
Here is the datasheet for the op amp.
You could get by with a single supply if your TV can accept AC coupled composite video, but you would need 100uF polarized caps in series with the luma input and the output, and a voltage divider with capacitor decoupling to reference the non-inverting inputs to.
Added 75 ohm termination resistors to the inputs.
I edited the schematic to add input termination resistors.
It will work with PAL or NTSC. To test for AC-coupled operation, you can add a 100uF cap in series with the luminance output on the s-video connector and connect that to the composite input of your TV. Don't forget to add a ground connection between the two connectors also. If you get a monochrome signal that looks good, then your TV is handling AC-coupled video. Watch for luminance-level (brightness) drift after scene changes where the brightness has made a sudden change. If this happens, you probably need to be direct (DC) coupled.
I have worked with video for many years, but as you can see, I'm not very familiar with TV input circuitry. My best guess is that, in order to handle all possible video sources, TVs are AC-coupled on the input, with a subsequent DC restore circuit (keyed off horizontal sync) to get back to DC. I think there were, and still may be, some cheap sets that are AC coupled all the way through.
I also came across this link. It shows a modulator which can take a
luma + chroma and give a composite out. I think it has a poor performance, though. It was used in the video output of the Commodore 64 computer (very old!).