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If I have a device that outputs HD YPbPr component video (through three cables: Y, Pb and Pr), can I use a single cable and connect it to only the green Y (luma)-jack to output SD composite video to a non-HD TV?

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If that "HD device" is set to output 480i (or other non-HD resolution that is compatible with the "non-HD TV"), then connecting the green Y (luma) output-jack to the composite input should produce a grey-scale (aka black&white) image.
Since there is no color (chroma) information in the Y signal, it's not really a composite video signal. But it does have H and V sync pulses to make a compatible signal.

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No. The "composite" part of the term indicates that a sync pulse, half a luminance frame and a compressed color burst have all be sent, in turn, on the same wire. The reason it is Standard Definition is because the color had to be compressed to fit it into the waveform, limiting its accuracy. Component video is high def because the color is output, uncompressed, on a separate wire, and because you can switch to a frame with more lines.

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