# Studying the schematic for educational purposes

I've been studying the schematic for the A520HD to better understand the process of converting RGB to YPbPr. I believe that I've come to understand how it works, but my new question is how the designer found appropriate values for the resistors.

From Wikipedia: Y = 0.2126 R + 0.7152 G + 0.0722 B
or as a ratio,
0.2126
0.7152
0.0722

Y_IN on the schematic is indeed a composite of R, G, and B, but appears at first glance to be very far out of the ratio described by Wikipedia. In my first look at the composition of Y_IN, I naively determined that it was formed solely by mixing R through R10, G through R11, and B through R13. The ratio I got from this assumption is

0.00119760479041916167664670658683
0.0023696682464454976303317535545
4.4247787610619469026548672566372e-4

0.2126
0.4207 (under by 0.3485)
0.0785 (over by 0.0722)

You can see that the Green value is way off. That's when I realized that Y_IN is not formed solely by the network of R10, R11, and R13, but is also formed by the network of R7, R9, R25, R27, and to a lesser extent R26/R8/Cr_O/Cb_O. (Throwing Cr_O and Cb_O into the mix is obviously not intentional but seems unavoidable to me.)

The resistance between Y_IN and G_BUF is not simply R11, but the parallel resistance of (R11, R10+R25+R27, R13+R9+R7). B_BUF and R_BUF are similarly complex.

Taking all this into account, the resistances that form Y_IN are actually 773.62 to R_BUF, 373.93 to G_BUF, and 1597.76 to B_BUF. That ratio is
0.00129262428582508208164214989271
0.00267429732837696895140801754339
6.2587622671740436611255758061286e-4

0.2126
0.4398 (under by 0.2754)
0.1029 (over by 0.0307)

That's much closer to the ratio given by Wikipedia, and it kind of blows my mind that someone was able to account for these resistances that I would consider to be parasitic.

I imagine that there's still something more about this design that I don't understand which might bring the ratio for calculating Luma even closer to perfection. Knowing that the relationship between Luma and Pb/Pr is cyclical by way of negative feedback, what sort of thinking brought the designer to these surprisingly precise resistor values?

### YPbPr Equations

The equation you quote reflects the HDTV signal conversion matrix (ITU-R BT.709).
The GS2HD follows the ITU-R BT.601 (formerly CCIR 601) standard for YPbPr conversion.
The BT.601 is the conversion used for SD signals which we believe is the right conversion matrix given HDTV did not exist in the 80s.
According to BT.601 the equation for Y is:
Y = 0.299 * R + 0.587 * G + 0.114 * B

substituting the resistor refdes:
Y = R * ((R11||R13)/(R10+(R11||R13))) + G * ((R13||R10)/(R11+(R13||R10)) + B * ((R11||R10)/(R13+(R11||R10)))