your got detect if use diierent w.balance at raw to convert b&w is diffrent?.
let say you use around 6500k(warm),you can found red channel is more bright,but also most blur,blue is most dark,but it is more sharp... if u use around 2350k(cold),is totally reverse with 6500k..so if use channel mix,i use diffrent way to convert it...normally is red +,green+,blue-,but it not suit for all w.balance....