I am learning about Butterworth filters right now, so we are also learning about frequency scaling. To find the new transfer function after you frequency scale something by Kf, you simply divide all 's' by Kf. I am doing a homework problem where you have to find the new location of the poles and the gain constant. Here is where my confusion happened. The DC gain of the transfer function does not change from what my calculations showed, but the answer was saying to multiply it by Knew=Kold*Kf^n where n is the order of the BW filter. I am rambling on now. From what I get in my book, DC gain is different from the transfer function gain constant. DC gain is what happens to an actual signal when you put it through. What does the transfer function gain constant represent then? All my confusion started when I assumed they were the same thing.