Recently I'm reading in-depth about butterworth filters, more specifically about the normalized values the tables give. Most of the tables give you the normalized values for the case of RL/RS=1 or RL/RS=∞ but I have found a table that gives the values for other ratios too.
Now the equation that these values come from (maybe this not the only way) is the Cauer topology equation that is shown here (equation 10.5.1):
But this equation is valid only for RS=RL=1Ohm so my goal is to find out the general equation that counts in the RS and RL to be able to calculate the normalized values for any resistors ratio.
For some reason I can't find where this equation came from or how it can be changed to include the resistors as parameters.
How can I generalize this equation?