Are Rin and Rl defined with the other end connected? For example, Rin must be right when a load is connected to the output, but can be different when the output is left open. The same question applies to the output impedance whether the input is connected or left open. I think you mean both input and output must be connected and of the correct impedance for the results to be valid, but I want to be sure before doing the math.

Yes, both are connected and both must see their respective impedances when they look into the taper-pad port (no tricks etc.). I'm probably going to post another unrelated question to give the site a boost. Maybe you should think about posting the odd question (that you can answer) given you are site maestro.

I have successfully solved your problem in the past using a spreadsheet to to determine all the correct values for a potentiometer to give the the desired s21 response from 5% to 100% of the pot value chosen.

I trust you can easily do the same.

Anectdotal

In my case I wanted to design a range of current to control an L317 with an NPN controlled bias to buffer10k thermistor to regulate fan voltage to correct thermal response from 40 to 50 'C on 48V fans from 0 to 100% voltage to smoothly regulate PSU hotspot temperature. (Tfmr) thus at 40'C fans would start slow and and 50'C under abnormal full load the fans could expel all the heat at 50'C max. I needed an effective plenum over the hotspots to maximize turbulence and linear air velocity for very low Rja. I chose the pad R values with a chosen thermistor and pot to set the 10 dec C range to spec. Goal seeking options in the spreadsheet made thus task trivial after the s21 and variables ('C) stated.or trials.

Good ruck.

Tony, why would I want to do what you did? It's a formulaic solution I require and not numbers.