Does anyone have good reading for how to calculate the frequency response of a CTLE equalizer?

Right now I model it as gain G1 from DC to Fz, linearly ramping to G2 at Fp1, constant G2 until Fp2, then instantly going to zero at Fp2.

I know this isn't ideal but how do I improve?

I'm reading stuff like https://www.serdesdesign.com/home/about-the-ctle-analysis-tool/ which is absolute Greek to me. Other docs show equivalent analog circuits.

If I can just get a frequency domain transfer function (gain,phase)=F(freq, config vars) I'm good, but WTF are "S domain" and "Z domain" transfer functions?

I think what I'm modeling is a very chonky version of a "2 pole 1 zero" equalizer but how the math produces anything that looks like this is just @_@.