Most conclusive would be to look up what paper it's from. (Does it say? Look in the help? Ask a developer? Check the source for comments?)
Offhand,
TanD (D is lowercase delta) = dielectric loss tangent (the dielectric isn't purely capacitive, but has an imaginary component as well; delta = real/imag)
rho = resistivity of copper
H = height (either copper trace thickness, or laminate thickness / height over ground plane)
H_t = height again? Oh probably height of trace, and other one is over plane.
T = thickness? Or maybe Trace width?
Rough = roughness parameter. Must be a good model to have this? Although I don't see frequency in here, which matters. Maybe it's just a scalar for resistivity.
mu = ? Would be permeability something or other, but who uses permeable materials? Don't understand the Rel, S and C parts.
In any case, a very accurate calculator isn't very useful, as fabs are only 5% tolerance -- and that's if you pay them enough to use the best materials, and measure the results! (Well, RF fabs are probably better than that, but...)
If you're doing controlled impedance for digital signaling, 20% (which is typical of most main line fabs) is good enough.
Note also that, if you have ground poured on the same layer, that reduces impedance. That structure is called a coplanar waveguide.
Note further that, for standard fab widths (minimum trace width) and component pitches (maximum practical trace width), you can't get impedances very low on two layer board (even 0.8mm thickness). A 50 ohm trace (CPW, minimum clearance) is about 1mm wide, on 1.6mm board. Typical impedances are in the 100 ohm range (which, by the way, works very nicely with most CMOS logic; add a 47-100 ohm source termination resistor, and you're mostly good to go). Controlled impedance designs, needing lower impedances (like 100 ohm diff pair), really have to be done on multilayer boards.
I like these calculators:
http://www.chemandy.com/calculators/calculator-index.htmThey include three different formulas for microstrip. Take your pick. Which one is best? I refer you to my above discussion on fab accuracy.
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Tim