Approximating Via Characteristics
Lets say I have a signal that is X GHz, is there a specific anti pad size to ensure I have correct signal propagation?
Does the anti pad only add a delay or extra capacitance?
"Correct" signal propagation is a quite difficult thing to quantify without knowing exactly what you are looking for.
It is true that varying the diameter of antipads will vary the parasitic capacitance, which - depending on what you are looking for - may be acceptable or desirable for maintaining line impedance.
Equation [7.6] in High-Speed Digital Design by Johnson and Graham provides an estimate for this capacitance -- by their own admission, a very coarse estimate. This model approximates the via as a coaxial, simplifying the geometry and omitting fringing fields.
[Equation 1]
Where D₂ is the clearance hole/antipad in inches, D₁ is via diameter in inches, T is board thickness in inches, εr is relative permeability, and C is parasitic capacitance in pF.
[Equation 2]
Where h is the via length in inches, d is via diameter in inches, and L is parasitic inductance in nH.
They go on to compose their capacitance approximation with the equation —
[Equation 3]
to give a coarse estimate of the rise time in the via, where T is in ps.
The Saturn PCB Toolkit also has a via calculator that can make estimates for these values.
Thus, given that, you can find a comfortable rise time for which the eye width of your whole system is acceptable with the addition of jitter. Every standard will have some guidance for when the signal must be settled, which ultimately translates into a diamond, usually called an eye mask. This report from Diodes Inc., seemingly exported directly from their 25GHz (!!!!)* oscilloscope, provides some realistic values for an HDMI 2.0 link, including showing the aforementioned eye mask on page 6.
Realistically, using simulation software like ADS is the best way to get a good picture of your signal integrity before fabrication and testing. So many approximations and empirical formulas are needed to characterize a whole link that the guidance they provide can become inaccurate by the end of a long chain of elements.
Bar that, this approximation in addition to a heap of other good practices will usually lead to a working system. The books High-Speed Digital Design and High-Speed Signal Propagation are usually considered a good primer on this subject. These books are aging, but still contain excellent advice.
*4x $33,000 20GHz active probes and an oscilloscope with an MSRP nearing $230,000, not to mention options.
