What is the effect of the anti-pad size on the impedance of a via in a high speed channel?

What is the effect of the anti-pad size on the impedance of a via in a high speed channel? The anti-pad is the clearance hole in each ground plane through which the via passes, and its size directly controls the capacitance and impedance of the via: (1) Via impedance model: the via acts as a coaxial transmission line: the via barrel is the center conductor, and the anti-pad edge (ground plane opening) is the outer conductor. The characteristic impedance: Z_via ≈ (60 / √Dk) × ln(D_antipad / D_drill). Where D_antipad is the anti-pad diameter and D_drill is the drill hole diameter. Smaller anti-pad → more capacitance → lower Z_via. Larger anti-pad → less capacitance → higher Z_via. (2) Typical values: standard anti-pad = 30 mil, drill = 12 mil, FR-4 (Dk=4): Z_via ≈ (60/2) × ln(30/12) = 30 × 0.916 = 27.5 ohm. This is well below the 50 ohm target, causing a reflection. Enlarged anti-pad = 50 mil: Z_via ≈ 30 × ln(50/12) = 30 × 1.427 = 42.8 ohm. Still below 50 ohm but much better. Anti-pad = 72 mil: Z_via ≈ 30 × ln(72/12) = 30 × 1.792 = 53.8 ohm ≈ 50 ohm target. (3) However, the anti-pad size has trade-offs: larger anti-pad weakens the ground plane (removes copper, reduces ground plane continuity). Larger anti-pad increases via-to-via coupling (less shielding between adjacent vias). Very large anti-pads can cause signal integrity issues for other signals routed near the via. (4) Optimization: the optimal anti-pad size is the one that brings Z_via closest to 50 ohm without excessively weakening the ground plane. Use 3D EM simulation to find the optimal size for your specific stackup. For differential vias: the anti-pad affects both the single-ended and differential (odd-mode) impedance. Separate anti-pads per via are often used (each via has its own clearance). Alternatively: an oval or "racetrack" anti-pad (one clearance hole for both vias of the differential pair) can be tuned for the differential impedance.