Via Transitions, Stubs, and Backdrilling

A via is the only component on a board whose geometry is dictated by the fabrication process rather than by the circuit. Its drill diameter is set by the smallest bit the shop will run, its pad by the registration tolerance, its length by the board thickness, and its position by the router. On a high-speed net the via is therefore almost always the worst-controlled impedance in the path, and on a thick backplane it can be the dominant source of loss.

The barrel as a coaxial section

A plated through-hole is, electrically, a short length of coaxial line. The barrel is the inner conductor; the planes it passes through are the outer conductor, with the clearance hole — the antipad — setting the outer radius. The impedance of that section is

$$Z_{via} \approx \frac{60}{\sqrt{\varepsilon_r}} \ln!\left(\frac{D_{antipad}}{d_{drill}}\right)$$

with both diameters in the same units. A 0.25 mm drill in a 0.75 mm antipad in FR-4 gives an impedance near 32 Ω by that approximation; a 0.45 mm antipad gives about 17 Ω, and reaching 50 Ω would need an antipad about 1.4 mm across, which no dense plane can afford. That is the central awkwardness of via design: the barrel is almost always lower in impedance than the trace it serves, and the only knob that would fix it costs plane copper and return-path quality. The problem is never the transition alone, though; it is what surrounds it.

Around the antipad the return current must divert. The plane has a hole in it, and the current that was flowing directly beneath the trace must travel around the hole to reach the other side. That detour adds local inductance, and it is the reason a via’s equivalent circuit is not a simple capacitor but a pi-network of shunt capacitance and series inductance, with the inductance concentrated in the plane’s clearance.

The unused barrel is a stub

On a through via in a thick board, the signal enters at one layer and leaves at another, but the barrel continues to the far side of the board. The portion below the exit layer is an open-circuited transmission line — a stub — attached to the signal path.

An open stub of length $l$ presents an input impedance of $-j Z_0 \cot(2\pi l / \lambda)$. At a quarter wavelength it looks like a short circuit; at a half wavelength, an open. A stub that is a quarter wavelength long at some frequency therefore presents a near-short across the through path at that frequency, which appears as a deep notch in the channel’s response. The frequency is set by the stub length and the effective permittivity:

$$f_{resonance} \approx \frac{c}{4 , l \sqrt{\varepsilon_{eff}}}$$

For a 3 mm stub in FR-4 the quarter-wave resonance falls near 12 GHz; for a 10 mm stub it falls near 3.6 GHz. That is the reason thick backplanes and long connectors are specified with care: the stub length is the board thickness minus the depth of the exit layer, and a signal that changes layer near the top of a 5 mm board carries several millimetres of stub with it.

Below resonance the stub still matters. It adds capacitance to the through path, lowering the local impedance and producing a reflection. The reflection coefficient depends on the stub’s electrical length relative to the edge: a stub shorter than about a tenth of the edge’s rise-time length is nearly invisible, while one comparable to it produces visible distortion. This is the same critical-length criterion applied to a short section of line, as set out in Rise Time, Electrical Length, and When a Trace Stops Being a Wire.

What backdrilling removes

Backdrilling is a fabrication step that removes the unused portion of the barrel with a drill slightly larger than the via, from the side of the board opposite the signal’s exit layer. The remaining barrel is only as long as the signal needs.

The process leaves a small residual stub, because the backdrill must stop short of the exit layer’s pad to avoid damaging it; the residual is typically a few tenths of a millimetre, and the depth control is the limiting tolerance. The result is a stub short enough that its quarter-wave resonance moves well above the channel’s bandwidth, and a through path with much less excess capacitance.

Backdrilling is expensive because it is a separate drilling operation, it must be done after plating, and it requires depth control on every panel. It is also not uniformly applicable: it works from the board surface inward and cannot remove a stub in the middle of a stack, so a signal that changes layer at an inner layer and continues to a deeper one keeps whatever stub remains between those layers.

The cheaper alternatives are to plan the layer assignment so that high-speed nets use vias whose exit is at or near the far surface, and to use blind or buried vias in high-density builds where the barrel spans only the layers it needs. Blind vias run from an outer layer to an inner one; buried vias connect only inner layers. Both eliminate the unused barrel by construction, at the cost of sequential lamination, which is the dominant cost driver in HDI boards.

Antipad sizing and the impedance trade

The antipad is the clearance in each plane the via passes through. Its diameter sets the barrel’s capacitance per unit length: a larger antipad reduces capacitance and raises the barrel’s impedance, while a smaller antipad does the opposite and also crowds the return current.

The two effects pull in opposite directions, which is why the antipad is a design parameter rather than a default. A generous antipad improves the barrel’s impedance match but increases the plane’s void, raising the return path’s inductance around the via. A tight antipad reduces the void but makes the barrel look capacitive and lowers its impedance.

The usual compromise is to size the antipad for the barrel impedance that matches the trace, and to accept the return-path cost, because the return current’s detour is short — the current flows around the antipad’s circumference, and the inductance of that detour scales with the antipad diameter but remains small for typical sizes. What must not happen is a plane with an oversized void around a via for mechanical reasons, such as a keep-out for a connector’s mounting hardware. That case produces a large return-path detour with no electrical benefit.

import math

def via_z0(d_antipad_mm, d_drill_mm, er=4.3):
    return 60 / math.sqrt(er) * math.log(d_antipad_mm / d_drill_mm)

def stub_resonance_ghz(length_mm, er_eff=4.0):
    c_mm_per_s = 2.998e11
    v = c_mm_per_s / math.sqrt(er_eff)         # mm/s
    return v / (4 * length_mm * 1e9)            # quarter-wave, GHz

for ap in (0.45, 0.60, 0.75):
    print(f"antipad {ap:.2f} mm -> {via_z0(ap, 0.25):.1f} ohm")
for l in (1.0, 3.0, 6.0):
    print(f"stub {l:.1f} mm -> resonance {stub_resonance_ghz(l):.1f} GHz")

Return vias and the transition as a whole

The signal via is only half the transition. The return current must change layers too, and it does so through a return via — a via tied to the reference plane on both the entry and exit sides, placed close to the signal via.

Spacing matters because the return current spreads around the signal via at a distance comparable to the plane spacing. A return via within about one dielectric height of the signal via captures most of the return current; one several millimetres away leaves the current to find its own path through the power distribution network, which is both longer and less predictable. For a differential pair, two return vias are usually placed symmetrically beside the pair, one on each side, so that both conductors’ returns are captured without introducing asymmetry.

The return via also sets the local reference for the via’s own capacitance. A signal via with no nearby return via has a much larger effective loop, and the transition’s discontinuity grows. The return-path argument in Return Current Paths and Why Loop Area Sets Trace Inductance applies at every via, which is why via placement rules and return-path rules are the same rule seen from two directions.

When the via is the limiting element

A single via on a 10 Gb/s channel shows up as a small bump in the impedance profile rather than as a large loss on its own. Several vias in series — through a connector footprint, through a backplane, through a mezzanine — accumulate, and the reflections add coherently at some frequencies because the spacing between them is fixed by the layout.

The diagnostic signature is a channel whose loss is worse than the trace length predicts, with periodic ripple in the frequency response. The period of the ripple corresponds to the round-trip delay between two discontinuities, and the depth corresponds to their reflection coefficients. Once the signature is recognised, the fix is geometric: shorten the stubs, add return vias, or remove the layer change entirely by keeping the net on one layer through the connector region.

The limit case is a via that cannot be fixed because the board is too thick for the data rate. At that point the answer is architectural rather than layout: move the connector to a thinner board, use an optical link, or accept a shorter reach. The stub resonance calculation gives the frequency at which that decision becomes unavoidable, and it is worth running early rather than after the stackup is frozen.