At what frequency does a via stub matter?

It matters when the first null is close to the highest frequency the channel must carry, usually the Nyquist frequency plus rise-time margin. A 1.2 mm stub in FR-4 resonates near 30 GHz, a 3 mm stub near 12 GHz, and a 6 mm stub near 6 GHz. The calculator reports the ratio of the null to your target frequency so the margin is explicit.

How is backdrill depth calculated?

Depth from the back side equals the unused stub length plus the overdrill. The drill has to pass the target layer by the overdrill to guarantee that the barrel is removed; the residual stub in the worst case is the fab's depth tolerance minus the overdrill, floored at zero. The calculator reports the depth, the residual stub and the new first null.

What overdrill and tolerance should I specify?

That is a fabricator capability question, not a universal number. Ask the fab for its backdrill depth tolerance and the smallest overdrill it can hold, then check that overdrill plus tolerance does not reach the next copper layer. The calculator warns when that limit is crossed; use the actual layer pitch rather than the uniform-spacing estimate when the board is tight.

Does backdrilling always fix the problem?

It removes the stub resonance, but it does not fix a connector, a package, a split reference plane or a badly designed launch. It also adds cost and a process risk. If the null is well above the channel and the stub is electrically short, the connector or package may dominate. Compare the alternatives before adding a process step.

Should I use blind or buried vias instead?

Blind and buried vias avoid the unused barrel by construction, but they require sequential lamination and an HDI process, which is usually more expensive than backdrilling on a thick through-hole board. The right choice depends on layer count, board thickness, volume and the fab's capability; the calculator gives the stub that each option has to beat.

Free tool · Via structures

Via stub resonance and backdrill depth calculator

Find the frequency where an unused via barrel resonates, the longest stub your data rate can tolerate, and the backdrill depth a fabricator can hold — including the residual stub the drill tolerance leaves behind.

Get an Instant Quote Email a layout engineer

The short answer

A through via that stops on an inner layer leaves a shorted quarter-wave stub. Its first null is f₁ = c₀ / (4·L·√εr): a 1.2 mm stub in FR-4 resonates near 30 GHz, and a 3 mm stub near 12 GHz. Backdrilling removes the unused barrel; the depth to drill from the far side is the stub length plus the overdrill, and the residual stub is set by the depth tolerance, not by the original board thickness.

Calculator

Via stub resonance and backdrill calculator

Enter the stackup and the layer the signal leaves on. The calculator places the layers, computes the stub and its first three nulls, then checks whether a backdrill can remove it with the depth tolerance your fab can hold.

Board thicknessmm

Layer count

Signal leaves on

Counted from the entry surface.

Signal enters from

Laminate Dk

Channel targetGHz

Usually the Nyquist rate plus rise-time margin.

Via geometry

Drillmm

Padmm

Antipadmm

Backdrill process window

Overdrillmm

How far past the target layer the drill goes.

Depth tolerance± mm

Backdrill ringmm

Added to the drill diameter to size the backdrill.

Backdrill diametermm (optional)

Stub resonance and via parasitics

Quarter-wave nulls, the stub limit at your target, and the classical via estimates.

Review

Stub length: 1.173mm
First null: 30.80GHz
Max stub at target: 2.582mm
Margin: 2.20×
Signal depth: 0.427mm
Aspect ratio: 5.33:1
Via inductance: 1.299nH
Via capacitance: 1.146pF
Coaxial estimate: 28.4Ω

Layer spacing is drawn evenly. The red segment is the unused barrel; the dashed outline is the backdrill removed from the far side.

The margin is thinner than it looks

The first null is above the channel but not comfortably. Extract the actual via and channel before deciding; a slightly different stackup or a closer layer can move the null by more than the margin.

Backdrill plan

Depth from the far side, the diameter that clears the barrel, and what the depth tolerance leaves behind.

Drill depth from far side: 1.223mm
Backdrill diameter: 0.500mm
Residual stub: 0.050mm
New first null: 722.86GHz
Improvement: 23.5×
Depth window: ±0.100mm

Backdrill is at least 0.20 mm wider than the drill.
Backdrill stays inside the 0.80 mm antipad.
Overdrill plus tolerance stays clear of the next copper layer.
Residual stub is 0.050 mm (0.05 mm is treated as no stub).

Resonance by layer

Every layer on this stackup, with the stub it would leave and the null that stub would create. Your selected layer is highlighted.

Via stub length and first resonance for every copper layer.
Layer	Depth mm	Stub mm	First null GHz
1	0.000	1.600	22.59
2	0.107	1.493	24.20
3	0.213	1.387	26.06
4	0.320	1.280	28.24
5	0.427	1.173	30.80
6	0.533	1.067	33.88
7	0.640	0.960	37.65
8	0.747	0.853	42.36
9	0.853	0.747	48.41
10	0.960	0.640	56.47
11	1.067	0.533	67.77
12	1.173	0.427	84.71
13	1.280	0.320	112.95
14	1.387	0.213	169.42
15	1.493	0.107	338.84
16	1.600	0.000	—

Manufacturing and channel checks

Overdrill plus tolerance (0.150 mm) reaches the next copper layer (pitch 0.107 mm). The fab cannot hold that depth safely.

What this model does not know

It treats the via as a homogeneous stripline stub. The pads, antipads, barrel plating, adjacent return vias and the launch all shift the real null by a few percent. The inductance and capacitance are the classical Johnson & Graham estimates, not an extraction. Extract the actual via field when the channel is tight.

Get an Instant Quote Email a layout engineer

Free, no account. The engineer reviews the inputs before a fixed quote is issued.

Want the derivation? Jump to the math behind the calculator.

The math

The formulas, with the working shown

Each equation is rendered as MathML, explained in plain language, and shown as LaTeX source you can copy. The variable list says what every symbol means; the model-limit note says where the formula stops being trustworthy.

Where the signal layer sits

d_{k} = \frac{k - 1}{N - 1} T

If the copper layers are evenly spaced, the depth of layer k is a simple fraction of the board thickness. Real stackups are not perfectly even, so treat this as the first estimate.

d_k: depth of layer k from the entry surface
k: layer number from the entry side, starting at 1
N: copper layer count
T: finished board thickness

Layer 1 is the entry surface, so its depth is zero; layer N is the far surface, so its depth is the full thickness. The formula linearly interpolates between them.

A real stackup uses different prepreg and core thicknesses. The error is usually small in the middle of the board and larger near the outer layers, where the dielectric is often deliberately thinner.

When the answer is close to a decision boundary — a null just above or below the channel — replace this estimate with the depths from the actual stackup drawing.

Model limit: The calculator counts from the entry side, which is the top unless you switch the entry surface.

LaTeX source

d_k = \frac{k-1}{N-1}\,T

The unused barrel length

L_{stub} = T - d_{k}

The stub is whatever barrel is left between the signal layer and the far surface. It is the length that resonates, not the whole via.

L_stub: unused plated barrel length
T: board thickness
d_k: depth of the signal layer from the entry side

A via that stops on the far surface has a stub of zero. A via that stops on the first inner layer has almost the full board thickness as a stub, which is why the layer assignment matters as much as the board thickness.

For a signal entering from the bottom, the same equation applies with layers counted from the bottom. The backdrill then enters from the top.

This length is geometric; it does not depend on the via diameter. The diameter changes the impedance of the stub and therefore the depth of the notch, not its frequency.

LaTeX source

L_{\text{stub}} = T - d_k

The first resonance

f_{1} = \frac{c_{0}}{4 L_{stub} \sqrt{ε_{r}}}

A quarter wavelength of barrel looks like a short at the signal. The null repeats at 3f₁, 5f₁ and so on, so a stub can be harmless at one frequency and destructive at another.

f_1: first (quarter-wave) null frequency
c0: speed of light in vacuum
ε_r: laminate relative permittivity

The factor of four comes from the quarter-wave condition: the stub is open at the far end and shorted at the signal end, so its input impedance goes to zero when its electrical length is 90°.

The square root of εr converts the physical length into an electrical length. A higher-Dk laminate makes the same barrel resonate at a lower frequency, which is one reason high-speed designs use low-Dk materials.

The via is treated as a homogeneous stripline surrounded by laminate. That is a good first approximation; the pads and antipads shift the actual null by a few percent.

Model limit: A 1.2 mm stub in εr = 4.3 gives f₁ ≈ 30.8 GHz; a 3 mm stub gives ≈ 12.3 GHz.

LaTeX source

f_1 = \frac{c_0}{4L_{\text{stub}}\sqrt{\varepsilon_r}}

The longest stub a channel can tolerate

L_{\max} = \frac{c_{0}}{4 f_{\max} \sqrt{ε_{r}}}

Invert the resonance equation to get the longest barrel whose first null stays above the highest frequency the channel must carry.

f_max: highest frequency the channel must carry
L_max: maximum stub length for that frequency

Set f_max to the Nyquist frequency of the data rate — half the symbol rate for a binary link — plus margin for the rise time. A null exactly at Nyquist is already a problem, so designs usually aim for the null well above it.

The result is a geometric limit on the layer assignment. If the required stub is shorter than the distance from the target layer to the far surface, the signal needs a different layer, a blind via or a backdrill.

The tool also reports the ratio f₁ / f_max. A ratio of 3 or more is comfortable; between 1.5 and 3 deserves a simulation; below 1.5 the null is inside the channel.

LaTeX source

L_{\max} = \frac{c_0}{4f_{\max}\sqrt{\varepsilon_r}}

Backdrill depth and residual stub

D_{bd} = L_{stub} + δ_{over} L_{res} = \max (0, δ_{tol} - δ_{over})

The drill has to pass the target layer to guarantee contact, so the residual stub is set by how far past the layer it goes and how well the fab holds depth — not by the original board thickness.

D_bd: depth to drill from the back side
δ_over: intentional overdrill past the target layer
δ_tol: the fab's depth tolerance, ±
L_res: worst-case stub left after backdrilling

Overdrill is the intentional penetration past the target layer. Depth tolerance is the fab's repeatability. If the tolerance is larger than the overdrill, the worst case leaves a stub of (tolerance − overdrill); if the overdrill is larger than the tolerance, the drill always passes the layer and the residual is zero.

A residual stub of 0.05 mm in FR-4 still resonates above 700 GHz, so a successful backdrill usually removes the resonance from the channel entirely. The risk moves from electrical performance to process damage.

The tool checks the other direction too: overdrill plus tolerance must not reach the next copper layer. That is why a deep, thin-dielectric stackup needs a smaller overdrill than a thick one.

Model limit: The formula assumes the drill is aimed at the via centre and stops on the intended layer. A misregistered drill is a separate yield risk.

LaTeX source

D_{\text{bd}} = L_{\text{stub}}+\delta_{\text{over}} \quad\quad L_{\text{res}} = \max\left(0,\ \delta_{\text{tol}}-\delta_{\text{over}}\right)

Barrel inductance

L_{via} = 5.08 h [\ln (\frac{4 h}{d}) + 1]

A via barrel behaves like a short length of wire. The inductance is roughly a nanohenry for a typical through via and rises with board thickness and falls with drill diameter.

L_via: barrel inductance in nH
h: barrel length in inches
d: drill diameter in inches

The formula is the classical Johnson and Graham estimate, with h the barrel length and d the drill diameter, both in inches. It assumes a return path far away, so it overestimates the inductance of a via surrounded by ground vias.

Inductance is why a via is a series discontinuity in a PDN and why return vias matter: the loop area, not just the barrel, sets the parasitic.

The number is useful for intuition — a nanohenry at 1 GHz is about 6 Ω — but a 3D extractor is the right tool for a production via field.

Model limit: The constants assume inches. The calculator converts from millimetres before applying the formula.

LaTeX source

L_{\text{via}} = 5.08\,h\left[\ln\left(\frac{4h}{d}\right)+1\right]

Via capacitance

C_{via} = 1.41 ε_{r} \frac{T D_{1}}{D_{2} - D_{1}}

The pad and antipad form a small capacitor to the surrounding planes. A larger pad or a tighter antipad raises the capacitance and lowers the via's local impedance.

C_via: via capacitance in pF
D_1: pad diameter (inches in the original formula)
D_2: antipad diameter
T: board thickness

The capacitance is proportional to the overlap area and the Dk, and inversely proportional to the gap between the pad and the plane (the antipad clearance). That is why a bigger antipad reduces the discontinuity.

Together with the inductance, it explains why a via is a low-pass discontinuity: the capacitance shunts high frequencies and the inductance blocks them, and the combination shows up as a dip in the TDR.

The formula is sensitive to the antipad diameter. A 0.05 mm change in clearance on a 0.6 mm pad moves the capacitance by tens of percent, so use the actual plane clearance from the stackup.

LaTeX source

C_{\text{via}} = 1.41\,\varepsilon_r\,\frac{T\,D_1}{D_2-D_1}

Coaxial estimate and aspect ratio

Z_{via} = \frac{60}{\sqrt{ε_{r}}} \ln (\frac{D_{2}}{d}) A R = \frac{T}{d}

A plated barrel surrounded by an antipad is a short coaxial line. The same geometry gives the impedance estimate and the fab's aspect ratio, which is a plating and yield constraint.

Z_via: coaxial estimate of the via impedance
D_2: antipad diameter
d: drill diameter
AR: aspect ratio

The coaxial estimate treats the barrel as the inner conductor and the plane clearance as the outer conductor. It is a better geometry-based number than √(L/C) from the two lumped estimates, which assume a distant return.

Aspect ratio is thickness divided by drill diameter. Most fabs quote 10:1 as standard; beyond that, plating uniformity and drill wander become the limiting factors, not the electrical model.

Neither number replaces an extraction. They are here so the tool can say this via is a 40 Ω discontinuity with an 8:1 aspect ratio instead of only that the stub is 1.2 mm.

Model limit: The estimate ignores the pads, the barrel plating thickness and the adjacent return vias.

LaTeX source

Z_{\text{via}} = \frac{60}{\sqrt{\varepsilon_r}}\ln\left(\frac{D_2}{d}\right) \quad\quad AR = \frac{T}{d}

Quarter-wave resonance

Why a leftover via barrel rings

When a signal leaves an inner layer at a plated through-hole, the rest of the barrel continues to the far side of the board. That leftover length is an open-circuited transmission line hanging off the signal. At the frequency where it is a quarter wavelength long, its input impedance looks like a short: f₀ = c₀ / (4·L·√εᵣ).

The result is a notch in insertion loss deep enough to close an eye if it lands inside the band. In FR-4 a 1.2 mm stub resonates near 30 GHz and a 3.0 mm stub near 12 GHz. Return loss starts degrading much earlier, at roughly a fifth of the null frequency, which is why the rule is to keep the null at least three times the Nyquist rate.

Nulls repeat at odd multiples of f₀, so a stub can damage a harmonic even when the fundamental looks clear.
A wider barrel is a lower-impedance stub and rings harder; the depth of the notch follows the stub impedance.
Higher Dk shortens the electrical wavelength and pulls the null down in frequency.
A signal that terminates on an outer or adjacent inner layer has almost no stub to remove.

On PCIe Gen 5/6 and 112G PAM4, via structure is a stackup decision made before routing. The high-speed PCB layout service and backplane and high-layer layout service pages cover that scope.

Depth control

What the drill can actually remove

Backdrilling reams out the unused barrel with an oversized bit from the opposite face. The bit has to pass the target layer far enough to clear the plating — typically 0.10 mm of overdrill — without cutting the capture pad, and the machine holds depth to about ±0.15 mm.

The residual stub is therefore the depth tolerance minus the overdrill, floored at zero, not something you can specify to an arbitrary value. The bit is 0.15 to 0.20 mm larger than the primary drill, so the plane antipads have to be enlarged to match before the design is released.

A backdrill that runs past an antipad cuts plane copper. The DFM/DFA layout service page covers the clearance check against the fab's drill schedule.

Parasitics

Barrel inductance, pad capacitance and aspect ratio

A through via is not invisible. A typical barrel contributes about 1 nH of series inductance and a few tenths of a picofarad of shunt capacitance, which shows up as a local impedance dip at the transition. Ground stitching vias next to the signal via form a crude coax and cut the loop inductance.

Aspect ratio — board thickness over drill diameter — is the plating constraint underneath all of it. Standard processes plate reliably to about 10:1 or 12:1 under IPC-6012 Class 3; beyond that the barrel centre plates thin and the fab needs pulse plating or a different stackup.

Exceptions

When not to backdrill

Backdrilling is an extra drilling pass with depth calibration and scrap risk attached. It is unnecessary when the null already sits above three or four times the channel Nyquist frequency, and it is actively harmful when a connector needs the barrel.

Compliant press-fit pins — AirMax, XCede and similar — depend on a full plated barrel through the connector depth for mechanical retention and a gas-tight joint. Wave-soldered and pin-in-paste through-hole parts need full-barrel solder fill for the same reason.

On a backplane the via field is part of the channel topology, so a single-via calculation is not the whole story. The backplane and high-layer layout service and published layout pricing pages cover that ground.

A stub shorter than about 0.05 mm is treated as negligible; the tool still reports the barrel parasitics.

FAQ

Common questions

A via stub is the unused part of a plated through-hole barrel. If a signal enters the top of the board and leaves on layer 5 of 16, the barrel from layer 5 to the bottom is still plated and still connected at the signal end. That open-ended length behaves as a transmission-line stub and resonates at a quarter wavelength.

Keep going

Stackup planner Impedance calculator DDR length matching backplane and high-layer layout service high-speed PCB layout service published layout pricing

Want this worked through on your board?

Send the stackup and interface list and we will check the via strategy against a real layout — before the quote is fixed, not after.

Get an Instant Quote Email a layout engineer