SIPI

Calculators / 06

Via Stub Resonance Calculator

Via stub notch against Nyquist exact
Insertion loss through a line with an open stub

The unused length of a via below the layer a signal leaves on is an open-circuited stub. At the frequency where it is a quarter wavelength long it looks like a short to the line, and energy that should pass through it is sent back instead. The fix is to keep that frequency well above everything the channel carries — by backdrilling, or by choosing layers that leave no stub.

Reading the numbers

Every value is in the address bar as you change it, so a link reproduces the calculation exactly. Type values with SI prefixes — 100n, 2.2p, 16G — or drag the sliders; a bare number keeps the prefix already shown.

The formulas

fnotch = c / ( 4 · l · √Dkeff )  ≈  2950 / ( lmil · √Dkeff )  GHz The stub is a quarter wavelength at this frequency.
S21 = 2 / ( 2 + j tanθ ),   θ = (π/2)(f/fnotch) An ideal open stub of the line's own impedance, shunted across a matched line.
Go deeper — assumptions, how it is checked, and sources

Assumptions. The stub is lossless and has the line's impedance, so the notch is infinitely deep. A real stub has loss and a different impedance, which make the notch finite and shift its shoulder; the frequency is the part to trust. The effective Dk of a via barrel is not simply the laminate's, because the field around it is not uniform.

How it is checked. |S21| is 0 dB at DC and at twice the notch frequency, where the stub is a half wave; it vanishes at the notch; and the notch is exactly where the stub is a quarter wavelength.

Source. D. M. Pozar, Microwave Engineering, 4th ed., Wiley, 2012, §2.3 and §5.2.

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