Decoupling Impedance Plot — PDN Anti-Resonance
Enter your decoupling banks. The calculator plots the bank impedance across frequency and finds the anti-resonant peaks between the capacitor self-resonances — the ones a flat count-the-capacitors estimate cannot see.
| Qty | Value (µF) | Mounted ESL (nH) | ESR (mΩ) | Self-resonance |
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The peak is the answer, not the average
Almost every quick decoupling estimate — including the one on our own PDN target impedance page — treats a capacitor bank as a resistance and an inductance in parallel and asks how many parts it takes to get under a target. That model is useful, and it is blind to the thing that most often makes a real board miss its target: anti-resonance.
Every capacitor is a series RLC. Below its self-resonant frequency it behaves capacitively; above it, inductively. Put two different values side by side and there is a frequency between their resonances where one is already inductive and the other is still capacitive. The inductive one and the capacitive one form a parallel resonant tank, and a parallel tank has high impedance. The bank gets worse at that frequency than either bank alone would have been.
The example loaded above is a design that looks safe by every flat measure. Four bulk capacitors and a hundred small ones, low ESR throughout, and an impedance under 3 mΩ across most of the band — a count-the-capacitors estimate would sign it off without comment. It has a 20 mΩ spike at 2.3 MHz, twice the target, because the two banks sit two full decades apart with nothing in between. Press Fix it: add the mid-band value and the peak drops by about a factor of three, from one added component value. Press Single value only to see the opposite failure: no peak at all, and a hopeless impedance below a megahertz.
How the curve is computed
Zbank(f) = ESR/n + j( 2πf · ESL/n − 1/(2πf · nC) )Ztotal(f) = 1 / Σ ( 1 / Zbank(f) ) — complex admittances, summedfSRF = 1 / (2π √(ESL · C))The admittances are summed as complex numbers, which is the whole point: adding magnitudes would average the peaks away and reproduce exactly the misleading answer the flat model gives. Each bank of n identical parts divides its ESR and ESL by n and multiplies its capacitance by n.
What to do about a peak
- Add an intermediate value between the two banks that straddle the peak. This is the usual fix and it is why real stackups carry three or four decades of capacitance rather than one.
- Do not chase it with more of the same part. Adding capacitors to an existing bank moves its resonance but does not remove the tank; sometimes it makes the peak sharper.
- Damp it. A little more ESR in one bank lowers the Q of the tank and flattens the peak. Controlled-ESR parts exist for exactly this, and the instinct that ESR is always bad is wrong here.
- Reduce mounted inductance first. It sets both the high-frequency floor and where the resonances sit. It is a layout decision — via placement and plane depth — not a purchasing one.
What this model still leaves out
- The planes are missing — both their capacitance, which helps at high frequency, and their spreading inductance and cavity resonances, which hurt. On a real board the planes often dominate above a few hundred megahertz.
- Position is missing. This model assumes every capacitor sees the same node. A capacitor two inches from the load is not the same capacitor, and above a few tens of megahertz that distance matters more than the part number.
- The VRM is missing. Below its control-loop crossover the regulator, not the bulk capacitance, sets the impedance.
- Tolerance and bias are missing. Class II ceramics lose a large fraction of their capacitance under DC bias and with temperature — the resonances move accordingly, and a bank designed at nominal can be materially different in circuit.
Where this fits
Signal and power integrity is one of our primary service lines — pre-layout constraints through post-layout verification in Ansys SIwave and Siemens HyperLynx, which model the planes, the positions and the VRM that this page deliberately cannot. A PDN and decoupling review runs about a week to a fixed scope and ends in a written report you keep.
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