Hot-plug inrush and LC ringing calculator
What the rail actually does in the first few microseconds after a live connection — and whether your input capacitors survive it.
Peak rail voltage
—V
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The physics
Connecting a live supply to a board with bulk capacitance is a voltage step into a series RLC circuit. The inductance is your cable, your connector and your traces. The capacitance is your input bulk. The resistance is whatever happens to be in the loop — and it is the only thing preventing the classic result.
The circuit
ω₀ = 1 / √(LC) undamped natural frequency
ζ = (R/2) · √(C/L) damping ratio
ω_d = ω₀ · √(1 − ζ²) damped ring frequencyFor an underdamped circuit — which is almost every real one — the step response is:
v(t) = V · [ 1 − e^(−ζω₀t) · ( cos ω_d t + (ζ/√(1−ζ²)) · sin ω_d t ) ]
peak = V · ( 1 + e^(−πζ/√(1−ζ²)) )
Set ζ = 0 and the peak is exactly 2V. That is the number
worth carrying around: a connection transient tries to double your rail,
and only loop resistance stops it.
Inrush current
i(t) = (V / (ω_d·L)) · e^(−ζω₀t) · sin(ω_d t)The first peak is what the connector contact carries, and it is frequently tens of amps for a few microseconds. Contacts are rated for continuous current, not for this — repeated hot-plugging is a contact-erosion mechanism as well as a capacitor one.
This tool integrates the circuit numerically rather than using the closed form, so the over-damped and critically-damped cases are handled correctly instead of falling out of an equation that assumes ringing.
What the fixes actually do
- Derating does not change the waveform at all. It changes whether the waveform matters. Cheapest fix available and the one most often skipped.
- An NTC thermistor adds series resistance, raising ζ. Simple, and it stays warm and lossy in normal operation.
- Active soft-start controls the rate of rise so the LC never gets a step to respond to. The proper answer above a few hundred microfarads.
- An RC snubber damps without the standing loss of a series element.
- A TVS clamps the peak. It does not stop the ring, and every connection becomes an energy event for the diode.
The mechanical failure that looks identical
Large ceramic capacitors crack under board flex, and a cracked MLCC often fails short — which looks exactly like an overvoltage failure and is not. On any board that gets handled, vibrated or impacted, use soft-termination parts in 1206 and above. We found both mechanisms present simultaneously on the same board once, and fixing only one looked like a partial fix.
Design guidance, not a manufacturing instruction. Verify every result against your fabricator's stack-up and the applicable standard before release. Closed-form models are approximations; the fab's field solver and process window are the authority.
Questions
What people ask about this
Why does connecting a supply cause an overvoltage at all?
Because the cable and the bulk capacitance form a series LC circuit, and a step into an undamped LC overshoots to twice the applied voltage. Nothing is faulty — it is the circuit you accidentally built by having a cable and a capacitor. Real wiring has resistance, so the ring is damped, but on a metre of cable into a few hundred microfarads you still routinely see 1.5× to 1.9×.
How much cable inductance should I assume?
Roughly 1 µH per metre for a typical two-wire run, less for a tightly twisted pair, more for widely separated conductors. It is worth measuring rather than assuming if the answer is marginal: loop area is what sets it, so how the cable is routed matters as much as its length.
Why does my board fail only sometimes?
Because the peak depends on where in the connector mating cycle contact is made, how discharged the bulk is, cable length and routing, and source impedance. It is genuinely intermittent, which is why the failure gets blamed on a bad batch of capacitors. If a fault only appears on some power-ups and never during operation, this is the first thing to measure.
What actually fixes it?
In order: derate the input capacitors for the transient rather than the rail; add inrush limiting so the rate of rise never lets the ring form; damp the circuit with a small series resistance or an RC snubber; and only then add a TVS as a backstop. A TVS alone clamps the peak but does not stop the ring, and relying on it means every connection is an energy event.
Does this apply to USB-C and similar connectors?
Yes. Staggered pins address contact sequencing, not the LC ring — the moment power connects, the circuit is the same. Any hot-pluggable input with meaningful bulk capacitance behind it needs inrush control regardless of the connector standard.
Capacitors failing and nobody can reproduce it?
Intermittent input-capacitor failure is one of the most misdiagnosed faults in embedded hardware. Send us the symptoms and the input schematic.