Hot-plug voltage overshoot: how cable inductance and an MLCC form a series resonance that nearly doubles the input voltage, and how to fix it

Q: Does adding MLCC capacitance solve it?

No. More C raises ζ and lowers the peak slightly, but the effect is limited. Raising R with deliberate ESR works much better on the peak.

Q: What about tantalum or polymer capacitors instead of an MLCC?

Their ESR of tens to hundreds of mΩ is higher than an MLCC's, so they damp somewhat on their own. Stopping the oscillation almost fully takes an ESR near critical damping, 2√(L/C), so a parallel electrolytic or a TVS may still be needed. Some tantalum types are weak against surge and reverse voltage, so check the surge rating.

Q: Isn't it fine if nobody hot-plugs?

Even if the intended procedure is to plug in first and then power on, people will plug in live cables. They carry an adapter plugged into the unit, swap a battery pack, or use a connector specified for live insertion. Leave margin on the circuit side.

Q: Any tips for checking this on a scope?

The resonant frequency is tens to hundreds of kHz and can fall near the switching frequency. To avoid confusing it with supply ripple, set the time base wider than one or two resonant periods. A long probe ground lead adds to L and changes the waveform, so keep the ground connection short.

Plugging in a live cable nearly doubles the input voltage

Take an AC adapter that is already putting out 12V and plug it into the jack of an unpowered board. From the board's side, 12V is suddenly connected: a step input.

A 1m power cable has about 0.5 to 1µH of inductance. The board input usually carries a few µF to tens of µF of low-ESR multilayer ceramic capacitors (MLCCs), so the cable's L and the input's C form a series LC circuit.

With only an aluminum electrolytic capacitor, or a battery, the resonance dies out quickly. An MLCC has an ESR of only a few mΩ and almost no damping, so the closer the resistance gets to zero, the closer the peak voltage gets to twice the input voltage. Plug in a 12V adapter and the input node briefly jumps to the 20V range.

This effect is reported in Linear Technology application note AN88.

Figure 1: the cable's L and R and the input MLCC's C form a series LC circuit. f₀ = 1/(2π√LC), ζ = (R/2)√(C/L).

Why the peak approaches twice the supply

When a step voltage V₀ is applied to a series RLC circuit, the capacitor voltage (the input node voltage) peaks at:

V_peak = V₀ × (1 + e^{−ζπ/√(1−ζ²)}) (ζ < 1, the oscillating case)

ζ is the damping ratio, ζ = (R/2)√(C/L), where R is the cable resistance plus the MLCC's ESR. As ζ approaches zero, V_peak approaches 2V₀.

R cannot be counted on, though. A low-ESR MLCC has an ESR of a few mΩ, and a 1m power cord has only about 0.05Ω. The low ESR the MLCC is chosen for works against you here.

Figure 2: stable at 12V before plug-in. At the moment of plug-in the LC circuit is excited, and the voltage jumps into the 20V range before settling to 12V.

Peak voltage and resonant frequency for L, C and R

Take a 1m power cable (L ≈ 0.6µH) and a board with a 10µF MLCC at the input, and vary R (V₀ = 12V).

Varying R with L = 0.6µH, C = 10µF, V₀ = 12V (calculated in node)
Total R	Damping ratio ζ	Resonant frequency f₀	Peak voltage	Typical case
0.02Ω	0.041	65kHz	22.6V	Thick cable, low-ESR MLCC alone
0.05Ω	0.102	65kHz	20.7V	Typical 1m power cord
0.1Ω	0.204	65kHz	18.2V	Thin cable, or 2m
0.2Ω	0.408	65kHz	14.9V	Resistance added on purpose
0.5Ω	1.02	65kHz	12.0V	Beyond critical damping, no oscillation

f₀ = 1/(2π√LC) does not depend on R. Raising R does not change the resonant frequency; it only lowers the peak voltage.

Where it breaks real hardware: USB PD at 20V and 24V industrial equipment

The effect does real damage when the margin to the input's absolute maximum rating is thin. Here are common conditions on a DC-DC input rated for 30V.

Peak voltage and margin on a DC-DC input rated for 30V (calculated in node)
System	Conditions	Peak voltage	Against 30V rating
12V	1m cable (0.6µH), 10µF MLCC, R = 0.05Ω	20.7V	Margin left
USB PD 20V	1m cable (1.0µH, thin), 10µF MLCC, R = 0.15Ω	29.3V	Right at the rating
24V industrial	2m cable (1.2µH), 22µF MLCC, R = 0.05Ω	41.1V	More than 10V over

On USB PD at 20V, the cable tends to be long and thin and the source is already live when you connect, so the effect occurs as is. A 30V rating looks comfortable, but the overshoot uses up most of the 10V static margin.

24V industrial equipment is worse. Cables of 2m or 3m from the distribution panel are common, and many machines put MLCCs at the input for high-frequency noise. 41V exceeds the absolute maximum rating of many DC-DC controllers. Damage happens only when you plug in at a bad moment, so finding the cause tends to take a long time.

DC bias on the MLCC makes it worse

An MLCC loses capacitance under DC voltage. A 10µF X7R at 12V can fall to under half its rated value, and on some parts to 3 to 4µF. When C drops, ζ = (R/2)√(C/L) drops too, so the overshoot gets worse with R and L unchanged.

R = 0.05Ω and L = 0.6µH fixed, MLCC effective capacitance varied (calculated in node)
MLCC effective capacitance	Resonant frequency f₀	Peak voltage
10µF (catalog value)	65kHz	20.7V
4µF (example after DC bias)	103kHz	21.8V

The peak differs by only about 1V, but the resonant frequency rises by about 1.6 times. The real resonance sits higher than f₀ calculated from the datasheet capacitance, so allow for it when you set the scope's time base.

Inrush current: worn contacts and a dropped upstream supply

Seen as current, the same effect is inrush current. As the voltage jumps, a large current briefly flows in the cable to charge C.

Standards with frequent plugging, such as USB, limit the local bulk capacitance to hold inrush down. USB 2.0 allows a bus-powered device at most 10µF directly on VBUS, and requires an inrush-limiting circuit beyond that.

Peak inrush current for VBUS 5V, C = 10µF (the USB 2.0 limit) and L = 0.2µH, by cable plus contact resistance R (calculated in node)
Total R	Peak inrush current
0.05Ω (thick cable, good contact)	27.5A
0.1Ω (typical cable)	22.4A
0.2Ω (thin cable, slightly worn contact)	16.1A

A single USB connector pin is rated for only about 1.5 to 3A continuous, so the currents in the table are an order of magnitude higher. They last only a few µs, so the connector will rarely melt on the spot. The problem is repetition. Each plug-in roughens the contact surface with tiny arcs (fretting, blackening), and the contact resistance creeps up. R rises and the overshoot falls, but it only trades into a heat and voltage-drop problem.

The other symptom is a brief drop in the upstream supply. A fuse, polyswitch or current-limited power IC can mistake the inrush peak for an overcurrent and trip. If the power LED goes out at plug-in, or the power IC's PG goes low briefly, suspect this inrush first.

Fix 1: add an aluminum electrolytic in parallel

The easiest fix is to add an aluminum electrolytic capacitor, which has ESR, in parallel with the MLCC. Low ESR is the problem, so use ESR to supply the damping.

There are two reference resistances. The characteristic impedance Z₀ = √(L/C) is about 0.245Ω for L = 0.6µH and C = 10µF. At R = Z₀, ζ = 0.5, and the overshoot drops a lot but does not vanish. Above critical damping R_crit = 2√(L/C) ≈ 0.49Ω (ζ = 1), the oscillation stops altogether.

The ESR of a small 100µF-class aluminum electrolytic is often 0.2 to 0.3Ω around 100kHz, right between Z₀ and R_crit. Bringing the peak below the absolute maximum rating is enough in practice, so aim for an ESR between Z₀ and R_crit. The electrolytic turns the energy of one resonance into heat in its ESR. Figure 3 treats the ESR as a series R as an estimate.

Figure 3: with the MLCC alone (left) the voltage jumps to 20.7V. With a 100µF electrolytic of about 0.3Ω ESR in parallel (right), the peak stays at 13.1V.

Peak voltage versus R

Figure 4 sweeps R on a log axis. Right of Z₀ and R_crit the overshoot almost vanishes, and left of them it rises steeply.

Figure 4: the red dot is the MLCC alone (R ≈ 0.05Ω, 20.7V), the green dot the case with an electrolytic added (R ≈ 0.3Ω, 13.1V).

Fix 2: TVS. Fix 3: load switch or hot-swap controller

A TVS diode does not stop the resonance. It conducts once the voltage passes its clamping voltage and lets the voltage rise no further. On a 12V rail, choose a standoff voltage (for example 15V) above the maximum steady voltage including ripple and tolerance. The clamping voltage of such a TVS at its rated surge current is often 1.3 to 1.4 times the standoff voltage (around 24V for a 15V part), so it can cap the overshoot in the 20V range. But the TVS absorbs current and heats up while clamping. The resonance energy does not shrink, so the TVS takes it on every time.

A load switch or hot-swap controller takes a fundamentally different approach. An electronic switch deliberately slows the rise of the output. The resonant period here is 1/f₀ = 1/65kHz ≈ 15µs. If the rise time is much longer than that (about 1 to 10ms), there is no step to excite the circuit and almost no resonance occurs.

Figure 5: connected abruptly (left), the voltage jumps to 20.7V. Ramped up over 1ms (right), the rise is slow against the 15µs resonant period and the overshoot almost vanishes.

Effects and side effects of each fix

The three fixes act differently and have different side effects, so they are usually combined.

Estimate the cable's L at 0.5 to 1µH per metre and calculate f₀ and ζ from the MLCC's effective capacitance after DC bias.
If ζ is 0.2 or less, assume the peak can reach 1.5 to 2 times the input voltage and compare it with the absolute maximum ratings of the input parts.
If the margin is short, first consider the inexpensive parallel aluminum electrolytic. Choose one whose ESR falls between Z₀ and R_crit.
If the voltage is still too high or there is no board area, cap it with a TVS. Estimate the TVS's average loss from the plug-in rate.
If plugging is frequent and you also worry about contact wear and false upstream protection, use a load switch or hot-swap controller.

Effects and side effects of each fix
Fix	How it works	Side effects and cautions
Parallel aluminum electrolytic	ESR between Z₀ and 2Z₀ (critical damping) damps the resonance and turns its energy into heat	Takes board area. ESR can rise several times at low temperature, so the effect varies with the environment. Electrolytics have a service life
TVS	Absorbs only the part above the clamping voltage. Resonant period and damping are unchanged	The resonance energy is not reduced, so the TVS heats on every plug-in. Watch average power with frequent plugging. Slight leakage even in normal operation
Load switch / hot-swap controller	Makes the rise much longer than the resonant period, so nothing is excited	Adds cost and board area. On-resistance causes voltage drop and heat. Fast transients such as contact bounce need separate measures

Frequently asked questions

Does adding MLCC capacitance solve it?