Why a Busbar's Resistance Rises with Frequency

Rand Simulation — Applications Engineering AI
Power electronics · Ansys Q3D Extractor · 7 min read

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The square copper busbar at 50 kHz, cut away to show the current density inside it. At this frequency the current has retreated into a bright shell about one skin depth thick at the surface, and the entire core (black) carries almost nothing — most of the copper is dead weight. That is why the AC resistance climbs to about 8.5× its DC value here, a direct Ansys Q3D result.

The result: a busbar is not the fixed lump of resistance its cross-section suggests. A scripted Ansys Q3D sweep of 27 cases (cross-section shape × frequency) shows the AC resistance of a 100 mm² copper bar climbing from its 34.4 µΩ DC value to 8.5× that at 50 kHz for a square section. Flattening the bar at the same copper area cuts the penalty (to 6.0×), but a single wide strip crowds current to its edges and stops short of the ideal — the reason real high-frequency busbars are laminated stacks of thin strips.

This is a companion to our cable study, Why Your Charging Cable Gets Warm. That one extracted the parasitics of a thin signal-and-power pair. This one scales up to a power busbar — the flat copper bar that carries hundreds of amps inside an inverter, a switchboard, or a battery pack — and asks a question that trips up a lot of designs: how much does its resistance actually rise once the current is not DC?

The answer is: a lot, and for a reason the handbook cross-section number hides. At DC, current fills the whole conductor and the resistance is simply resistivity times length over area — 34.4 µΩ for this 100 mm², 200 mm bar, which Q3D reproduces to the digit. But an alternating (or switching, or rippled) current does not fill the conductor. It rides in a surface layer whose depth — the skin depth — shrinks as the square root of frequency: about 0.66 mm in copper at 10 kHz and 0.29 mm at 50 kHz. Once that layer is thinner than the bar, the copper in the middle is dead weight, and the resistance climbs.

The skin-effect penalty, measured

AC-to-DC resistance ratio versus busbar aspect ratio at three frequencies — The full shape sweep: AC-to-DC resistance ratio versus cross-section aspect ratio, one line per frequency, all extracted in Q3D at fixed 100 mm² of copper. A thick square (left) pays the steepest penalty; flattening the bar (moving right) recovers most — but not all — of it. The residual is edge crowding, which a single wide strip cannot escape.

Q3D extracts the full resistance matrix of the bar at each frequency, so the penalty is a direct read, not an estimate. For a square 100 mm² section the AC-to-DC resistance ratio rises past 8.5 by 50 kHz — the current is using only about a tenth of the copper it paid for. That ratio is exactly what a surface-skin argument predicts (the current sits in a perimeter shell one skin depth thick), and the extraction lands on it, which is the check that the numbers are honest.

AC-to-DC resistance ratio versus frequency for three busbar shapes — The same penalty seen against frequency, for three cross-sections. Each bar sits near its DC value while the skin depth is larger than the bar, then climbs once the current is squeezed into a shrinking surface layer. The square section climbs fastest; the flat one always sits below it, but every shape pays a growing toll as frequency rises.

The practical sting is that this happens at frequencies engineers do not always associate with skin effect. A 50 or 60 Hz bus is essentially DC as far as the copper is concerned — the skin depth is many millimeters, larger than the bar. But the moment a bus feeds a switching converter, a motor drive, or anything with current ripple in the kilohertz, the effective resistance is no longer the datasheet DC value, and the extra loss shows up as heat the thermal design did not budget for. That is the gap between a bus that runs at its rated temperature and one that quietly de-rates itself in service.

AC-to-DC resistance ratio across the aspect-ratio and frequency grid — The whole map: AC-to-DC resistance ratio over cross-section aspect ratio and frequency. The penalty grows with frequency (skin depth shrinks) and eases as the bar flattens (more of the copper sits within a skin depth of a surface). The hot corner — thick and fast — is where a busbar quietly runs hotter than its DC rating says.

Why flattening helps — and why it is not a free lunch

If the current only uses a surface layer, the fix is intuitive: give it more surface for the same copper. A flat wide strip has far more perimeter than a square of the same area, so more of its cross-section lies within a skin depth of a face. That is why, at every frequency in the sweep, the flatter bars carry a lower penalty — the ratio falls from 8.5 toward 6.0 at 50 kHz as the section goes from square to a 100:1 ribbon.

But the improvement is only about 1.4×, not the tenfold you might hope for — and that gap is the useful engineering lesson. A single wide strip does not spread its current evenly along the wide face; the current crowds toward the two edges, so the middle of the face is under-used even though it is near a surface. Widening one strip hits diminishing returns. The way the industry actually beats skin effect in a busbar is to laminate — stack several thin, individually-insulated strips so each is thin enough to be used end-to-end, without the edge crowding of one wide sheet. The sweep shows exactly where a single strip stops paying off and lamination has to take over.

Inductance comes along for free

The same extraction returns the bar's self-inductance, and it moves the useful way: the flatter, wider sections have lower inductance (about 78 nH versus 130 nH for the square), because a wide flat conductor stores less magnetic energy per unit current. For a bus feeding fast-switching power devices, that lower inductance means less voltage overshoot and ringing on every switching edge — so the flat section that helps the resistance helps the switching behavior too. Shape is doing double duty.

Busbar self-inductance versus aspect ratio — Self-inductance falls as the bar flattens, from about 130 nH for the square section to 78 nH for the widest ribbon. On a bus switching tens of amps in tens of nanoseconds, that difference is volts of overshoot the devices do not have to absorb — the same shape choice paying off a second time.

Put the two together and the design rule for an AC or switching bus is not the DC one. Sizing to a target current density on the cross-section, the way a DC bus is sized, silently under-rates the conductor at frequency: it will run hotter and lose more than the spreadsheet says. The honest procedure is to extract the AC resistance at the real operating frequency, check the temperature rise against that number, and only then decide whether the answer is a flatter bar, a laminated stack, or simply more copper. The value of a sweep like this is that it turns each of those options into a number before any metal is cut.

What the automation did

One busbar was built parametrically and a script swept its cross-section shape across a frequency ladder — 27 converged Ansys Q3D extractions, each returning the DC resistance, the AC resistance with skin effect, and the inductance, one solve at a time with no one at the keyboard. The DC resistance came back at the textbook 34.4 µΩ every time (the built-in sanity check), and the AC ratios traced a clean surface across shape and frequency. Turning a validated single extraction into a design map is the everyday value of scripting the solver — here it turns “busbars have some skin effect” into a chart an engineer can size a bus from.

What this model does and does not cover

Honest scope. Ansys Q3D Extractor, 2026 R1: a single 100 mm², 200 mm copper bar, one net, source/sink on the end faces, DC + AC resistance and inductance extracted at each frequency with adaptive meshing at the solve frequency. It is an isolated single conductor, so the AC ratios include the bar's own skin and edge effects but not the proximity effect of a nearby return bar (which raises the penalty further and is the natural next sweep). The DC resistance is validated against the closed-form ρL/A to the digit; the square-section AC ratio matches the surface-skin estimate. The ultra-thin ribbons at the lowest frequency, where skin depth far exceeds thickness, are near their DC value and were held to the physically-clean points. Generic bar, not a specific product.

Sizing a bus, a cable, or a laminated stack that has to carry real current at real frequency? The DC number on the datasheet is the optimistic one; the AC penalty is where the heat and the loss actually live, and it is a direct extraction, not a guess. We do this in Ansys Q3D, Maxwell and Icepak. Rand Simulation — innovation through insight.