Broadside-Coupled Pairs: Half the Width, One Big Risk

Two ways to build a pair

Edge-coupled is the default: two traces side by side on the same layer. Broadside-coupled stacks them instead — one directly above the other on adjacent layers.

The payoff is width. A broadside pair occupies roughly half the routing channel of an edge-coupled pair with similar coupling. On a dense rigid board that's real estate you can spend elsewhere. On flex it's often the only sensible option, because bend radius and width both matter and the two conductors bend together instead of one taking the longer path around the outside of a curve.

The maths is nicer than you'd guess

A symmetric pair driven differentially has a useful property: the plane exactly midway between the two traces sits at zero volts. Not approximately — by symmetry.

That virtual ground is an electric wall, and it turns a messy four-conductor problem into two independent single-line problems. Each trace becomes an offset stripline: virtual ground at half the separation on one side, the real plane on the other. Then:

What's nice is that this isn't an approximation. Working the two-strip Green's function through algebraically, the odd-mode kernel turns out to be identical to that of a single strip in a half-height cavity. So if your single-line stripline model is good, your differential impedance is good, for free.

Even mode is the harder half — magnetic wall instead of electric, no equivalent identity — but even mode only matters for common-mode impedance, which is a secondary concern in most designs.

Unshielded flex: common mode has nowhere to go

On a two-layer flex with no ground planes, the virtual ground is the only reference in the structure. Each trace becomes a strip at half the separation above a ground plane in a homogeneous dielectric, and Hammerstad's microstrip forms apply directly with εr in place of εeff, because there's no air–substrate boundary to average over.

Differential impedance is well defined and easy to hit.

Common mode is not. It's not small — it's undefined. Common mode means both conductors swinging together, which needs a return path somewhere else in the system, and there isn't one. Any common-mode current the cable picks up has nowhere to go except out into free space.

That's why unshielded broadside flex radiates, and why you fit common-mode chokes at both ends. Not as belt-and-braces — as the actual mitigation for a mode the geometry cannot terminate.

Copper thickness matters here more than anywhere

Worth calling out because it's easy to skip.

On a typical flex pair with 0.2 mm between the layers, the virtual ground sits just 0.1 mm below each trace. One ounce of copper is 35 µm — a third of that height.

Ignore thickness and you overstate differential impedance by more than 10%. In practice that means designing a 0.18 mm trace when 0.15 mm was right, or believing you're at 100 Ω when you're at 89 Ω. Neither is subtle enough to hide.

Any calculator that lets you enter copper weight but produces the same answer regardless is not using it. Worth a ten-second check.

The real risk: registration

Here's the thing that actually goes wrong in production, and it isn't impedance.

The entire analysis above assumes the two traces sit squarely above each other. Every fabricator holds etch width tightly, because that's what impedance coupons measure. Layer-to-layer registration is held much more loosely — it's a mechanical alignment problem across a lamination press, not a photolithography one.

A lateral shift breaks the symmetry the analysis depends on. And broken symmetry in a differential pair means differential-to-common-mode conversion. You are, mechanically, building a mode converter.

Common mode is the mode that radiates, and the mode a differential receiver cannot reject. So a registration problem shows up as an EMC failure and a jitter problem, not as a failed impedance coupon. The coupon passes. The board doesn't.

What to do about it

• Ask for the registration spec before you pick trace widths. Not the etch tolerance — the layer-to-layer number.
• Size traces so a worst-case shift is a small fraction of the width. A 25 µm shift on a 0.15 mm trace is a 17% overlap error. On a 0.3 mm trace it's 8%. Wider traces desensitise the design, and on flex you often have the room.
• Keep via transitions symmetric. Where the pair breaks out of the stacked geometry, keep the two vias close together and mirrored. An asymmetric transition is another mode converter, and it's one you control completely.

Quick model checks

If you're validating a tool or your own maths:

• Differential impedance must be exactly twice the odd-mode impedance. Not approximately.
• Odd mode must sit below the uncoupled single-line value — coupling lowers it.
• Bringing the traces together must drive differential impedance down. If it goes up, the model is broken.
• Common-mode impedance on an unshielded pair should be reported as undefined, not as some finite number.

The broadside-coupled pair calculator handles both the shielded case between planes and the unshielded flex case, and includes the copper-thickness effect that the simple forms drop.