Differential Signaling and Mode Conversion

Why two wires beat one

The idea behind differential signalling is something you already understand from a noisy phone call. If both people hear the same background hum, the listener's brain subtracts it out and hears only the voice. A differential receiver does the same thing electrically: it listens to the difference between two wires, so any disturbance that hits both equally — power supply noise, an external electromagnetic field, a ground shift — cancels when the receiver subtracts one signal from the other.

That is why every modern high-speed serial link — PCIe, USB, HDMI, MIPI, DDR's data strobe — is differential. As data rates climb and timing margins shrink to single-digit picoseconds, the noise rejection that comes from subtraction is no longer a bonus; it is a requirement. But the cancellation only works when the two halves of the pair are truly identical. Every interesting differential failure — mode conversion, skew-induced EMI, common- mode voltage excursions — traces back to the two halves not being the same.

A single-ended signal is a voltage measured against a reference plane. That works, and it has two weaknesses. Any noise that appears on the reference appears on the signal, because the receiver cannot tell them apart. And the return current has to find its own way home through the plane, so the loop it takes is whatever the geometry allows rather than something you designed.

A differential pair sends the signal twice, in opposite polarity, on two adjacent conductors. The receiver subtracts one from the other. Two things follow immediately:

Noise that hits both wires equally cancels. Subtracting removes anything common to both — plane noise, an external field, a shared ground shift. This is the benefit people quote.
The return current has somewhere defined to go. The current going out on one wire comes back on the other, so the loop is the gap between the pair rather than whatever route the plane offered. A smaller, defined loop radiates less and is less susceptible.

Both benefits have the same precondition: the two halves must be the same. Everything below follows from taking that precondition seriously.

Two modes, not two wires

A coupled pair does not have one impedance, it has two, depending on what the two conductors are doing. Drive them in opposition and each sees the odd-mode impedance; drive them together and each sees the even-mode impedance. Every differential number in a spec is derived from those:

Z_diff = 2 · Z_odd Z_common = Z_even / 2 Z_odd is lower than the isolated single-ended Z₀ and Z_even higher, because in odd mode the neighbour's opposite swing adds coupling capacitance. So Z_diff is always less than 2·Z₀ — the tighter the coupling, the bigger the gap.

That last point catches people out regularly. Two 50 Ω traces routed close together are not a 100 Ω differential pair; they are perhaps 85–90 Ω, and getting to 100 Ω differential means either moving them apart or narrowing them. PCIe signs off at 85 Ω, USB 3.x at 90 Ω, MIPI at 100 Ω — and those numbers come from the receiver's on-die termination, so they are not negotiable at layout.

Tight coupling is a trade, not a virtue

Tight coupling improves immunity to outside aggressors and shrinks the loop area, so it lowers emissions. It also makes the pair much more sensitive to its own geometry: any width or spacing variation moves Z_diff more, and the pair becomes harder to escape from a dense BGA without breaking symmetry. Loosely coupled pairs are more tolerant to route around and rely more on the reference plane — which is fine, as long as that plane is continuous.

Mode conversion is the real failure

Symmetry is the entire mechanism. When the two halves are no longer identical, part of the differential signal converts into common mode — measured as S_CD21 — and common mode is bad in three separate ways at once. It is largely rejected — subtracting one wire from the other is exactly what removes it, and an ideal receiver rejects equal common mode completely. But rejection is finite: real parts specify a common-mode rejection ratio, and a level outside the input's common-mode range stops the front end working rather than merely degrading it. Whatever survives eats margin. It has no controlled return path — the current does return, through reference planes, a chassis, a cable shield, whatever parasitic route exists, but none of those were designed for it, so the loop is large and it radiates. That is the usual root cause of a failed emissions scan. And when it meets an asymmetric discontinuity it converts partly back into differential noise at a delay, arriving as an echo the equaliser was not designed for.

Where the asymmetry comes from Intra-pair skew from length mismatch is the obvious one and the easiest to fix. The one that bites is glass weave skew: the two traces of a pair can sit over different amounts of glass and resin, giving them genuinely different propagation velocities even at identical routed lengths. Serpentine-matching the lengths does not fix it. Routing at an angle to the weave, or specifying a spread-glass style, is what fixes it — and both are stackup decisions made long before layout.

Why this decides how your board behaves

Get Z_diff wrong and you reflect. The receiver's on-die termination is a fixed value; if the pair does not match it, part of every edge comes back. See reflections.
Skew becomes common mode, and common mode becomes an EMC problem. The radiated emissions of a well-matched pair are tiny because the two currents cancel in the far field. Break the match and the cancellation is incomplete in exactly proportion to the skew.
Converted common mode comes back as differential noise later. Any asymmetric discontinuity downstream — a connector, a via pair with unequal antipads — converts some of it back, arriving delayed. It behaves like an echo that the receiver's equaliser was never designed for.
Common mode outside the input range stops the receiver working. Not degrades — stops. Rejection is finite and specified, and beyond the input common-mode range the front end is simply out of its operating region.

What to do about it

Design to the differential impedance the receiver wants, not to 2×50 Ω. Two 50 Ω traces routed close together are about 85–90 Ω differential, not 100. Give the fab the differential target and the tolerance and let them solve for width and spacing together.

Match length within the pair far more tightly than between pairs. Intra-pair skew converts to common mode and is the thing that matters. Inter-pair skew is a timing budget item and is usually allowed to be an order of magnitude larger.

Keep the pair symmetric through discontinuities, not just along the straights. The places symmetry breaks are the places it is hardest to see: a bend where the inner trace is shorter, a via pair with different antipad clearances, a connector where one pin has a neighbour and the other does not, an escape where one trace leaves before the other. Length matching after the fact does not undo an asymmetric discontinuity.

Decide tight versus loose coupling deliberately. Tight coupling improves external immunity and lowers emissions, but makes the pair more sensitive to its own geometry and harder to escape from a dense BGA without breaking symmetry. Loose coupling is more tolerant to route and leans harder on the reference plane being continuous — which is fine right up until it is not.

Using this to find a fault

A failed radiated emissions scan on a differential interface. Measure S_CD21 if you can, or look for intra-pair skew in the layout. A pair radiating at all means the cancellation is incomplete, and skew is the usual reason.
An eye with a clean top and bottom but jitter at the crossings. Skew shows up as timing, not amplitude, because the two halves arrive at different moments and the crossing moves.
Lengths match perfectly and skew is still present. Glass weave. The two traces sit over different amounts of glass and resin and genuinely propagate at different speeds. No amount of serpentine fixes it.
A pair that works on the bench and fails through a connector. Suspect asymmetry in the connector footprint or the mating structure, and measure the common-mode conversion through the connector alone before blaming the board.

Go deeper — where the mode impedances come from, and reading the mixed-mode matrix

A coupled pair has two ways to be excited, and each has its own impedance because the coupling between the conductors either helps or hinders depending on what the neighbour is doing.

In odd mode the two conductors swing in opposition. The voltage across the gap between them is twice the single-ended swing, so the mutual capacitance is charged harder — it behaves as a larger effective capacitance to ground. More C means lower impedance, so Z_odd < Z₀. In even mode both swing together, so there is no voltage across the gap, the mutual capacitance does nothing, and the mutual inductance adds instead: Z_even > Z₀.

The differential impedance a receiver sees is the voltage between the conductors divided by the current in the loop, which is 2·Z_odd; the common-mode impedance is Z_even/2 because the two conductors are in parallel for that mode. This is why tighter coupling always drags Z_diff further below 2·Z₀.

Reading the mixed-mode matrix. A four-port measurement of a pair gets rearranged into blocks named by mode: SDD, SDC, SCD and SCC. The naming is output mode first. Keeping that order explicit makes the terms easier to read:

SDD21 — differential in, differential out. Your actual insertion loss.
SDD11 — differential return loss. What the termination match costs you.
SCD21 — differential in, common out. This is mode conversion, and it is the number that predicts an emissions problem.
SDC21 — common in, differential out. Susceptibility: how much external common-mode noise turns into signal-band noise.
SCC21 — common in, common out. How well common mode propagates, which matters for what arrives at the far end to radiate.

For a perfectly symmetric structure SCD and SDC are identically zero. They are, in other words, a direct measurement of how good your symmetry is — which makes SCD21 the single most useful plot for diagnosing a differential channel, and the one least often looked at. See S-Parameters: Insertion Loss, Return Loss, and Mixed Mode.

One caveat about the two-mode picture: it assumes the pair is uniform and isolated. A pair inside a bus has neighbours, and a full treatment needs the whole coupled system rather than two modes. The two-mode description is exact for an isolated pair and a very good approximation for a pair with a guard of empty space either side.

In the real world

Differential signalling is often described as noise-immune, and that framing causes trouble. It is not immune to noise; it rejects noise that arrives equally on both halves, and the whole discipline is about preserving the conditions under which that is true. A pair that has been routed asymmetrically has thrown away the property it was chosen for while keeping all of its cost.

It helps to treat the pair as one structure whose symmetry you are protecting, rather than as two unrelated traces. This leads to a useful review question: question — is anything here happening to one half and not the other?