Docs › App Notes › AN-01 Coupled lines and EM ports

AN-01 — Coupled Lines, EM Ports, terminations and de-embedding

How to EM-simulate a pair of coupled lines — which kernel, where the ports go, what circuitRF does when two feeds are coupled at the same reference plane, and how to read the run.

The structure

Two parallel microstrips over a ground plane. Each is 254 µm wide and 3.83 mm long, and they are 246 µm apart edge to edge, on 0.9 mm FR-4 (ε_r 4.4, tan δ 0.02). Ports 1 and 2 are the ends of the lower line, ports 3 and 4 the ends of the upper one. The sweep is 1–7 GHz.

Every number and every curve on this page came out of this design or one of its siblings in testdata/portcal/. One command runs it:

circuitrf em testdata/portcal/coupled-pair/em/coupled-pair.cem

Choosing the kernel

Two straight coupled lines are a uniform cross-section, and circuitRF has a kernel for exactly that: it solves the section per unit length and has no de-embedding step to get wrong. Leaving Analysis on Auto picks it and says so:

Automatic chose "Uniform transmission line": this geometry is a uniform cross-section, which
that analysis solves exactly and is about a thousand times cheaper than "Full-wave planar".

On this pair that is 0.16 s against 9.0 s for the same seven points on ten cores. So the first question to ask about any coupled-line structure is whether it is uniform end to end. If it is — straight coupled lines, a broadside pair, a single transmission line — you are done, and nothing below applies.

Reach for the full-wave planar kernel when the cross-section is not uniform: a coupler with bends or tapers at its ends, lines that fan in and out, anything with a pad or a stub on it. That kernel does have a de-embedding step, and the rest of this note is about the one part of it a coupled-line layout makes interesting.

Coupled feeds are calibrated together

This is the part that is specific to coupled lines, and it needs no action from you — but it is worth knowing what circuitRF is doing, because it decides what the run can and cannot accept.

The planar kernel de-embeds each port by solving calibration standards beside your structure and peeling the port discontinuity off the raw answer. A standard is a uniform extrusion of whatever crosses the reference plane. For a single isolated line that is one conductor, one mode, and an error box that is one number per port.

Two driven conductors at one plane are not that. They support two modes there — with different propagation constants and different characteristic impedances — and no pair of per-port scalars can describe them. So the unit of calibration stops being the port and becomes the group:

• one standard carrying both conductors, built from your own mesh at your own gridlines, with a port on each conductor at each end — a four-port standard for a pair;
• one modal error box, whose blocks are matrices rather than scalars;
• one γ and one Z_c per mode, reported per frequency.

The run says so by name, and prints what it extracted:

Ports 1, 3 form one CALIBRATION GROUP: their feeds are mutually coupled at the reference plane,
the nearest pair 246 µm apart. They share one 2-conductor calibration standard and one MODAL
error box of 2×2 blocks, because 2 coupled conductors support 2 modes there and a per-port
scalar box cannot represent them. The profile spans 0 µm to 754 µm across.
  1 GHz, ports 1+3: modes 40.2° / ε_eff 2.718 / Z_c 71.53Ω · 42.8° / ε_eff 3.073 / Z_c 157.51Ω;
  separation 2.55°, …

What this means for you

• The modes are extracted from the standard, never assumed. Even and odd is right for two identical lines and wrong for almost anything else, so nothing here assumes it — an asymmetric pair and a group of three unequal conductors are the same code path.
• The two numbers in that line are the design quantities. 71.53 Ω and 157.51 Ω with ε_eff 2.718 and 3.073 are this pair's own modal impedances and effective permittivities, per frequency, for free, on every run that forms a group.
• Mode separation is the number everything rests on, and it is reported on every point. If two modes are too close to tell apart (the floor is 0.5° of electrical length) the run refuses rather than publishing a smooth, plausible answer built on a modal basis decided by round-off. Three conductors of equal width at this spacing are refused for exactly that reason — 0.369° apart at 1 GHz.
• It costs almost nothing. The standard carries the same metal either way, so it is the same mesh and the same ~9× the DUT's unknowns; the four-port coupled pair runs about 13 % slower than the two-port case.
• Groups hold up to three conductors. More than that is refused by name rather than discovered as a run time.

The result

Same file, same mesh, 1–7 GHz at 200 MHz — plotted in the Data Display exactly as any other result.

A 254 µm line on 0.9 mm FR-4 is about 116 Ω, so against a 50 Ω reference it is a mismatch that grows with frequency: S(1,1) climbs from −17 dB to −5.7 dB across the band while S(2,1) falls from −0.14 dB to −2.1 dB. S(3,1) — the backward-coupled port — rises from −20.8 dB to −11.9 dB.

Ports 1 and 2 are the two ends of one uniform conductor, so S(1,1) and S(2,2) must coincide. They do, to every digit plotted. That is worth checking on your own structures: where they separate on geometry that is symmetric, the mesh or the ports are not.

Against the cross-section kernel on the same unmodified file:

Worst-case |ΔS| = 0.0454 over the whole matrix and the whole band, against the 0.0521 the two kernels differ by on the same conductors moved 9 mm apart — where there is no coupled feed and nothing to get wrong. The de-embedding is inside the floor it is being measured against.

The run still reports a small passivity excess here — σ_max(S) = 1.0023 at 1 GHz, on 4 of the 31 points plotted. Read it as the smoke alarm it is: below for what it is reliable at and what it is not.

When a group cannot be formed, and what to do

A group is one standard cut at one plane, so every member has to cross that plane, running straight, on the same level, facing the same way. Where that does not hold — the neighbour's own port is somewhere else along the line, or the neighbour bends or ends inside the run the standard reproduces, or it is on another conductor level, or the group would exceed three conductors — the run is refused, and no Touchstone is written. This is testdata/portcal/offset-pair — the same two lines, with the neighbour shortened so its ports sit at a different station:

Calibrated port feeds are not isolated: port 1 has other metal 246 µm away (0.27 substrate
heights, against the 5 a neighbour that carries a port of its own needs)… Move the feed away
from its neighbour, or put the port where the line is already isolated.

Why this feed's calibration standard could not simply reproduce the neighbour: Port 3's feed
has a conductor 246 µm away carrying a port of its own (2 port(s) on it), none of which sits at
this reference plane facing the same way…

It refuses rather than warns because a .sNp on disk carries no notes. Whoever opens that file next — in the Data Display, in a circuit, next month — would see a plausible curve and nothing else. The refusal is on a measurable geometric fact about the port, and it names both what it found and which flag answers it. Two escapes exist in Solver options and neither is quiet: turn port de-embedding off and read the raw solve, which includes the port discontinuity; or turn on "de-embed outside the calibration's validity", which publishes and stamps the Touchstone with a line recording that the calibration was applied outside the geometry it is valid for.

A neighbour with no port on it

The commonest case on a board is not two driven lines at all — it is a conductor that is simply near your feed and carries no port: the other half of a pair you are not driving, an adjacent net, a ground pour. That needs nothing from you either. One driven conductor at the plane means one mode, so the error box stays scalar and the standard is simply widened to contain the neighbour, copied from your own mesh with the gap reproduced as a gap and the neighbour driven by nothing:

Its calibration standard reproduces 1 neighbouring conductor(s) beside the feed, the nearest
246 µm away, over the whole of the standard's run: the profile spans 0 µm to 754 µm across,
against 0 µm to 254 µm for the port's own conductor. The neighbour carries no port, so the error
box is still the scalar one; it is present in the standard and driven by nothing, exactly as it
is in the structure.

Three things are still declined and each falls back to the refusal above: a neighbour that bends, ends or changes width inside the standard's run (a standard is a uniform extrusion, and guessing would invent metal you did not draw); a neighbour on another conductor level; and a neighbour carrying a port, which is the group case. There is one cost and one caveat: the standards get about twice as large, which the run reports, and the reproduced neighbour is open at both ends, so where the standard is half a wavelength long it resonates — the run lists those frequencies.

Move the ports, not the circuit

This is usually the real answer on a board, and it is not a redesign.

A coupled section is almost never coupled all the way to where you would naturally put a port — the traces arrive from somewhere, and that approach is often already separated. Put the port on the isolated run instead, and the coupled section you care about stays exactly as drawn. You are choosing where the reference plane sits, not changing the circuit.

What comes back is then referenced to that plane, so the extra line is part of the answer. De-embed it in the circuit — a length of ideal line of the same impedance in series, or the cross-section kernel's own answer for that run — the same thing you would do with a measured fixture.

Give every port an isolated feed

If neither applies, the structure has to supply the isolated run. Same coupled section, unchanged: 4 mm of line added at each port with the other conductor held 6 mm away there.

Every port reports its own margin — "6.38 substrate heights, against the 5 a neighbour that carries a port of its own needs" — and the result is passive at every frequency. As in the option above, the 8 mm of extra line is genuinely part of the structure now and comes out in the circuit if you want the planes back at the coupled section's own ends.

Best practice

Let Auto choose the kernel. A uniform cross-section is solved exactly, in a fraction of the time, with no de-embedding step to get wrong. Forcing the planar kernel on geometry that does not need it buys a calibration you then have to satisfy.

Measure port clearance in SUBSTRATE HEIGHTS, not in millimetres and not in line widths. How much a calibrated feed needs was measured on this very geometry, by sweeping the separation and comparing against the cross-section kernel at every point:

Three things are worth knowing about that table.

• It is the substrate height that matters. Making the lines four times wider moved the requirement by 5 %; making the substrate four times thinner moved it by nearly four times. A ground pour behaves exactly like a thin trace at the same distance — the neighbour's own width does not enter.
• You get the margin even when nothing is wrong. Every de-embedded port reports its clearance in substrate heights on every run, so "comfortable" and "just passed" are distinguishable without re-running anything. Do not confuse that margin with the separate sentence about the 2.7 mm of line the standard reproduces: the first is the measured requirement, the second is how far into the structure the standard looks.
• A pad or flare on the port's own conductor is a different thing and is already handled — circuitRF grows a uniform lead for it and removes it exactly, which is the automatic feed lead reported in the notes, and a port that sits on a pad can still join a group.

Read the notes under the run, every time. The kernel choice, the calibration groups and their modes, every port's clearance and reference plane, the passivity verdict — all of it is printed before you plot anything.

Start from the default mesh and justify every reduction. Cells per wavelength defaults to 20 and cells across to 4. The fixture on this page runs at 5 and 2 because it is a deliberately hard case; below about 10 is not a serious answer on real work, and a coarse mesh moves the reference planes off your drawn edges.

Sanity-check one number by hand. A single microstrip section is a closed-form calculation. If the solver disagrees with it by 20 dB at the bottom of the band, stop there.

Check passivity across the whole band, not at one marker. De-embedding error is strongly frequency-dependent: the peel divides by a₂₁², which grows as frequency falls, so the bottom of the sweep is always the worst place and is always where to look first.

And read NOT PASSIVE as a smoke alarm, not as a thermometer. It is reliable at telling you that something is wrong. It is not reliable at telling you how wrong — the worst case measured during this work reported a smaller passivity excess than a case with half the error. Do not rank two runs by their σ_max.

Comparing two port configurations properly

An S-parameter is defined with every other port terminated in its own reference impedance — that is what a_k = 0 means — so a port is a load as well as a source, and on coupled lines the neighbour's load is exactly where the coupled power goes. Deleting a port label removes the load and the excitation; it never removes the conductor, which goes on being meshed and goes on coupling, now open at both ends.

So if what you want to know is how does this network behave with its other ports loaded differently, do not delete the ports. Simulate once with every port present, then change the loads in the circuit:

• Place the resulting .sNp as an SnP component in a schematic.
• Put Terms on the ports you want to measure.
• Put the real load on each remaining port — a resistor to ground for a matched termination, whatever the neighbour actually drives otherwise.
• Run S-parameters.

The mesh, the calibration, the feed leads and the frequency plan are then identical across every comparison, and the only thing that varies is the thing you meant to vary. It is also faster: one EM run serves every load case.

Two runs with different port counts are not a controlled comparison in any case. Port labels seed gridlines, so the mesh can differ; de-embedding grows a feed lead where a port sits on metal that changes cross-section, so the solved geometry can differ; and adaptive sampling converges against the whole S-matrix, which is 16 entries in one run and 4 in the other, so the solved frequencies can differ too.

Delete ports from the layout only when you are deliberately changing the experiment.

Checklist before you trust an EM result