Circuit Response
every model has an edge, and the figure carries it
Concept

Ground plane — where it appears

A layer of copper under a circuit that carries every signal's return current and holds a common reference. At high frequency each return gathers under its own track; at low frequency it spreads across the whole plane, where returns can share its resistance.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

A 0.4 mm slot between the tracks leaves all of the resistance shared at DC and raises the in-band share from 4.03% to 4.98%. computed by solving, not by drawing, across the plane in strips. Two tracks 200 µm above a 50 mm plane and 2 mm apart, one driven and the other listened to: the share of the driven loop's resistance that the quiet loop's return also carries, against frequency, over an uncut plane (dashed) and with a slot 0.4 mm wide cut along the plane midway between the tracks (solid). The slot's two halves are one conductor, joined where the run ends, so at direct current the return still spreads across both and the whole of the plane's resistance is shared, 1.0000 of it. Above the band each return has gathered under its own track, and the share is 4.98% with the slot against 4.03% without: the slot is where the copper nearest the other track used to be.

The slot that does not separate

Cutting a slot in the plane between two tracks is the common response to coupling between their returns, and in a cross-section it looks as if it separates them. It does not, if the plane is one ground: the halves stay joined where the run ends, so at direct current both returns still spread across the whole plane and share all of its resistance — 1.0000 with a 0.4 mm slot — and above the band the slot makes the sharing worse, 4.98% against 4.03%, rising to 15.7% as the slot widens to 1.6 mm, because it takes away the copper between the tracks and pushes each return towards the other. Only a split into two grounds removes the shared resistance at DC, at the price of each loop's resistance multiplied by 2.10, and it leaves the in-band coupling 29% lower, not gone: most of two tracks' coupling at 100 MHz is their own magnetic field, which the plane's copper does not carry.

lines · Return path A 0.6 mm guard between the tracks leaves all the resistance shared at DC and moves the in-band share from 4.03% to 3.50%. computed by solving, not by drawing, across the plane and the guard in strips. Two tracks 200 µm above a 50 mm plane and 2 mm apart, one driven and the other listened to, with a grounded trace of 0.2, 0.6, 1.2 mm centred between them at the tracks' height and joined to the plane at the ends of the run: the share of the driven loop's resistance that the quiet loop's return also carries, against frequency. The guard is part of the return net, so at direct current it changes nothing — the whole plane's resistance is still shared. Above the band a 0.6 mm guard moves the share from 4.03% to 3.50%.

The guard that is part of the return

Where a slot between two tracks makes their returns share more of the plane, adding copper instead — a grounded trace between them — makes them share less. But not much, and not at every width. At direct current a guard joined to the plane at the ends of the run is part of the same return and changes nothing: the whole plane's resistance is still shared. At 100 MHz a guard 1.4 mm wide in the 2 mm gap cuts the shared resistance from 4.03 to 2.55 per cent and the mutual inductance by half; a guard 0.1 mm wide raises the sharing to 4.44 per cent, since a thin trace beside both tracks carries both returns through its own small cross-section. The guard works by taking return current the quiet track's plane would have carried — 7 per cent of the neighbour's for a 0.6 mm guard — and it is bounded by exactly that.

lines · Return path

Named alongside it

The objects these essays reach for when they reach for this one.

Common-impedanceCrosstalkMutual inductanceSkin effectGuard traceReturn currentReturn path

All concepts