Why does the return current in the ground plane of a circuit board follow the path directly beneath the...

Thomas Gray <ai380@FreeNet.Carleton.CA> wrote:
>An equivalent way of looking at this is to consider the current
>in the trace and the current in the ground plane. These currents
>are moving in opposite directions. Thus they will produce
>magnetic fields of different direction. These currents will
>attract each other. If the current by chance took a
>path that did not mirror the trace, it will be attracted back to
>the trace.

I think you have a sign wrong.

-- Dave Ring <dwr2560@tam2000.tamu.edu>

[ Editor: parallel currents attract and antiparallel currents repel, so
the trace current and its opposite return current push each other
apart; that is the sign Ring objects to.  The posting titled "Return
Current Path - the answer", to which Gray's text belongs, was not
found in the collected material. ]

[ Editor: Thomas Gray's posting "Return Current Path - the answer"
(November 1994), from which the entry above quotes, in full. ]

Recently the problem of a pcb with a single trace on one side and a
ground plane on the other was posted.  In the problem the trace was
conected via a plated through hole to the ground plane.  The trace ran
diagonally from one edge of the board to the other.  A voltage source
(with finite output resistance as all voltage sources have) was placed
at the end of the trace.  The ground plane (copper sheet of even
thickness) was connected to ground potential uniformly along the edge
of the board at the same side as the voltage source.  A current thus
ran from the voltage source, along the trace, through the PTH, through
the ground plane and then to ground.

The problem was to identify the path the current took in the ground
plane.

The answer is that the current will flow directly under the trace
mirroring its width, shape and path.  The same will be true if the
trace is curved or rectilinear with 90 degree bends.

Consider the circuit.  It is a current loop and is therefore creating
a magnetic flux.  The size of this flux depends on the area of the
interior of the loop and the current.  For our purposes the current is
fixed.  The area consists of two components, one parallel to the plane
of the board and one vertical.  The current in the ground plane will
adjust itself to minimize the energy stored in the magnetic field.  It
will do so by minimizing the area of the loop.  There is nothing that
can be done about the vertical loop since its area is fixed by the
length of the trace and the thickness of the board.  On the other hand,
the size of the horizontal component of the area can be reduced to zero
(and therefore the energy in the magnetic field minimized) if the path
moves to mirror the trace.

An equivalent way of looking at this is to consider the current in the
trace and the current in the ground plane.  These currents are moving
in opposite directions.  Thus they will produce magnetic fields of
different direction.  These currents will attract each other.  If the
current by chance took a path that did not mirror the trace, it will be
attracted back to the trace.

-- Thomas Gray <ai380@FreeNet.Carleton.CA>