From a modelling standpoint the structure is like a paired wire
transmission line. However the questions arise — how do you model
the structure with the Si8000/9000 field solvers and as this is a differential
structure but with no ground plane how should you test the impedance?

Fig. 1 Broadsidecoupled differential
structure

When
the tracks are driven in equal but opposite sense the potential at
every point equidistant from the two is always 0V (half way between +V
and –V). We can use this to our advantage because those points form
a virtual ground plane which lies exactly equidistant from each track.
Here's the same structure as in Figure 1 above but showing this virtual ground plane —
Figure 2, right.

Fig. 2 Broadsidecoupled differential
structure


Modelling
this structure
The Si8/9000
field solvers do not include a structure exactly like this, but do
offer the Surface
Microstrip structure
— shown in the figure below
— which is exactly half of it.

The track in Figure 3
corresponds to the upper track in Figure 2, and the planes
correspond. By turning Figure 3 upside down, the track corresponds
to the lower track in Figure 2. Notice the significance of H in the
three figures, where H1 in Figure 3 = H in Figure 2.

Fig. 3 Surface
Microstrip

The impedance of the
differential pair shown in Figure 1 will be the same as their impedance in
Figure 2, which in turn will be twice the impedance of the Surface
Microstrip in Figure 3. This is because in the structures shown in Figure 1
and Figure 2 both
signal tracks are driven, one by +V and the other by –V, so the
total driving voltage = +V – (–V) = 2V which is double that in Figure 3.
However, the resulting current will be the same and therefore the impedance is
double.
So, in order to calculate the
differential impedance of Figure 1, simply calculate the impedance
of Figure 3 and double it. The Si8000/9000 Quick Solvers are
convenient to use for this purpose.
When choosing a
suitable model for differential structures look for virtual ground
planes between differential tracks to see if a single ended model
with ground can be adapted to fit your needs. The virtual ground is
a useful tool
— and at first sight it may not be obvious that one exists between
two conductors driven differentially. Look beyond the obvious to see
if this tool can be adapted to suit your needs and use it to your
advantage.

Testing the structure
In the
structure to be tested all the signal current flows out through one
conductor and the return current comes back through the other. As
noted earlier, with
a signal of equal positive and negative going potential a virtual
ground exists midway between the two traces.
How do I connect probes to this?
Imagine
using a differential probe with + on one line and – on the
other —
you are left with nowhere to connect the ground. So in order to
test you need to think of this structure as a single ended
transmission line and consider connecting to it via a single
ended probe. The signal goes to one side of the transmission line and
the ground connects to the other.
Using
a single ended TDR and probe connection you can connect the probe
either way around and measure the impedance of the structure using
the system set for single ended measurements. The measurement
returned will represent the differential impedance of the transmission line.
For this structure this will equal Zo, the singleended impedance.

Footnote by Dr Alan Staniforth
The impedance of the
structure is the ratio of the voltage between, and the current in, the
conductors. The concept of driving the conductors as a differential
pair implies the presence of a zero voltage ground. The definition of the controlled
impedance for this configuration does not require a ground. Hence, without loss of generality, one
conductor can have zero voltage assigned to it.
Thus only a singleended measurement is required, even though one pin of the measurement probe is at ground potential. A three pin differential measurement probe requires a track configuration which already has a ground to which the ground pin is connected. A differential probe, in practice, measures the impedance between the two active pins and the ground pin. The differential impedance is calculated from these two impedances. If the ground pin is not connected, the impedance at the active pins will be incorrect and so will be the differential impedance.
